Theoretical Chemistry Accounts

, 117:185 | Cite as

QM/MM: what have we learned, where are we, and where do we go from here?

  • Hai Lin
  • Donald G. Truhlar
Open Access
Feature Article


This paper briefly reviews the current status of the most popular methods for combined quantum mechanical/molecular mechanical (QM/MM) calculations, including their advantages and disadvantages. There is a special emphasis on very general link-atom methods and various ways to treat the charge near the boundary. Mechanical and electric embedding are contrasted. We consider methods applicable to gas-phase organic chemistry, liquid-phase organic and organometallic chemistry, biochemistry, and solid-state chemistry. Then we review some recent tests of QM/MM methods and summarize what we learn about QM/MM from these studies. We also discuss some available software. Finally, we present a few comments about future directions of research in this exciting area, where we focus on more intimate blends of QM with MM.


Boundary treatment Combined QM/MM Electrostatic interactions Embedding scheme Link atom Multi-configuration molecular mechanics Potential energy surfaces 


  1. 1.
    van Gunsteren WF, Berendsen HJC, Geurtsen RG, Zwinderman HRJ (1986). Ann NY Acad Sci 482:287Google Scholar
  2. 2.
    Allinger NL, Yuh YH, Lii JH (1989). J Am Chem Soc 111:8551Google Scholar
  3. 3.
    Lii JH, Allinger NL (1989). J Am Chem Soc 111:8566Google Scholar
  4. 4.
    Lii JH, Allinger NL (1989). J Am Chem Soc 111:8576Google Scholar
  5. 5.
    Mayo SL, Olafson BD, Goddard WA III (1990). J Phys Chem 94:8897Google Scholar
  6. 6.
    Rappé AK, Casewit CJ, Colwell KS, Goddard III WA, Skid WM (1992). J Am Chem Soc 114:10024Google Scholar
  7. 7.
    Casewit CJ, Colwell KS, Rappé AK (1992). J Am Chem Soc 114:10035Google Scholar
  8. 8.
    Casewit CJ, Colwell KS, Rappé AK (1992). J Am Chem Soc 114:10046Google Scholar
  9. 9.
    Rappé AK, Colwell KS, Casewit CJ (1993). Inorg Chem 32:3438Google Scholar
  10. 10.
    Cornell WD, Cieplak P, Bayly CI, Gould IR, Merz KM Jr, Ferguson DM, Spellmeyer DC, Fox T, Caldwell JW, Kollman PA (1995). J Am Chem Soc 117:5179Google Scholar
  11. 11.
    Pearlman DA, Case DA, Caldwell JW, Ross WS, Cheatham TEI, DeBolt S, Ferguson D, Seibel G, Kollman PA (1995). Comp Phys Commun 91:1Google Scholar
  12. 12.
    Halgren TA (1996). J Comput Chem 17:490Google Scholar
  13. 13.
    Halgren TA (1996). J Comput Chem 17:520Google Scholar
  14. 14.
    Halgren TA (1996). J Comput Chem 17:552Google Scholar
  15. 15.
    Halgren TA, Nachbar RB (1996). J Comput Chem 17:587Google Scholar
  16. 16.
    Halgren TA (1996). J Comput Chem 17:616Google Scholar
  17. 17.
    Jorgensen WL, Maxwell DS, Tirado-Rives J (1996). J Am Chem Soc 118:11225Google Scholar
  18. 18.
    MacKerell AD Jr, Bashford D, Bellott M, Dunbrack RL, Evanseck JD, Field MJ, Fischer S, Gao J, Guo H, Ha S, Joseph-McCarthy D, Kuchnir L, Kuczera K, Lau FTK, Mattos C, Michnick S, Ngo T, Nguyen DT, Prodhom B, Reiher WE III, Roux B, Schlenkrich M, Smith JC, Stote R, Straub J, Watanabe M, Wiorkiewicz-Kuczera J, Yin D, Karplus M (1998). J Phys Chem B 102:3586Google Scholar
  19. 19.
    Jorgensen WL, McDonald NA (1998). Theochem 424:145Google Scholar
  20. 20.
    McDonald NA, Jorgensen WL (1998). J Phys Chem B 102:8049Google Scholar
  21. 21.
