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Chemistry, 91Ó°ÊÓÆÆ½â°æ.¡J‚(2 ' Y¦: ð¢ ð8 ƒ ð0€˜öš¿�ƒ¿ÀÿðP ú4Ë ð¿Ÿ¨The geometries and energies of six-coordinated amine complexes of Fe2+ at both spin states were explored using the DommiMOE program. Then the model parameters were refined using simulated annealing to give the correct geometries and predict the correct spin state of the metal, initially with [Fe(NH3)6]2+, then with three other amine complexes. The parameters found were applied to about 80 imine complexes, and after a slight modification, approximated the geometries reasonably well and most of the time predicted the correct spin state.¡xD å çÿ çÿ ë¦: ðB² ð. # ð Aÿ"ñ¿`ð- ¨ð¼¢ ð9 s ð*€lX¿�3ÌÌ¿Àÿ"ñ¿`ðü'z� ðTŸ¨ Introduction¡ 2 $¦: ðÖ¢ ð: £ ð<€4CX¿�ƒ¿ Àÿ?“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nðg'.4Õ ð,Ÿ îThe importance of organometallic proteins in biochemistry has long been recognised, which the metal instrumental in many of these protein s catalytic or binding functions. At the moment there are very few methods that model transition metal-containing organometallic proteins effectively, either using quantum or classical mechanical methods. Here is outlined a very promising new Molecular Modelling approach to deal with transition metal complexes which can be used to model biological macromolecules.¡øø¦: ðç¢ ð< s ð*€ôOX¿�3ÌÌ¿Àÿ"ñ¿`ð'zâ ðŸ¨Molecular Modelling¡B 2 $, $¦: ð¨ ð? ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðmið¨ ðA ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðmið¢ ð= £ ð<€8TX¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð"'.4ƒ ðVŸ¨Molecular Modelling (MM) of Force-Field (FF) methods of finding molecular structures determine the relationship between the energy and structure by application of empirical rules based on classical mechanics. To find an optimal structure in MM, we optimise the total strain energy¡¦: ðD¢ ðB £ ð<€èfX¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðë'\4€& 𚟨\where the terms correspond to the deviation from the optimal bond lengths, bond angles, torsions, non-bonded interactions and electrostatic interactions from those given by the a particular forcefield. Modelling transition metals using conventional MM has always been difficult as they can have variable oxidation states, spin states and electronic effects, and can coordinate from 4 to 12 different ligands in a complex. Rob Deeth has addressed this problem by developing this Ligand Field Molecular Mechanics model of dealing with transition metal centres using an approach called Ligand Field Theory.¡]]¦: ð¨ ðD ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðF$miF$ðj² ðC S ð AÁ ??"ñ?ð� &ð Á ðÑ¢ ðT £ ð<€tvX¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð}('am7 ð'Ÿ¨ In a free transition metal ion, the preference of the d-electrons is to occupy each of the five d-orbitals, and when there are more than five d electrons, spin-pairing occurs. In an octahedrally-coordinated complex, the dxy, dyz and dxz orbitals become lower in energy than the dx2-y2 and dz2 orbitals and are filled first. Ligand Field Theory states that this is because the former orbitals repel the ligand electron densities less than the latter (the d-orbitals are mostly antibonding and repel ligand electron clouds). Depending on the ligands (the so-called ligand field strength), the d-electrons may desert the dx2-y2 and dz2 orbitals completely as the electron pairing becomes energetically more favourable than the electron repulsion of ligand bonding orbitals.¡® Ý çÿ çÿ çÿ, çÿ çÿM çÿ çÿ‹ª>ܦ: ðV² ðW C ð.€€AÁdorbitals2ðÔ%m¶4·+ð¢ ð\ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð_ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ðb £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð‰ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ðŒ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð� £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ðÄðF ð2)p*–2 3 ð’  ðˆðÚ+`)Ä2v4ðN² ðÑ S ðÂA ÿÿÿ¿ˆð2)p*’2€-ðN² ðÒ S ðfA ÿÿÿ¿ˆð2)_-–2n0ð² ðÓ ã ðT¿ÇÂAÿÿÿ�ƒ¿ Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð2)L0’2 3ðæ ðF ð`B*Ã23 ð‘  ðˆðÚ+èK3µ4ðþ ð¸ à ðH€8^X¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(*0Ã23 ð@Ÿ¡¦ø: Wtð� ð· ³ ðB€X§X¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`*0{(3 ðØŸ¨:(2) High Ligand Field strength (e.g. CN-, phenantroline) ¡J;(&þ.þ&þª+ ¦ø: Wtðþ ð¶ à ðH€¼°X¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(6-Ã2*0 ð@Ÿ¡¦ø: WtðÑ ðµ ³ ðB€Ø*X¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`6-{(*0 ðŸ¨7(1) Low Ligand Field strength (e.g. Cl-, I-, F-, H2O) ¡°8'&þ.þ&þ.þ&þ.þ&þ.þçÿ&þ¦ø: Wtðþ ð´ à ðH€¸ÈX¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(B*Ã26- ð@Ÿ¡,¦ø: WtðA ð³ ³ ðB€ÓX¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`B*{(6- ð‰Ÿ¨Free Fe2+ ion (high spin)¡> ¦ø: WtðªB ð¹ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`B*Ã2B*ð¤B 𺠣 ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`6-Ã26-ð¤B ð» £ ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`*0Ã2*0ðªB ð¼ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`3Ã23ðªB ð½ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`B*`3ð¤B ð¾ £ ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð{(B*{(3ðªB ð¿ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÃ2B*Ã23ð/ðF ð$ °ÔÌ ðä ðˆðu>’Ù �?ði¢ ðå  ð€”×Xð$ °ÄÌ ð+Ÿ¨ High Spin¦: ðh¢ ðæ  ð€háXð4°ÔÌ ð*Ÿ¨Low Spin¦: ðj² ðè S ð A Á  ??"ñ?ðà?ó%yBð Á  ð_ ðê à ðH€ØéX‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðFB'L%ÁG 𩟨yDeeth has implemented LFMM into the Molecular Operating Environment (MOE), a popular MM dynamics program, to form DommiMOE, which uses the forcefield MMFF94 for non-transition metals. DommiMOE can optimise the geometry a complex for a given spin state, and so can give hypothetical structures of transition metal complexes for both spin states with the same set of parameters.¡zzðö ðë à ðH€|Y‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð~ ‰4ã^: ð@Ÿ ØThis is an octahedral high-spin complex where the Fe  N bond lengths were 2.20 ú (from X-ray crystallographic data). To obtain data on the a hypothetical low-spin structure, QM techniques were used, which predict that the Fe  N bond lengths to be around 2.00 ú. An estimate of 11 kcal/mol was also imposed on the energetic favourability of the high spin state to the low spin state. As with all MM-based methods, some model parameters have to be found which fit the required geometries and energies. Parameters modified included the Morse function parameters (Fe N bond length potential was modelled by a Morse function), octahedral-field splitting term, the ligand-ligand repulsion term and some electron-pairing energy terms. To measure the  fit of the parameters, a cost function was constructed such that the smaller its value, the better the parameters fit the data.¡mmª0P ³ gðt² ðì c ð>A Á·m ¸ÿFe_hexammine"ñ¿`ð 0_Ïgðâ ðî s ð*€ôòX¿�3ÌÌ¿Àÿ"ñ¿`ðz·4ÜJ ð[Ÿ¨Simulated Annealing¡ 2$¦: ð" 𬠳 ðB€hY¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð¹7D\4N? ðrŸ öThe difference between low spin and high spin states is the metal-ligand bond lengths of low spin states are much smaller than those of high spin. For example, the Fe  N bond length in low spin and high spin amine complexes are about 2.00 and 2.20ú respectively. This is because of the smaller repulsion of the ligands from the d-electron cloud at low spin. Deeth summarises this effect by the Ligand Field Stabilisation Energy (LFSE), and incorporated into the MM framework by adding to the MM equation:¡.üù"ªù ¦: ðv ð­ ³ ðB€ÐY¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðä4p–287 ðÆŸ¨r(1) is known as the high-spin state of Fe2+ as the total spin is greater than in (2), known as the low spin state.¡*s) H¦: ðj² ð¯  S ð A Á '??"ñ?ð17¯` ‚>ð Á 'ð( ð² à ðH€L$Y‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð·4¿gs ðrŸ ¾Simulated Annealing (SA) is a method of finding the maximum or minimum of a distribution À(x) by using Markov Chain Monte Carlo (MCMC) to sample the parameter space, in this case the distribution needed to be minimised is the cost function A Markov chain (a  random walk ) is constructed whose limiting distribution is À(x) - the target distribution. ¡d`[""å"""""ª,Yãð¨ ð¶ ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð+$mi+$ð ð» à ðH€˜þX‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð§%‰46g* ð`Ÿ BIn simulated annealing, the target distribution À(x) is changed to À(x)1/T (T is known as the  temperature ), which has the same maxima and minima as À(x) but is rather  steeper as T decreases from 1 to 0, and this makes the Markov chain less likely to escape local minima. If the temperature is carefully reduced, then (hopefully) at the end of the procedure the Markov chain will reside near the global minimum. ¡΢2"""""**""K""""è"ª,0c ð¿¢ ð¼ s ð*€ HY¿�3ÌÌ¿Àÿ"ñ¿`ð�*·4 K1, ðWŸ¨Amine Complexes¡ 2$¦: ðì ð¿ à ðH€XJY‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð5,‰4:\½2 ð6Ÿ¨6The simulated annealing procedure yielded some good parameters for the iron hexaammine complex, which were applied to three other amine complexes. From the bond lengths in their X-ray crystallographic structures, (1) and (2) were low spin complexes, while (3) was a high spin complex, which illustrates the sensitivity of the spin state of Fe2+ with nitrogen ligands. The parameters found for [Fe(NH3)6]2+ were found to reproduce the geometry of the complexes very well in their native spin states, and also the spin states of the complexes were correctly predicted.¡Â7Ý""  S"*7"*âÿ"*âÿ"*¢"ªL áð¿¢ ðÛ s ð*€8cY¿�3ÌÌ¿Àÿ"ñ¿`ðÃ2·4 KW4 ðWŸ¨Imine Complexes¡ 2$¦: ðy ðÝ Ã ðH€ðdY‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð\4‰46gÞ; ðߨ¥Can these parameters transfer to imine complexes? Unlike amine nitrogens, imine nitrogens are aromatic, and most Fe2+ imine complexes are low-spin. It was found that after some modification of the parameters, although the bond lengths were not very accurately reproduced, DommiMOE correctly predicted the spin state for most of the complexes (but not all). The most striking result was the predicted spin states of the low spin complex [Fe(1-10-phenantroline)3]2+ and the high spin [Fe(2-methyl-1-10-phenantroline)3]2+. Although the ligands in these complexes were very similar, DommiMOE correctly deduced their spin states, which correspond to a large change in geometry.¡Îi= t"*ò"f"*âÿ"*3"*âÿ"*œ"ª,@  Lðœ ð “ ð6…¿�¿Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðt!Î.ž:t!ðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@ÖD¦Pð@ðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð‘GÖD¦P‘Gð–B ð “ ð6‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@ÖDÖD¬GðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@¦P¦P‘GððF ðdYÝ<hæE ðF  ðˆðÍ;dYhÖDð^ ð  ³ ðB€ÔyY¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðk`@DhæE 𦟨$[Fe(2-methyl-1-10-phenantroline)3]2+¡f% eÿÿÿþmÿÿÿþâÿeÿÿÿþmÿÿÿþAðe ð  ³ ðB€H�Y¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðdY@Dk`æE 𭟨e(1-10-phenantroline)3]2+¡v%ÿÿÿþeÿÿÿþmÿÿÿþâÿeÿÿÿþmÿÿÿþAðö ð  ³ ðB€d�Y¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðdYÝ< h@D ð>Ÿ¡¦ø: Wtðt² ð  “ ðD‚„# "AÁÇ .?ˆBUHKAQð�YÝ<ð`7Dðt² ð  “ ðD‚F5 "AÁ€ Â5?ˆCEPZOMðÜ`Ý<|g7Dð¼¢ ð s ð*€@™Y¿�3ÌÌ¿Àÿ"ñ¿`ðÝ<·4 Kq> ðTŸ¨ Applications¡ 2 $¦: ðø¢ ð3 à ðH€ ›Y¿�ƒ¿ Àÿ?¿ÿ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðu>‰4‘YýD ðBŸ (The next step is to model iron(II) porphyrins, which are planar complexes with the Fe2+ surrounded by four aromatic nitrogens (chemically similar to imine nitrogens). The most important example of an iron(II) porphyrin is the O2 -binding site for haemoglobin, heme. Fe2+ in heme changes from high spin to low spin when it binds to an oxygen molecule, which changes the shape of the whole molecule. This change is important in the uptake and transport of oxygen. It would be very interesting to find out if DommiMOE can model this  %¡†U Œ çÿ  "ªb G  $F¦: ð|ð~ ð3 í  � ð< 3 ð€€ˆ¿ c"ñ$��‘’¿ð�) \øg�3ðN² ð=  S ðX99¿ÿ?ð3 í  �ðJ ð>  # ð �¿"ñ¿`ð3 í  �ðb² ð?  c ð2€€A Á†, .DETTOLð3 í Ôðb² ð@  c ð2€€AÁ†, .PAZXAPðí  Îðb² ðA  c ð2€€AÁOì f&PURYIKð3 �Ú�𨢠ðB  3 ð€x§Y�¿"ñ¿`ðÐ í ¦ -  ðPŸ¨1.¡$ ÿÿÿþ¦: 𨢠ðC  3 ð€ä”Y�¿"ñ¿`ðmí D-  ðPŸ¨2.¡$ ÿÿÿþ¦: 𨢠ðD  3 ð€XÉY�¿"ñ¿`ðÐ í¦ - ðPŸ¨3.¡$ ÿÿÿþ¦: ðNð8 ðä4E7YaH ðN ðEä47YaHð¼ ð9  Ó ðN‡¿�¿ÀÎÿ?¿ÿˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nðä4E7YaHðÚ¢ ð7  Ó ðN€tÁY¿�¿ÀÎÿ?¿ÿˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?NðÊ81E™QäG ðŸ¨ØThe author would like to thank the MOAC Doctoral Centre staff and colleagues for their guidance and the Engineering and Physical Sciences Research Council Life Sciences Interface Programme for their generous support.¡ÙÙ¦: ð†² ð5  £ ðH€€AÁ �¿ÀÎÿˆmoacc"ñ¿`ðl51El8OHðÒ² ðJ  ƒ 𔀀 X3”¹AÁdDownloads_Images_Logos_Version1Colour_EPSRC1RGBHI"ñ¿`ð=Q^E­X7Hðj² ðL C ðB€€AÁ*the_warwick_uni_blueðx¡ š ð2ð8 ð‰4S©Av& ð† ðpä4B“%ðÚð@ ð7�$DÀ% ðm ð‰4S©Av&ðz² ð  “ ð<€€Ó œAÁ¿?ˆsa"ñ¿`ð7�$DÀ%ðÈB ð   ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðr;sW?ƒ ðÈB ð B  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÌ;ƒ W? !ðÈB ð ‚  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðú;ë•@ !ðÈB ð B  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÙ9ë•@V ðÈB ð   ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð:V ‚<f!ðÈB ð! 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ðT€€ÖAÁé" ¤ðÿÿ¿ÿMOE_Screenshot"ñ¿`ðH>%4EHð¨ ð ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nði$þ0CW½,𸢠ð$ s ð*€äçš¿�3ÌÌ¿Àÿ"ñ¿`ð¸ 'zL  ðPŸ¨Abstract¡ 2 $¦: ðÌ¢ ð& s ð*€œéš¿�3ÌÌ¿Àÿ"ñ¿`ðŠ&'z( ðdŸ¨A bit of Ligand Field Theory¡ 2$¦: ðg¢ ð' s ð*€ÔX¿�3ÌÌ¿Àÿ"ñ¿`ð‹ ä47K  ðÿŸ¨Iron(II) Hexammine [Fe(NH3)6]2+¡Š 2'$/$âÿ'$/$âÿ'$/$ª$ ¦: ð'ðF ðÒTÈbl  ð1 ðˆðùxnb ðS¢ ð ƒ ð0€tõš¿�3ÌÌ¿Àÿˆ"ñ¿`ðTÈbŽ ðÝŸ¨qFinding optimal parameters for spin-state changes in Iron(II) amine complexes in Ligand Field Molecular Mechanics¡ r(2rPª56¦: ð ¢ ð “ ð6€üX¿�ƒ¿ÀÿˆðÒZšbš  ð�Ÿ¨Prakash Patel1 , Rob Deeth2¡X(2 6 6 6 66¦: ðc¢ ð+ “ ð6€ X¿�ƒ¿ÀÿˆðÒM šbl  ðõŸ¨�1MOAC Doctoral Training Centre, and the 2Inorganic Computational Chemistry Group, Department of Chemistry, 91Ó°ÊÓÆÆ½â°æ.¡J‚(2 ' Y¦: ð¢ ð8 ƒ ð0€˜öš¿�ƒ¿ÀÿðP ú4Ë ð¿Ÿ¨The geometries and energies of six-coordinated amine complexes of Fe2+ at both spin states were explored using the DommiMOE program. Then the model parameters were refined using simulated annealing to give the correct geometries and predict the correct spin state of the metal, initially with [Fe(NH3)6]2+, then with three other amine complexes. The parameters found were applied to about 80 imine complexes, and after a slight modification, approximated the geometries reasonably well and most of the time predicted the correct spin state.¡xD å çÿ çÿ ë¦: ðB² ð. # ð Aÿ"ñ¿`ð- ¨ð¼¢ ð9 s ð*€lX¿�3ÌÌ¿Àÿ"ñ¿`ðü'z� ðTŸ¨ Introduction¡ 2 $¦: ðÖ¢ ð: £ ð<€4CX¿�ƒ¿ Àÿ?“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nðg'.4Õ ð,Ÿ îThe importance of organometallic proteins in biochemistry has long been recognised, which the metal instrumental in many of these protein s catalytic or binding functions. At the moment there are very      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFG&ýÿÿÿýÿÿÿKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~€ few methods that model transition metal-containing organometallic proteins effectively, either using quantum or classical mechanical methods. Here is outlined a very promising new Molecular Modelling approach to deal with transition metal complexes which can be used to model biological macromolecules.¡øø¦: ðç¢ ð< s ð*€ôOX¿�3ÌÌ¿Àÿ"ñ¿`ð'zâ ðŸ¨Molecular Modelling¡B 2 $, $¦: ð¨ ð? ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðmið¨ ðA ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðmið¢ ð= £ ð<€8TX¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð"'.4ƒ ðVŸ¨Molecular Modelling (MM) of Force-Field (FF) methods of finding molecular structures determine the relationship between the energy and structure by application of empirical rules based on classical mechanics. To find an optimal structure in MM, we optimise the total strain energy¡¦: ðD¢ ðB £ ð<€èfX¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðë'\4€& 𚟨\where the terms correspond to the deviation from the optimal bond lengths, bond angles, torsions, non-bonded interactions and electrostatic interactions from those given by the a particular forcefield. Modelling transition metals using conventional MM has always been difficult as they can have variable oxidation states, spin states and electronic effects, and can coordinate from 4 to 12 different ligands in a complex. Rob Deeth has addressed this problem by developing this Ligand Field Molecular Mechanics model of dealing with transition metal centres using an approach called Ligand Field Theory.¡]]¦: ð¨ ðD ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðF$miF$ðj² ðC S ð AÁ ??"ñ?ð� &ð Á ðÑ¢ ðT £ ð<€tvX¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð}('am7 ð'Ÿ¨ In a free transition metal ion, the preference of the d-electrons is to occupy each of the five d-orbitals, and when there are more than five d electrons, spin-pairing occurs. In an octahedrally-coordinated complex, the dxy, dyz and dxz orbitals become lower in energy than the dx2-y2 and dz2 orbitals and are filled first. Ligand Field Theory states that this is because the former orbitals repel the ligand electron densities less than the latter (the d-orbitals are mostly antibonding and repel ligand electron clouds). Depending on the ligands (the so-called ligand field strength), the d-electrons may desert the dx2-y2 and dz2 orbitals completely as the electron pairing becomes energetically more favourable than the electron repulsion of ligand bonding orbitals.¡® Ý çÿ çÿ çÿ, çÿ çÿM çÿ çÿ‹ª>ܦ: ðV² ðW C ð.€€AÁdorbitals2ðÔ%m¶4·+ð¢ ð\ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð_ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ðb £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð‰ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ðŒ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð� £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ðÄðF ð2)p*–2 3 ð’  ðˆðÚ+`)Ä2v4ðN² ðÑ S ðÂA ÿÿÿ¿ˆð2)p*’2€-ðN² ðÒ S ðfA ÿÿÿ¿ˆð2)_-–2n0ð² ðÓ ã ðT¿ÇÂAÿÿÿ�ƒ¿ Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð2)L0’2 3ðæ ðF ð`B*Ã23 ð‘  ðˆðÚ+èK3µ4ðþ ð¸ à ðH€8^X¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(*0Ã23 ð@Ÿ¡¦ø: Wtð� ð· ³ ðB€X§X¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`*0{(3 ðØŸ¨:(2) High Ligand Field strength (e.g. CN-, phenantroline) ¡J;(&þ.þ&þª+ ¦ø: Wtðþ ð¶ à ðH€¼°X¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(6-Ã2*0 ð@Ÿ¡¦ø: WtðÑ ðµ ³ ðB€Ø*X¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`6-{(*0 ðŸ¨7(1) Low Ligand Field strength (e.g. Cl-, I-, F-, H2O) ¡°8'&þ.þ&þ.þ&þ.þ&þ.þçÿ&þ¦ø: Wtðþ ð´ à ðH€¸ÈX¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(B*Ã26- ð@Ÿ¡,¦ø: WtðA ð³ ³ ðB€ÓX¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`B*{(6- ð‰Ÿ¨Free Fe2+ ion (high spin)¡> ¦ø: WtðªB ð¹ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`B*Ã2B*ð¤B 𺠣 ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`6-Ã26-ð¤B ð» £ ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`*0Ã2*0ðªB ð¼ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`3Ã23ðªB ð½ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`B*`3ð¤B ð¾ £ ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð{(B*{(3ðªB ð¿ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÃ2B*Ã23ð/ðF ð$ °ÔÌ ðä ðˆðu>’Ù �?ði¢ ðå  ð€”×Xð$ °ÄÌ ð+Ÿ¨ High Spin¦: ðh¢ ðæ  ð€háXð4°ÔÌ ð*Ÿ¨Low Spin¦: ðj² ðè S ð A Á  ??"ñ?ðà?ó%yBð Á  ð_ ðê à ðH€ØéX‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðFB'L%ÁG 𩟨yDeeth has implemented LFMM into the Molecular Operating Environment (MOE), a popular MM dynamics program, to form DommiMOE, which uses the forcefield MMFF94 for non-transition metals. DommiMOE can optimise the geometry a complex for a given spin state, and so can give hypothetical structures of transition metal complexes for both spin states with the same set of parameters.¡zzðö ðë à ðH€|Y‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðP ä4>_  ð@Ÿ ØThis is an octahedral high-spin complex where the Fe  N bond lengths were 2.20 ú (from X-ray crystallographic data). To obtain data on the a hypothetical low-spin structure, QM techniques were used, which predict that the Fe  N bond lengths to be around 2.00 ú. An estimate of 11 kcal/mol was also imposed on the energetic favourability of the high spin state to the low spin state. As with all MM-based methods, some model parameters have to be found which fit the required geometries and energies. Parameters modified included the Morse function parameters (Fe N bond length potential was modelled by a Morse function), octahedral-field splitting term, the ligand-ligand repulsion term and some electron-pairing energy terms. To measure the  fit of the parameters, a cost function was constructed such that the smaller its value, the better the parameters fit the data.¡mmª0P ³ gðt² ðì c ð>A Á·m ¸ÿFe_hexammine"ñ¿`ð 0_Ïgðâ ðî s ð*€ôòX¿�3ÌÌ¿Àÿ"ñ¿`ðzä4 K ð[Ÿ¨Simulated Annealing¡ 2$¦: ð" 𬠳 ðB€hY¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð¹7D\4N? ðrŸ öThe difference between low spin and high spin states is the metal-ligand bond lengths of low spin states are much smaller than those of high spin. For example, the Fe  N bond length in low spin and high spin amine complexes are about 2.00 and 2.20ú respectively. This is because of the smaller repulsion of the ligands from the d-electron cloud at low spin. Deeth summarises this effect by the Ligand Field Stabilisation Energy (LFSE), and incorporated into the MM framework by adding to the MM equation:¡.