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Theoretical Chemistry Accounts

, Volume 120, Issue 1–3, pp 215–241 | Cite as

The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals

  • Yan Zhao
  • Donald G. TruhlarEmail author
Open Access
Regular Article
First Online:

Abstract

We present two new hybrid meta exchange- correlation functionals, called M06 and M06-2X. The M06 functional is parametrized including both transition metals and nonmetals, whereas the M06-2X functional is a high-nonlocality functional with double the amount of nonlocal exchange (2X), and it is parametrized only for nonmetals.The functionals, along with the previously published M06-L local functional and the M06-HF full-Hartree–Fock functionals, constitute the M06 suite of complementary functionals. We assess these four functionals by comparing their performance to that of 12 other functionals and Hartree–Fock theory for 403 energetic data in 29 diverse databases, including ten databases for thermochemistry, four databases for kinetics, eight databases for noncovalent interactions, three databases for transition metal bonding, one database for metal atom excitation energies, and three databases for molecular excitation energies. We also illustrate the performance of these 17 methods for three databases containing 40 bond lengths and for databases containing 38 vibrational frequencies and 15 vibrational zero point energies. We recommend the M06-2X functional for applications involving main-group thermochemistry, kinetics, noncovalent interactions, and electronic excitation energies to valence and Rydberg states. We recommend the M06 functional for application in organometallic and inorganometallic chemistry and for noncovalent interactions.

Keywords

Density functional theory Exchange Correlation Metals Organic molecules 
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Supplementary material