    Ewig CS, Thacher TS, Hagler AT (1999). J Phys Chem B 103:6999Google Scholar
  22. 22.
    Rizzo RC, Jorgensen WL (1999). J Am Chem Soc 121:4827Google Scholar
  23. 23.
    Allinger NL, Durkin KA (2000). J Comput Chem 21:1229Google Scholar
  24. 24.
    Kaminski GA, Friesner RA, Tirado-Rives J, Jorgensen WL (2001). J Phys Chem B 105:6474Google Scholar
  25. 25.
    Price MLP, Ostrovsky D, Jorgensen WL (2001). J Comput Chem 22:1340Google Scholar
  26. 26.
    Hill J-R, Sauer J (1994). J Phys Chem 98:1238Google Scholar
  27. 27.
    Hill J-R, Sauer J (1995). J Phys Chem 99:9536Google Scholar
  28. 28.
    Schröder K-P, Sauer J (1996). J Phys Chem 100:11043Google Scholar
  29. 29.
    Sierka M, Sauer J (1997). Faraday Discuss 106:41Google Scholar
  30. 30.
    Landis CR, Cleveland T, Firman TK (1998). J Am Chem Soc 120:2641Google Scholar
  31. 31.
    Firman TK, Landis CR (2001). J Am Chem Soc 123:11728Google Scholar
  32. 32.
    Warshel A, Levitt M (1976). J Mol Biol 103:227Google Scholar
  33. 33.
    Singh UC, Kollmann PA (1986). J Comput Chem 7:718Google Scholar
  34. 34.
    Field MJ, Bash PA, Karplus M (1990). J Comput Chem 11:700Google Scholar
  35. 35.
    Ferenczy GG, Rivail J-L, Surjan PR, Naray-Szabo G (1992). J Comput Chem 13:830Google Scholar
  36. 36.
    Gao J, Xia X (1992). Science 258:631Google Scholar
  37. 37.
    Åaqvist J, Warshel A (1993). Chem Rev 93:2523Google Scholar
  38. 38.
    Thery V, Rinaldi D, Rivail J-L, Maigret B, Ferenczy GG (1994). J Comput Chem 15:269Google Scholar
  39. 39.
    Maseras F, Morokuma K (1995). J Comput Chem 16:1170Google Scholar
  40. 40.
    Stanton RV, Hartsough DS, Merz KM Jr, (1995). J Comput Chem 16:113Google Scholar
  41. 41.
    Thompson MA (1995). J Phys Chem 99:4794Google Scholar
  42. 42.
    Thompson MA, Schenter GK (1995). J Phys Chem 99:6374Google Scholar
  43. 43.
    Assfeld X, Rivail J-L (1996). Chem Phys Lett 263:100Google Scholar
  44. 44.
    Bakowies D, Thiel W (1996). J Phys Chem 100:10580Google Scholar
  45. 45.
    Bakowies D, Thiel W (1996). J Comput Chem 17:87Google Scholar
  46. 46.
    Day PN, Jensen JH, Gordon MS, Webb SP, Stevens WJ, Krauss M, Garmer D, Basch H, Cohen D (1996). J Chem Phys 105:1968Google Scholar
  47. 47.
    Eichler U, Kölmel CM, Sauer J (1996). J Comput Chem 18:463Google Scholar
  48. 48.
    Eurenius KP, Chatfield DC, Brooks BR, Hodoscek M (1996). Int J Quantum Chem 60:1189Google Scholar
  49. 49.
    Gao (1996). J Rev Comput Chem 7:119Google Scholar
  50. 50.
    Kerdcharoen T, Liedl KR, Rode BM (1996). Chem Phys 211:313Google Scholar
  51. 51.
    Monard G, Loos M, Thery V, Baka K, Rivail J-L (1996). Int J Quantum Chem 58:153Google Scholar
  52. 52.
    Svensson M, Humbel S, Froese RDJ, Matsubara T, Sieber S, Morokuma K (1996). J Phys Chem 100:19357Google Scholar
  53. 53.
    Bersuker IB, Leong MK, Boggs JE, Pearlman RS (1997). Int J Quantum Chem 63:1051Google Scholar
  54. 54.