üù"ªù ¦: ðv ð­ ³ ðB€ÐY¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðä4p–287 ðÆŸ¨r(1) is known as the high-spin state of Fe2+ as the total spin is greater than in (2), known as the low spin state.¡*s) H¦: ðj² ð¯  S ð A Á '??"ñ?ð17¯` ‚>ð Á 'ð( ð² à ðH€L$Y‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðä4ìgs ðrŸ ¾Simulated Annealing (SA) is a method of finding the maximum or minimum of a distribution À(x) by using Markov Chain Monte Carlo (MCMC) to sample the parameter space, in this case the distribution needed to be minimised is the cost function A Markov chain (a  random walk ) is constructed whose limiting distribution is À(x) - the target distribution. ¡d`[""å"""""ª,Yãð¨ ð¶ ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð+$mi+$ð ð» à ðH€˜þX‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð§%·4dg* ð`Ÿ BIn simulated annealing, the target distribution À(x) is changed to À(x)1/T (T is known as the  temperature ), which has the same maxima and minima as À(x) but is rather  steeper as T decreases from 1 to 0, and this makes the Markov chain less likely to escape local minima. If the temperature is carefully reduced, then (hopefully) at the end of the procedure the Markov chain will reside near the global minimum. ¡΢2"""""**""K""""è"ª,0c ð¿¢ ð¼ s ð*€ HY¿�3ÌÌ¿Àÿ"ñ¿`ð�*ä47K1, ðWŸ¨Amine Complexes¡ 2$¦: ðì ð¿ à ðH€XJY‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð5,ä4•\½2 ð6Ÿ¨6The simulated annealing procedure yielded some good parameters for the iron hexaammine complex, which were applied to three other amine complexes. From the bond lengths in their X-ray crystallographic structures, (1) and (2) were low spin complexes, while (3) was a high spin complex, which illustrates the sensitivity of the spin state of Fe2+ with nitrogen ligands. The parameters found for [Fe(NH3)6]2+ were found to reproduce the geometry of the complexes very well in their native spin states, and also the spin states of the complexes were correctly predicted.¡Â7Ý""  S"*7"*âÿ"*âÿ"*¢"ªL áð¿¢ ðÛ s ð*€8cY¿�3ÌÌ¿Àÿ"ñ¿`ðÃ2ä47KW4 ðWŸ¨Imine Complexes¡ 2$¦: ðy ðÝ Ã ðH€ðdY‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð\4ä4‘gÞ; ðߨ¥Can these parameters transfer to imine complexes? Unlike amine nitrogens, imine nitrogens are aromatic, and most Fe2+ imine complexes are low-spin. It was found that after some modification of the parameters, although the bond lengths were not very accurately reproduced, DommiMOE correctly predicted the spin state for most of the complexes (but not all). The most striking result was the predicted spin states of the low spin complex [Fe(1-10-phenantroline)3]2+ and the high spin [Fe(2-methyl-1-10-phenantroline)3]2+. Although the ligands in these complexes were very similar, DommiMOE correctly deduced their spin states, which correspond to a large change in geometry.¡Îi= t"*ò"f"*âÿ"*3"*âÿ"*œ"ª,@  Lðœ ð “ ð6…¿�¿Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðt!Î.ž:t!ðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@ÖD¦Pð@ðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð‘GÖD¦P‘Gð–B ð “ ð6‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@ÖDÖD¬GðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@¦P¦P‘GððF ðdYÝ<hæE ðF  ðˆðÍ;dYhÖDð^ ð  ³ ðB€ÔyY¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðk`@DhæE 𦟨$[Fe(2-methyl-1-10-phenantroline)3]2+¡f% eÿÿÿþmÿÿÿþâÿeÿÿÿþmÿÿÿþAðe ð  ³ ðB€H�Y¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðdY@Dk`æE 𭟨e(1-10-phenantroline)3]2+¡v%ÿÿÿþeÿÿÿþmÿÿÿþâÿeÿÿÿþmÿÿÿþAðö ð  ³ ðB€d�Y¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðdYÝ< h@D ð>Ÿ¡¦ø: Wtðt² ð  “ ðD‚„# "AÁÇ .?ˆBUHKAQð�YÝ<ð`7Dðt² ð  “ ðD‚F5 "AÁ€ Â5?ˆCEPZOMðÜ`Ý<|g7Dð¼¢ ð s ð*€@™Y¿�3ÌÌ¿Àÿ"ñ¿`ðÝ<ä47Kq> ðTŸ¨ Applications¡ 2 $¦: ðø¢ ð3 à ðH€ ›Y¿�ƒ¿ Àÿ?¿ÿ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðu>ä4ìYýD ðBŸ (The next step is to model Iron(II) porphyrins, which are planar complexes with the Fe2+ surrounded by four aromatic nitrogens (chemically similar to imine nitrogens). The most important example of an Iron(II) porphyrin is the O2 -binding site for haemoglobin, heme. Fe2+ in heme changes from high spin to low spin when it binds to an oxygen molecule, which changes the shape of the whole molecule. This change is important in the uptake and transport of oxygen. It would be very interesting to find out if DommiMOE can model this  %¡†U Œ çÿ  "ªb G  $F¦: ð|ð~ ð3 í  � ð< 3 ð€€ˆ¿ c"ñ$��‘’¿ð�) \øg�3ðN² ð=  S ðX99¿ÿ?ð3 í  �ðJ ð>  # ð �¿"ñ¿`ð3 í  �ðb² ð?  c ð2€€A Á†, .DETTOLð3 í Ôðb² ð@  c ð2€€AÁ†, .PAZXAPðí  Îðb² ðA  c ð2€€AÁOì f&PURYIKð3 �Ú�𨢠ðB  3 ð€x§Y�¿"ñ¿`ðÐ í ¦ -  ðPŸ¨1.¡$ ÿÿÿþ¦: 𨢠ðC  3 ð€ä”Y�¿"ñ¿`ðmí D-  ðPŸ¨2.¡$ ÿÿÿþ¦: 𨢠ðD  3 ð€XÉY�¿"ñ¿`ðÐ í¦ - ðPŸ¨3.¡$ ÿÿÿþ¦: ðNð8 ðä4E7YaH ðN ðEä47YaHð¼ ð9  Ó ðN‡¿�¿ÀÎÿ?¿ÿˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nðä4E7YaHðÚ¢ ð7  Ó ðN€tÁY¿�¿ÀÎÿ?¿ÿˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?NðÊ81E™QäG ðŸ¨ØThe author would like to thank the MOAC Doctoral Centre staff and colleagues for their guidance and the Engineering and Physical Sciences Research Council Life Sciences Interface Programme for their generous support.¡ÙÙ¦: ð†² ð5  £ ðH€€AÁ �¿ÀÎÿˆmoacc"ñ¿`ðl51El8OHðÒ² ðJ  ƒ 𔀀 X3”¹AÁdDownloads_Images_Logos_Version1Colour_EPSRC1RGBHI"ñ¿`ð=Q^E­X7Hðj² ðL C ðB€€AÁ*the_warwick_uni_blueðx¡ š ð2ð8 ð‰4S©Av& ð† ðpä4B“%ðÚð@ ð7�$DÀ% ðm ð‰4S©Av&ðz² ð  “ ð<€€Ó œAÁ¿?ˆsa"ñ¿`ð7�$DÀ%ðÈB ð   ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðr;sW?ƒ ðÈB ð B  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÌ;ƒ W? !ðÈB ð ‚  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðú;ë•@ !ðÈB ð B  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÙ9ë•@V ðÈB ð   ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð:V ‚<f!ðÈB ð! 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Then the model parameters were refined using simulated annealing to give the correct geometries and predict the correct spin state of the metal, initially with [Fe(NH3)6]2+, then with three other amine complexes. The parameters found were applied to about 80 imine complexes, and after a slight modification, approximated the geometries reasonably well and most of the time predicted the correct spin state.¡xD å çÿ çÿ ë¦: ðB² ð. # ð Aÿ"ñ¿`ð- ¨ð¼¢ ð9 s ð*€lX¿�3ÌÌ¿Àÿ"ñ¿`ðü'z� ðTŸ¨ Introduction¡ 2 $¦: ðÖ¢ ð: £ ð<€4CX¿�ƒ¿ Àÿ?“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nðg'.4Õ ð,Ÿ îThe importance of organometallic proteins in biochemistry has long been recognised, which the metal instrumental in many of these protein s catalytic or binding functions. At the moment there are very few methods that model transition metal-containing organometallic proteins effectively, either using quantum or classical mechanical methods. Here is outlined a very promising new Molecular Modelling approach to deal with transition metal complexes which can be used to model biological macromolecules.¡øø¦: ðç¢ ð< s ð*€ôOX¿�3ÌÌ¿Àÿ"ñ¿`ð'zâ ðŸ¨Molecular Modelling¡B 2 $, $¦: ð¨ ð? ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðmið¨ ðA ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðmið¢ ð= £ ð<€8TX¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð"'.4ƒ ðVŸ¨Molecular Modelling (MM) of Force-Field (FF) methods of finding molecular structures determine the relationship between the energy and structure by application of empirical rules based on classical mechanics. To find an optimal structure in MM, we optimise the total strain energy¡¦: ðD¢ ðB £ ð<€èfX¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðë'\4€& 𚟨\where the terms correspond to the deviation from the optimal bond lengths, bond angles, torsions, non-bonded interactions and electrostatic interactions from those given by the a particular forcefield. Modelling transition metals using conventional MM has always been difficult as they can have variable oxidation states, spin states and electronic effects, and can coordinate from 4 to 12 different ligands in a complex. Rob Deeth has addressed this problem by developing this Ligand Field Molecular Mechanics model of dealing with transition metal centres using an approach called Ligand Field Theory.¡]]¦: ð¨ ðD ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðF$miF$ðj² ðC S ð AÁ ??"ñ?ð� &ð Á ðÑ¢ ðT £ ð<€tvX¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð}('am7 ð'Ÿ¨ In a free transition metal ion, the preference of the d-electrons is to occupy each of the five d-orbitals, and when there are more than five d electrons, spin-pairing occurs. In an octahedrally-coordinated complex, the dxy, dyz and dxz orbitals become lower in energy than the dx2-y2 and dz2 orbitals and are filled first. Ligand Field Theory states that this is because the former orbitals repel the ligand electron densities less than the latter (the d-orbitals are mostly antibonding and repel ligand electron clouds). Depending on the ligands (the so-called ligand field strength), the d-electrons may desert the dx2-y2 and dz2 orbitals completely as the electron pairing becomes energetically more favourable than the electron repulsion of ligand bonding orbitals.¡® Ý çÿ çÿ çÿ, çÿ çÿM çÿ çÿ‹ª>ܦ: ðV² ðW C ð.€€AÁdorbitals2ðÔ%m¶4·+ð¢ ð\ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð_ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ðb £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð‰ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ðŒ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð� £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ðÄðF ð2)p*–2 3 ð’  ðˆðÚ+`)Ä2v4ðN² ðÑ S ðÂA ÿÿÿ¿ˆð2)p*’2€-ðN² ðÒ S ðfA ÿÿÿ¿ˆð2)_-–2n0ð² ðÓ ã ðT¿ÇÂAÿÿÿ�ƒ¿ Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð2)L0’2 3ðæ ðF ð`B*Ã23 ð‘  ðˆðÚ+èK3µ4ðþ ð¸ à ðH€8^X¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(*0Ã23 ð@Ÿ¡¦ø: Wtð� ð· ³ ðB€X§X¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`*0{(3 ðØŸ¨:(2) High Ligand Field strength (e.g. CN-, phenantroline) ¡J;(&þ.þ&þª+ ¦ø: Wtðþ ð¶ à ðH€¼°X¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(6-Ã2*0 ð@Ÿ¡¦ø: WtðÑ ðµ ³ ðB€Ø*X¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`6-{(*0 ðŸ¨7(1) Low Ligand Field strength (e.g. Cl-, I-, F-, H2O) ¡°8'&þ.þ&þ.þ&þ.þ&þ.þçÿ&þ¦ø: Wtðþ ð´ à ðH€¸ÈX¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(B*Ã26- ð@Ÿ¡,¦ø: WtðA ð³ ³ ðB€ÓX¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`B*{(6- ð‰Ÿ¨Free Fe2+ ion (high spin)¡> ¦ø: WtðªB ð¹ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`B*Ã2B*ð¤B 𺠣 ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`6-Ã26-ð¤B ð» £ ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`*0Ã2*0ðªB ð¼ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`3Ã23ðªB ð½ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`B*`3ð¤B ð¾ £ ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð{(B*{(3ðªB ð¿ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÃ2B*Ã23ð/ðF ð$ °ÔÌ ðä ðˆðu>’Ù �?ði¢ ðå  ð€”×Xð$ °ÄÌ ð+Ÿ¨ High Spin¦: ðh¢ ðæ  ð€háXð4°ÔÌ ð*Ÿ¨Low Spin¦: ðj² ðè S ð A Á  ??"ñ?ðà?ó%yBð Á  ð_ ðê à ðH€ØéX‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðFB'L%ÁG 𩟨yDeeth has implemented LFMM into the Molecular Operating Environment (MOE), a popular MM dynamics program, to form DommiMOE, which uses the forcefield MMFF94 for non-transition metals. DommiMOE can optimise the geometry a complex for a given spin state, and so can give hypothetical structures of transition metal complexes for both spin states with the same set of parameters.¡zzðö ðë à ðH€|Y‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðP ä4>_  ð@Ÿ ØThis is an octahedral high-spin complex where the Fe  N bond lengths were 2.20 ú (from X-ray crystallographic data). To obtain data on the a hypothetical low-spin structure, QM techniques were used, which predict that the Fe  N bond lengths to be around 2.00 ú. An estimate of 11 kcal/mol was also imposed on the energetic favourability of the high spin state to the low spin state. As with all MM-based methods, some model parameters have to be found which fit the required geometries and energies. Parameters modified included the Morse function parameters (Fe N bond length potential was modelled by a Morse function), octahedral-field splitting term, the ligand-ligand repulsion term and some electron-pairing energy terms. To measure the  fit of the parameters, a cost function was constructed such that the smaller its value, the better the parameters fit the data.¡mmª0P ³ gðt² ðì c ð>A Á·m ¸ÿFe_hexammine"ñ¿`ð 0_Ïgðâ ðî s ð*€ôòX¿�3ÌÌ¿Àÿ"ñ¿`ðzä4 K ð[Ÿ¨Simulated Annealing¡ 2$¦: ð" 𬠳 ðB€hY¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð¹7D\4N? ðrŸ öThe difference between low spin and high spin states is the metal-ligand bond lengths of low spin states are much smaller than those of high spin. For example, the Fe  N bond length in low spin and high spin amine complexes are about 2.00 and 2.20ú respectively. This is because of the smaller repulsion of the ligands from the d-electron cloud at low spin. Deeth summarises this effect by the Ligand Field Stabilisation Energy (LFSE), and incorporated into the MM framework by adding to the MM equation:¡.üù"ªù ¦: ðv ð­ ³ ðB€ÐY¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðä4p–287 ðÆŸ¨r(1) is known as the high-spin state of Fe2+ as the total spin is greater than in (2), known as the low spin state.¡*s) H¦: ðj² ð¯  S ð A Á '??"ñ?ð17¯` ‚>ð Á 'ð( ð² à ðH€L$Y‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðä4ìgs ðrŸ ¾Simulated Annealing (SA) is a method of finding the maximum or minimum of a distribution À(x) by using Markov Chain Monte Carlo (MCMC) to sample the parameter space, in this case the distribution needed to be minimised is the cost function A Markov chain (a  random walk ) is constructed whose limiting distribution is À(x) - the target distribution. ¡d`[""å"""""ª,Yãð¨ ð¶ ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð+$mi+$ð ð» à ðH€˜þX‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð§%·4dg* ð`Ÿ BIn simulated annealing, the target distribution À(x) is changed to À(x)1/T (T is known as the  temperature ), which has the same maxima and minima as À(x) but is rather  steeper as T decreases from 1 to 0, and this makes the Markov chain less likely to escape local minima. If the temperature is carefully reduced, then (hopefully) at the end of the procedure the Markov chain will reside near the global minimum. ¡΢2"""""**""K""""è"ª,0c ð¿¢ ð¼ s ð*€ HY¿�3ÌÌ¿Àÿ"ñ¿`ð�*ä47K1, ðWŸ¨Amine Complexes¡ 2$¦: ðì ð¿ à ðH€XJY‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð5,ä4•\½2 ð6Ÿ¨6The simulated annealing procedure yielded some good parameters for the iron hexaammine complex, which were applied to three other amine complexes. From the bond lengths in their X-ray crystallographic structures, (1) and (2) were low spin complexes, while (3) was a high spin complex, which illustrates the sensitivity of the spin state of Fe2+ with nitrogen ligands. The parameters found for [Fe(NH3)6]2+ were found to reproduce the geometry of the complexes very well in their native spin states, and also the spin states of the complexes were correctly predicted.¡Â7Ý""  S"*7"*âÿ"*âÿ"*¢"ªL áð¿¢ ðÛ s ð*€8cY¿�3ÌÌ¿Àÿ"ñ¿`ðÃ2ä47KW4 ðWŸ¨Imine Complexes¡ 2$¦: ðy ðÝ Ã ðH€ðdY‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð\4ä4‘gÞ; ðߨ¥Can these parameters transfer to imine complexes? Unlike amine nitrogens, imine nitrogens are aromatic, and most Fe2+ imine complexes are low-spin. It was found that after some modification of the parameters, although the bond lengths were not very accurately reproduced, DommiMOE correctly predicted the spin state for most of the complexes (but not all). The most striking result was the predicted spin states of the low spin complex [Fe(1-10-phenantroline)3]2+ and the high spin [Fe(2-methyl-1-10-phenantroline)3]2+. Although the ligands in these complexes were very similar, DommiMOE correctly deduced their spin states, which correspond to a large change in geometry.¡Îi= t"*ò"f"*âÿ"*3"*âÿ"*œ"ª,@  Lðœ ð “ ð6…¿�¿Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðt!Î.ž:t!ðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@ÖD¦Pð@ðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð‘GÖD¦P‘Gð–B ð “ ð6‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@ÖDÖD¬GðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@¦P¦P‘GððF ðdYÝ<hæE ðF  ðˆðÍ;dYhÖDð^ ð  ³ ðB€ÔyY¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðk`@DhæE 𦟨$[Fe(2-methyl-1-10-phenantroline)3]2+¡f% eÿÿÿþmÿÿÿþâÿeÿÿÿþmÿÿÿþAðe ð  ³ ðB€H�Y¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðdY@Dk`æE 𭟨e(1-10-phenantroline)3]2+¡v%ÿÿÿþeÿÿÿþmÿÿÿþâÿeÿÿÿþmÿÿÿþAðö ð  ³ ðB€d�Y¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðdYÝ< h@D ð>Ÿ¡¦ø: Wtðt² ð  “ ðD‚„# "AÁÇ .?ˆBUHKAQð�YÝ<ð`7Dðt² ð  “ ðD‚F5 "AÁ€ Â5?ˆCEPZOMðÜ`Ý<|g7Dð¼¢ ð s ð*€@™Y¿�3ÌÌ¿Àÿ"ñ¿`ðÝ<ä47Kq> ðTŸ¨ Applications¡ 2 $¦: ðn² ð  s ð8€€AÁ®G (\?Image1"ñ¿`ðr;:NjWoCðø¢ ð3 à ðH€ ›Y¿�ƒ¿ Àÿ?¿ÿ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðu>ä4ìYýD ðBŸ (The next step is to model Iron(II) porphyrins, which are planar complexes with the Fe2+ surrounded by four aromatic nitrogens (chemically similar to imine nitrogens). The most important example of an Iron(II) porphyrin is the O2 -binding site for haemoglobin, heme. Fe2+ in heme changes from high spin to low spin when it binds to an oxygen molecule, which changes the shape of the whole molecule. This change is important in the uptake and transport of oxygen. It would be very interesting to find out if DommiMOE can model this  %¡†U Œ çÿ  "ªb G  $F¦: ð|ð~ ð3 í  � ð< 3 ð€€ˆ¿ c"ñ$��‘’¿ð�) \øg�3ðN² ð=  S ðX99¿ÿ?ð3 í  �ðJ ð>  # ð �¿"ñ¿`ð3 í  �ðb² ð?  c ð2€€A Á†, .DETTOLð3 í Ôðb² ð@  c ð2€€AÁ†, .PAZXAPðí  Îðb² ðA  c ð2€€AÁOì f&PURYIKð3 �Ú�𨢠ðB  3 ð€x§Y�¿"ñ¿`ðÐ í ¦ -  ðPŸ¨1.¡$ ÿÿÿþ¦: 𨢠ðC  3 ð€ä”Y�¿"ñ¿`ðmí D-  ðPŸ¨2.¡$ ÿÿÿþ¦: 𨢠ðD  3 ð€XÉY�¿"ñ¿`ðÐ í¦ - ðPŸ¨3.¡$ ÿÿÿþ¦: ðNð8 ðä4E7YaH ðN ðEä47YaHð¼ ð9  Ó ðN‡¿�¿ÀÎÿ?¿ÿˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nðä4E7YaHðÚ¢ ð7  Ó ðN€tÁY¿�¿ÀÎÿ?¿ÿˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?NðÊ81E™QäG ðŸ¨ØThe author would like to thank the MOAC Doctoral Centre staff and colleagues for their guidance and the Engineering and Physical Sciences Research Council Life Sciences Interface Programme for their generous support.¡ÙÙ¦: ð†² ð5  £ ðH€€AÁ �¿ÀÎÿˆmoacc"ñ¿`ðl51El8OHðÒ² ðJ  ƒ 𔀀 X3”¹AÁdDownloads_Images_Logos_Version1Colour_EPSRC1RGBHI"ñ¿`ð=Q^E­X7Hðj² ðL C ðB€€AÁ*the_warwick_uni_blueðx¡ š ð2ð8 ð‰4S©Av& ð† ðpä4B“%ðÚð@ ð7�$DÀ% ðm ð‰4S©Av&ðz² ð  “ ð<€€Ó œAÁ¿?ˆsa"ñ¿`ð7�$DÀ%ðÈB ð   ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðr;sW?ƒ ðÈB ð B  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÌ;ƒ W? !ðÈB ð ‚  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðú;ë•@ !ðÈB ð B  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÙ9ë•@V ðÈB ð   ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð:V ‚<f!ðÈB ð! 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Then the model parameters were refined using simulated annealing to give the correct geometries and predict the correct spin state of the metal, initially with [Fe(NH3)6]2+, then with three other amine complexes. The parameters found were applied to about 80 imine complexes, and after a slight modification, approximated the geometries reasonably well and most of the time predicted the correct spin state.¡xD å çÿ çÿ ë¦: ðB² ð. # ð Aÿ"ñ¿`ð'T ¨ð¼¢ ð9 s ð*€lX¿�3ÌÌ¿Àÿ"ñ¿`ðü'z� ðTŸ¨ Introduction¡ 2 $¦: ðÖ¢ ð: £ ð<€4CX¿�ƒ¿ Àÿ?“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nðg'.4Õ ð,Ÿ îThe importance of organometallic proteins in biochemistry has long been recognised, which the metal instrumental in many of these protein s catalytic or binding functions. At the moment there are very few methods that model transition metal-containing organometallic proteins effectively, either using quantum or classical mechanical methods. Here is outlined a very promising new Molecular Modelling approach to deal with transition metal complexes which can be used to model biological macromolecules.¡øø¦: ðç¢ ð< s ð*€ôOX¿�3ÌÌ¿Àÿ"ñ¿`ð'zâ ðŸ¨Molecular Modelling¡B 2 $, $¦: ð¨ ð? ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðmið¨ ðA ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðmið¢ ð= £ ð<€8TX¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð"'.4ƒ ðVŸ¨Molecular Modelling (MM) of Force-Field (FF) methods of finding molecular structures determine the relationship between the energy and structure by application of empirical rules based on classical mechanics. To find an optimal structure in MM, we optimise the total strain energy¡¦: ðD¢ ðB £ ð<€èfX¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðë'\4€& 𚟨\where the terms correspond to the deviation from the optimal bond lengths, bond angles, torsions, non-bonded interactions and electrostatic interactions from those given by the a particular forcefield. Modelling transition metals using conventional MM has always been difficult as they can have variable oxidation states, spin states and electronic effects, and can coordinate from 4 to 12 different ligands in a complex. Rob Deeth has addressed this problem by developing this Ligand Field Molecular Mechanics model of dealing with transition metal centres using an approach called Ligand Field Theory.