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References

  1. 1.
    Boese AD and Handy NC (2002). J Chem Phys 116: 9559 Google Scholar
  2. 2.
    Tao J, Perdew JP, Staroverov VN and Scuseria GE (2003). Phys Rev Lett 91: 146401 Google Scholar
  3. 3.
    Staroverov VN, Scuseria GE, Tao J and Perdew JP (2003). J Chem Phys 119: 12129 Google Scholar
  4. 4.
    Zhao Y, Lynch BJ and Truhlar DG (2004). J Phys Chem A 108: 2715 Google Scholar
  5. 5.
    Boese AD and Martin JML (2004). J Chem Phys 121: 3405 Google Scholar
  6. 6.
    Zhao Y and Truhlar DG (2004). J Phys Chem A 108: 6908 Google Scholar
  7. 7.
    Xu X and Goddard WA (2004). Proc Natl Acad Sci USA 101: 2673 Google Scholar
  8. 8.
    Zhao Y, Lynch BJ and Truhlar DG (2005). Phys Chem Chem Phys 7: 43 Google Scholar
  9. 9.
    Perdew JP, Ruzsinszky A, Tao J, Staroverov VN, Scuseria GE and Csonka GI (2005). J Chem Phys 123: 62201 Google Scholar
  10. 10.
    Zhao Y and Truhlar DG (2005). J Phys Chem A 109: 5656 Google Scholar
  11. 11.
    Keal TW and Tozer DJ (2005). J Chem Phys 123: 121103 Google Scholar
  12. 12.
    Zhao Y, Schultz NE and Truhlar DG (2005). J Chem Phys 123: 161103 Google Scholar
  13. 13.
    Becke AD (2005). J Chem Phys 122: 64101 Google Scholar
  14. 14.
    Zhao Y, Schultz NE and Truhlar DG (2006). J Chem Theory Comput 2: 364 Google Scholar
  15. 15.
    Mori-Sanchez P, Cohen AJ and Yang W (2006). J Chem Phys 124: 91102 Google Scholar
  16. 16.
    Zhao Y and Truhlar DG (2006). J Chem Phys 125: 194101 Google Scholar
  17. 17.
    Grimme S (2006). J Chem Phys 124: 034108 Google Scholar
  18. 18.
    Grimme S (2006). J Comp Chem 27: 1787 Google Scholar
  19. 19.
    Zhao Y and Truhlar DG (2006). J Phys Chem A 110: 13126 Google Scholar
  20. 20.
    Scuseria GE, Staroverov VN (2005). In: Dykstra CE, Frenking G, Kim KS, Scuseria GE (eds) Theory and application of computational chemistry: the first 40 years. Elsevier, Amsterdam, pp 669–724 Google Scholar
  21. 21.
    Voorhis TV and Scuseria GE (1998). J Chem Phys 109: 400 Google Scholar
  22. 22.
    Becke AD (1998). J Chem Phys 109: 2092 Google Scholar
  23. 23.
    Baerends EJ, Ellis DE and Ros P (1973). Chem Phys 2: 41 Google Scholar
  24. 24.
    Dunlap BI, Connolly JWD and Sabin JR (1979). J Chem Phys 71: 3396 Google Scholar
  25. 25.
    Vahtras O, Almlöf J and Feyereisen MW (1993). Chem Phys Lett 213: 514 Google Scholar
  26. 26.
    Kendall RA, Apra E, Bernholdt DE, Bylaska EJ, Dupuis M, Fann GI, Harrison RJ, Ju J, Nichols JA, Nieplocha J, Straatsma TP, Windus TL and Wong AT (2000). Comput Phys Commun 128: 260 Google Scholar
  27. 27.
    Te Velde G, Bickelhaupt FM, Baerends EJ, Fonseca Guerra C, Van Gisbergen SJA, Snijders JG and Ziegler T (2001). J Comp Chem 22: 931 Google Scholar
  28. 28.
    VandeVondele J, Krack M, Mohamed F, Parrinello M, Chassaing T and Hutter J (2005). Comput Phys Commun 167: 103 Google Scholar
  29. 29.
    Jung Y, Sodt A, Gill PMW and Head-Gordon M (2005). Proc Natl Acad Sci USA 102: 6692 Google Scholar
  30. 30.
    Eichkorn K, Treutler O, Oehm H, Haeser M and Ahlrichs R (1995). Chem Phys Lett 240: 283 Google Scholar
  31. 31.
    Eichkorn K, Weigend F, Treutler O and Ahlrichs R (1997). Theo Chem Acc 97: 119 Google Scholar
  32. 32.
    Füsti-Molnár L and Pulay P (2003). Theochem 25: 666–667 Google Scholar
  33. 33.
    Skylaris C-K, Haynes PD, Mostofi AA and Payne MC (2006). Phys Status Solidi B, Basic Res 243: 973 Google Scholar
  34. 34.
    Dreuw A and Head-Gordon M (2006). Chem Rev 105: 4009 Google Scholar
  35. 35.
    Zhao Y and Truhlar DG (2006). Org Lett 8: 5753 Google Scholar
  36. 36.
    Lynch BJ, Fast PL, Harris M and Truhlar DG (2000). J Phys Chem A 104: 4811 Google Scholar
  37. 37.
    Zhao Y and Truhlar DG (2005). J Chem Theory Comput 1: 415 Google Scholar
  38. 38.