    Cummins PL, Gready JE (1997). J Comput Chem 18:1496Google Scholar
  55. 55.
    Gao J, Alhambra C (1997). J Chem Phys 107:1212Google Scholar
  56. 56.
    Sherwood P, De Vries AH, Collins SJ, Greatbanks SP, Burton NA, Vincent MA, Hillier IH, (1997). Faraday Discuss 106:79Google Scholar
  57. 57.
    Tongraar A, Liedl KR, Rode BM (1997). J Phys Chem A 101:6299Google Scholar
  58. 58.
    Antes I, Thiel W (1998). ACS Symp Ser 712:50Google Scholar
  59. 59.
    Bentzien J, Florian J, Glennon TM, Warshel A (1998). ACS Symp Ser 712:16Google Scholar
  60. 60.
    Bersuker IB, Leong MK, Boggs JE, Pearlman RS (1998). ACS Symp Ser 712:66Google Scholar
  61. 61.
    Burton NA, Harrison MJ, Hart JC, Hillier IH, Sheppard DW (1998). Faraday Discuss 110:463Google Scholar
  62. 62.
    Froese RDJ, Musaev DG, Morokuma K (1998). J Am Chem Soc 120:1581Google Scholar
  63. 63.
    Gao J, Amara P, Alhambra C, Field MJ (1998). J Phys Chem A 102:4714Google Scholar
  64. 64.
    Kaminski GA, Jorgensen WL (1998). J Phys Chem B 102:1787Google Scholar
  65. 65.
    Merz KM Jr (1998). ACS Symp Ser 712:2Google Scholar
  66. 66.
    Mordasini T, Thiel W (1998). Chimia 52:288Google Scholar
  67. 67.
    Sinclair PE, de Vries A, Sherwood P, Catlow CRA, van Santen RA (1998). J Chem Soc Faraday Trans 94:3401Google Scholar
  68. 68.
    Stefanovich EV, Truong TN (1998). ACS Symp Ser 712:92Google Scholar
  69. 69.
    Woo TK, Cavallo L, Ziegler T (1998). Theor Chem Acc 100:307Google Scholar
  70. 70.
    Antes I, Thiel W (1999). J Phys Chem A 103:9290Google Scholar
  71. 71.
    de Vries AH, Sherwood P, Collins SJ, Rigby AM, Rigutto M, Kramer GJ (1999). J Phys Chem B 103:6133Google Scholar
  72. 72.
    Dapprich S, Komiromi I, Byun KS, Morokuma K, Frisch MJ (1999). Theochem 461–462:1Google Scholar
  73. 73.
    Eichinger M, Tavan P, Hutter J, Parrinello M (1999). J Chem Phys 110:10452Google Scholar
  74. 74.
    Hillier IH (1999). THEOCHEM 463:45Google Scholar
  75. 75.
    Monard G, Merz KM Jr (1999). Acc Chem Res 32:904Google Scholar
  76. 76.
    Lyne PD, Hodoscek M, Karplus M (1999). J Phys Chem A 103:3462Google Scholar
  77. 77.
    Marini GW, Liedl KR, Rode BM (1999). J Phys Chem A 103:11387Google Scholar
  78. 78.
    Philipp DM, Friesner RA (1999). J Comput Chem 20:1468Google Scholar
  79. 79.
    Pitarch J, Pascual-Ahuir JL, Silla E, Tunon I, Ruiz-Lopez MF (1999). J Comput Chem 20:1401Google Scholar
  80. 80.
    Turner AJ, Moliner V, Williams IH (1999). Phys Chem Chem Phys 1:1323Google Scholar
  81. 81.
    Woo TK, Margl PM, Deng L, Cavallo L, Ziegler T (1999). ACS Symp Ser 721:173Google Scholar
  82. 82.
    Zhang Y, Lee T-S, Yang W (1999). J Chem Phys 110:46Google Scholar
  83. 83.
    Amara P, Field MJ, Alhambra C, Gao J (2000). Theor Chem Acc 104:336Google Scholar
  84. 84.
    Byun K, Gao J (2000). J Mol Graph Model 18:50Google Scholar
  85. 85.
    Derenzo SE, Klintenberg MK, Weber MJ (2000). J Chem Phys 112:2074Google Scholar
  86. 86.