¡]]¦: ð¨ ðD ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðF$miF$ðj² ðC S ð AÁ ??"ñ?ð� &ð Á ðÑ¢ ðT £ ð<€tvX¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð}('am7 ð'Ÿ¨ In a free transition metal ion, the preference of the d-electrons is to occupy each of the five d-orbitals, and when there are more than five d electrons, spin-pairing occurs. In an octahedrally-coordinated complex, the dxy, dyz and dxz orbitals become lower in energy than the dx2-y2 and dz2 orbitals and are filled first. Ligand Field Theory states that this is because the former orbitals repel the ligand electron densities less than the latter (the d-orbitals are mostly antibonding and repel ligand electron clouds). Depending on the ligands (the so-called ligand field strength), the d-electrons may desert the dx2-y2 and dz2 orbitals completely as the electron pairing becomes energetically more favourable than the electron repulsion of ligand bonding orbitals.¡® Ý çÿ çÿ çÿ, çÿ çÿM çÿ çÿ‹ª>ܦ: ðV² ðW C ð.€€AÁdorbitals2ðÔ%m¶4·+ð¢ ð\ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð_ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ðb £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð‰ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ðŒ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð� £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ðÄðF ð2)p*–2 3 ð’  ðˆðÚ+`)Ä2v4ðN² ðÑ S ðÂA ÿÿÿ¿ˆð2)p*’2€-ðN² ðÒ S ðfA ÿÿÿ¿ˆð2)_-–2n0ð² ðÓ ã ðT¿ÇÂAÿÿÿ�ƒ¿ Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð2)L0’2 3ðæ ðF ð`B*Ã23 ð‘  ðˆðÚ+èK3µ4ðþ ð¸ à ðH€8^X¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(*0Ã23 ð@Ÿ¡¦ø: Wtð� ð· ³ ðB€X§X¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`*0{(3 ðØŸ¨:(2) High Ligand Field strength (e.g. CN-, phenantroline) ¡J;(&þ.þ&þª+ ¦ø: Wtðþ ð¶ à ðH€¼°X¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(6-Ã2*0 ð@Ÿ¡¦ø: WtðÑ ðµ ³ ðB€Ø*X¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`6-{(*0 ðŸ¨7(1) Low Ligand Field strength (e.g. Cl-, I-, F-, H2O) ¡°8'&þ.þ&þ.þ&þ.þ&þ.þçÿ&þ¦ø: Wtðþ ð´ à ðH€¸ÈX¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(B*Ã26- ð@Ÿ¡,¦ø: WtðA ð³ ³ ðB€ÓX¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`B*{(6- ð‰Ÿ¨Free Fe2+ ion (high spin)¡> ¦ø: WtðªB ð¹ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`B*Ã2B*ð¤B 𺠣 ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`6-Ã26-ð¤B ð» £ ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`*0Ã2*0ðªB ð¼ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`3Ã23ðªB ð½ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`B*`3ð¤B ð¾ £ ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð{(B*{(3ðªB ð¿ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÃ2B*Ã23ð/ðF ð$ °ÔÌ ðä ðˆðu>’Ù �?ði¢ ðå  ð€”×Xð$ °ÄÌ ð+Ÿ¨ High Spin¦: ðh¢ ðæ  ð€háXð4°ÔÌ ð*Ÿ¨Low Spin¦: ðj² ðè S ð A Á  ??"ñ?ðà?ó%yBð Á  ð_ ðê à ðH€ØéX‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðFB'L%ÁG 𩟨yDeeth has implemented LFMM into the Molecular Operating Environment (MOE), a popular MM dynamics program, to form DommiMOE, which uses the forcefield MMFF94 for non-transition metals. DommiMOE can optimise the geometry a complex for a given spin state, and so can give hypothetical structures of transition metal complexes for both spin states with the same set of parameters.¡zzðö ðë à ðH€|Y‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðP ä4>_  ð@Ÿ ØThis is an octahedral high-spin complex where the Fe  N bond lengths were 2.20 ú (from X-ray crystallographic data). To obtain data on the a hypothetical low-spin structure, QM techniques were used, which predict that the Fe  N bond lengths to be around 2.00 ú. An estimate of 11 kcal/mol was also imposed on the energetic favourability of the high spin state to the low spin state. As with all MM-based methods, some model parameters have to be found which fit the required geometries and energies. Parameters modified included the Morse function parameters (Fe N bond length potential was modelled by a Morse function), octahedral-field splitting term, the ligand-ligand repulsion term and some electron-pairing energy terms. To measure the  fit of the parameters, a cost function was constructed such that the smaller its value, the better the parameters fit the data.¡mmª0P ³ gðt² ðì c ð>A Á·m ¸ÿFe_hexammine"ñ¿`ð 0_Ïgðâ ðî s ð*€ôòX¿�3ÌÌ¿Àÿ"ñ¿`ðzä4 K ð[Ÿ¨Simulated Annealing¡ 2$¦: ð" 𬠳 ðB€hY¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð¹7D\4N? ðrŸ öThe difference between low spin and high spin states is the metal-ligand bond lengths of low spin states are much smaller than those of high spin. For example, the Fe  N bond length in low spin and high spin amine complexes are about 2.00 and 2.20ú respectively. This is because of the smaller repulsion of the ligands from the d-electron cloud at low spin. Deeth summarises this effect by the Ligand Field Stabilisation Energy (LFSE), and incorporated into the MM framework by adding to the MM equation:¡.üù"ªù ¦: ðv ð­ ³ ðB€ÐY¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðä4p–287 ðÆŸ¨r(1) is known as the high-spin state of Fe2+ as the total spin is greater than in (2), known as the low spin state.¡*s) H¦: ðj² ð¯  S ð A Á '??"ñ?ð17¯` ‚>ð Á 'ð( ð² à ðH€L$Y‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðä4ìgs ðrŸ ¾Simulated Annealing (SA) is a method of finding the maximum or minimum of a distribution À(x) by using Markov Chain Monte Carlo (MCMC) to sample the parameter space, in this case the distribution needed to be minimised is the cost function A Markov chain (a  random walk ) is constructed whose limiting distribution is À(x) - the target distribution. ¡d`[""å"""""ª,Yãð¨ ð¶ ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð+$mi+$ð ð» à ðH€˜þX‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð§%·4dg* ð`Ÿ BIn simulated annealing, the target distribution À(x) is changed to À(x)1/T (T is known as the  temperature ), which has the same maxima and minima as À(x) but is rather  steeper as T decreases from 1 to 0, and this makes the Markov chain less likely to escape local minima. If the temperature is carefully reduced, then (hopefully) at the end of the procedure the Markov chain will reside near the global minimum. ¡΢2"""""**""K""""è"ª,0c ð¿¢ ð¼ s ð*€ HY¿�3ÌÌ¿Àÿ"ñ¿`ð�*ä47K1, ðWŸ¨Amine Complexes¡ 2$¦: ðì ð¿ à ðH€XJY‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð5,ä4•\½2 ð6Ÿ¨6The simulated annealing procedure yielded some good parameters for the iron hexaammine complex, which were applied to three other amine complexes. From the bond lengths in their X-ray crystallographic structures, (1) and (2) were low spin complexes, while (3) was a high spin complex, which illustrates the sensitivity of the spin state of Fe2+ with nitrogen ligands. The parameters found for [Fe(NH3)6]2+ were found to reproduce the geometry of the complexes very well in their native spin states, and also the spin states of the complexes were correctly predicted.¡Â7Ý""  S"*7"*âÿ"*âÿ"*¢"ªL áð¿¢ ðÛ s ð*€8cY¿�3ÌÌ¿Àÿ"ñ¿`ðÃ2ä47KW4 ðWŸ¨Imine Complexes¡ 2$¦: ðy ðÝ Ã ðH€ðdY‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð\4ä4‘gÞ; ðߨ¥Can these parameters transfer to imine complexes? Unlike amine nitrogens, imine nitrogens are aromatic, and most Fe2+ imine complexes are low-spin. It was found that after some modification of the parameters, although the bond lengths were not very accurately reproduced, DommiMOE correctly predicted the spin state for most of the complexes (but not all). The most striking result was the predicted spin states of the low spin complex [Fe(1-10-phenantroline)3]2+ and the high spin [Fe(2-methyl-1-10-phenantroline)3]2+. Although the ligands in these complexes were very similar, DommiMOE correctly deduced their spin states, which correspond to a large change in geometry.¡Îi= t"*ò"f"*âÿ"*3"*âÿ"*œ"ª,@  Lðœ ð “ ð6…¿�¿Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðt!Î.ž:t!ðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@ÖD¦Pð@ðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð‘GÖD¦P‘Gð–B ð “ ð6‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@ÖDÖD¬GðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@¦P¦P‘GððF ðdYÝ<hæE ðF  ðˆðÍ;dYhÖDð^ ð  ³ ðB€ÔyY¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðk`@DhæE 𦟨$[Fe(2-methyl-1-10-phenantroline)3]2+¡f% eÿÿÿþmÿÿÿþâÿeÿÿÿþmÿÿÿþAðe ð  ³ ðB€H�Y¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðdY@Dk`æE 𭟨e(1-10-phenantroline)3]2+¡v%ÿÿÿþeÿÿÿþmÿÿÿþâÿeÿÿÿþmÿÿÿþAðö ð  ³ ðB€d�Y¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðdYÝ< h@D ð>Ÿ¡¦ø: Wtðt² ð  “ ðD‚„# "AÁÇ .?ˆBUHKAQð�YÝ<ð`7Dðt² ð  “ ðD‚F5 "AÁ€ Â5?ˆCEPZOMðÜ`Ý<|g7Dð¼¢ ð s ð*€@™Y¿�3ÌÌ¿Àÿ"ñ¿`ðÝ<ä47Kq> ðTŸ¨ Applications¡ 2 $¦: ðn² ð  s ð8€€AÁ®G (\?Image1"ñ¿`ðr;:NjWoCðø¢ ð3 à ðH€ ›Y¿�ƒ¿ Àÿ?¿ÿ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðu>ä4ìYýD ðBŸ (The next step is to model Iron(II) porphyrins, which are planar complexes with the Fe2+ surrounded by four aromatic nitrogens (chemically similar to imine nitrogens). The most important example of an Iron(II) porphyrin is the O2 -binding site for haemoglobin, heme. Fe2+ in heme changes from high spin to low spin when it binds to an oxygen molecule, which changes the shape of the whole molecule. This change is important in the uptake and transport of oxygen. It would be very interesting to find out if DommiMOE can model this  %¡†U Œ çÿ  "ªb G  $F¦: ð|ð~ ð3 í  � ð< 3 ð€€ˆ¿ c"ñ$��‘’¿ð�) \øg�3ðN² ð=  S ðX99¿ÿ?ð3 í  �ðJ ð>  # ð �¿"ñ¿`ð3 í  �ðb² ð?  c ð2€€A Á†, .DETTOLð3 í Ôðb² ð@  c ð2€€AÁ†, .PAZXAPðí  Îðb² ðA  c ð2€€AÁOì f&PURYIKð3 �Ú�𨢠ðB  3 ð€x§Y�¿"ñ¿`ðÐ í ¦ -  ðPŸ¨1.¡$ ÿÿÿþ¦: 𨢠ðC  3 ð€ä”Y�¿"ñ¿`ðmí D-  ðPŸ¨2.¡$ ÿÿÿþ¦: 𨢠ðD  3 ð€XÉY�¿"ñ¿`ðÐ í¦ - ðPŸ¨3.¡$ ÿÿÿþ¦: ðNð8 ðä4E7YaH ðN ðEä47YaHð¼ ð9  Ó ðN‡¿�¿ÀÎÿ?¿ÿˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nðä4E7YaHðÚ¢ ð7  Ó ðN€tÁY¿�¿ÀÎÿ?¿ÿˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?NðÊ81E™QäG ðŸ¨ØThe author would like to thank the MOAC Doctoral Centre staff and colleagues for their guidance and the Engineering and Physical Sciences Research Council Life Sciences Interface Programme for their generous support.¡ÙÙ¦: ð†² ð5  £ ðH€€AÁ �¿ÀÎÿˆmoacc"ñ¿`ðl51El8OHðÒ² ðJ  ƒ 𔀀 X3”¹AÁdDownloads_Images_Logos_Version1Colour_EPSRC1RGBHI"ñ¿`ð=Q^E­X7Hðj² ðL C ðB€€AÁ*the_warwick_uni_blueðx¡ š ð2ð8 ð‰4S©Av& ð† ðpä4B“%ðÚð@ ð7�$DÀ% ðm ð‰4S©Av&ðz² ð  “ ð<€€Ó œAÁ¿?ˆsa"ñ¿`ð7�$DÀ%ðÈB ð   ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðr;sW?ƒ ðÈB ð B  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÌ;ƒ W? !ðÈB ð ‚  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðú;ë•@ !ðÈB ð B  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÙ9ë•@V ðÈB ð   ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð:V ‚<f!ðÈB ð! 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Then the model parameters were refined using simulated annealing to give the correct geometries and predict the correct spin state of the metal, initially with [Fe(NH3)6]2+, then with three other amine complexes. The parameters found were applied to about 80 imine complexes, and after a slight modification, approximated the geometries reasonably well and most of the time predicted the correct spin state.¡xD å çÿ çÿ ë¦: ðB² ð. # ð Aÿ"ñ¿`ð'T ¨ð¼¢ ð9 s ð*€lX¿�3ÌÌ¿Àÿ"ñ¿`ðü'z� ðTŸ¨ Introduction¡ 2 $¦: ðÖ¢ ð: £ ð<€4CX¿�ƒ¿ Àÿ?“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nðg'.4Õ ð,Ÿ îThe importance of organometallic proteins in biochemistry has long been recognised, which the metal instrumental in many of these protein s catalytic or binding functions. At the moment there are very few methods that model transition metal-containing organometallic proteins effectively, either using quantum or classical mechanical methods. Here is outlined a very promising new Molecular Modelling approach to deal with transition metal complexes which can be used to model biological macromolecules.¡øø¦: ðç¢ ð< s ð*€ôOX¿�3ÌÌ¿Àÿ"ñ¿`ð'zâ ðŸ¨Molecular Modelling¡B 2 $, $¦: ð¨ ð? ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðmið¨ ðA ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðmið¢ ð= £ ð<€8TX¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð"'.4ƒ ðVŸ¨Molecular Modelling (MM) of Force-Field (FF) methods of finding molecular structures determine the relationship between the energy and structure by application of empirical rules based on classical mechanics. To find an optimal structure in MM, we optimise the total strain energy¡¦: ðD¢ ðB £ ð<€èfX¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðë'\4€& 𚟨\where the terms correspond to the deviation from the optimal bond lengths, bond angles, torsions, non-bonded interactions and electrostatic interactions from those given by the a particular forcefield. Modelling transition metals using conventional MM has always been difficult as they can have variable oxidation states, spin states and electronic effects, and can coordinate from 4 to 12 different ligands in a complex. Rob Deeth has addressed this problem by developing this Ligand Field Molecular Mechanics model of dealing with transition metal centres using an approach called Ligand Field Theory.¡]]¦: ð¨ ðD ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðF$miF$ðj² ðC S ð AÁ ??"ñ?ð� &ð Á ðÑ¢ ðT £ ð<€tvX¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð}('am7 ð'Ÿ¨ In a free transition metal ion, the preference of the d-electrons is to occupy each of the five d-orbitals, and when there are more than five d electrons, spin-pairing occurs. In an octahedrally-coordinated complex, the dxy, dyz and dxz orbitals become lower in energy than the dx2-y2 and dz2 orbitals and are filled first. Ligand Field Theory states that this is because the former orbitals repel the ligand electron densities less than the latter (the d-orbitals are mostly antibonding and repel ligand electron clouds). Depending on the ligands (the so-called ligand field strength), the d-electrons may desert the dx2-y2 and dz2 orbitals completely as the electron pairing becomes energetically more favourable than the electron repulsion of ligand bonding orbitals.¡® Ý çÿ çÿ çÿ, çÿ çÿM çÿ çÿ‹ª>ܦ: ðV² ðW C ð.€€AÁdorbitals2ðÔ%m¶4·+ð¢ ð\ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð_ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ðb £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð‰ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ðŒ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð� £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ðÄðF ð2)p*–2 3 ð’  ðˆðÚ+`)Ä2v4ðN² ðÑ S ðÂA ÿÿÿ¿ˆð2)p*’2€-ðN² ðÒ S ðfA ÿÿÿ¿ˆð2)_-–2n0ð² ðÓ ã ðT¿ÇÂAÿÿÿ�ƒ¿ Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð2)L0’2 3ðæ ðF ð`B*Ã23 ð‘  ðˆðÚ+èK3µ4ðþ ð¸ à ðH€8^X¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(*0Ã23 ð@Ÿ¡¦ø: Wtð� ð· ³ ðB€X§X¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`*0{(3 ðØŸ¨:(2) High Ligand Field strength (e.g. CN-, phenantroline) ¡J;(&þ.þ&þª+ ¦ø: Wtðþ ð¶ à ðH€¼°X¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(6-Ã2*0 ð@Ÿ¡¦ø: WtðÑ ðµ ³ ðB€Ø*X¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`6-{(*0 ðŸ¨7(1) Low Ligand Field strength (e.g. Cl-, I-, F-, H2O) ¡°8'&þ.þ&þ.þ&þ.þ&þ.þçÿ&þ¦ø: Wtðþ ð´ à ðH€¸ÈX¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(B*Ã26- ð@Ÿ¡,¦ø: WtðA ð³ ³ ðB€ÓX¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`B*{(6- ð‰Ÿ¨Free Fe2+ ion (high spin)¡> ¦ø: WtðªB ð¹ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`B*Ã2B*ð¤B 𺠣 ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`6-Ã26-ð¤B ð» £ ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`*0Ã2*0ðªB ð¼ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`3Ã23ðªB ð½ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`B*`3ð¤B ð¾ £ ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð{(B*{(3ðªB ð¿ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÃ2B*Ã23ð/ðF ð$ °ÔÌ ðä ðˆðu>’Ù �?ði¢ ðå  ð€”×Xð$ °ÄÌ ð+Ÿ¨ High Spin¦: ðh¢ ðæ  ð€háXð4°ÔÌ ð*Ÿ¨Low Spin¦: ðj² ðè S ð A Á  ??"ñ?ðà?ó%yBð Á  ð_ ðê à ðH€ØéX‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðFB'L%ÁG 𩟨yDeeth has implemented LFMM into the Molecular Operating Environment (MOE), a popular MM dynamics program, to form DommiMOE, which uses the forcefield MMFF94 for non-transition metals. DommiMOE can optimise the geometry a complex for a given spin state, and so can give hypothetical structures of transition metal complexes for both spin states with the same set of parameters.¡zzð ðë à ðH€|Y‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðP ä4>_  ðJŸ ÐThis is an octahedral high-spin complex where the Fe  N bond lengths were 2.20 ú (from X-ray crystallographic data). To obtain data on a hypothetical low-spin structure, QM techniques were used, which predict that the Fe  N bond lengths to be around 2.00 ú. An estimate of 11 kcal/mol was also imposed on the energetic favourability of the high spin state to the low spin state. As with all MM-based methods, some model parameters have to be found which fit the required geometries and energies. Parameters modified included the Morse function parameters (Fe N bond length potential was modelled by a Morse function), octahedral-field splitting term, the ligand-ligand repulsion term and some electron-pairing energy terms. To measure the  fit of the parameters, a cost function was constructed such that the smaller its value, the better the parameters fit the data.¡iiªBP 3z gðt² ðì c ð>A Á·m ¸ÿFe_hexammine"ñ¿`ð 0_Ïgðâ ðî s ð*€ôòX¿�3ÌÌ¿Àÿ"ñ¿`ðzä4 K ð[Ÿ¨Simulated Annealing¡ 2$¦: ð" 𬠳 ðB€hY¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð¹7D\4N? ðrŸ öThe difference between low spin and high spin states is the metal-ligand bond lengths of low spin states are much smaller than those of high spin. For example, the Fe  N bond length in low spin and high spin amine complexes are about 2.00 and 2.20ú respectively. This is because of the smaller repulsion of the ligands from the d-electron cloud at low spin. Deeth summarises this effect by the Ligand Field Stabilisation Energy (LFSE), and incorporated into the MM framework by adding to the MM equation:¡.üù"ªù ¦: ðv ð­ ³ ðB€ÐY¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðä4p–287 ðÆŸ¨r(1) is known as the high-spin state of Fe2+ as the total spin is greater than in (2), known as the low spin state.¡*s) H¦: ðj² ð¯  S ð A Á '??"ñ?ð17¯` ‚>ð Á 'ð( ð² à ðH€L$Y‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðä4ìgs ðrŸ ¾Simulated Annealing (SA) is a method of finding the maximum or minimum of a distribution À(x) by using Markov Chain Monte Carlo (MCMC) to sample the parameter space, in this case the distribution needed to be minimised is the cost function A Markov chain (a  random walk ) is constructed whose limiting distribution is À(x) - the target distribution. ¡d`[""å"""""ª,Yãð¨ ð¶ ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð+$mi+$ð ð» à ðH€˜þX‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð§%·4dg* ð`Ÿ BIn simulated annealing, the target distribution À(x) is changed to À(x)1/T (T is known as the  temperature ), which has the same maxima and minima as À(x) but is rather  steeper as T decreases from 1 to 0, and this makes the Markov chain less likely to escape local minima. If the temperature is carefully reduced, then (hopefully) at the end of the procedure the Markov chain will reside near the global minimum. ¡΢2"""""**""K""""è"ª,0c ð¿¢ ð¼ s ð*€ HY¿�3ÌÌ¿Àÿ"ñ¿`ð�*ä47K1, ðWŸ¨Amine Complexes¡ 2$¦: ðì ð¿ à ðH€XJY‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð5,ä4•\½2 ð6Ÿ¨6The simulated annealing procedure yielded some good parameters for the iron hexaammine complex, which were applied to three other amine complexes. From the bond lengths in their X-ray crystallographic structures, (1) and (2) were low spin complexes, while (3) was a high spin complex, which illustrates the sensitivity of the spin state of Fe2+ with nitrogen ligands. The parameters found for [Fe(NH3)6]2+ were found to reproduce the geometry of the complexes very well in their native spin states, and also the spin states of the complexes were correctly predicted.¡Â7Ý""  S"*7"*âÿ"*âÿ"*¢"ªL áð¿¢ ðÛ s ð*€8cY¿�3ÌÌ¿Àÿ"ñ¿`ðÃ2ä47KW4 ðWŸ¨Imine Complexes¡ 2$¦: ðy ðÝ Ã ðH€ðdY‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð\4ä4‘gÞ; ðߨ¥Can these parameters transfer to imine complexes? Unlike amine nitrogens, imine nitrogens are aromatic, and most Fe2+ imine complexes are low-spin. It was found that after some modification of the parameters, although the bond lengths were not very accurately reproduced, DommiMOE correctly predicted the spin state for most of the complexes (but not all). The most striking result was the predicted spin states of the low spin complex [Fe(1-10-phenantroline)3]2+ and the high spin [Fe(2-methyl-1-10-phenantroline)3]2+. Although the ligands in these complexes were very similar, DommiMOE correctly deduced their spin states, which correspond to a large change in geometry.¡Îi= t"*ò"f"*âÿ"*3"*âÿ"*œ"ª,@  Lðœ ð “ ð6…¿�¿Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðt!Î.ž:t!ðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@ÖD¦Pð@ðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð‘GÖD¦P‘Gð–B ð “ ð6‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@ÖDÖD¬GðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@¦P¦P‘GððF ðdYÝ<hæE ðF  ðˆðÍ;dYhÖDð^ ð  ³ ðB€ÔyY¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðk`@DhæE 𦟨$[Fe(2-methyl-1-10-phenantroline)3]2+¡f% eÿÿÿþmÿÿÿþâÿeÿÿÿþmÿÿÿþAðe ð  ³ ðB€H�Y¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðdY@Dk`æE 𭟨e(1-10-phenantroline)3]2+¡v%ÿÿÿþeÿÿÿþmÿÿÿþâÿeÿÿÿþmÿÿÿþAðö ð  ³ ðB€d�Y¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðdYÝ< h@D ð>Ÿ¡¦ø: Wtðt² ð  “ ðD‚„# "AÁÇ .?ˆBUHKAQð�YÝ<ð`7Dðt² ð  “ ðD‚F5 "AÁ€ Â5?ˆCEPZOMðÜ`Ý<|g7Dð¼¢ ð s ð*€@™Y¿�3ÌÌ¿Àÿ"ñ¿`ðÝ<ä47Kq> ðTŸ¨ Applications¡ 2 $¦: ðn² ð  s ð8€€AÁ®G (\?Image1"ñ¿`ðr;:NjWoCðø¢ ð3 à ðH€ ›Y¿�ƒ¿ Àÿ?¿ÿ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðu>ä4ìYýD ðBŸ (The next step is to model Iron(II) porphyrins, which are planar complexes with the Fe2+ surrounded by four aromatic nitrogens (chemically similar to imine nitrogens). The most important example of an Iron(II) porphyrin is the O2 -binding site for haemoglobin, heme. Fe2+ in heme changes from high spin to low spin when it binds to an oxygen molecule, which changes the shape of the whole molecule. This change is important in the uptake and transport of oxygen. It would be very interesting to find out if DommiMOE can model this  %¡†U Œ çÿ  "ªb G  $F¦: ð|ð~ ð3 í  � ð< 3 ð€€ˆ¿ c"ñ$��‘’¿ð�) \øg�3ðN² ð=  S ðX99¿ÿ?ð3 í  �ðJ ð>  # ð �¿"ñ¿`ð3 í  �ðb² ð?  c ð2€€A Á†, .DETTOLð3 í Ôðb² ð@  c ð2€€AÁ†, .PAZXAPðí  Îðb² ðA  c ð2€€AÁOì f&PURYIKð3 �Ú�𨢠ðB  3 ð€x§Y�¿"ñ¿`ðÐ í ¦ -  ðPŸ¨1.¡$ ÿÿÿþ¦: 𨢠ðC  3 ð€ä”Y�¿"ñ¿`ðmí D-  ðPŸ¨2.¡$ ÿÿÿþ¦: 𨢠ðD  3 ð€XÉY�¿"ñ¿`ðÐ í¦ - ðPŸ¨3.¡$ ÿÿÿþ¦: ðNð8 ðä4E7YaH ðN ðEä47YaHð¼ ð9  Ó ðN‡¿�¿ÀÎÿ?¿ÿˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nðä4E7YaHðÚ¢ ð7  Ó ðN€tÁY¿�¿ÀÎÿ?¿ÿˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?NðÊ81E™QäG ðŸ¨ØThe author would like to thank the MOAC Doctoral Centre staff and colleagues for their guidance and the Engineering and Physical Sciences Research Council Life Sciences Interface Programme for their generous support.¡ÙÙ¦: ð†² ð5  £ ðH€€AÁ �¿ÀÎÿˆmoacc"ñ¿`ðl51El8OHðÒ² ðJ  ƒ 𔀀 X3”¹AÁdDownloads_Images_Logos_Version1Colour_EPSRC1RGBHI"ñ¿`ð=Q^E­X7Hðj² ðL C ðB€€AÁ*the_warwick_uni_blueðx¡ š ð2ð8 ð‰4S©Av& ð† ðpä4B“%ðÚð@ ð7�$DÀ% ðm ð‰4S©Av&ðz² ð  “ ð<€€Ó œAÁ¿?ˆsa"ñ¿`ð7�$DÀ%ðÈB ð   ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðr;sW?ƒ ðÈB ð B  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÌ;ƒ W? !ðÈB ð ‚  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðú;ë•@ !ðÈB ð B  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÙ9ë•@V ðÈB ð   ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð:V ‚<f!ðÈB ð! 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Then the model parameters were refined using simulated annealing to give the correct geometries and predict the correct spin state of the metal, initially with [Fe(NH3)6]2+, then with three other amine complexes. The parameters found were applied to about 80 imine complexes, and after a slight modification, approximated the geometries reasonably well and most of the time predicted the correct spin state.¡xD å çÿ çÿ ë¦: ðB² ð. # ð Aÿ"ñ¿`ð'T ¨ð¼¢ ð9 s ð*€lX¿�3ÌÌ¿Àÿ"ñ¿`ðü'z� ðTŸ¨ Introduction¡ 2 $¦: ðÖ¢ ð: £ ð<€4CX¿�ƒ¿ Àÿ?“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nðg'.4Õ ð,Ÿ îThe importance of organometallic proteins in biochemistry has long been recognised, which the metal instrumental in many of these protein s catalytic or binding functions. At the moment there are very few methods that model transition metal-containing organometallic proteins effectively, either using quantum or classical mechanical methods. Here is outlined a very promising new Molecular Modelling approach to deal with transition metal complexes which can be used to model biological macromolecules.¡øø¦: ðç¢ ð< s ð*€ôOX¿�3ÌÌ¿Àÿ"ñ¿`ð'zâ ðŸ¨Molecular Modelling¡B 2 $, $¦: ð¨ ð? ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðmið¨ ðA ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðmið¢ ð= £ ð<€8TX¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð"'.4ƒ ðVŸ¨Molecular Modelling (MM) of Force-Field (FF) methods of finding molecular structures determine the relationship between the energy and structure by application of empirical rules based on classical mechanics. To find an optimal structure in MM, we optimise the total strain energy¡¦: ðD¢ ðB £ ð<€èfX¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðë'\4€& 𚟨\where the terms correspond to the deviation from the optimal bond lengths, bond angles, torsions, non-bonded interactions and electrostatic interactions from those given by the a particular forcefield. Modelling transition metals using conventional MM has always been difficult as they can have variable oxidation states, spin states and electronic effects, and can coordinate from 4 to 12 different ligands in a complex. Rob Deeth has addressed this problem by developing this Ligand Field Molecular Mechanics model of dealing with transition metal centres using an approach called Ligand Field Theory.¡]]¦: ð¨ ðD ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðF$miF$ðj² ðC S ð AÁ ??"ñ?ð� &ð Á ðÑ¢ ðT £ ð<€tvX¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð}('am7 ð'Ÿ¨ In a free transition metal ion, the preference of the d-electrons is to occupy each of the five d-orbitals, and when there are more than five d electrons, spin-pairing occurs. In an octahedrally-coordinated complex, the dxy, dyz and dxz orbitals become lower in energy than the dx2-y2 and dz2 orbitals and are filled first. Ligand Field Theory states that this is because the former orbitals repel the ligand electron densities less than the latter (the d-orbitals are mostly antibonding and repel ligand electron clouds). Depending on the ligands (the so-called ligand field strength), the d-electrons may desert the dx2-y2 and dz2 orbitals completely as the electron pairing becomes energetically more favourable than the electron repulsion of ligand bonding orbitals.¡® Ý çÿ çÿ çÿ, çÿ çÿM çÿ çÿ‹ª>ܦ: ðV² ðW C ð.€€AÁdorbitals2ðÔ%m¶4·+ð¢ ð\ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð_ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ðb £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð‰ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ðŒ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð� £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ðÄðF ð2)p*–2 3 ð’  ðˆðÚ+`)Ä2v4ðN² ðÑ S ðÂA ÿÿÿ¿ˆð2)p*’2€-ðN² ðÒ S ðfA ÿÿÿ¿ˆð2)_-–2n0ð² ðÓ ã ðT¿ÇÂAÿÿÿ�ƒ¿ Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð2)L0’2 3ðæ ðF ð`B*Ã23 ð‘  ðˆðÚ+èK3µ4ðþ ð¸ à ðH€8^X¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(*0Ã23 ð@Ÿ¡¦ø: Wtð� ð· ³ ðB€X§X¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`*0{(3 ðØŸ¨:(2) High Ligand Field strength (e.g. CN-, phenantroline) ¡J;(&þ.þ&þª+ ¦ø: Wtðþ ð¶ à ðH€¼°X¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(6-Ã2*0 ð@Ÿ¡¦ø: WtðÑ ðµ ³ ðB€Ø*X¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`6-{(*0 ðŸ¨7(1) Low Ligand Field strength (e.g. Cl-, I-, F-, H2O) ¡°8'&þ.þ&þ.þ&þ.þ&þ.þçÿ&þ¦ø: Wtðþ ð´ à ðH€¸ÈX¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(B*Ã26- ð@Ÿ¡,¦ø: WtðA ð³ ³ ðB€ÓX¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`B*{(6- ð‰Ÿ¨Free Fe2+ ion (high spin)¡> ¦ø: WtðªB ð¹ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`B*Ã2B*ð¤B 𺠣 ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`6-Ã26-ð¤B ð» £ ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ�‚ƒ„…†‡ˆ‰Š‹Œ�Ž��‘’“”•–—˜™š›œ�žŸ ¡¢£¤¥¦§¨©ª«¬­®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈÉÊËÌÍÎÏÐÑÒÓÔÕÖרÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øúýÿÿÿûüýþÿ €¿‚‚N¿NÿN?Nð`*0Ã2*0ðªB ð¼ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`3Ã23ðªB ð½ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`B*`3ð¤B ð¾ £ ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð{(B*{(3ðªB ð¿ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÃ2B*Ã23ð/ðF ð$ °ÔÌ ðä ðˆðu>’Ù �?ði¢ ðå  ð€”×Xð$ °ÄÌ ð+Ÿ¨ High Spin¦: ðh¢ ðæ  ð€háXð4°ÔÌ ð*Ÿ¨Low Spin¦: ðj² ðè S ð A Á  ??"ñ?ðà?ó%yBð Á  ð_ ðê à ðH€ØéX‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðFB'L%ÁG 𩟨yDeeth has implemented LFMM into the Molecular Operating Environment (MOE), a popular MM dynamics program, to form DommiMOE, which uses the forcefield MMFF94 for non-transition metals. DommiMOE can optimise the geometry a complex for a given spin state, and so can give hypothetical structures of transition metal complexes for both spin states with the same set of parameters.¡zzðú ðë à ðH€|Y‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðP ä4>_  ðDŸ ÊThis is an octahedral high-spin complex where the Fe  N bond lengths were 2.20 ú (from X-ray crystallographic data). To obtain data on a hypothetical low-spin structure, QM techniques were used, which predict that the Fe  N bond lengths to be around 2.00 ú. Also, an estimate of 11 kcal/mol was set on the energetic favourability of the high spin state to the low spin state. As with all MM-based methods, some model parameters have to be found which fit the required geometries and energies. Parameters modified included the Morse function parameters (Fe N bond length potential was modelled by a Morse function), octahedral-field splitting term, the ligand-ligand repulsion term and some electron-pairing energy terms. To measure the  fit of the parameters, a cost function was constructed such that the smaller its value, the better the parameters fit the data.¡ffªBP ¯ Yðt² ðì c ð>A Á·m ¸ÿFe_hexammine"ñ¿`ð 0_Ïgðâ ðî s ð*€ôòX¿�3ÌÌ¿Àÿ"ñ¿`ðzä4 K ð[Ÿ¨Simulated Annealing¡ 2$¦: ð" 𬠳 ðB€hY¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð¹7D\4N? ðrŸ öThe difference between low spin and high spin states is the metal-ligand bond lengths of low spin states are much smaller than those of high spin. For example, the Fe  N bond length in low spin and high spin amine complexes are about 2.00 and 2.20ú respectively. This is because of the smaller repulsion of the ligands from the d-electron cloud at low spin. Deeth summarises this effect by the Ligand Field Stabilisation Energy (LFSE), and incorporated into the MM framework by adding to the MM equation:¡.üù"ªù ¦: ðv ð­ ³ ðB€ÐY¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðä4p–287 ðÆŸ¨r(1) is known as the high-spin state of Fe2+ as the total spin is greater than in (2), known as the low spin state.¡*s) H¦: ðj² ð¯  S ð A Á '??"ñ?ð17¯` ‚>ð Á 'ð( ð² à ðH€L$Y‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðä4ìgs ðrŸ ¾Simulated Annealing (SA) is a method of finding the maximum or minimum of a distribution À(x) by using Markov Chain Monte Carlo (MCMC) to sample the parameter space, in this case the distribution needed to be minimised is the cost function A Markov chain (a  random walk ) is constructed whose limiting distribution is À(x) - the target distribution. ¡d`[""å"""""ª,Yãð¨ ð¶ ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð+$mi+$ð ð» à ðH€˜þX‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð§%·4dg* ð`Ÿ BIn simulated annealing, the target distribution À(x) is changed to À(x)1/T (T is known as the  temperature ), which has the same maxima and minima as À(x) but is rather  steeper as T decreases from 1 to 0, and this makes the Markov chain less likely to escape local minima. If the temperature is carefully reduced, then (hopefully) at the end of the procedure the Markov chain will reside near the global minimum. ¡΢2"""""**""K""""è"ª,0c ð¿¢ ð¼ s ð*€ HY¿�3ÌÌ¿Àÿ"ñ¿`ð�*ä47K1, ðWŸ¨Amine Complexes¡ 2$¦: ðì ð¿ à ðH€XJY‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð5,ä4•\½2 ð6Ÿ¨6The simulated annealing procedure yielded some good parameters for the iron hexaammine complex, which were applied to three other amine complexes. From the bond lengths in their X-ray crystallographic structures, (1) and (2) were low spin complexes, while (3) was a high spin complex, which illustrates the sensitivity of the spin state of Fe2+ with nitrogen ligands. The parameters found for [Fe(NH3)6]2+ were found to reproduce the geometry of the complexes very well in their native spin states, and also the spin states of the complexes were correctly predicted.¡Â7Ý""  S"*7"*âÿ"*âÿ"*¢"ªL áð¿¢ ðÛ s ð*€8cY¿�3ÌÌ¿Àÿ"ñ¿`ðÃ2ä47KW4 ðWŸ¨Imine Complexes¡ 2$¦: ðy ðÝ Ã ðH€ðdY‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð\4ä4‘gÞ; ðߨ¥Can these parameters transfer to imine complexes? Unlike amine nitrogens, imine nitrogens are aromatic, and most Fe2+ imine complexes are low-spin. It was found that after some modification of the parameters, although the bond lengths were not very accurately reproduced, DommiMOE correctly predicted the spin state for most of the complexes (but not all). The most striking result was the predicted spin states of the low spin complex [Fe(1-10-phenantroline)3]2+ and the high spin [Fe(2-methyl-1-10-phenantroline)3]2+. Although the ligands in these complexes were very similar, DommiMOE correctly deduced their spin states, which correspond to a large change in geometry.¡Îi= t"*ò"f"*âÿ"*3"*âÿ"*œ"ª,@  Lðœ ð “ ð6…¿�¿Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðt!Î.ž:t!ðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@ÖD¦Pð@ðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð‘GÖD¦P‘Gð–B ð “ ð6‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@ÖDÖD¬GðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@¦P¦P‘GððF ðdYÝ<hæE ðF  ðˆðÍ;dYhÖDð^ ð  ³ ðB€ÔyY¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðk`@DhæE 𦟨$[Fe(2-methyl-1-10-phenantroline)3]2+¡f% eÿÿÿþmÿÿÿþâÿeÿÿÿþmÿÿÿþAðe ð  ³ ðB€H�Y¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðdY@Dk`æE 𭟨e(1-10-phenantroline)3]2+¡v%ÿÿÿþeÿÿÿþmÿÿÿþâÿeÿÿÿþmÿÿÿþAðö ð  ³ ðB€d�Y¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðdYÝ< h@D ð>Ÿ¡¦ø: Wtðt² ð  “ ðD‚„# "AÁÇ .?ˆBUHKAQð�YÝ<ð`7Dðt² ð  “ ðD‚F5 "AÁ€ Â5?ˆCEPZOMðÜ`Ý<|g7Dð¼¢ ð s ð*€@™Y¿�3ÌÌ¿Àÿ"ñ¿`ðÝ<ä47Kq> ðTŸ¨ Applications¡ 2 $¦: ðn² ð  s ð8€€AÁ®G (\?Image1"ñ¿`ðr;:NjWoCðø¢ ð3 à ðH€ ›Y¿�ƒ¿ Àÿ?¿ÿ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðu>ä4ìYýD ðBŸ (The next step is to model Iron(II) porphyrins, which are planar complexes with the Fe2+ surrounded by four aromatic nitrogens (chemically similar to imine nitrogens). The most important example of an Iron(II) porphyrin is the O2 -binding site for haemoglobin, heme. Fe2+ in heme changes from high spin to low spin when it binds to an oxygen molecule, which changes the shape of the whole molecule. This change is important in the uptake and transport of oxygen. It would be very interesting to find out if DommiMOE can model this  %¡†U Œ çÿ  "ªb G  $F¦: ð|ð~ ð3 í  � ð< 3 ð€€ˆ¿ c"ñ$��‘’¿ð�) \øg�3ðN² ð=  S ðX99¿ÿ?ð3 í  �ðJ ð>  # ð �¿"ñ¿`ð3 í  �ðb² ð?  c ð2€€A Á†, .DETTOLð3 í Ôðb² ð@  c ð2€€AÁ†, .PAZXAPðí  Îðb² ðA  c ð2€€AÁOì f&PURYIKð3 �Ú�𨢠ðB  3 ð€x§Y�¿"ñ¿`ðÐ í ¦ -  ðPŸ¨1.¡$ ÿÿÿþ¦: 𨢠ðC  3 ð€ä”Y�¿"ñ¿`ðmí D-  ðPŸ¨2.¡$ ÿÿÿþ¦: 𨢠ðD  3 ð€XÉY�¿"ñ¿`ðÐ í¦ - ðPŸ¨3.¡$ ÿÿÿþ¦: ðNð8 ðä4E7YaH ðN ðEä47YaHð¼ ð9  Ó ðN‡¿�¿ÀÎÿ?¿ÿˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nðä4E7YaHðÚ¢ ð7  Ó ðN€tÁY¿�¿ÀÎÿ?¿ÿˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?NðÊ81E™QäG ðŸ¨ØThe author would like to thank the MOAC Doctoral Centre staff and colleagues for their guidance and the Engineering and Physical Sciences Research Council Life Sciences Interface Programme for their generous support.¡ÙÙ¦: ð†² ð5  £ ðH€€AÁ �¿ÀÎÿˆmoacc"ñ¿`ðl51El8OHðÒ² ðJ  ƒ 𔀀 X3”¹AÁdDownloads_Images_Logos_Version1Colour_EPSRC1RGBHI"ñ¿`ð=Q^E­X7Hðj² ðL C ðB€€AÁ*the_warwick_uni_blueðx¡ š ð2ð8 ð‰4S©Av& ð† ðpä4B“%ðÚð@ ð7�$DÀ% ðm ð‰4S©Av&ðz² ð  “ ð<€€Ó œAÁ¿?ˆsa"ñ¿`ð7�$DÀ%ðÈB ð   ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðr;sW?ƒ ðÈB ð B  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÌ;ƒ W? !ðÈB ð ‚  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðú;ë•@ !ðÈB ð B  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÙ9ë•@V ðÈB ð   ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð:V ‚<f!ðÈB ð! 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Then the model parameters were refined using simulated annealing to give the correct geometries and predict the correct spin state of the metal, initially with [Fe(NH3)6]2+, then with three other amine complexes. The parameters found were applied to about 80 imine complexes, and after a slight modification, approximated the geometries reasonably well and most of the time predicted the correct spin state.¡xD å çÿ çÿ ë¦: ðB² ð. # ð Aÿ"ñ¿`ð'T ¨ð¼¢ ð9 s ð*€lX¿�3ÌÌ¿Àÿ"ñ¿`ðü'z� ðTŸ¨ Introduction¡ 2 $¦: ðÖ¢ ð: £ ð<€4CX¿�ƒ¿ Àÿ?“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nðg'.4Õ ð,Ÿ îThe importance of organometallic proteins in biochemistry has long been recognised, which the metal instrumental in many of these protein s catalytic or binding functions. At the moment there are very few methods that model transition metal-containing organometallic proteins effectively, either using quantum or classical mechanical methods. Here is outlined a very promising new Molecular Modelling approach to deal with transition metal complexes which can be used to model biological macromolecules.¡øø¦: ðç¢ ð< s ð*€ôOX¿�3ÌÌ¿Àÿ"ñ¿`ð'zâ ðŸ¨Molecular Modelling¡B 2 $, $¦: ð¨ ð? ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðmið¨ ðA ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðmið¢ ð= £ ð<€8TX¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð"'.4ƒ ðVŸ¨Molecular Modelling (MM) of Force-Field (FF) methods of finding molecular structures determine the relationship between the energy and structure by application of empirical rules based on classical mechanics. To find an optimal structure in MM, we optimise the total strain energy¡¦: ðD¢ ðB £ ð<€èfX¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðë'\4€& 𚟨\where the terms correspond to the deviation from the optimal bond lengths, bond angles, torsions, non-bonded interactions and electrostatic interactions from those given by the a particular forcefield. Modelling transition metals using conventional MM has always been difficult as they can have variable oxidation states, spin states and electronic effects, and can coordinate from 4 to 12 different ligands in a complex. Rob Deeth has addressed this problem by developing this Ligand Field Molecular Mechanics model of dealing with transition metal centres using an approach called Ligand Field Theory.¡]]¦: ð¨ ðD ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðF$miF$ðj² ðC S ð AÁ ??"ñ?ð� &ð Á ðÑ¢ ðT £ ð<€tvX¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð}('am7 ð'Ÿ¨ In a free transition metal ion, the preference of the d-electrons is to occupy each of the five d-orbitals, and when there are more than five d electrons, spin-pairing occurs. In an octahedrally-coordinated complex, the dxy, dyz and dxz orbitals become lower in energy than the dx2-y2 and dz2 orbitals and are filled first. Ligand Field Theory states that this is because the former orbitals repel the ligand electron densities less than the latter (the d-orbitals are mostly antibonding and repel ligand electron clouds). Depending on the ligands (the so-called ligand field strength), the d-electrons may desert the dx2-y2 and dz2 orbitals completely as the electron pairing becomes energetically more favourable than the electron repulsion of ligand bonding orbitals.¡® Ý çÿ çÿ çÿ, çÿ çÿM çÿ çÿ‹ª>ܦ: ðV² ðW C ð.€€AÁdorbitals2ðÔ%m¶4·+ð¢ ð\ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð_ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ðb £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð‰ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ðŒ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð� £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ðÄðF ð2)p*–2 3 ð’  ðˆðÚ+`)Ä2v4ðN² ðÑ S ðÂA ÿÿÿ¿ˆð2)p*’2€-ðN² ðÒ S ðfA ÿÿÿ¿ˆð2)_-–2n0ð² ðÓ ã ðT¿ÇÂAÿÿÿ�ƒ¿ Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð2)L0’2 3ðæ ðF ð`B*Ã23 ð‘  ðˆðÚ+èK3µ4ðþ ð¸ à ðH€8^X¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(*0Ã23 ð@Ÿ¡¦ø: Wtð� ð· ³ ðB€X§X¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`*0{(3 ðØŸ¨:(2) High Ligand Field strength (e.g. CN-, phenantroline) ¡J;(&þ.þ&þª+ ¦ø: Wtðþ ð¶ à ðH€¼°X¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(6-Ã2*0 ð@Ÿ¡¦ø: WtðÑ ðµ ³ ðB€Ø*X¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`6-{(*0 ðŸ¨7(1) Low Ligand Field strength (e.g. Cl-, I-, F-, H2O) ¡°8'&þ.þ&þ.þ&þ.þ&þ.þçÿ&þ¦ø: Wtðþ ð´ à ðH€¸ÈX¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(B*Ã26- ð@Ÿ¡,¦ø: WtðA ð³ ³ ðB€ÓX¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`B*{(6- ð‰Ÿ¨Free Fe2+ ion (high spin)¡> ¦ø: WtðªB ð¹ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`B*Ã2B*ð¤B 𺠣 ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`6-Ã26-ð¤B ð» £ ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`*0Ã2*0ðªB ð¼ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`3Ã23ðªB ð½ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`B*`3ð¤B ð¾ £ ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð{(B*{(3ðªB ð¿ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÃ2B*Ã23ð/ðF ð$ °ÔÌ ðä ðˆðu>’Ù �?ði¢ ðå  ð€”×Xð$ °ÄÌ ð+Ÿ¨ High Spin¦: ðh¢ ðæ  ð€háXð4°ÔÌ ð*Ÿ¨Low Spin¦: ðj² ðè S ð A Á  ??"ñ?ðà?ó%yBð Á  ð_ ðê à ðH€ØéX‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðFB'L%ÁG 𩟨yDeeth has implemented LFMM into the Molecular Operating Environment (MOE), a popular MM dynamics program, to form DommiMOE, which uses the forcefield MMFF94 for non-transition metals. DommiMOE can optimise the geometry a complex for a given spin state, and so can give hypothetical structures of transition metal complexes for both spin states with the same set of parameters.