    Field MJ, Albe M, Bret C, Martin FP-D, Thomas A (2000). J Comput Chem 21:1088Google Scholar
  87. 87.
    Gogonea V, Westerhoff LM, Merz KM Jr (2000). J Chem Phys 113:5604Google Scholar
  88. 88.
    Hall RJ, Hindle SA, Burton NA, Hillier IH (2000). J Comput Chem 21:1433Google Scholar
  89. 89.
    Kairys V, Jensen JH (2000). J Phys Chem A 104:6656Google Scholar
  90. 90.
    Moliner V, Williams IH (2000). Chem Commun 1843Google Scholar
  91. 91.
    Murphy RB, Philipp DM, Friesner RA (2000). J Comput Chem 21:1442Google Scholar
  92. 92.
    Murphy RB, Philipp DM, Friesner RA (2000). Chem Phys Lett 321:113Google Scholar
  93. 93.
    Reuter N, Dejaegere A, Maigret B, Karplus M (2000). J Phys Chem A 104:1720Google Scholar
  94. 94.
    Röthlisberger U, Carloni P, Doclo K, Parrinello M (2000). J Biol Inorg Chem 5:236Google Scholar
  95. 95.
    Sherwood P (2000). In: Grotendorst J (ed) Modern methods and algorithms of quantum chemistry. NIC-Directors: Princeton, vol 3, pp 285Google Scholar
  96. 96.
    Sierka M, Sauer J (2000). J Chem Phys 112:6983Google Scholar
  97. 97.
    Sushko PV, Shluger AL, Catlow CRA (2000). Surface Science 450:153Google Scholar
  98. 98.
    Vreven T, Morokuma K (2000). J Comput Chem 21:1419Google Scholar
  99. 99.
    Woo TK, Blöchl PE, Ziegler T (2000). Theochem 506:313Google Scholar
  100. 100.
    Cui Q, Elstner M, Kaxiras E, Frauenheim T, Karplus M (2001). J Phys Chem B 105:569Google Scholar
  101. 101.
    French SA, Sokol AA, Bromley ST, Catlow CRA, Rogers SC, King F, Sherwood P (2001). Angew Chem 113:4569Google Scholar
  102. 102.
    Khaliullin RZ, Bell AT, Kazansky VB (2001). J Phys Chem A 105:10454Google Scholar
  103. 103.
    Nasluzov VA, Rivanenkov VV, Gordienko AB, Neyman KM, Birkenheuer U, Rösch N (2001). J Chem Phy 115:8157Google Scholar
  104. 104.
    Nicoll RM, Hindle SA, MacKenzie G, Hillier IH, Burton NA (2001). Theor Chem Acc 106:105Google Scholar
  105. 105.
    Poteau R, Ortega I, Alary F, Solis AR, Barthelat JC, Daudey JP (2001). J Phys Chem A 105:198Google Scholar
  106. 106.
    Vreven T, Mennucci B, da Silva CO, Morokuma K, Tomasi J (2001). J Chem Phys 115:62Google Scholar
  107. 107.
    Worthington SE, Krauss M (2001). J Phys Chem B 105:7096Google Scholar
  108. 108.
    Batista ER, Friesner RA (2002). J Phys Chem B 106:8136Google Scholar
  109. 109.
    Colombo MC, Guidoni L, Laio A, Magistrato A, Maurer P, Piana S, Rohrig U, Spiegel K, Sulpizi M, VandeVondele J, Zumstein M, Röthlisberger U (2002). Chimia 56:13Google Scholar
  110. 110.
    Das D, Eurenius KP, Billings EM, Sherwood P, Chatfield DC, Hodoscek M, Brooks BR (2002). J Chem Phys 117:10534Google Scholar
  111. 111.
    DiLabio GA, Hurley MM, Christiansen PA (2002). J Chem Phys 116:9578Google Scholar
  112. 112.
    Ferré Nicolas, Assfeld X Rivail J-L (2002). J Comput Chem 23:610Google Scholar
  113. 113.
    Gao J, Truhlar DG, (2002). Annu Rev Phys Chem 53:467Google Scholar
  114. 114.
    Gogonea V (2002). Internet Electron J Mol Design 1:173Google Scholar
  115. 115.
    Hermida-Ramón JM, Karlström G, Lindh R (2002). J Phys Chem B 106:7115Google Scholar
  116. 116.
    Kerdcharoen T, Morokuma K (2002). Chem Phys Lett 355:257Google Scholar
  117. 117.
    Laio A, Vande Vondele J, Röthlisberger U (2002). J Chem Phys 116:6941Google Scholar
  118. 118.
    Lennartz C, Schaefer A, Terstegen F, Thiel W (2002). J Phys Chem B 106:1758Google Scholar
  119. 119.
    Morokuma K (2002). Phil Trans Roy Soc London, Ser A 360:1149Google Scholar
  120. 120.
    Rajamani R, Gao J (2002). J Comput Chem 23:96Google Scholar
  121. 121.
    Schöneboom JC, Lin H, Reuter N, Thiel W, Cohen S, Ogliaro F, Shaik S (2002). J Am Chem Soc 124:8142Google Scholar
  122. 122.
    Titmuss SJ, Cummins PL, Rendell AP, Bliznyuk AA, Gready JE (2002). J Comput Chem 23:1314Google Scholar
  123. 123.
    Truhlar DG, Gao J, Alhambra C, Garcia-Viloca M, Corchado J, Sanchez ML, Villa (2002). J Acc Chem Res 35:341Google Scholar
  124. 124.
    Amara P, Field MJ (2003). Theor Chem Acc 109:43Google Scholar
  125. 125.
    Devi-Kesavan LS, Garcia-Viloca M, Gao J (2003). Theor Chem Acc 109:133Google Scholar
  126. 126.
    Dinner AR, Lopez X, Karplus M (2003). Theor Chem Acc 109:118Google Scholar
  127. 127.
    Hu H, Elstner M, Hermans J (2003). Proteins 50:451Google Scholar
  128. 128.
    Kongsted J, Osted A, Mikkelsen KV, Christiansen O (2003). J Phys Chem A 107:2578Google Scholar
  129. 129.
    Li G, Zhang X, Cui Q (2003). J Phys Chem B 107:8643Google Scholar
  130. 130.
    Loferer MJ, Loeffler HH, Liedl KR (2003). J Comput Chem 24:1240Google Scholar
  131. 131.
    Molina PA, Sikorski RS, Jensen JH (2003). Theor Chem Acc 109:100Google Scholar
  132. 132.
    Mordasini T, Curioni A, Andreoni W (2003). J Biol Chem 278:4381Google Scholar
  133. 133.
    Sherwood P, de Vries AH, Guest MF, Schreckenbach G, Catlow CRA, French SA, Sokol AA, Bromley ST, Thiel W, Turner AJ, Billeter S, Terstegen F, Thiel S, Kendrick J, Rogers SC, Casci J, Watson M, King F, Karlsen E, Sjovoll M, Fahmi A, Schafer A, Lennartz C (2003). Theochem 632:1Google Scholar
  134. 134.
    Sulpizi M, Laio A, Vande Vondele J, Cattaneo A, Röthlisberger U, Carloni P (2003). Proteins 52:212Google Scholar
  135. 135.
    Swart M (2003). Int J Quantum Chem 91:177Google Scholar
  136. 136.
    Tresadern G, Faulder PF, Gleeson MP, Tai Z, MacKenzie G, NA, Hillier IH (2003). Theor Chem Acc 109:108Google Scholar
  137. 137.
    Vreven T, Morokuma K, Farkas O, Schlegel HB, Frisch MJ (2003). J Comput Chem 24:760Google Scholar
  138. 138.
    Vreven T, Morokuma K (2003). Theor Chem Acc 109:125Google Scholar
  139. 139.
    Yang W, Drueckhammer DG (2003). J Phys Chem B 107:5986Google Scholar
  140. 140.
    Herschend B, Baudin M, Hermansson K (2004). J Chem Phys 120:4939Google Scholar
  141. 141.
    Laio A, Gervasio FL, Vande Vondele J, Sulpizi M, Röthlisberger U (2004). J Phys Chem B 108:7963Google Scholar
  142. 142.
    Pu J, Gao J, Truhlar DG (2004). J Phys Chem A 108:632Google Scholar
  143. 143.