¡zzðè ðë à ðH€|Y‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðP ä4>_  ð2Ÿ ÊThis is an octahedral high-spin complex where the Fe  N bond lengths were 2.20 ú (from X-ray crystallographic data). To obtain data on a hypothetical low-spin structure, QM techniques were used, which predict that the Fe  N bond lengths to be around 2.00 ú. Also, an estimate of 11 kcal/mol was set on the energetic favourability of the high spin state to the low spin state. As with all MM-based methods, some model parameters have to be found which fit the required geometries and energies. Parameters modified included the Morse function parameters (Fe N bond length potential was modelled by a Morse function), octahedral-field splitting term, the ligand-ligand repulsion term and some electron-pairing energy terms. To measure the  fit of the parameters, a cost function was constructed such that the smaller its value, the better the parameters fit the data.¡ffª0P ¯ dðt² ðì c ð>A Á·m ¸ÿFe_hexammine"ñ¿`ð 0_Ïgðâ ðî s ð*€ôòX¿�3ÌÌ¿Àÿ"ñ¿`ðzä4 K ð[Ÿ¨Simulated Annealing¡ 2$¦: ðF 𬠳 ðB€hY¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð¹7D\4N? ð–Ÿ The difference between low spin and high spin states is the metal-ligand bond lengths of low spin states are much smaller than those of high spin. For example, the Fe  N bond length in low spin and high spin amine complexes are about 2.00 and 2.20ú respectively. This is because of the smaller repulsion of the ligands from the d-electron cloud at low spin than at high spin. Deeth summarises this effect by the Ligand Field Stabilisation Energy (LFSE), and incorporated into the MM framework by adding to the MM equation:¡.ù"ªù ¦: ðv ð­ ³ ðB€ÐY¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðä4p–287 ðÆŸ¨r(1) is known as the high-spin state of Fe2+ as the total spin is greater than in (2), known as the low spin state.¡*s) H¦: ðj² ð¯  S ð A Á '??"ñ?ð17¯` ‚>ð Á 'ð( ð² à ðH€L$Y‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðä4ìgs ðrŸ ¾Simulated Annealing (SA) is a method of finding the maximum or minimum of a distribution À(x) by using Markov Chain Monte Carlo (MCMC) to sample the parameter space, in this case the distribution needed to be minimised is the cost function A Markov chain (a  random walk ) is constructed whose limiting distribution is À(x) - the target distribution. ¡d`[""å"""""ª,Yãð¨ ð¶ ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð+$mi+$ð ð» à ðH€˜þX‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð§%·4dg* ð`Ÿ BIn simulated annealing, the target distribution À(x) is changed to À(x)1/T (T is known as the  temperature ), which has the same maxima and minima as À(x) but is rather  steeper as T decreases from 1 to 0, and this makes the Markov chain less likely to escape local minima. If the temperature is carefully reduced, then (hopefully) at the end of the procedure the Markov chain will reside near the global minimum. ¡΢2"""""**""K""""è"ª,0c ð¿¢ ð¼ s ð*€ HY¿�3ÌÌ¿Àÿ"ñ¿`ð�*ä47K1, ðWŸ¨Amine Complexes¡ 2$¦: ðì ð¿ à ðH€XJY‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð5,ä4•\½2 ð6Ÿ¨6The simulated annealing procedure yielded some good parameters for the iron hexaammine complex, which were applied to three other amine complexes. From the bond lengths in their X-ray crystallographic structures, (1) and (2) were low spin complexes, while (3) was a high spin complex, which illustrates the sensitivity of the spin state of Fe2+ with nitrogen ligands. The parameters found for [Fe(NH3)6]2+ were found to reproduce the geometry of the complexes very well in their native spin states, and also the spin states of the complexes were correctly predicted.¡Â7Ý""  S"*7"*âÿ"*âÿ"*¢"ªL áð¿¢ ðÛ s ð*€8cY¿�3ÌÌ¿Àÿ"ñ¿`ðÃ2ä47KW4 ðWŸ¨Imine Complexes¡ 2$¦: ðy ðÝ Ã ðH€ðdY‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð\4ä4‘gÞ; ðߨ¥Can these parameters transfer to imine complexes? Unlike amine nitrogens, imine nitrogens are aromatic, and most Fe2+ imine complexes are low-spin. It was found that after some modification of the parameters, although the bond lengths were not very accurately reproduced, DommiMOE correctly predicted the spin state for most of the complexes (but not all). The most striking result was the predicted spin states of the low spin complex [Fe(1-10-phenantroline)3]2+ and the high spin [Fe(2-methyl-1-10-phenantroline)3]2+. Although the ligands in these complexes were very similar, DommiMOE correctly deduced their spin states, which correspond to a large change in geometry.¡Îi= t"*ò"f"*âÿ"*3"*âÿ"*œ"ª,@  Lðœ ð “ ð6…¿�¿Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðt!Î.ž:t!ðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@ÖD¦Pð@ðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð‘GÖD¦P‘Gð–B ð “ ð6‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@ÖDÖD¬GðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@¦P¦P‘GððF ðdYÝ<hæE ðF  ðˆðÍ;dYhÖDð^ ð  ³ ðB€ÔyY¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðk`@DhæE 𦟨$[Fe(2-methyl-1-10-phenantroline)3]2+¡f% eÿÿÿþmÿÿÿþâÿeÿÿÿþmÿÿÿþAðe ð  ³ ðB€H�Y¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðdY@Dk`æE 𭟨e(1-10-phenantroline)3]2+¡v%ÿÿÿþeÿÿÿþmÿÿÿþâÿeÿÿÿþmÿÿÿþAðö ð  ³ ðB€d�Y¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðdYÝ< h@D ð>Ÿ¡¦ø: Wtðt² ð  “ ðD‚„# "AÁÇ .?ˆBUHKAQð�YÝ<ð`7Dðt² ð  “ ðD‚F5 "AÁ€ Â5?ˆCEPZOMðÜ`Ý<|g7Dð¼¢ ð s ð*€@™Y¿�3ÌÌ¿Àÿ"ñ¿`ðÝ<ä47Kq> ðTŸ¨ Applications¡ 2 $¦: ðn² ð  s ð8€€AÁ®G (\?Image1"ñ¿`ðr;:NjWoCðø¢ ð3 à ðH€ ›Y¿�ƒ¿ Àÿ?¿ÿ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðu>ä4ìYýD ðBŸ (The next step is to model Iron(II) porphyrins, which are planar complexes with the Fe2+ surrounded by four aromatic nitrogens (chemically similar to imine nitrogens). The most important example of an Iron(II) porphyrin is the O2 -binding site for haemoglobin, heme. Fe2+ in heme changes from high spin to low spin when it binds to an oxygen molecule, which changes the shape of the whole molecule. This change is important in the uptake and transport of oxygen. It would be very interesting to find out if DommiMOE can model this  %¡†U Œ çÿ  "ªb G  $F¦: ð|ð~ ð3 í  � ð< 3 ð€€ˆ¿ c"ñ$��‘’¿ð�) \øg�3ðN² ð=  S ðX99¿ÿ?ð3 í  �ðJ ð>  # ð �¿"ñ¿`ð3 í  �ðb² ð?  c ð2€€A Á†, .DETTOLð3 í Ôðb² ð@  c ð2€€AÁ†, .PAZXAPðí  Îðb² ðA  c ð2€€AÁOì f&PURYIKð3 �Ú�𨢠ðB  3 ð€x§Y�¿"ñ¿`ðÐ í ¦ -  ðPŸ¨1.¡$ ÿÿÿþ¦: 𨢠ðC  3 ð€ä”Y�¿"ñ¿`ðmí D-  ðPŸ¨2.¡$ ÿÿÿþ¦: 𨢠ðD  3 ð€XÉY�¿"ñ¿`ðÐ í¦ - ðPŸ¨3.¡$ ÿÿÿþ¦: ðNð8 ðä4E7YaH ðN ðEä47YaHð¼ ð9  Ó ðN‡¿�¿ÀÎÿ?¿ÿˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nðä4E7YaHðÚ¢ ð7  Ó ðN€tÁY¿�¿ÀÎÿ?¿ÿˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?NðÊ81E™QäG ðŸ¨ØThe author would like to t                          ! 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Then the model parameters were refined using simulated annealing to give the correct geometries and predict the correct spin state of the metal, initially with [Fe(NH3)6]2+, then with three other amine complexes. The parameters found were applied to about 80 imine complexes, and after a slight modification, approximated the geometries reasonably well and most of the time predicted the correct spin state.¡xD å çÿ çÿ ë¦: ðB² ð. # ð Aÿ"ñ¿`ð'T ¨ð ¢ ð9 à ðH€,fŠ ¿?�3ÌÌ¿Àÿ?¿ÿ“"ñ6?@¿`ÿÀ¿‚‚N¿NÿN?Nðü'z� ðTŸ¨ Introduction¡ 2 $¦: ðÖ¢ ð: £ ð<€8—Š ¿�ƒ¿ Àÿ?“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nðg'.4Õ ð,Ÿ îThe importance of organometallic proteins in biochemistry has long been recognised, which the metal instrumental in many of these protein s catalytic or binding functions. At the moment there are very few methods that model transition metal-containing organometallic proteins effectively, either using quantum or classical mechanical methods. Here is outlined a very promising new Molecular Modelling approach to deal with transition metal complexes which can be used to model biological macromolecules.¡øø¦: ð¢ ð< à ðH€��Š ¿?�3ÌÌ¿Àÿ?¿ÿ“"ñ6?@¿`ÿÀ¿‚‚N¿NÿN?Nð'z– ð[Ÿ¨Molecular Modelling¡ 2$¦: ð¨ ð? ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðmið¨ ðA ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðmið¢ ð= £ ð<€±Š ¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð"'.4ƒ ðVŸ¨Molecular Modelling (MM) of Force-Field (FF) methods of finding molecular structures determine the relationship between the energy and structure by application of empirical rules based on classical mechanics. To find an optimal structure in MM, we optimise the total strain energy¡¦: ðD¢ ðB £ ð<€øºŠ ¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðë'\4€& 𚟨\where the terms correspond to the deviation from the optimal bond lengths, bond angles, torsions, non-bonded interactions and electrostatic interactions from those given by the a particular forcefield. Modelling transition metals using conventional MM has always been difficult as they can have variable oxidation states, spin states and electronic effects, and can coordinate from 4 to 12 different ligands in a complex. Rob Deeth has addressed this problem by developing this Ligand Field Molecular Mechanics model of dealing with transition metal centres using an approach called Ligand Field Theory.¡]]¦: ð¨ ðD ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðF$miF$ðj² ðC S ð AÁ ??"ñ?ð� &ð Á ðÑ¢ ðT £ ð<€¸ÊŠ ¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð}('am7 ð'Ÿ¨ In a free transition metal ion, the preference of the d-electrons is to occupy each of the five d-orbitals, and when there are more than five d electrons, spin-pairing occurs. In an octahedrally-coordinated complex, the dxy, dyz and dxz orbitals become lower in energy than the dx2-y2 and dz2 orbitals and are filled first. Ligand Field Theory states that this is because the former orbitals repel the ligand electron densities less than the latter (the d-orbitals are mostly antibonding and repel ligand electron clouds). Depending on the ligands (the so-called ligand field strength), the d-electrons may desert the dx2-y2 and dz2 orbitals completely as the electron pairing becomes energetically more favourable than the electron repulsion of ligand bonding orbitals.¡® Ý çÿ çÿ çÿ, çÿ çÿM çÿ çÿ‹ª>ܦ: ðV² ðW C ð.€€AÁdorbitals2ðÔ%m¶4·+ð¢ ð\ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð_ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ðb £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð‰ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ðŒ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð� £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ðÄðF ð2)p*–2 3 ð’  ðˆðÚ+`)Ä2v4ðN² ðÑ S ðÂA ÿÿÿ¿ˆð2)p*’2€-ðN² ðÒ S ðfA ÿÿÿ¿ˆð2)_-–2n0ð² ðÓ ã ðT¿ÇÂAÿÿÿ�ƒ¿ Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð2)L0’2 3ðæ ðF ð`B*Ã23 ð‘  ðˆðÚ+èK3µ4ðþ ð¸ à ðH€ÖŠ ¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(*0Ã23 ð@Ÿ¡¦ø: Wtð� ð· ³ ðB€´úŠ ¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`*0{(3 ðØŸ¨:(2) High Ligand Field strength (e.g. CN-, phenantroline) ¡J;(&þ.þ&þª+ ¦ø: Wtðþ ð¶ à ðH€‹ ¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(6-Ã2*0 ð@Ÿ¡¦ø: WtðÑ ðµ ³ ðB€¼‹ ¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`6-{(*0 ðŸ¨7(1) Low Ligand Field strength (e.g. Cl-, I-, F-, H2O) ¡°8'&þ.þ&þ.þ&þ.þ&þ.þçÿ&þ¦ø: Wtðþ ð´ à ðH€è~Š ¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(B*Ã26- ð@Ÿ¡,¦ø: WtðA ð³ ³ ðB€x‹ ¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`B*{(6- ð‰Ÿ¨Free Fe2+ ion (high spin)¡> ¦ø: WtðªB ð¹ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`B*Ã2B*ð¤B 𺠣 ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`6-Ã26-ð¤B ð» £ ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`*0Ã2*0ðªB ð¼ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`3Ã23ðªB ð½ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`B*`3ð¤B ð¾ £ ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð{(B*{(3ðªB ð¿ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÃ2B*Ã23ð/ðF ð$ °ÔÌ ðä ðˆðu>’Ù �?ði¢ ðå  ð€-‹ ð$ °ÄÌ ð+Ÿ¨ High Spin¦: ðh¢ ðæ  ð€¸6‹ ð4°ÔÌ ð*Ÿ¨Low Spin¦: ðj² ðè S ð A Á  ??"ñ?ðà?ó%yBð Á  ð_ ðê à ðH€(?‹ ‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðFB'L%ÁG 𩟨yDeeth has implemented LFMM into the Molecular Operating Environment (MOE), a popular MM dynamics program, to form DommiMOE, which uses the forcefield MMFF94 for non-transition metals. DommiMOE can optimise the geometry a complex for a given spin state, and so can give hypothetical structures of transition metal complexes for both spin states with the same set of parameters.¡zzðè ðë à ðH€\H‹ ‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðP ä4>_  ð2Ÿ ÊThis is an octahedral high-spin complex where the Fe  N bond lengths were 2.20 ú (from X-ray crystallographic data). To obtain data on a hypothetical low-spin structure, QM techniques were used, which predict that the Fe  N bond lengths to be around 2.00 ú. Also, an estimate of 11 kcal/mol was set on the energetic favourability of the high spin state to the low spin state. As with all MM-based methods, some model parameters have to be found which fit the required geometries and energies. Parameters modified included the Morse function parameters (Fe N bond length potential was modelled by a Morse function), octahedral-field splitting term, the ligand-ligand repulsion term and some electron-pairing energy terms. To measure the  fit of the parameters, a cost function was constructed such that the smaller its value, the better the parameters fit the data.¡ffª0P ¯ dðt² ðì c ð>A Á·m ¸ÿFe_hexammine"ñ¿`ð 0_Ïgð%¢ ðî à ðH€œ_‹ ¿?�3ÌÌ¿Àÿ?¿ÿ“"ñ6?@¿`ÿÀ¿‚‚N¿NÿN?Nðzä4 K ðoŸ¨Simulated Annealing¡2 2 $ '$¦: ðF 𬠳 ðB€d‹ ¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð¹7D\4N? ð–Ÿ The difference between low spin and high spin states is the metal-ligand bond lengths of low spin states are much smaller than those of high spin. For example, the Fe  N bond length in low spin and high spin amine complexes are about 2.00 and 2.20ú respectively. This is because of the smaller repulsion of the ligands from the d-electron cloud at low spin than at high spin. Deeth summarises this effect by the Ligand Field Stabilisation Energy (LFSE), and incorporated into the MM framework by adding to the MM equation:¡.ù"ªù ¦: ðv ð­ ³ ðB€ðl‹ ¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðä4p–287 ðÆŸ¨r(1) is known as the high-spin state of Fe2+ as the total spin is greater than in (2), known as the low spin state.¡*s) H¦: ðj² ð¯  S ð A Á '??"ñ?ð17¯` ‚>ð Á 'ð( ð² à ðH€pw‹ ‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðä4ìgs ðrŸ ¾Simulated Annealing (SA) is a method of finding the maximum or minimum of a distribution À(x) by using Markov Chain Monte Carlo (MCMC) to sample the parameter space, in this case the distribution needed to be minimised is the cost function A Markov chain (a  random walk ) is constructed whose limiting distribution is À(x) - the target distribution. ¡d`[""å"""""ª,Yãð¨ ð¶ ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð+$mi+$ð ð» à ðH€l€‹ ‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð§%·4dg* ð`Ÿ BIn simulated annealing, the target distribution À(x) is changed to À(x)1/T (T is known as the  temperature ), which has the same maxima and minima as À(x) but is rather  steeper as T decreases from 1 to 0, and this makes the Markov chain less likely to escape local minima. If the temperature is carefully reduced, then (hopefully) at the end of the procedure the Markov chain will reside near the global minimum. ¡΢2"""""**""K""""è"ª,0c ðÓ¢ ð¼ s ð*€ð›‹ ¿�3ÌÌ¿Àÿ"ñ¿`ð�*ä47K1, ðkŸ¨Amine Complexes¡2 2$ '$¦: ðì ð¿ à ðH€¨�‹ ‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð5,ä4•\½2 ð6Ÿ¨6The simulated annealing procedure yielded some good parameters for the iron hexaammine complex, which were applied to three other amine complexes. From the bond lengths in their X-ray crystallographic structures, (1) and (2) were low spin complexes, while (3) was a high spin complex, which illustrates the sensitivity of the spin state of Fe2+ with nitrogen ligands. The parameters found for [Fe(NH3)6]2+ were found to reproduce the geometry of the complexes very well in their native spin states, and also the spin states of the complexes were correctly predicted.¡Â7Ý""  S"*7"*âÿ"*âÿ"*¢"ªL áðÓ¢ ðÛ s ð*€ìµ‹ ¿�3ÌÌ¿Àÿ"ñ¿`ðÃ2ä47KW4 ðkŸ¨Imine Complexes¡2 2$ '$¦: ðy ðÝ Ã ðH€ô·‹ ‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð\4ä4‘gÞ; ðߨ¥Can these parameters transfer to imine complexes? Unlike amine nitrogens, imine nitrogens are aromatic, and most Fe2+ imine complexes are low-spin. It was found that after some modification of the parameters, although the bond lengths were not very accurately reproduced, DommiMOE correctly predicted the spin state for most of the complexes (but not all). The most striking result was the predicted spin states of the low spin complex [Fe(1-10-phenantroline)3]2+ and the high spin [Fe(2-methyl-1-10-phenantroline)3]2+. Although the ligands in these complexes were very similar, DommiMOE correctly deduced their spin states, which correspond to a large change in geometry.¡Îi= t"*ò"f"*âÿ"*3"*âÿ"*œ"ª,@  Lðœ ð “ ð6…¿�¿Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðt!Î.ž:t!ðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@ÖD¦Pð@ðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð‘GÖD¦P‘Gð–B ð “ ð6‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@ÖDÖD¬GðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@¦P¦P‘GððF ðdYÝ<hæE ðF  ðˆðÍ;dYhÖDð^ ð  ³ ðB€ÄÌ‹ ¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðk`@DhæE 𦟨$[Fe(2-methyl-1-10-phenantroline)3]2+¡f% eÿÿÿþmÿÿÿþâÿeÿÿÿþmÿÿÿþAðe ð  ³ ðB€ôÓ‹ ¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðdY@Dk`æE 𭟨e(1-10-phenantroline)3]2+¡v%ÿÿÿþeÿÿÿþmÿÿÿþâÿeÿÿÿþmÿÿÿþAðö ð  ³ ðB€8â‹ ¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðdYÝ< h@D ð>Ÿ¡¦ø: Wtðt² ð  “ ðD‚„# "AÁÇ .?ˆBUHKAQð�YÝ<ð`7Dðt² ð  “ ðD‚F5 "AÁ€ Â5?ˆCEPZOMðÜ`Ý<|g7Dð¼¢ ð s ð*€ì‹ ¿�3ÌÌ¿Àÿ"ñ¿`ðÝ<ä47Kq> ðTŸ¨ Applications¡ 2 $¦: ðn² ð  s ð8€€AÁ®G (\?Image1"ñ¿`ðr;:NjWoCðø¢ ð3 à ðH€„� ¿�ƒ¿ Àÿ?¿ÿ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðu>ä4ìYýD ðBŸ (The next step is to model Iron(II) porphyrins, which are planar complexes with the Fe2+ surrounded by four aromatic nitrogens (chemically similar to imine nitrogens). The most important example of an Iron(II) porphyrin is the O2 -binding site for haemoglobin, heme. Fe2+ in heme changes from high spin to low spin when it binds to an oxygen molecule, which changes the shape of the whole molecule. This change is important in the uptake and transport of oxygen. It would be very interesting to find out if DommiMOE can model this  %¡†U Œ çÿ  "ªb G  $F¦: ð|ð~ ð3 í  � ð< 3 ð€€ˆ¿ c"ñ$��‘’¿ð�) \øg�3ðN² ð=  S ðX99¿ÿ?ð3 í  �ðJ ð>  # ð �¿"ñ¿`ð3 í  �ðb² ð?  c ð2€€A Á†, .DETTOLð3 í Ôðb² ð@  c ð2€€AÁ†, .PAZXAPðí  Îðb² ðA  c ð2€€AÁOì f&PURYIKð3 �Ú�𨢠ðB  3 ð€p� �¿"ñ¿`ðÐ í ¦ -  ðPŸ¨1.¡$ ÿÿÿþ¦: 𨢠ðC  3 ð€ìü‹ �¿"ñ¿`ðmí D-  ðPŸ¨2.¡$ ÿÿÿþ¦: 𨢠ðD  3 ð€P� �¿"ñ¿`ðÐ í¦ - ðPŸ¨3.¡$ ÿÿÿþ¦: ðNð8 ðä4E7YaH ðN ðEä47YaHð¼ ð9  Ó ðN‡¿�¿ÀÎÿ?¿ÿˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nðä4E7YaHðÚ¢ ð7  Ó ðN€`)� ¿�¿ÀÎÿ?¿ÿˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?NðÊ81E™QäG ðŸ¨ØThe author would like to thank the MOAC Doctoral Centre staff and colleagues for their guidance and the Engineering and Physical Sciences Research Council Life Sciences Interface Programme for their generous support.¡ÙÙ¦: ð†² ð5  £ ðH€€AÁ �¿ÀÎÿˆmoacc"ñ¿`ðl51El8OHðÒ² ðJ  ƒ 𔀀 X3”¹AÁdDownloads_Images_Logos_Version1Colour_EPSRC1RGBHI"ñ¿`ð=Q^E­X7Hðj² ðL C ðB€€AÁ*the_warwick_uni_blueðx¡ š ð2ð8 ð‰4S©Av& ð† ðpä4B“%ðÚð@ ð7�$DÀ% ðm ð‰4S©Av&ðz² ð  “ ð<€€Ó œAÁ¿?ˆsa"ñ¿`ð7�$DÀ%ðÈB ð   ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðr;sW?ƒ ðÈB ð B  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÌ;ƒ W? !ðÈB ð ‚  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðú;ë•@ !ðÈB ð B  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÙ9ë•@V ðÈB ð   ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð:V ‚<f!ðÈB ð! 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Then the model parameters were refined using simulated annealing to give the correct geometries and predict the correct spin state of the metal, initially with [Fe(NH3)6]2+, then with three other amine complexes. The parameters found were applied to about 80 imine complexes, and after a slight modification, approximated the geometries reasonably well and most of the time predicted the correct spin state.¡xD å çÿ çÿ ë¦: ðB² ð. # ð Aÿ"ñ¿`ð'T ¨ð ¢ ð9 à ðH€,fŠ ¿?�3ÌÌ¿Àÿ?¿ÿ“"ñ6?@¿`ÿÀ¿‚‚N¿NÿN?Nðü'z� ðTŸ¨ Introduction¡ 2 $¦: ðÖ¢ ð: £ ð<€8—Š ¿�ƒ¿ Àÿ?“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nðg'.4Õ ð,Ÿ îThe importance of organometallic proteins in biochemistry has long been recognised, which the metal instrumental in many of these protein s catalytic or binding functions. At the moment there are very few methods that model transition metal-containing organometallic proteins effectively, either using quantum or classical mechanical methods. Here is outlined a very promising new Molecular Modelling approach to deal with transition metal complexes which can be used to model biological macromolecules.¡øø¦: ð¢ ð< à ðH€��Š ¿?�3ÌÌ¿Àÿ?¿ÿ“"ñ6?@¿`ÿÀ¿‚‚N¿NÿN?Nð]'zñ ð[Ÿ¨Molecular Modelling¡ 2$¦: ð¨ ð? ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðmið¨ ðA ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðmið¢ ð= £ ð<€±Š ¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð"'.4ƒ ðVŸ¨Molecular Modelling (MM) of Force-Field (FF) methods of finding molecular structures determine the relationship between the energy and structure by application of empirical rules based on classical mechanics. To find an optimal structure in MM, we optimise the total strain energy¡¦: ðD¢ ðB £ ð<€øºŠ ¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðë'\4€& 𚟨\where the terms correspond to the deviation from the optimal bond lengths, bond angles, torsions, non-bonded interactions and electrostatic interactions from those given by the a particular forcefield. Modelling transition metals using conventional MM has always been difficult as they can have variable oxidation states, spin states and electronic effects, and can coordinate from 4 to 12 different ligands in a complex. Rob Deeth has addressed this problem by developing this Ligand Field Molecular Mechanics model of dealing with transition metal centres using an approach called Ligand Field Theory.¡]]¦: ð¨ ðD ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðF$miF$ðj² ðC S ð AÁ ??"ñ?ð� &ð Á ðÑ¢ ðT £ ð<€¸ÊŠ ¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð}('am7 ð'Ÿ¨ In a free transition metal ion, the preference of the d-electrons is to occupy each of the five d-orbitals, and when there are more than five d electrons, spin-pairing occurs. In an octahedrally-coordinated complex, the dxy, dyz and dxz orbitals become lower in energy than the dx2-y2 and dz2 orbitals and are filled first. Ligand Field Theory states that this is because the former orbitals repel the ligand electron densities less than the latter (the d-orbitals are mostly antibonding and repel ligand electron clouds). Depending on the ligands (the so-called ligand field strength), the d-electrons may desert the dx2-y2 and dz2 orbitals completely as the electron pairing becomes energetically more favourable than the electron repulsion of ligand bonding orbitals.¡® Ý çÿ çÿ çÿ, çÿ çÿM çÿ çÿ‹ª>ܦ: ðV² ðW C ð.€€AÁdorbitals2ðÔ%m¶4·+ð¢ ð\ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð_ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ðb £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð‰ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ðŒ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð� £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ðÄðF ð2)p*–2 3 ð’  ðˆðÚ+`)Ä2v4ðN² ðÑ S ðÂA ÿÿÿ¿ˆð2)p*’2€-ðN² ðÒ S ðfA ÿÿÿ¿ˆð2)_-–2n0ð² ðÓ ã ðT¿ÇÂAÿÿÿ�ƒ¿ Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð2)L0’2 3ðæ ðF ð`B*Ã23 ð‘  ðˆðÚ+èK3µ4ðþ ð¸ à ðH€ÖŠ ¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(*0Ã23 ð@Ÿ¡¦ø: Wtð� ð· ³ ðB€´úŠ ¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`*0{(3 ðØŸ¨:(2) High Ligand Field strength (e.g. CN-, phenantroline) ¡J;(&þ.þ&þª+ ¦ø: Wtðþ ð¶ à ðH€‹ ¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(6-Ã2*0 ð@Ÿ¡¦ø: WtðÑ ðµ ³ ðB€¼‹ ¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`6-{(*0 ðŸ¨7(1) Low Ligand Field strength (e.g. Cl-, I-, F-, H2O) ¡°8'&þ.þ&þ.þ&þ.þ&þ.þçÿ&þ¦ø: Wtðþ ð´ à ðH€è~Š ¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(B*Ã26- ð@Ÿ¡,¦ø: WtðA ð³ ³ ðB€x‹ ¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`B*{(6- ð‰Ÿ¨Free Fe2+ ion (high spin)¡> ¦ø: WtðªB ð¹ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`B*Ã2B*ð¤B 𺠣 ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`6-Ã26-ð¤B ð» £ ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`*0Ã2*0ðªB ð¼ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`3Ã23ðªB ð½ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`B*`3ð¤B ð¾ £ ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð{(B*{(3ðªB ð¿ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÃ2B*Ã23ð/ðF ð$ °ÔÌ ðä ðˆðu>’Ù �?ði¢ ðå  ð€-‹ ð$ °ÄÌ ð+Ÿ¨ High Spin¦: ðh¢ ðæ  ð€¸6‹ ð4°ÔÌ ð*Ÿ¨Low Spin¦: ðj² ðè S ð A Á  ??"ñ?ðà?ó%yBð Á  ð_ ðê à ðH€(?‹ ‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðFB'L%ÁG 𩟨yDeeth has implemented LFMM into the Molecular Operating Environment (MOE), a popular MM dynamics program, to form DommiMOE, which uses the forcefield MMFF94 for non-transition metals. DommiMOE can optimise the geometry a complex for a given spin state, and so can give hypothetical structures of transition metal complexes for both spin states with the same set of parameters.¡zzðè ðë à ðH€\H‹ ‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðP ä4>_  ð2Ÿ ÊThis is an octahedral high-spin complex where the Fe  N bond lengths were 2.20 ú (from X-ray crystallographic data). To obtain data on a hypothetical low-spin structure, QM techniques were used, which predict that the Fe  N bond lengths to be around 2.00 ú. Also, an estimate of 11 kcal/mol was set on the energetic favourability of the high spin state to the low spin state. As with all MM-based methods, some model parameters have to be found which fit the required geometries and energies. Parameters modified included the Morse function parameters (Fe N bond length potential was modelled by a Morse function), octahedral-field splitting term, the ligand-ligand repulsion term and some electron-pairing energy terms. To measure the  fit of the parameters, a cost function was constructed such that the smaller its value, the better the parameters fit the data.¡ffª0P ¯ dðt² ðì c ð>A Á·m ¸ÿFe_hexammine"ñ¿`ð 0_Ïgð%¢ ðî à ðH€œ_‹ ¿?�3ÌÌ¿Àÿ?¿ÿ“"ñ6?@¿`ÿÀ¿‚‚N¿NÿN?Nðzä4 K ðoŸ¨Simulated Annealing¡2 2 $ '$¦: ðF 𬠳 ðB€d‹ ¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð¹7D\4N? ð–Ÿ The difference between low spin and high spin states is the metal-ligand bond lengths of low spin states are much smaller than those of high spin. For example, the Fe  N bond length in low spin and high spin amine complexes are about 2.00 and 2.20ú respectively. This is because of the smaller repulsion of the ligands from the d-electron cloud at low spin than at high spin. Deeth summarises this effect by the Ligand Field Stabilisation Energy (LFSE), and incorporated into the MM framework by adding to the MM equation:¡.ù"ªù ¦: ðv ð­ ³ ðB€ðl‹ ¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðä4p–287 ðÆŸ¨r(1) is known as the high-spin state of Fe2+ as the total spin is greater than in (2), known as the low spin state.¡*s) H¦: ðj² ð¯  S ð A Á '??"ñ?ð17¯` ‚>ð Á 'ð( ð² à ðH€pw‹ ‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðä4ìgs ðrŸ ¾Simulated Annealing (SA) is a method of finding the maximum or minimum of a distribution À(x) by using Markov Chain Monte Carlo (MCMC) to sample the parameter space, in this case the distribution needed to be minimised is the cost function A Markov chain (a  random walk ) is constructed whose limiting distribution is À(x) - the target distribution. ¡d`[""å"""""ª,Yãð¨ ð¶ ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð+$mi+$ð ð» à ðH€l€‹ ‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð§%·4dg* ð`Ÿ BIn simulated annealing, the target distribution À(x) is changed to À(x)1/T (T is known as the  temperature ), which has the same maxima and minima as À(x) but is rather  steeper as T decreases from 1 to 0, and this makes the Markov chain less likely to escape local minima. If the temperature is carefully reduced, then (hopefully) at the end of the procedure the Markov chain will reside near the global minimum. ¡΢2"""""**""K""""è"ª,0c ðÓ¢ ð¼ s ð*€ð›‹ ¿�3ÌÌ¿Àÿ"ñ¿`ð�*ä47K1, ðkŸ¨Amine Complexes¡2 2$ '$¦: ðì ð¿ à ðH€¨�‹ ‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð5,ä4•\½2 ð6Ÿ¨6The simulated annealing procedure yielded some good parameters for the iron hexaammine complex, which were applied to three other amine complexes. From the bond lengths in their X-ray crystallographic structures, (1) and (2) were low spin complexes, while (3) was a high spin complex, which illustrates the sensitivity of the spin state of Fe2+ with nitrogen ligands. The parameters found for [Fe(NH3)6]2+ were found to reproduce the geometry of the complexes very well in their native spin states, and also the spin states of the complexes were correctly predicted.¡Â7Ý""  S"*7"*âÿ"*âÿ"*¢"ªL áðÓ¢ ðÛ s ð*€ìµ‹ ¿�3ÌÌ¿Àÿ"ñ¿`ðÃ2ä47KW4 ðkŸ¨Imine Complexes¡2 2$ '$¦: ðy ðÝ Ã ðH€ô·‹ ‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð\4ä4‘gÞ; ðߨ¥Can these parameters transfer to imine complexes? Unlike amine nitrogens, imine nitrogens are aromatic, and most Fe2+ imine complexes are low-spin. It was found that after some modification of the parameters, although the bond lengths were not very accurately reproduced, DommiMOE correctly predicted the spin state for most of the complexes (but not all). The most striking result was the predicted spin states of the low spin complex [Fe(1-10-phenantroline)3]2+ and the high spin [Fe(2-methyl-1-10-phenantroline)3]2+. Although the ligands in these complexes were very similar, DommiMOE correctly deduced their spin states, which correspond to a large change in geometry.¡Îi= t"*ò"f"*âÿ"*3"*âÿ"*œ"ª,@  Lðœ ð “ ð6…¿�¿Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðt!Î.ž:t!ðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@ÖD¦Pð@ðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð‘GÖD¦P‘Gð–B ð “ ð6‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@ÖDÖD¬GðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@¦P¦P‘GððF ðdYÝ<hæE ðF  ðˆðÍ;dYhÖDð^ ð  ³ ðB€ÄÌ‹ ¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðk`@DhæE 𦟨$[Fe(2-methyl-1-10-phenantroline)3]2+¡f% eÿÿÿþmÿÿÿþâÿeÿÿÿþmÿÿÿþAðe ð  ³ ðB€ôÓ‹ ¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðdY@Dk`æE 𭟨e(1-10-phenantroline)3]2+¡v%ÿÿÿþeÿÿÿþmÿÿÿþâÿeÿÿÿþmÿÿÿþAðö ð  ³ ðB€8â‹ ¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðdYÝ< h@D ð>Ÿ¡¦ø: Wtðt² ð  “ ðD‚„# "AÁÇ .?ˆBUHKAQð�YÝ<ð`7Dðt² ð  “ ðD‚F5 "AÁ€ Â5?ˆCEPZOMðÜ`Ý<|g7Dð¼¢ ð s ð*€ì‹ ¿�3ÌÌ¿Àÿ"ñ¿`ðÝ<ä47Kq> ðTŸ¨ Applications¡ 2 $¦: ðn² ð  s ð8€€AÁ®G (\?Image1"ñ¿`ðr;:NjWoCðø¢ ð3 à ðH€„� ¿�ƒ¿ Àÿ?¿ÿ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðu>ä4ìYýD ðBŸ (The next step is to model Iron(II) porphyrins, which are planar complexes with the Fe2+ surrounded by four aromatic nitrogens (chemically similar to imine nitrogens). The most important example of an Iron(II) porphyrin is the O2 -binding site for haemoglobin, heme. Fe2+ in heme changes from high spin to low spin when it binds to an oxygen molecule, which changes the shape of the whole molecule. This change is important in the uptake and transport of oxygen. It would be very interesting to find out if DommiMOE can model this  %¡†U Œ çÿ  "ªb G  $F¦: ð|ð~ ð3 í  � ð< 3 ð€€ˆ¿ c"ñ$��‘’¿ð�) \øg�3ðN² ð=  S ðX99¿ÿ?ð3 í  �ðJ ð>  # ð �¿"ñ¿`ð3 í  �ðb² ð?  c ð2€€A Á†, .DETTOLð3 í Ôðb² ð@  c ð2€€AÁ†, .PAZXAPðí  Îðb² ðA  c ð2€€AÁOì f&PURYIKð3 �Ú�𨢠ðB  3 ð€p� �¿"ñ¿`ðÐ í ¦ -  ðPŸ¨1.¡$ ÿÿÿþ¦: 𨢠ðC  3 ð€ìü‹ �¿"ñ¿`ðmí D-  ðPŸ¨2.¡$ ÿÿÿþ¦: 𨢠ðD  3 ð€P� �¿"ñ¿`ðÐ í¦ - ðPŸ¨3.¡$ ÿÿÿþ¦: ðNð8 ðä4E7YaH ðN ðEä47YaHð¼ ð9  Ó ðN‡¿�¿ÀÎÿ?¿ÿˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nðä4E7YaHðÚ¢ ð7  Ó ðN€`)� ¿�¿ÀÎÿ?¿ÿˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?NðÊ81E™QäG ðŸ¨ØThe author would like to thank the MOAC Doctoral Centre staff and colleagues for their guidance and the Engineering and Physical Sciences Research Council Life Sciences Interface Programme for their generous support.¡ÙÙ¦: ð†² ð5  £ ðH€€AÁ �¿ÀÎÿˆmoacc"ñ¿`ðl51El8OHðÒ² ðJ  ƒ 𔀀 X3”¹AÁdDownloads_Images_Logos_Version1Colour_EPSRC1RGBHI"ñ¿`ð=Q^E­X7Hðj² ðL C ðB€€AÁ*the_warwick_uni_blueðx¡ š ð2ð8 ð‰4S©Av& ð† ðpä4B“%ðÚð@ ð7�$DÀ% ðm ð‰4S©Av&ðz² ð  “ ð<€€Ó œAÁ¿?ˆsa"ñ¿`ð7�$DÀ%ðÈB ð   ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðr;sW?ƒ ðÈB ð B  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÌ;ƒ W? !ðÈB ð ‚  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðú;ë•@ !ðÈB ð B  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÙ9ë•@V ðÈB ð   ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð:V ‚<f!ðÈB ð! 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Then the model parameters were refined using simulated annealing to give the correct geometries and predict the correct spin state of the metal, initially with [Fe(NH3)6]2+, then with three other amine complexes. The parameters found were applied to about 80 imine complexes, and after a slight modification, approximated the geometries reasonably well and most of the time predicted the correct spin state.¡xD å çÿ çÿ ë¦: ðB² ð. # ð Aÿ"ñ¿`ð'T ¨ð ¢ ð9 à ðH€”._¿?�3ÌÌ¿Àÿ?¿ÿ“"ñ6?@¿`ÿÀ¿‚‚N¿NÿN?Nðü'z� ðTŸ¨ Introduction¡ 2 $¦: ðÖ¢ ð: £ ð<€ D_¿�ƒ¿ Àÿ?“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nðg'.4Õ ð,Ÿ îThe importance of organometallic proteins in biochemistry has long been recognised, which the metal instrumental in many of these protein s catalytic or binding functions. At the moment there are very few methods that model transition metal-containing organometallic proteins effectively, either using quantum or classical mechanical methods. Here is outlined a very promising new Molecular Modelling approach to deal with transition metal complexes which can be used to model biological macromolecules.¡øø¦: ð¢ ð< à ðH€Q_¿?�3ÌÌ¿Àÿ?¿ÿ“"ñ6?@¿`ÿÀ¿‚‚N¿NÿN?Nð]'zñ ð[Ÿ¨Molecular Modelling¡ 2$¦: ð¨ ð? ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðmið¨ ðA ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðmið¢ ð= £ ð<€àZ_¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð"'.4ƒ ðVŸ¨Molecular Modelling (MM) of Force-Field (FF) methods of finding molecular structures determine the relationship between the energy and structure by application of empirical rules based on classical mechanics. To find an optimal structure in MM, we optimise the total strain energy¡¦: ðD¢ ðB £ ð<€lf_¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðë'\4€& 𚟨\where the terms correspond to the deviation from the optimal bond lengths, bond angles, torsions, non-bonded interactions and electrostatic interactions from those given by the a particular forcefield. Modelling transition metals using conventional MM has always been difficult as they can have variable oxidation states, spin states and electronic effects, and can coordinate from 4 to 12 different ligands in a complex. Rob Deeth has addressed this problem by developing this Ligand Field Molecular Mechanics model of dealing with transition metal centres using an approach called Ligand Field Theory.¡]]¦: ð¨ ðD ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðF$miF$ðj² ðC S ð AÁ ??"ñ?ð� &ð Á ðÑ¢ ðT £ ð<€øu_¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð}('am7 ð'Ÿ¨ In a free transition metal ion, the preference of the d-electrons is to occupy each of the five d-orbitals, and when there are more than five d electrons, spin-pairing occurs. In an octahedrally-coordinated complex, the dxy, dyz and dxz orbitals become lower in energy than the dx2-y2 and dz2 orbitals and are filled first. Ligand Field Theory states that this is because the former orbitals repel the ligand electron densities less than the latter (the d-orbitals are mostly antibonding and repel ligand electron clouds). Depending on the ligands (the so-called ligand field strength), the d-electrons may desert the dx2-y2 and dz2 orbitals completely as the electron pairing becomes energetically more favourable than the electron repulsion of ligand bonding orbitals.¡® Ý çÿ çÿ çÿ, çÿ çÿM çÿ çÿ‹ª>ܦ: ðV² ðW C ð.€€AÁdorbitals2ðÔ%m¶4·+ð¢ ð\ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð_ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ðb £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð‰ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ðŒ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð� £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ðÄðF ð2)p*–2 3 ð’  ðˆðÚ+`)Ä2v4ðN² ðÑ S ðÂA ÿÿÿ¿ˆð2)p*’2€-ðN² ðÒ S ðfA ÿÿÿ¿ˆð2)_-–2n0ð² ðÓ ã ðT¿ÇÂAÿÿÿ�ƒ¿ Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð2)L0’2 3ðæ ðF ð`B*Ã23 ð‘  ðˆðÚ+èK3µ4ðþ ð¸ à ðH€l›_¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(*0Ã23 ð@Ÿ¡¦ø: Wtð� ð· ³ ðB€ §_¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`*0{(3 ðØŸ¨:(2) High Ligand Field strength (e.g. CN-, phenantroline) ¡J;(&þ.þ&þª+ ¦ø: Wtðþ ð¶ à ðH€„°_¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(6-Ã2*0 ð@Ÿ¡¦ø: WtðÑ ðµ ³ ðB€ À_¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`6-{(*0 ðŸ¨7(1) Low Ligand Field strength (e.g. Cl-, I-, F-, H2O) ¡°8'&þ.þ&þ.þ&þ.þ&þ.þçÿ&þ¦ø: Wtðþ ð´ à ðH€`É_¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(B*Ã26- ð@Ÿ¡,¦ø: WtðA ð³ ³ ðB€LÔ_¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`B*{(6- ð‰Ÿ¨Free Fe2+ ion (high spin)¡> ¦ø: WtðªB ð¹ ³ ðB¿¿ÀËŸo×ÿ ?¿¦ÿÿÿÿ§ÿÿÿÿ¿ ÙÿÿÿÿÚÿÿÿÿÛ ÜÝÿÿÿÿÞÿÿÿÿß àáÿÿÿÿâÿÿÿÿÿÀÿÿÿÿÿÿÿÿ ÿÿÿÿÿÿÿÿ ÿÿÿÿÿÿÿÿ‰ÿÿÿÿŠÿÿÿÿ‹ Œ�ÿÿÿÿ��‘’¿‚‚@ABÿÿÿC DEEFGHIJK5%LMNOPQRSTUWYÿÿÿÿZÿÿÿÿ[ \]ÿÿÿÿ^ÿÿÿÿ_ `aÿÿÿÿbÿÿÿÿN€�‚ÿÿÿƒ „…E†‡ˆ‰Š‹5%Œ�Ž��ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`B*Ã2B*ð¤B 𺠣 ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`6-Ã26-ð¤B ð» £ ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`*0Ã2*0ðªB ð¼ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`3Ã23ðªB ð½ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`B*`3ð¤B ð¾ £ ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð{(B*{(3ðªB ð¿ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÃ2B*Ã23ð/ðF ð$ °ÔÌ ðä ðˆðu>’Ù �?ði¢ ðå  ð€Ù_ð$ °ÄÌ ð+Ÿ¨ High Spin¦: ðh¢ ðæ  ð€Àâ_ð4°ÔÌ ð*Ÿ¨Low Spin¦: ðj² ðè S ð A Á  ??"ñ?ðà?ó%yBð Á  ð_ ðê à ðH€0ë_‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðFB'L%ÁG 𩟨yDeeth has implemented LFMM into the Molecular Operating Environment (MOE), a popular MM dynamics program, to form DommiMOE, which uses the forcefield MMFF94 for non-transition metals. DommiMOE can optimise the geometry a complex for a given spin state, and so can give hypothetical structures of transition metal complexes for both spin states with the same set of parameters.¡zzðè ðë à ðH€l`‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðP ä4>_  ð2Ÿ ÊThis is an octahedral high-spin complex where the Fe  N bond lengths were 2.20 ú (from X-ray crystallographic data). To obtain data on a hypothetical low-spin structure, QM techniques were used, which predict that the Fe  N bond lengths to be around 2.00 ú. Also, an estimate of 11 kcal/mol was set on the energetic favourability of the high spin state to the low spin state. As with all MM-based methods, some model parameters have to be found which fit the required geometries and energies. Parameters modified included the Morse function parameters (Fe N bond length potential was modelled by a Morse function), octahedral-field splitting term, the ligand-ligand repulsion term and some electron-pairing energy terms. To measure the  fit of the parameters, a cost function was constructed such that the smaller its value, the better the parameters fit the data.¡ffª0P ¯ dðt² ðì c ð>A Á·m ¸ÿFe_hexammine"ñ¿`ð 0_Ïgð%¢ ðî à ðH€ï_¿?�3ÌÌ¿Àÿ?¿ÿ“"ñ6?@¿`ÿÀ¿‚‚N¿NÿN?Nðzä4 K ðoŸ¨Simulated Annealing¡2 2 $ '$¦: ðF 𬠳 ðB€T`¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð¹7D\4N? ð–Ÿ The difference between low spin and high spin states is the metal-ligand bond lengths of low spin states are much smaller than those of high spin. For example, the Fe  N bond length in low spin and high spin amine complexes are about 2.00 and 2.20ú respectively. This is because of the smaller repulsion of the ligands from the d-electron cloud at low spin than at high spin. Deeth summarises this effect by the Ligand Field Stabilisation Energy (LFSE), and incorporated into the MM framework by adding to the MM equation:¡.ù"ªù ¦: ðv ð­ ³ ðB€È!`¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðä4p–287 ðÆŸ¨r(1) is known as the high-spin state of Fe2+ as the total spin is greater than in (2), known as the low spin state.¡*s) H¦: ðj² ð¯  S ð A Á _??"ñ?ð17¯` ‚>ð Á _ð( ð² à ðH€¨þ_‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðä4ìgs ðrŸ ¾Simulated Annealing (SA) is a method of finding the maximum or minimum of a distribution À(x) by using Markov Chain Monte Carlo (MCMC) to sample the parameter space, in this case the distribution needed to be minimised is the cost function A Markov chain (a  random walk ) is constructed whose limiting distribution is À(x) - the target distribution. ¡d`[""å"""""ª,Yãð¨ ð¶ ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð+$mi+$ð ð» à ðH€|0`‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð§%·4dg* ð`Ÿ BIn simulated annealing, the target distribution À(x) is changed to À(x)1/T (T is known as the  temperature ), which has the same maxima and minima as À(x) but is rather  steeper as T decreases from 1 to 0, and this makes the Markov chain less likely to escape local minima. If the temperature is carefully reduced, then (hopefully) at the end of the procedure the Markov chain will reside near the global minimum. ¡΢2"""""**""K""""è"ª,0c ðÓ¢ ð¼ s ð*€L`¿�3ÌÌ¿Àÿ"ñ¿`ð�*ä47K1, ðkŸ¨Amine Complexes¡2 2$ '$¦: ðì ð¿ à ðH€œN`‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð5,ä4•\½2 ð6Ÿ¨6The simulated annealing procedure yielded some good parameters for the iron hexaammine complex, which were applied to three other amine complexes. From the bond lengths in their X-ray crystallographic structures, (1) and (2) were low spin complexes, while (3) was a high spin complex, which illustrates the sensitivity of the spin state of Fe2+ with nitrogen ligands. The parameters found for [Fe(NH3)6]2+ were found to reproduce the geometry of the complexes very well in their native spin states, and also the spin states of the complexes were correctly predicted.