    Riccardi D, Li GH, Cui Q (2004). J Phys Chem B 108:6467Google Scholar
  144. 144.
    Pu J, Gao J, Truhlar DG (2004). J Phys Chem A 108:5454Google Scholar
  145. 145.
    Bludsky O, Silhan M, Nachtigall P (2005). J Phys Chem B (in press)Google Scholar
  146. 146.
    Gregersen BA, York DM (2005). J Phys Chem B 109:536Google Scholar
  147. 147.
    Lin H, Truhlar DG (2005). J Phys Chem A 109:3991Google Scholar
  148. 148.
    Nam K, Gao J, York DM (2005). J Chem Theory Comput 1:2Google Scholar
  149. 149.
    Pu J, Truhlar DG (2005). Chem Phys Chem (in press)Google Scholar
  150. 150.
    Wanko M, Hoffmann M, Strodel P, Koslowski A, Thiel W, Neese F, Frauenheim T, Elstner M (2005). J Phys Chem B 109:3606Google Scholar
  151. 151.
    Zhang Y (2005). J Chem Phys 122:024114Google Scholar
  152. 152.
    Politzer P, Truhlar DG ed. (1981). Chemical Applications of Atomic and Molecular Electrostatic Potentials Reactivity. Plenum, New YorkGoogle Scholar
  153. 153.
    Price SL, Stone AJ (1992). J Chem Soc Faraday Trans 88:1755Google Scholar
  154. 154.
    Koch U, Popelier PLA, Stone A (1995). J Chem Phys Lett 238:253Google Scholar
  155. 155.
    Matta CF, Bader RFW (2000). Proteins: Struct Func Genet 40:310Google Scholar
  156. 156.
    Minikis RM, Kairys V, Jensen JH (2001). J Phys Chem A 105:3829Google Scholar
  157. 157.
    Stillinger FH, David CW (1978). J Chem Phys 69:1473Google Scholar
  158. 158.
    Sprik M, Klein ML (1988). J Chem Phys 89:7556Google Scholar
  159. 159.
    Dick Jr BG, Overhauser AW (1958). Phy Rev 112:90Google Scholar
  160. 160.
    Van Belle D, Prevost M, Lippens G, Wodak SJ (1994). ACS Symp Ser 568:318Google Scholar
  161. 161.
    Kowall T, Foglia F, Helm L, Merbach AE (1995). J Am Chem Soc 117:3790Google Scholar
  162. 162.
    Banks JL, Kaminski GA, Zhou R, Mainz DT, Berne BJ, Friesner RA (1999). J Chem Phys 110:741Google Scholar
  163. 163.
    Martinez JM, Hernandez-Cobos J, Saint-Martin H, Pappalardo RR, Ortega-Blake I, Marcos ES (2000). J Chem Phys 112:2339Google Scholar
  164. 164.
    Rick SW, Stuart SJ (2002). Rev Comput Chem 18:89Google Scholar
  165. 165.
    Lamoureux G, MacKerell AD, Roux B (2003). J Chem Phys 119:5185Google Scholar
  166. 166.
    Ponder JW, Case DA (2003). Adv Protein Chem 66:27CrossRefGoogle Scholar
  167. 167.
    Ren P, Ponder JW (2003). J Phys Chem B 107:5933Google Scholar
  168. 168.
    Kaminski GA, Stern HA, Berne BJ, Friesner RA (2004). J Phys Chem A 108:621Google Scholar
  169. 169.
    Patel S, Mackerell AD Jr, Brooks CL III (2004). J Comput Chem 25:1504Google Scholar
  170. 170.
    Rinaldi D, Rivail JL (1973). Theor Chim Acta 32:57Google Scholar
  171. 171.
    Storer JW, Giesen DJ, Hawkins GD, Lynch GC, Cramer CJ, Truhlar DG, Liotard DA (1994). ACS Symp Ser 568:24CrossRefGoogle Scholar
  172. 172.
    Tomasi J (1994). ACS Symp Ser 1994:10Google Scholar
  173. 173.
    Cramer CJ, Truhlar Donald G (1996). Continuum solvation models. In: Tapia O, Bertran J (eds). Solvents effects and chemical reactivity. Kluwer, Dordrecht, pp 1Google Scholar
  174. 174.
    Bacalis NC, Kunz AB (1985). Phys Rev B 32:4857Google Scholar
  175. 175.
    Pascual J, Pettersson LGM (1997). Chem Phys Lett 270:351Google Scholar
  176. 176.
    Stefanovich EV, Truong TN (1998). J Phys Chem B 102:3018Google Scholar
  177. 177.
    Li J, Cramer CJ, Truhlar DG (2000). Int J Quantum Chem 77:264Google Scholar
  178. 178.
    Yagüe JI, Mohammed AM, Loeffler H, Rode BM, (2001). J Phys Chem A 105:7646Google Scholar
  179. 179.
    Brooks BR, Bruccoleri RE, Olafson BD, States DJ, Swaminathan S, Karplus M (1983). J Comput Chem 4:187Google Scholar
  180. 180.
    Humbel S, Sieber S, Morokuma K (1996). J Chem Phys 105:1959Google Scholar
  181. 181.
    Waszkowycz B, Hillier IH, Gensmantel N, Payling DW (1991). J Chem Soc Perkin Trans 2, 2025Google Scholar
  182. 182.
    Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Montgomery JJA, Vreven T, Kudin KN, Burant JC, Millam JM, Iyengar SS, Tomasi J, Barone V, Mennucci B, Cossi M, Scalmani G, Rega N, Petersson GA, Nakatsuji H, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Klene M, Li X, Knox JE, Hratchian HP, Cross JB, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Ayala PY, Morokuma K, Voth GA, Salvador P, Dannenberg JJ, Zakrzewski VG, Dapprich S, Daniels AD, Strain MC, Farkas O, Malick DK, Rabuck AD, Raghavachari K, Foresman JB, Ortiz JV, Cui Q, Baboul AG Clifford S, Cioslowski J, Stefanov BB, Liu G, Liashenko A, Piskorz P, Komaromi I, Martin RL, Fox DJ, Keith T, Al-Laham MA, Peng CY, Nanayakkara A, Challacombe M, Gill PMW, Johnson B, Chen W, Wong MW, Gonzalez C, Pople JA (2003)Gaussian03 Gaussian, Inc: Pittsburgh PAGoogle Scholar
  183. 183.
    Besler BH, Merz KM Jr, Kollman PA (1990). J Comput Chem 11:431Google Scholar
  184. 184.
    Truhlar DG, Gordon MS (1990). Science 249:491Google Scholar
  185. 185.
    Morse PM (1929). Phy Rev 34:57Google Scholar
  186. 186.
    London FZ (1929). Elektrochemistry 35:552Google Scholar
  187. 187.
    Eyring H, Polanyi MZ (1931). Phys Chem B 12:279Google Scholar
  188. 188.
    Parr CA, Truhlar DG (1971). J Phys Chem 75:1844Google Scholar
  189. 189.
    Raff LM (1974). J Chem Phys 60:2220Google Scholar
  190. 190.
    Steckler R, Dykema KJ, Brown FB, Hancock GC, Truhlar DG, Valencich T (1987). J Chem Phys 87:7024Google Scholar
  191. 191.
    Jordan MJT, Gilbert RG (1995). J Chem Phys 102:5669Google Scholar
  192. 192.
    Espinosa-García J, Corchado JC (1996). J Chem Phys 105:3517Google Scholar
  193. 193.
    Espinosa-García J, Corchado JC (2000). J Chem Phys 112:5731Google Scholar
  194. 194.
    Espinosa-Garcia J, Rangel C, Navarrete M, Corchado JC (2004). J Chem Phys 121:5098Google Scholar
  195. 195.
    Navarrete M, Rangel C, Espinosa-Garcia J, Corchado JC (2005). J Chem Theory Comput 1:337Google Scholar
  196. 196.
    Rangel C, Espinosa-Garcia J (2005). J Chem Phys 122:134315Google Scholar
  197. 197.
    Rangel C, Navarrete M, Espinosa-Garcia J (2005). J Phys Chem A 109:1441Google Scholar
  198. 198.
    Brenner DW (1990). Phys Rev B 42:9458Google Scholar
  199. 199.
    Brenner DW (2000). Phys Stat Sol (b) 217:23Google Scholar
  200. 200.