¡Â7Ý""  S"*7"*âÿ"*âÿ"*¢"ªL áðÓ¢ ðÛ s ð*€T+`¿�3ÌÌ¿Àÿ"ñ¿`ðÃ2ä47KW4 ðkŸ¨Imine Complexes¡2 2$ '$¦: ðy ðÝ Ã ðH€ i`‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð\4ä4‘gÞ; ðߨ¥Can these parameters transfer to imine complexes? Unlike amine nitrogens, imine nitrogens are aromatic, and most Fe2+ imine complexes are low-spin. It was found that after some modification of the parameters, although the bond lengths were not very accurately reproduced, DommiMOE correctly predicted the spin state for most of the complexes (but not all). The most striking result was the predicted spin states of the low spin complex [Fe(1-10-phenantroline)3]2+ and the high spin [Fe(2-methyl-1-10-phenantroline)3]2+. Although the ligands in these complexes were very similar, DommiMOE correctly deduced their spin states, which correspond to a large change in geometry.¡Îi= t"*ò"f"*âÿ"*3"*âÿ"*œ"ª,@  Lðœ ð “ ð6…¿�¿Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðt!Î.ž:t!ðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@ÖD¦Pð@ðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð‘GÖD¦P‘Gð–B ð “ ð6‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@ÖDÖD¬GðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@¦P¦P‘GððF ðdYÝ<hæE ðF  ðˆðÍ;dYhÖDð^ ð  ³ ðB€(}`¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðk`@DhæE 𦟨$[Fe(2-methyl-1-10-phenantroline)3]2+¡f% eÿÿÿþmÿÿÿþâÿeÿÿÿþmÿÿÿþAðe ð  ³ ðB€œ„`¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðdY@Dk`æE 𭟨e(1-10-phenantroline)3]2+¡v%ÿÿÿþeÿÿÿþmÿÿÿþâÿeÿÿÿþmÿÿÿþAðö ð  ³ ðB€¸’`¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðdYÝ< h@D ð>Ÿ¡¦ø: Wtðt² ð  “ ðD‚„# "AÁÇ .?ˆBUHKAQð�YÝ<ð`7Dðt² ð  “ ðD‚F5 "AÁ€ Â5?ˆCEPZOMðÜ`Ý<|g7Dð¼¢ ð s ð*€”œ`¿�3ÌÌ¿Àÿ"ñ¿`ðÝ<ä47Kq> ðTŸ¨ Applications¡ 2 $¦: ðn² ð  s ð8€€AÁ®G (\?Image1"ñ¿`ðr;:NjWoCðø¢ ð3 à ðH€tž`¿�ƒ¿ Àÿ?¿ÿ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðu>ä4ìYýD ðBŸ (The next step is to model Iron(II) porphyrins, which are planar complexes with the Fe2+ surrounded by four aromatic nitrogens (chemically similar to imine nitrogens). The most important example of an Iron(II) porphyrin is the O2 -binding site for haemoglobin, heme. Fe2+ in heme changes from high spin to low spin when it binds to an oxygen molecule, which changes the shape of the whole molecule. This change is important in the uptake and transport of oxygen. It would be very interesting to find out if DommiMOE can model this  %¡†U Œ çÿ  "ªb G  $F¦: ð|ð~ ð3 í  � ð< 3 ð€€ˆ¿ c"ñ$��‘’¿ð�) \øg�3ðN² ð=  S ðX99¿ÿ?ð3 í  �ðJ ð>  # ð �¿"ñ¿`ð3 í  �ðb² ð?  c ð2€€A Á†, .DETTOLð3 í Ôðb² ð@  c ð2€€AÁ†, .PAZXAPðí  Îðb² ðA  c ð2€€AÁOì f&PURYIKð3 �Ú�𨢠ðB  3 ð€H©`�¿"ñ¿`ðÐ í ¦ -  ðPŸ¨1.¡$ ÿÿÿþ¦: 𨢠ðC  3 ð€<Ã`�¿"ñ¿`ðmí D-  ðPŸ¨2.¡$ ÿÿÿþ¦: 𨢠ðD  3 ð€¬Ó`�¿"ñ¿`ðÐ í¦ - ðPŸ¨3.¡$ ÿÿÿþ¦: ðNð8 ðä4E7YaH ðN ðEä47YaHð¼ ð9  Ó ðN‡¿�¿ÀÎÿ?¿ÿˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nðä4E7YaHðÚ¢ ð7  Ó ðN€ Ö`¿�¿ÀÎÿ?¿ÿˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?NðÊ81E™QäG ðŸ¨ØThe author would like to thank the MOAC Doctoral Centre staff and colleagues for their guidance and the Engineering and Physical Sciences Research Council Life Sciences Interface Programme for their generous support.¡ÙÙ¦: ð†² ð5  £ ðH€€AÁ �¿ÀÎÿˆmoacc"ñ¿`ðl51El8OHðÒ² ðJ  ƒ 𔀀 X3”¹AÁdDownloads_Images_Logos_Version1Colour_EPSRC1RGBHI"ñ¿`ð=Q^E­X7Hðj² ðL C ðB€€AÁ*the_warwick_uni_blueðx¡ š ð2ð8 ð‰4S©Av& ð† ðpä4B“%ðÚð@ ð7�$DÀ% ðm ð‰4S©Av&ðz² ð  “ ð<€€Ó œAÁ¿?ˆsa"ñ¿`ð7�$DÀ%ðÈB ð   ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðr;sW?ƒ ðÈB ð B  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÌ;ƒ W? !ðÈB ð ‚  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðú;ë•@ !ðÈB ð B  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÙ9ë•@V ðÈB ð   ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð:V ‚<f!ðÈB ð! 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Then the model parameters were refined using simulated annealing to give the correct geometries and predict the correct spin state of the metal, initially with [Fe(NH3)6]2+, then with three other amine complexes. The parameters found were applied to about 80 imine complexes, and after a slight modification, approximated the geometries reasonably well and most of the time predicted the correct spin state.¡xD å çÿ çÿ ë¦: ðB² ð. # ð Aÿ"ñ¿`ð'T ¨ð ¢ ð9 à ðH€”._¿?�3ÌÌ¿Àÿ?¿ÿ“"ñ6?@¿`ÿÀ¿‚‚N¿NÿN?Nðü'z� ðTŸ¨ Introduction¡ 2 $¦: ðÖ¢ ð: £ ð<€ D_¿�ƒ¿ Àÿ?“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nðg'.4Õ ð,Ÿ îThe importance of organometallic proteins in biochemistry has long been recognised, which the metal instrumental in many of these protein s catalytic or binding functions. At the moment there are very few methods that model transition metal-containing organometallic proteins effectively, either using quantum or classical mechanical methods. Here is outlined a very promising new Molecular Modelling approach to deal with transition metal complexes which can be used to model biological macromolecules.¡øø¦: ð¢ ð< à ðH€Q_¿?�3ÌÌ¿Àÿ?¿ÿ“"ñ6?@¿`ÿÀ¿‚‚N¿NÿN?Nð]'zñ ð[Ÿ¨Molecular Modelling¡ 2$¦: ð¨ ð? ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðmið¨ ðA ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðmið¢ ð= £ ð<€àZ_¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð"'.4ƒ ðVŸ¨Molecular Modelling (MM) of Force-Field (FF) methods of finding molecular structures determine the relationship between the energy and structure by application of empirical rules based on classical mechanics. To find an optimal structure in MM, we optimise the total strain energy¡¦: ðD¢ ðB £ ð<€lf_¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðë'\4€& 𚟨\where the terms correspond to the deviation from the optimal bond lengths, bond angles, torsions, non-bonded interactions and electrostatic interactions from those given by the a particular forcefield. Modelling transition metals using conventional MM has always been difficult as they can have variable oxidation states, spin states and electronic effects, and can coordinate from 4 to 12 different ligands in a complex. Rob Deeth has addressed this problem by developing this Ligand Field Molecular Mechanics model of dealing with transition metal centres using an approach called Ligand Field Theory.¡]]¦: ð¨ ðD ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðF$miF$ðj² ðC S ð AÁ ??"ñ?ð� &ð Á ðÑ¢ ðT £ ð<€øu_¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð}('am7 ð'Ÿ¨ In a free transition metal ion, the preference of the d-electrons is to occupy each of the five d-orbitals, and when there are more than five d electrons, spin-pairing occurs. In an octahedrally-coordinated complex, the dxy, dyz and dxz orbitals become lower in energy than the dx2-y2 and dz2 orbitals and are filled first. Ligand Field Theory states that this is because the former orbitals repel the ligand electron densities less than the latter (the d-orbitals are mostly antibonding and repel ligand electron clouds). Depending on the ligands (the so-called ligand field strength), the d-electrons may desert the dx2-y2 and dz2 orbitals completely as the electron pairing becomes energetically more favourable than the electron repulsion of ligand bonding orbitals.¡® Ý çÿ çÿ çÿ, çÿ çÿM çÿ çÿ‹ª>ܦ: ðV² ðW C ð.€€AÁdorbitals2ðÔ%m¶4·+ð¢ ð\ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð_ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ðb £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð‰ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ðŒ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð� £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ðÄðF ð2)p*–2 3 ð’  ðˆðÚ+`)Ä2v4ðN² ðÑ S ðÂA ÿÿÿ¿ˆð2)p*’2€-ðN² ðÒ S ðfA ÿÿÿ¿ˆð2)_-–2n0ð² ðÓ ã ðT¿ÇÂAÿÿÿ�ƒ¿ Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð2)L0’2 3ðæ ðF ð`B*Ã23 ð‘  ðˆðÚ+èK3µ4ðþ ð¸ à ðH€l›_¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(*0Ã23 ð@Ÿ¡¦ø: Wtð� ð· ³ ðB€ §_¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`*0{(3 ðØŸ¨:(2) High Ligand Field strength (e.g. CN-, phenantroline) ¡J;(&þ.þ&þª+ ¦ø: Wtðþ ð¶ à ðH€„°_¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(6-Ã2*0 ð@Ÿ¡¦ø: WtðÑ ðµ ³ ðB€ À_¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`6-{(*0 ðŸ¨7(1) Low Ligand Field strength (e.g. Cl-, I-, F-, H2O) ¡°8'&þ.þ&þ.þ&þ.þ&þ.þçÿ&þ¦ø: Wtðþ ð´ à ðH€`É_¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(B*Ã26- ð@Ÿ¡,¦ø: WtðA ð³ ³ ðB€LÔ_¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`B*{(6- ð‰Ÿ¨Free Fe2+ ion (high spin)¡> ¦ø: WtðªB ð¹ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`B*Ã2B*ð¤B 𺠣 ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`6-Ã26-ð¤B ð» £ ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`*0Ã2*0ðªB ð¼ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`3Ã23ðªB ð½ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`B*`3ð¤B ð¾ £ ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð{(B*{(3ðªB ð¿ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÃ2B*Ã23ð/ðF ð$ °ÔÌ ðä ðˆðu>’Ù �?ði¢ ðå  ð€Ù_ð$ °ÄÌ ð+Ÿ¨ High Spin¦: ðh¢ ðæ  ð€Àâ_ð4°ÔÌ ð*Ÿ¨Low Spin¦: ðj² ðè S ð A Á  ??"ñ?ðà?ó%yBð Á  ð_ ðê à ðH€0ë_‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðFB'L%ÁG 𩟨yDeeth has implemented LFMM into the Molecular Operating Environment (MOE), a popular MM dynamics program, to form DommiMOE, which uses the forcefield MMFF94 for non-transition metals. DommiMOE can optimise the geometry a complex for a given spin state, and so can give hypothetical structures of transition metal complexes for both spin states with the same set of parameters.¡zzðè ðë à ðH€l`‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðP ä4>_  ð2Ÿ ÊThis is an octahedral high-spin complex where the Fe  N bond lengths were 2.20 ú (from X-ray crystallographic data). To obtain data on a hypothetical low-spin structure, QM techniques were used, which predict that the Fe  N bond lengths to be around 2.00 ú. Also, an estimate of 11 kcal/mol was set on the energetic favourability of the high spin state to the low spin state. As with all MM-based methods, some model parameters have to be found which fit the required geometries and energies. Parameters modified included the Morse function parameters (Fe N bond length potential was modelled by a Morse function), octahedral-field splitting term, the ligand-ligand repulsion term and some electron-pairing energy terms. To measure the  fit of the parameters, a cost function was constructed such that the smaller its value, the better the parameters fit the data.¡ffª0P ¯ dðt² ðì c ð>A Á·m ¸ÿFe_hexammine"ñ¿`ð 0_Ïgð%¢ ðî à ðH€ï_¿?�3ÌÌ¿Àÿ?¿ÿ“"ñ6?@¿`ÿÀ¿‚‚N¿NÿN?Nðzä4 K ðoŸ¨Simulated Annealing¡2 2 $ '$¦: ðF 𬠳 ðB€T`¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð¹7D\4N? ð–Ÿ The difference between low spin and high spin states is the metal-ligand bond lengths of low spin states are much smaller than those of high spin. For example, the Fe  N bond length in low spin and high spin amine complexes are about 2.00 and 2.20ú respectively. This is because of the smaller repulsion of the ligands from the d-electron cloud at low spin than at high spin. Deeth summarises this effect by the Ligand Field Stabilisation Energy (LFSE), and incorporated into the MM framework by adding to the MM equation:¡.ù"ªù ¦: ðv ð­ ³ ðB€È!`¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðä4p–287 ðÆŸ¨r(1) is known as the high-spin state of Fe2+ as the total spin is greater than in (2), known as the low spin state.¡*s) H¦: ðj² ð¯  S ð A Á _??"ñ?ð17¯` ‚>ð Á _ð( ð² à ðH€¨þ_‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðä4ìgs ðrŸ ¾Simulated Annealing (SA) is a method of finding the maximum or minimum of a distribution À(x) by using Markov Chain Monte Carlo (MCMC) to sample the parameter space, in this case the distribution needed to be minimised is the cost function A Markov chain (a  random walk ) is constructed whose limiting distribution is À(x) - the target distribution. ¡d`[""å"""""ª,Yãð¨ ð¶ ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð+$mi+$ð ð» à ðH€|0`‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð§%·4dg* ð`Ÿ BIn simulated annealing, the target distribution À(x) is changed to À(x)1/T (T is known as the  temperature ), which has the same maxima and minima as À(x) but is rather  ste‘’“”•—™ÿÿÿÿšÿÿÿÿ› œ�ÿÿÿÿžÿÿÿÿŸ  ¡ÿÿÿÿ¢ÿÿÿÿ¿NÀÁÂÿÿÿà ÄÅEÆÇÈÉÊË5%ÌÍÎÏÐÑÒÓÔÕ×ÙÿÿÿÿÚÿÿÿÿÛ ÜÝÿÿÿÿÞÿÿÿÿß àáÿÿÿÿâÿÿÿÿÿNÿÿÿ F   5%  ÿÿÿÿÿÿÿÿ ÿÿÿÿÿÿÿÿ !ÿÿÿÿ"ÿÿÿÿ?N@eper as T decreases from 1 to 0, and this makes the Markov chain less likely to escape local minima. If the temperature is carefully reduced, then (hopefully) at the end of the procedure the Markov chain will reside near the global minimum. ¡΢2"""""**""K""""è"ª,0c ðÓ¢ ð¼ s ð*€L`¿�3ÌÌ¿Àÿ"ñ¿`ð�*ä47K1, ðkŸ¨Amine Complexes¡2 2$ '$¦: ðì ð¿ à ðH€œN`‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð5,ä4•\½2 ð6Ÿ¨6The simulated annealing procedure yielded some good parameters for the iron hexaammine complex, which were applied to three other amine complexes. From the bond lengths in their X-ray crystallographic structures, (1) and (2) were low spin complexes, while (3) was a high spin complex, which illustrates the sensitivity of the spin state of Fe2+ with nitrogen ligands. The parameters found for [Fe(NH3)6]2+ were found to reproduce the geometry of the complexes very well in their native spin states, and also the spin states of the complexes were correctly predicted.¡Â7Ý""  S"*7"*âÿ"*âÿ"*¢"ªL áðÓ¢ ðÛ s ð*€T+`¿�3ÌÌ¿Àÿ"ñ¿`ðÃ2ä47KW4 ðkŸ¨Imine Complexes¡2 2$ '$¦: ðy ðÝ Ã ðH€ i`‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð\4ä4‘gÞ; ðߨ¥Can these parameters transfer to imine complexes? Unlike amine nitrogens, imine nitrogens are aromatic, and most Fe2+ imine complexes are low-spin. It was found that after some modification of the parameters, although the bond lengths were not very accurately reproduced, DommiMOE correctly predicted the spin state for most of the complexes (but not all). The most striking result was the predicted spin states of the low spin complex [Fe(1-10-phenantroline)3]2+ and the high spin [Fe(2-methyl-1-10-phenantroline)3]2+. Although the ligands in these complexes were very similar, DommiMOE correctly deduced their spin states, which correspond to a large change in geometry.¡Îi= t"*ò"f"*âÿ"*3"*âÿ"*œ"ª,@  Lðœ ð “ ð6…¿�¿Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðt!Î.ž:t!ðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@ÖD¦Pð@ðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð‘GÖD¦P‘Gð–B ð “ ð6‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@ÖDÖD¬GðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@¦P¦P‘GððF ðdYÝ<hæE ðF  ðˆðÍ;dYhÖDð^ ð  ³ ðB€(}`¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðk`@DhæE 𦟨$[Fe(2-methyl-1-10-phenantroline)3]2+¡f% eÿÿÿþmÿÿÿþâÿeÿÿÿþmÿÿÿþAðe ð  ³ ðB€œ„`¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðdY@Dk`æE 𭟨e(1-10-phenantroline)3]2+¡v%ÿÿÿþeÿÿÿþmÿÿÿþâÿeÿÿÿþmÿÿÿþAðö ð  ³ ðB€¸’`¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðdYÝ< h@D ð>Ÿ¡¦ø: Wtðt² ð  “ ðD‚„# "AÁÇ .?ˆBUHKAQð�YÝ<ð`7Dðt² ð  “ ðD‚F5 "AÁ€ Â5?ˆCEPZOMðÜ`Ý<|g7Dð¼¢ ð s ð*€”œ`¿�3ÌÌ¿Àÿ"ñ¿`ðÝ<ä47Kq> ðTŸ¨ Applications¡ 2 $¦: ðn² ð  s ð8€€AÁ®G (\?Image1"ñ¿`ðr;:NjWoCðø¢ ð3 à ðH€tž`¿�ƒ¿ Àÿ?¿ÿ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðu>ä4ìYýD ðBŸ (The next step is to model Iron(II) porphyrins, which are planar complexes with the Fe2+ surrounded by four aromatic nitrogens (chemically similar to imine nitrogens). The most important example of an Iron(II) porphyrin is the O2 -binding site for haemoglobin, heme. Fe2+ in heme changes from high spin to low spin when it binds to an oxygen molecule, which changes the shape of the whole molecule. This change is important in the uptake and transport of oxygen. It would be very interesting to find out if DommiMOE can model this  %¡†U Œ çÿ  "ªb G  $F¦: ð|ð~ ð3 í  � ð< 3 ð€€ˆ¿ c"ñ$��‘’¿ð�) \øg�3ðN² ð=  S ðX99¿ÿ?ð3 í  �ðJ ð>  # ð �¿"ñ¿`ð3 í  �ðb² ð?  c ð2€€A Á†, .DETTOLð3 í Ôðb² ð@  c ð2€€AÁ†, .PAZXAPðí  Îðb² ðA  c ð2€€AÁOì f&PURYIKð3 �Ú�𨢠ðB  3 ð€H©`�¿"ñ¿`ðÐ í ¦ -  ðPŸ¨1.¡$ ÿÿÿþ¦: 𨢠ðC  3 ð€<Ã`�¿"ñ¿`ðmí D-  ðPŸ¨2.¡$ ÿÿÿþ¦: 𨢠ðD  3 ð€¬Ó`�¿"ñ¿`ðÐ í¦ - ðPŸ¨3.¡$ ÿÿÿþ¦: ðNð8 ðä4E7YaH ðN ðEä47YaHð¼ ð9  Ó ðN‡¿�¿ÀÎÿ?¿ÿˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nðä4E7YaHðÚ¢ ð7  Ó ðN€ Ö`¿�¿ÀÎÿ?¿ÿˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?NðÊ81E™QäG ðŸ¨ØThe author would like to thank the MOAC Doctoral Centre staff and colleagues for their guidance and the Engineering and Physical Sciences Research Council Life Sciences Interface Programme for their generous support.¡ÙÙ¦: ð†² ð5  £ ðH€€AÁ �¿ÀÎÿˆmoacc"ñ¿`ðl51El8OHðÒ² ðJ  ƒ 𔀀 X3”¹AÁdDownloads_Images_Logos_Version1Colour_EPSRC1RGBHI"ñ¿`ð=Q^E­X7Hðj² ðL C ðB€€AÁ*the_warwick_uni_blueðx¡ š ð2ð8 ð‰4S©Av& ð† ðpä4B“%ðÚð@ ð7�$DÀ% ðm ð‰4S©Av&ðz² ð  “ ð<€€Ó œAÁ¿?ˆsa"ñ¿`ð7�$DÀ%ðÈB ð   ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðr;sW?ƒ ðÈB ð B  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÌ;ƒ W? !ðÈB ð ‚  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðú;ë•@ !ðÈB ð B  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÙ9ë•@V ðÈB ð   ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð:V ‚<f!ðÈB ð! 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" # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x z Ì { | } ~  € ý ‚ ƒ „ … † ‡ ˆ ‰ Š ‹ Œ � Ž � � ‘ ’ “ ” • – — ˜ ™ š › œ � ž Ÿ   ¡ ¢ £ ¤ ¥ ¦ § ¨ © ª « ¬ ­ ® ¯ ° ± ² ³ ´ µ ¶ · ¸ ¹ º » ¼ ½ ¾ ¿ À Á Â Ã Ä Å Æ Ç È É Ê Ë Ì Í Î Ï Ð Ñ Ò Ó Ô Õ Ö × Ø Ù Ú Û Ü Ý Þ ß à á â ã ä å æ ç è é ê ë ì í î ï ð ñ ò ó ô õ ö ÷ ø ù ú û ü þ y ÿ µ+2ð$ Å?•Mú‚¥J±Ñ0¡×ÿ-cQËRð$xdãj¶?ª8’ÊpW‰ôÿ~.2ð$(-‚rf/ÎAóZ6›æþÿõ�>¸éð$+ÉÆ±è´¥<Ówåk@t;ÿÓ;’@bð$§Œ¢Ä3ÉÁ Rð$á?‰UfÍsÙZ87â[¿Éÿ-3ˆ bð$ÓøPf;)r±Dcžã5@ÿ¹·µ;  ð�0e‚˜²ƒ0e„˜²…‡ˆ‰¿ ô   €�‚ƒ„… †A‡Áˆ‰Š‹Œ�Ž��‘’“”•–—Á˜™š›œ@¿ ÀÁÂÿÿÿà ÄÅAÆÁÇÈÉÊË5%ÌÍÎÏÁ×ÿËËË 8c8c     ?€�‚ƒœ1„…ðù†‡÷ˆ ¿ÀÁÂdÃÄÅÆÇÈÉÊ0uËÐÌ0íìÿÍ@T‰Î€Ï€ÿÿÐyÿÑ2Ò NÓPÃÔÕ'Öp”×°<ÿÿØÙ'Úp”ÿA¨)BCD|¾E„|¾…†|¾‡s "ñ Œ�0e@žÿÿÿÿŸÿÿÿÿ  ¡Á¢ÿÿÿÿ£ÿÿÿÿ¤ ¥Á¦ÿÿÿÿ§ÿÿÿABÿÿÿC DEFFGHIJK5%LMNOPQRSTUWYÿÿÿÿZÿÿÿÿ[ \]ÿÿÿÿ^ÿÿÿÿ_ `aÿÿÿÿbÿÿÿÿ@ñ÷ðó€Ð»=‹ŽÊš;d,;Êš;úgþý4-d-dvÇ 0pÚ¢LpûÄ$pû·4<ý4dd`ó 0,ÞhdÉÿ <ý4!d!dœÚÙô 0,Þ<ý4BdBdœÚÙô 0,Þˆ8Š0º___PPT10‹ pµpµ?Ù Ú %ðóêîë¤ï€ ¤ðú£ð˜¡ 0ñL ðþ¢ð( ð ððR² ð� C ð*€€AÁPicture1ð] Ì h Hðв ð4 “ ðT€€ÖAÁé" ¤ðÿÿ¿ÿMOE_Screenshot"ñ¿`ðH>%4EHð¨ ð ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nði$þ0CW½,𸢠ð$ s ð*€ðñÉ¿�3ÌÌ¿Àÿ"ñ¿`ð¸ 'zL  ðPŸ¨Abstract¡ 2 $¦: ð¢ ð& à ðH€ÐÝ¿?�3ÌÌ¿Àÿ?¿ÿ“"ñ6?@¿`ÿÀ¿‚‚N¿NÿN?NðŠ&'z( ðdŸ¨A bit of Ligand Field Theory¡ 2$¦: ðµ¢ ð' à ðH€(Ý¿?�3ÌÌ¿Àÿ?¿ÿ“"ñ6?@¿`ÿÀ¿‚‚N¿NÿN?Nð‹ ä47K  ðÿŸ¨Iron(II) Hexammine [Fe(NH3)6]2+¡Š 2'$/$çÿ'$/$çÿ'$/$ª$ ¦: ð'ðF ðÒTÈbi  ð1 ðˆðÌÅò_ ðS¢ ð ƒ ð0€HÝ¿�3ÌÌ¿Àÿˆ"ñ¿`ðTÈby ðÝŸ¨qFinding optimal parameters for spin-state changes in Iron(II) amine complexes in Ligand Field Molecular Mechanics¡ r(2rPª56¦: ð ¢ ð “ ð6€ðÝ¿�ƒ¿ÀÿˆðÒZšb“  ð�Ÿ¨Prakash Patel1 , Rob Deeth2¡X(2 6 6 6 66¦: ðc¢ ð+ “ ð6€4-Ý¿�ƒ¿ÀÿˆðÒM šbi  ðõŸ¨�1MOAC Doctoral Training Centre, and the 2Inorganic Computational Chemistry Group, Department of Chemistry, 91Ó°ÊÓÆÆ½â°æ.¡J‚(2 ' Y¦: ð¢ ð8 ƒ ð0€41Ý¿�ƒ¿ÀÿðP ú4Ë ð¿Ÿ¨The geometries and energies of six-coordinated amine complexes of Fe2+ at both spin states were explored using the DommiMOE program. Then the model parameters were refined using simulated annealing to give the correct geometries and predict the correct spin state of the metal, initially with [Fe(NH3)6]2+, then with three other amine complexes. The parameters found were applied to about 80 imine complexes, and after a slight modification, approximated the geometries reasonably well and most of the time predicted the correct spin state.¡xD å çÿ çÿ ë¦: ðB² ð. # ð Aÿ"ñ¿`ð'T ¨ð ¢ ð9 à ðH€´HÝ¿?�3ÌÌ¿Àÿ?¿ÿ“"ñ6?@¿`ÿÀ¿‚‚N¿NÿN?Nðü'z� ðTŸ¨ Introduction¡ 2 $¦: 𜢠ð: £ ð<€4JÝ¿�ƒ¿ Àÿ?“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nðg'.4Õ ðòŸ¨ðThe importance of metalloproteins in biochemistry has long been recognised. Metal centres are instrumental in many catalytic and binding functions. Computer modelling can help probe their properties but few methods exist that model transition metal-containing proteins effectively, either using quantum or classical mechanical methods. Here is outlined a very promising new molecular modelling approach to deal with transition metal complexes which can be used to model biological macromolecules.¡ññª¼ 6 #j  h¦: ð3¢ ð< à ðH€ÈNÝ¿?�3ÌÌ¿Àÿ?¿ÿ“"ñ6?@¿`ÿÀ¿‚‚N¿NÿN?Nð]'zñ ð}Ÿ¨Molecular Mechanics¡ 2$ª ¦: ð¨ ð? ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðmið¨ ðA ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðmiðo¢ ð= £ ð<€¼gÝ¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð"'.4ƒ ðÅŸ¨Molecular Mechanics (MM), or Force-Field (FF) methods, of finding molecular structures determine the relationship between the energy and structure by application of empirical rules based on classical mechanics. To find an optimal structure in MM, we optimise the total potential energy¡ªb × ¦: ðÀ¢ ðB £ ð<€Ü¦: ðV² ðW C ð.€€AÁdorbitals2ðÔ%m¶4·+ð¢ ð\ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð_ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ðb £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð‰ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ðŒ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð� £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ðÄðF ð2)p*–2 3 ð’  ðˆðÚ+`)Ä2v4ðN² ðÑ S ðÂA ÿÿÿ¿ˆð2)p*’2€-ðN² ðÒ S ðfA ÿÿÿ¿ˆð2)_-–2n0ð² ðÓ ã ðT¿ÇÂAÿÿÿ�ƒ¿ Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð2)L0’2 3ð ðF ð`B*Ã23 ð‘  ðˆðÚ+èK3µ4ð ð¸ à ðH€Ý¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(*0Ã23 ðRŸ¡ª ¦ø: Wtð� ð· ³ ðB€H}Ý¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`*0{(3 ðØŸ¨:(2) High Ligand Field strength (e.g. CN-, phenantroline) ¡J;(&þ.