    Brenner DW, Shenderova OA, Harrison JA, Stuart SJ, Ni B, SB (2002). J Phys: Condens Matter 14:782Google Scholar
  201. 201.
    Duin ACTv, Dasgupta S, Lorant F, Goddard WA (2001). J Phys Chem A 105:9396Google Scholar
  202. 202.
    Goddard WA III, Zhang Q, Uludogan M, Strachan A, Cagin T (2002). In: Cohen RE (eds). Fundamental physics of ferroelectrics 2002. American Institute of Physcis, Pasadena, , vol 626, pp 45Google Scholar
  203. 203.
    Duin ACTv, Strachan A, Stewman S, Zhang Q, Xu X, Goddard WA (2003). J Phys Chem A 107:3803Google Scholar
  204. 204.
    Cheung S, Deng W-Q, van Duin ACT, Goddard WA (2005). J Phys Chem A 109:851Google Scholar
  205. 205.
    Kim Y, Corchado JC, Villa J, Xing J, Truhlar DG (2000). J Chem Phys 112:2718Google Scholar
  206. 206.
    Albu TV, Corchado JC, Truhlar DG (2001). J Phys Chem A 105:8465Google Scholar
  207. 207.
    Truhlar DG (2002). J Phys Chem A 106:5048Google Scholar
  208. 208.
    Lin H, Pu JZ, Albu TV, Truhlar DG (2004). J Phys Chem A 108:4112Google Scholar
  209. 209.
    Kim KH, Kim Y (2004). J Chem Phys 120:623Google Scholar
  210. 210.
    Warshel A, Weiss RM (1980). J Am Chem Soc 102:6218Google Scholar
  211. 211.
    Lin H, Truhlar DG (in press)Google Scholar
  212. 212.
    Bayly CI, Cieplak P, Cornell WD, Kollman PA (1993). J Phys Chem 97:10269Google Scholar
  213. 213.
    Laio A, VandeVondele J, Rothlisberger U (2002). J Phys Chem B 106Google Scholar
  214. 214.
    Storer JW, Giesen DJ, Cramer CJ, Truhlar DG (1995). J Comput-Aid Mol Des 9:87Google Scholar
  215. 215.
    Li J, Zhu T, Cramer CJ, Truhlar DG (1998). J Phys Chem A 102:1820Google Scholar
  216. 216.
    Li J, Williams B, Cramer CJ, Truhlar DG (1999). J Chem Phys 110:724Google Scholar
  217. 217.
    Winget P, Thompson JD, Xidos JD, Cramer CJ, Truhlar DG (2002). J Phys Chem A 106:10707Google Scholar
  218. 218.
    Brom JM, Schmitz BJ, Thompson JD, Cramer CJ, Truhlar DG, (2003). J Phys Chem A 107:6483Google Scholar
  219. 219.
    Thompson JD, Cramer CJ, Truhlar DG (2003). J Comput Chem 24:1291Google Scholar
  220. 220.
    Kelly C, Cramer CJ, Truhlar Donald G (in press)Google Scholar
  221. 221.
    Mortier WJ, Ghosh SK, Shankar S (1986). J Am Chem Soc 108:4315Google Scholar
  222. 222.
    Rappé AK, Goddard WA (1991). J Phys Chem 95:3358Google Scholar
  223. 223.
    Kitao O, Ogawa T (2003). Mol Phys 101:3Google Scholar
  224. 224.
    Ogawa T, Kurita N, Sekino H, Kitao O, Tanaka S (2003). Chem Phys Lett 374:271Google Scholar
  225. 225.
    Ogawa T, Kurita N, Sekino H, Kitao O, Tanaka S (2004). Chem Phys Lett 397:382Google Scholar
  226. 226.
    Gogonea V, Merz KM Jr (2000). J Phys Chem B 104:2117Google Scholar
  227. 227.
    Ackland GJ, Finnis MW, Vitek V (1988). J Phys F: Met Phys 18:L153Google Scholar
  228. 228.
    Jasper AW, Schultz NE, Truhlar DG (2005). J Phys Chem B 109:3915Google Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Chemistry Department and Supercomputing InstituteUniversity of MinnesotaMinneapolisUSA
  2. 2.Chemistry DepartmentUniversity of Colorado at DenverDenverUSA

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