þ&þª+ ¦ø: Wtð ð¶ à ðH€è›Ý¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(6-Ã2*0 ðRŸ¡ª ¦ø: WtðÑ ðµ ³ ðB€´«Ý¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`6-{(*0 ðŸ¨7(1) Low Ligand Field strength (e.g. Cl-, I-, F-, H2O) ¡°8'&þ.þ&þ.þ&þ.þ&þ.þçÿ&þ¦ø: Wtð ð´ à ðH€À®Ý¿�‚=J¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð{(B*Ã26- ðRŸ¡,ª ¦ø: WtðA ð³ ³ ðB€ÜÁÝ¿�¿Àÿ?ˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð`B*{(6- ð‰Ÿ¨Free Fe2+ ion (high spin)¡> ¦ø: WtðªB ð¹ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`B*Ã2B*ð¤B 𺠣 ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`6-Ã26-ð¤B ð» £ ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`*0Ã2*0ðªB ð¼ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`3Ã23ðªB ð½ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`B*`3ð¤B ð¾ £ ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð{(B*{(3ðªB ð¿ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÃ2B*Ã23ð/ðF ð$ °ÔÌ ðä ðˆðu>’Ù �?ði¢ ðå  ð€TÔÝð$ °ÄÌ ð+Ÿ¨ High Spin¦: ðh¢ ðæ  ð€�ÖÝð4°ÔÌ ð*Ÿ¨Low Spin¦: ð\² ðè S ð A Á  ??ðà?ó%yBð Á  ð° ðê à ðH€èÞ݇¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðFB'L%ÁG ðúŸ¨rDeeth has implemented LFMM into the Molecular Operating Environment (MOE), a popular modelling program, to form DommiMOE, which uses the MMFF94 FF for non-transition metals. DommiMOE can optimise the geometry of a complex for a given spin state, and so can give hypothetical structures of transition metal complexes for both spin states with the same set of parameters.¡ssªPU ' <�ð  ðë à ðH€(ç݇¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðP ä4>_  ðjŸ ÈThis is an octahedral high-spin complex where the Fe  N bond lengths are 2.20 ú (from X-ray crystallographic data). To obtain data on a hypothetical low-spin structure, QM techniques were used, which predict that the Fe  N bond lengths are around 2.00 ú. Also, an estimate of 11 kcal/mol was set on the energetic favourability of the high spin state over the low spin state. As with all MM-based methods, some model parameters have to be found which fit the required geometries and energies. Parameters modified included the Morse function parameters (Fe N bond length potential was modelled by a Morse function), octahedral-field splitting term, the ligand-ligand repulsion term and some electron-pairing energy terms. To measure the  fit of the parameters, a cost function was constructed such that the smaller its value, the better the parameters fit the data.¡eeªjF �  bðt² ðì c ð>A Á·m ¸ÿFe_hexammine"ñ¿`ð 0_Ïgð%¢ ðî à ðH€êÝ¿?�3ÌÌ¿Àÿ?¿ÿ“"ñ6?@¿`ÿÀ¿‚‚N¿NÿN?Nðzä4 K ðoŸ¨Simulated Annealing¡2 2 $ '$¦: ðZ 𬠳 ðB€¨ùÝ¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð¹7D\4N? 𪟠The difference between low spin and high spin states is the metal-ligand bond lengths of low spin states are much smaller than those of high spin. For example, the Fe  N bond length in low spin and high spin amine complexes are about 2.00 and 2.20ú respectively. This is because of the smaller repulsion of the ligands from the d-electron cloud at low spin than at high spin. Deeth summarised this effect by the Ligand Field Stabilisation Energy (LFSE), and incorporated into the MM framework by adding to the MM equation:¡.ù"ª0ù ‡ ƒ¦: ðv ð­ ³ ðB€dÞ¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðä4p–287 ðÆŸ¨r(1) is known as the high-spin state of Fe2+ as the total spin is greater than in (2), known as the low spin state.¡*s) H¦: ð\² ð¯  S ð A Á _??ð17¯` ‚>ð Á _ð< ð² à ðH€ÄÞ‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðä4ìgs ð†Ÿ ÀSimulated Annealing (SA) is a method of finding the maximum or minimum of a distribution À(x) by using Markov Chain Monte Carlo (MCMC) to sample the parameter space, in this case the distribution needed to be minimised is the cost function. A Markov chain (a  random walk ) is constructed whose limiting distribution is À(x) - the target distribution. ¡da[""æ"""""ª>Y‹ Pð¨ ð¶ ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð+$mi+$ð ð» à ðH€äÞ‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð§%·4dg* ð`Ÿ BIn simulated annealing, the target distribution À(x) is changed to À(x)1/T (T is known as the  temperature ), which has the same maxima and minima as À(x) but is rather  steeper as T decreases from 1 to 0, and this makes the Markov chain less likely to escape local minima. If the temperature is carefully reduced, then (hopefully) at the end of the procedure the Markov chain will reside near the global minimum. ¡΢2"""""**""K""""è"ª,0c ðÓ¢ ð¼ s ð*€l5Þ¿�3ÌÌ¿Àÿ"ñ¿`ð�*ä47K1, ðkŸ¨Amine Complexes¡2 2$ '$¦: ðì ð¿ à ðH€8Þ‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð5,ä4•\½2 ð6Ÿ¨6The simulated annealing procedure yielded some good parameters for the iron hexaammine complex, which were applied to three other amine complexes. From the bond lengths in their X-ray crystallographic structures, (1) and (2) were low spin complexes, while (3) was a high spin complex, which illustrates the sensitivity of the spin state of Fe2+ with nitrogen ligands. The parameters found for [Fe(NH3)6]2+ were found to reproduce the geometry of the complexes very well in their native spin states, and also the spin states of the complexes were correctly predicted.¡Â7Ý""  S"*7"*âÿ"*âÿ"*¢"ªL áðÓ¢ ðÛ s ð*€œOÞ¿�3ÌÌ¿Àÿ"ñ¿`ðÃ2ä47KW4 ðkŸ¨Imine Complexes¡2 2$ '$¦: ðî ðÝ Ã ðH€ PÞ‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð\4ä4‘gÞ; ð8Ÿ¨’Can these parameters transfer to imine complexes? Unlike amine nitrogens, imine nitrogens are unsaturated, and most Fe2+ imine complexes are low-spin. After further refinement of the parameters to account for p bonding, DommiMOE correctly predicted the spin state for most of the complexes, although the geometries require more analysis. The most striking result was the predicted spin states of the low spin complex [Fe(1-10-phenantroline)3]2+ and the high spin [Fe(2-methyl-1-10-phenantroline)3]2+. Although the ligands in these complexes were very similar, DommiMOE correctly deduced their spin states, which correspond to a large change in geometry.¡êV= w"*Z"c�"f"*âÿ"*3"*âÿ"*œ"ª˜@   .k!@ðœ ð “ ð6…¿�¿Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðt!Î.ž:t!ðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@ÖD¦Pð@ðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð‘GÖD¦P‘Gð–B ð “ ð6‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿ÿ¿ ÙÿÿÿÿÚÿÿÿÿÛ ÜÁÝÿÿÿÿÞÿÿÿÿß àÁáÿÿÿÿâÿÿÿÿÿÀÿÿÿÿÿÿÿÿ Âÿÿÿÿÿÿÿÿ Âÿÿÿÿÿÿÿÿ‰ÿÿÿÿŠÿÿÿÿ‹ ŒÂ�ÿÿÿÿ��‘’¿‚‚@ABÿÿÿC DEEFÅGHIJK5%LMNOÅPQRSTUWYÿÿÿÿZÿÿÿÿ[ \Å]ÿÿÿÿ^ÿÿÿÿ_ `ÅaÿÿÿÿbÿÿÿÿN€�‚ÿÿÿƒ „…E†Å‡ˆ‰Š‹5%Œ�Ž�Å�‘’“NÿN?Nðð@ÖDÖD¬GðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@¦P¦P‘Gð)ðF ðdYÝ<hæE ðF  ðˆðÍ;dYhÖDð^ ð  ³ ðB€œcÞ¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðk`@DhæE 𦟨$[Fe(2-methyl-1-10-phenantroline)3]2+¡f% eÿÿÿþmÿÿÿþâÿeÿÿÿþmÿÿÿþAðe ð  ³ ðB€jÞ¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðdY@Dk`æE 𭟨e(1-10-phenantroline)3]2+¡v%ÿÿÿþeÿÿÿþmÿÿÿþâÿeÿÿÿþmÿÿÿþAð ð  ³ ðB€XpÞ¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðdYÝ< h@D ðPŸ¡ª ¦ø: Wtðt² ð  “ ðD‚„# "AÁÇ .?ˆBUHKAQð�YÝ<ð`7Dðt² ð  “ ðD‚F5 "AÁ€ Â5?ˆCEPZOMðÜ`Ý<|g7Dð¼¢ ð s ð*€DxÞ¿�3ÌÌ¿Àÿ"ñ¿`ðÝ<ä47Kq> ðTŸ¨ Applications¡ 2 $¦: ðn² ð  s ð8€€AÁ®G (\?Image1"ñ¿`ðr;:NjWoCð¢ ð3 à ðH€�Þ¿�ƒ¿ Àÿ?¿ÿ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðu>ä4ìYýD ðRŸ The next step is to model iron porphyrins. The porphyrin is a symmetric planar ligand which binds the metal via four aromatic nitrogens (chemically similar to imine nitrogens). An important example of an iron porphyrin is the O2 -binding site for haemoglobin. Fe2+ in heme changes from high spin to low spin when it binds to an oxygen molecule, which changes the shape of the whole molecule. This change is important in the uptake and transport of oxygen. It would be very interesting to find out if DommiMOE can model this  %¡Zã çÿ" "ªª(  '  ¦: ð|ð~ ð3 í  � ð< 3 ð€€ˆ¿ c"ñ$��‘’¿ð�) \øg�3ðN² ð=  S ðX99¿ÿ?ð3 í  �ðJ ð>  # ð �¿"ñ¿`ð3 í  �ðb² ð?  c ð2€€A Á†, .DETTOLð3 í Ôðb² ð@  c ð2€€AÁ†, .PAZXAPðí  Îðb² ðA  c ð2€€AÁOì f&PURYIKð3 �Ú�𨢠ðB  3 ð€ŸÞ�¿"ñ¿`ðÐ í ¦ -  ðPŸ¨1.¡$ ÿÿÿþ¦: 𨢠ðC  3 ð€ü„Þ�¿"ñ¿`ðmí D-  ðPŸ¨2.¡$ ÿÿÿþ¦: 𨢠ðD  3 ð€°Þ�¿"ñ¿`ðÐ í¦ - ðPŸ¨3.¡$ ÿÿÿþ¦: ð¹ðF ðä4EÀfaH ð¡  ðˆðEä4ÀfaHð¼ ð9  Ó ðN‡¿�¿ÀÎÿ?¿ÿˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nðä4EÀfaHð%¢ ð7  Ó ðN€d²Þ¿�¿ÀÎÿ?¿ÿˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð>:1EK\äG ðaŸ¨ïThe author would like to thank Rob Deeth and the MOAC Doctoral Centre staff and colleagues for their help and guidance and the Engineering and Physical Sciences Research Council Life Sciences Interface Programme for their generous support.¡ððª,5z¦: ð†² ð5  £ ðH€€AÁ �¿ÀÎÿˆmoacc"ñ¿`ðŸ51E½9OHðä² ðJ  ³ 𦀀 X3”¹AÁd¿ÿˆDownloads_Images_Logos_Version1Colour_EPSRC1RGBHI"ñ¿`ð�]`Eþd9Hðj² ðL C ðB€€AÁ*the_warwick_uni_blueðx¡ š ð2ð8 ð‰4S©Av& ð† ðpä4B“%ðÚð@ ð7�$DÀ% ðm ð‰4S©Av&ðz² ð  “ ð<€€Ó œAÁ¿?ˆsa"ñ¿`ð7�$DÀ%ðÈB ð   ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðr;sW?ƒ ðÈB ð B  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÌ;ƒ W? !ðÈB ð ‚  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðú;ë•@ !ðÈB ð B  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÙ9ë•@V ðÈB ð   ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð:V ‚<f!ðÈB ð! 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Then the model parameters were refined using simulated annealing to give the correct geometries and predict the correct spin state of the metal, initially with [Fe(NH3)6]2+, then with three other amine complexes. The parameters found were applied to about 80 imine complexes, and after a slight modification, approximated the geometries reasonably well and most of the time predicted the correct spin state.¡xD å çÿ çÿ ë¦: ðB² ð. # ð Aÿ"ñ¿`ð'T ¨ð ¢ ð9 à ðH€Œy?¿?�3ÌÌ¿Àÿ?¿ÿ“"ñ6?@¿`ÿÀ¿‚‚N¿NÿN?Nðü'z� ðTŸ¨ Introduction¡ 2 $¦: ðú¢ ð: £ ð<€Hq ¿�ƒ¿ Àÿ?“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nðg'.4Õ ðPŸ¨ðThe importance of metalloproteins in biochemistry has long been recognised. Metal centres are instrumental in many catalytic and binding functions. Computer modelling can help probe their properties but few methods exist that model transition metal-containing proteins effectively, either using quantum or classical mechanical methods. Here is outlined a very promising new molecular modelling approach to deal with transition metal complexes which can be used to model biological macromolecules.¡ññªÐ¦: ð¢ ð< à ðH€|õi¿?�3ÌÌ¿Àÿ?¿ÿ“"ñ6?@¿`ÿÀ¿‚‚N¿NÿN?Nð]'zñ ð[Ÿ¨Molecular Mechanics¡ 2$¦: ð¨ ð? ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðmið¨ ðA ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðmið¢ ð= £ ð<€Øõi¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð"'.4ƒ ð[Ÿ¨Molecular Mechanics (MM), or Force-Field (FF) methods, of finding molecular structures determine the relationship between the energy and structure by application of empirical rules based on classical mechanics. To find an optimal structure in MM, we optimise the total potential energy¡¦: ðD¢ ðB £ ð<€4öi¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðë'\4€& 𚟨\where the terms correspond to the deviation from the reference bond lengths, bond angles, torsions, non-bonded interactions and electrostatic interactions from those given by the a particular force field. Modelling transition metals using conventional MM has always been difficult as they can have variable oxidation states, spin states and electronic effects, and can coordinate from 4 to 12 different ligands in a complex. This has been addressed in Warwick by developing the Ligand Field Molecular Mechanics model of dealing with transition metal centres using an approach called Ligand Field Theory.¡]]¦: ð¨ ðD ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðF$miF$ð\² ðC S ð AÁ ??ð� &ð Á ðÑ¢ ðT £ ð<€<íI¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð}('am7 ð'Ÿ¨ In a free transition metal ion, the preference of the d-electrons is to occupy each of the five d-orbitals, and when there are more than five d electrons, spin-pairing occurs. In an octahedrally-coordinated complex, the dxy, dyz and dxz orbitals become lower in energy than the dx2-y2 and dz2 orbitals and are filled first. Ligand Field Theory states that this is because the former orbitals repel the ligand electron densities less than the latter (the d-orbitals are mostly antibonding and repel ligand electron clouds). Depending on the ligands (the so-called ligand field strength), the d-electrons may desert the dx2-y2 and dz2 orbitals completely as the electron pairing becomes energetically more favourable than the electron repulsion of ligand bonding orbitals.¡® Ý çÿ çÿ çÿ, çÿ çÿM çÿ çÿ‹ª>ܦ: ðV² ðW C ð.€€AÁdorbitals2ðÔ%m¶4·+ð¢ ð\ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð_ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ðb £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð‰ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ðŒ £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ð¢ ð� £ ð<…¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð.¶4ðÄðF ð2)p*–2 3 ð’  ðˆðÚ+`)Ä2v4ðN² ðÑ S ðÂA ÿÿÿ¿ˆð2)p*’2€-ðN² ðÒ S ðfA ÿÿÿ¿ˆð2)_-–2n0ð² ðÓ ã ðT¿ÇÂAÿÿÿ�ƒ¿ Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð2)L0’2 3ðæ ðF ð`B*Ã23 ð‘  ðˆðÚ+èK3µ4ðþ ð¸ à ðH€€ ¦ø: WtðªB ð¹ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`B*Ã2B*ð¤B 𺠣 ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`6-Ã26-ð¤B ð» £ ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`*0Ã2*0ðªB ð¼ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`3Ã23ðªB ð½ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð`B*`3ð¤B ð¾ £ ð<¿¿ÀËœ1ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð{(B*{(3ðªB ð¿ ³ ðB¿¿ÀËŸo×ÿ ?¿ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÃ2B*Ã23ð/ðF ð$ °ÔÌ ðä ðˆðu>’Ù �?ði¢ ðå  ð€xIð$ °ÄÌ ð+Ÿ¨ High Spin¦: ðh¢ ðæ  ð€ä$Ið4°ÔÌ ð*Ÿ¨Low Spin¦: ð\² ðè S ð A Á  ??ðà?ó%yBð Á  ðX ðê à ðH€�rI‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðFB'L%ÁG 𢟨rDeeth has implemented LFMM into the Molecular Operating Environment (MOE), a popular modelling program, to form DommiMOE, which uses the MMFF94 FF for non-transition metals. DommiMOE can optimise the geometry of a complex for a given spin state, and so can give hypothetical structures of transition metal complexes for both spin states with the same set of parameters.¡ssðæ ðë à ðH€ìï?‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðP ä4>_  ð0Ÿ ÈThis is an octahedral high-spin complex where the Fe  N bond lengths are 2.20 ú (from X-ray crystallographic data). To obtain data on a hypothetical low-spin structure, QM techniques were used, which predict that the Fe  N bond lengths are around 2.00 ú. Also, an estimate of 11 kcal/mol was set on the energetic favourability of the high spin state over the low spin state. As with all MM-based methods, some model parameters have to be found which fit the required geometries and energies. Parameters modified included the Morse function parameters (Fe N bond length potential was modelled by a Morse function), octahedral-field splitting term, the ligand-ligand repulsion term and some electron-pairing energy terms. To measure the  fit of the parameters, a cost function was constructed such that the smaller its value, the better the parameters fit the data.¡eeª0O ­ fðt² ðì c ð>A Á·m ¸ÿFe_hexammine"ñ¿`ð 0_Ïgð%¢ ðî à ðH€X»Ÿ¿?�3ÌÌ¿Àÿ?¿ÿ“"ñ6?@¿`ÿÀ¿‚‚N¿NÿN?Nðzä4 K ðoŸ¨Simulated Annealing¡2 2 $ '$¦: ðF 𬠳 ðB€T±Ÿ¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð¹7D\4N? ð–Ÿ The difference between low spin and high spin states is the metal-ligand bond lengths of low spin states are much smaller than those of high spin. For example, the Fe  N bond length in low spin and high spin amine complexes are about 2.00 and 2.20ú respectively. This is because of the smaller repulsion of the ligands from the d-electron cloud at low spin than at high spin. Deeth summarised this effect by the Ligand Field Stabilisation Energy (LFSE), and incorporated into the MM framework by adding to the MM equation:¡.ù"ªù ¦: ðv ð­ ³ ðB€¨¼Ÿ¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðä4p–287 ðÆŸ¨r(1) is known as the high-spin state of Fe2+ as the total spin is greater than in (2), known as the low spin state.¡*s) H¦: ð\² ð¯  S ð A Á _??ð17¯` ‚>ð Á _ð* ð² à ðH€F‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðä4ìgs ðtŸ ÀSimulated Annealing (SA) is a method of finding the maximum or minimum of a distribution À(x) by using Markov Chain Monte Carlo (MCMC) to sample the parameter space, in this case the distribution needed to be minimised is the cost function. A Markov chain (a  random walk ) is constructed whose limiting distribution is À(x) - the target distribution. ¡da[""æ"""""ª,Yäð¨ ð¶ ³ ðB…‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð+$mi+$ð ð» à ðH€ F‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð§%·4dg* ð`Ÿ BIn simulated annealing, the target distribution À(x) is changed to À(x)1/T (T is known as the  temperature ), which has the same maxima and minima as À(x) but is rather  steeper as T decreases from 1 to 0, and this makes the Markov chain less likely to escape local minima. If the temperature is carefully reduced, then (hopefully) at the end of the procedure the Markov chain will reside near the global minimum. ¡΢2"""""**""K""""è"ª,0c ðÓ¢ ð¼ s ð*€ F¿�3ÌÌ¿Àÿ"ñ¿`ð�*ä47K1, ðkŸ¨Amine Complexes¡2 2$ '$¦: ðì ð¿ à ðH€$+F‡¿�ƒ¿ Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nð5,ä4•\½2 ð6Ÿ¨6The simulated annealing procedure yielded some good parameters for the iron hexaammine complex, which were applied to three other amine complexes. From the bond lengths in their X-ray crystallographic structures, (1) and (2) were low spin complexes, while (3) was a high spin complex, which illustrates the sensitivity of the spin state of Fe2+ with nitrogen ligands. The parameters found for [Fe(NH3)6]2+ were found to reproduce the geometry of the complexes very well in their native spin states, and also the spin states of the complexes were correctly predicted.¡Â7Ý""  S"*7"*âÿ"*âÿ"*¢"ªL áðÓ¢ ðÛ s ð*€ CF¿�3ÌÌ¿Àÿ"ñ¿`ðÃ2ä47KW4 ðkŸ¨Imine Complexes¡2 2$ '$¦: ð” ðÝ Ã ðH€@  „­ðœ ð “ ð6…¿�¿Àÿ?“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðt!Î.ž:t!ðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@ÖD¦Pð@ðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð‘GÖD¦P‘Gð–B ð “ ð6‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@ÖDÖD¬GðœB ð £ ð<…‡¿¿Àÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðð@¦P¦P‘GððF ðdYÝ<hæE ðF  ðˆðÍ;dYhÖDð^ ð  ³ ðB€@^F¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðk`@DhæE 𦟨$[Fe(2-methyl-1-10-phenantroline)3]2+¡f% eÿÿÿþmÿÿÿþâÿeÿÿÿþmÿÿÿþAðe ð  ³ ðB€´eF¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðdY@Dk`æE 𭟨e(1-10-phenantroline)3]2+¡v%ÿÿÿþeÿÿÿþmÿÿÿþâÿeÿÿÿþmÿÿÿþAðö ð  ³ ðB€(tF¿�¿Àÿ?ˆ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?NðdYÝ< h@D ð>Ÿ¡¦ø: Wtðt² ð  “ ðD‚„# "AÁÇ .?ˆBUHKAQð�YÝ<ð`7Dðt² ð  “ ðD‚F5 "AÁ€ Â5?ˆCEPZOMðÜ`Ý<|g7Dð¼¢ ð s ð*€(~F¿�3ÌÌ¿Àÿ"ñ¿`ðÝ<ä47Kq> ðTŸ¨ Applications¡ 2 $¦: ðn² ð  s ð8€€AÁ®G (\?Image1"ñ¿`ðr;:NjWoC𮢠ð3 à ðH€àF¿�ƒ¿ Àÿ?¿ÿ“"ñ6@¿ ÿÀ¿‚‚N¿NÿN?Nðu>ä4ìYýD ðøŸ The next step is to model iron porphyrins. The porphyrin is a symmetric planar ligand which binds the metal via four aromatic nitrogens (chemically similar to imine nitrogens). An important example of an iron porphyrin is the O2 -binding site for haemoglobin. Fe2+ in heme changes from high spin to low spin when it binds to an oxygen molecule, which changes the shape of the whole molecule. This change is important in the uptake and transport of oxygen. It would be very interesting to find out if DommiMOE can model this  %¡Zã çÿ" "ªP  F  a¦: ð|ð~ ð3 í  � ð< 3 ð€€ˆ¿ c"ñ$��‘’¿ð�) \øg�3ðN² ð=  S ðX99¿ÿ?ð3 í  �ðJ ð>  # ð �¿"ñ¿`ð3 í  �ðb² ð?  c ð2€€A Á†, .DETTOLð3 í Ôðb² ð@  c ð2€€AÁ†, .PAZXAPðí  Îðb² ðA  c ð2€€AÁOì f&PURYIKð3 �Ú�𨢠ðB  3 ð€$ƒF�¿"ñ¿`ðÐ í ¦ -  ðPŸ¨1.¡$ ÿÿÿþ¦: 𨢠ðC  3 ð€ ›F�¿"ñ¿`ðmí D-  ðPŸ¨2.¡$ ÿÿÿþ¦: 𨢠ðD  3 ð€ô±F�¿"ñ¿`ðÐ í¦ - ðPŸ¨3.¡$ ÿÿÿþ¦: ð§ðF ðä4EÀfaH ð¢  ðˆðEä4ÀfaHð¼ ð9  Ó ðN‡¿�¿ÀÎÿ?¿ÿˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nðä4EÀfaHð¢ ð7  Ó ðN€µF¿�¿ÀÎÿ?¿ÿˆ“"ñ6@¿`ÿÀ¿‚‚N¿NÿN?Nð;1E$]äG ðOŸ¨ïThe author would like to thank Rob Deeth and the MOAC Doctoral Centre staff and colleagues for their help and guidance and the Engineering and Physical Sciences Research Council Life Sciences Interface Programme for their generous support.¡ððª#Ȧ: ð†² ð5  £ ðH€AÁ �¿ÀÎÿˆmoacc"ñ¿`ð©61Eª9OHðä² ðJ  ³ 𦀀 X3”¹AÁd¿ÿˆDownloads_Images_Logos_Version1Colour_EPSRC1RGBHI"ñ¿`ð¥]^Ee7Hðj² ðL C ðB€€AÁ*the_warwick_uni_blueðx¡ š ð2ð8 ð‰4S©Av& ð† ðpä4B“%ðÚð@ ð7�$DÀ% ðm ð‰4S©Av&ðz² ð  “ ð<€€Ó œAÁ¿?ˆsa"ñ¿`ð7�$DÀ%ðÈB ð   ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðr;sW?ƒ ðÈB ð B  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÌ;ƒ W? !ðÈB ð ‚  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nðú;ë•@ !ðÈB ð B  ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?NðÙ9ë•@V ðÈB ð   ð`…‡¿D¿ÀÑÿ?¿ÿ?ˆƒ"ñ0@ÿ€¿‚‚N¿NÿN?Nð:V ‚<f!ðÈB ð! 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