    Schultz N, Zhao Y and Truhlar DG (2005). J Phys Chem A 109: 4388 Google Scholar
  39. 39.
    Schultz N, Zhao Y and Truhlar DG (2005). J Phys Chem A 109: 11127 Google Scholar
  40. 40.
    Zhao Y and Truhlar DG (2006). J Phys Chem A 110: 10478 Google Scholar
  41. 41.
    Zhao Y and Truhlar DG (2006). J Chem Theory Comput 2: 1009 Google Scholar
  42. 42.
    Zhao Y and Truhlar DG (2006). J Phys Chem A 110: 5121 Google Scholar
  43. 43.
    Zhao Y and Truhlar DG (2006). J Chem Phys 124: 224105 Google Scholar
  44. 44.
    Zhao Y and Truhlar DG (2007). J Chem Theory Comput 3: 289 Google Scholar
  45. 45.
    Zhang Y, Li ZH and Truhlar DG (2007). J Chem Theory Comput 3: 593 Google Scholar
  46. 46.
    Kabelác M, Sherer EC, Cramer CJ and Hobza P (2006). Chem Eur J 13: 2067 Google Scholar
  47. 47.
    Schultz NE, Gherman BF, Cramer CJ and Truhlar DG (2006). J Phys Chem B 110: 24030 Google Scholar
  48. 48.
    Zhao Y and Truhlar DG (2007). J Org Chem 72: 295 Google Scholar
  49. 49.
    Zhao Y, Lynch BJ and Truhlar DG (2004). J Phys Chem A 108: 4786 Google Scholar
  50. 50.
    Zhao Y, González-García N and Truhlar DG (2005). J Phys Chem A 109: 2012 Google Scholar
  51. 51.
    Chakravorty SJ, Gwaltney SR, Davidson ER, Parpia FA and Fischer CFF (1993). Phys Rev A 47: 3649 Google Scholar
  52. 52.
    Lynch BJ, Zhao Y and Truhlar DG (2003). J Phys Chem A 107: 1384 Google Scholar
  53. 53.
    Zheng JJ, Zhao Y and Truhlar DG (2007). J Chem Theory Comput 3: 569 Google Scholar
  54. 54.
    Pople JA, Head-Gordon M and Raghavachari K (1987). J Chem Phys 87: 5968 Google Scholar
  55. 55.
    Fast PL, Sanchez ML and Truhlar DG (1999). Chem Phys Lett 306: 407 Google Scholar
  56. 56.
    Curtiss LA, Redfern PC, Raghavachari K, Rassolov V and Pople JA (1999). J Chem Phys 110: 4703 Google Scholar
  57. 57.
    Curtiss LA, Raghavachari K, Redfern PC, Rassolov V and Pople JA (1998). J Chem Phys 109: 7764 Google Scholar
  58. 58.
    Frisch MJ, Pople JA and Binkley JS (1984). J Chem Phys 80: 3265 Google Scholar
  59. 59.
    Hehre WJ, Radom L, Schleyer PvR and Pople JA (1986). Ab initio molecular orbital theory, 1st ed.   , Wiley, New York Google Scholar
  60. 60.
    Izgorodina EI, Coote ML and Radom L (2005). J Phys Chem A 109: 7558 Google Scholar
  61. 61.
    Weigend F, Furche F and Ahlrichs R (2003). J Chem Phys 119: 12753 Google Scholar
  62. 62.
    Fast PL and Truhlar DG (2000). J Phys Chem A 104: 6111 Google Scholar
  63. 63.
    Lynch BJ and Truhlar DG (2003). J Phys Chem A 107: 3898 Google Scholar
  64. 64.
    Sinnokrot MO and Sherrill CD (2004). J Phys Chem A 108: 10200 Google Scholar
  65. 65.
    Jurecka P, Sponer J, Cerny J and Hobza P (2006). Phys Chem Chem Phys 8: 1985 Google Scholar
  66. 66.
    Runge E and Gross EKU (1984). Phys Rev Lett 52: 997 Google Scholar
  67. 67.
    Casida ME (1996) . In: Seminario JM(ed) Recent developments and applications of modern density functional theory. Elsevier, Amsterdam, p 391 Google Scholar
  68. 68.
    Bauernschmitt R and Ahlrichs R (1996). Chem Phys Lett 256: 454 Google Scholar
  69. 69.
    Stratmann RE, Scuseria GE and Frisch MJ (1998). J Chem Phys 109: 8218 Google Scholar
  70. 70.
    Marques MAL and Gross EKU (2004). Annu Rev Phys Chem 55: 427 Google Scholar
  71. 71.
    Furche F and Rappoport D (2005). Comp Theor Chem 16: 93 CrossRefGoogle Scholar
  72. 72.
    Sadlej AJ (1991). Theor Chim Acta 79: 123 Google Scholar
  73. 73.
    Casida ME, Jamorski C, Casida KC and Salahub DR (1998). J Chem Phys 108: 4439 Google Scholar
  74. 74.
    Hamprecht FA, Cohen AJ, Tozer DJ and Handy NC (1998). J Chem Phys 109: 6264 Google Scholar
  75. 75.
    NIST Computational Chemistry Comparison and Benchmark DataBase, http://srdata.nist.gov/cccbdb/Google Scholar
  76. 76.
    Furche F and Perdew JP (2006). J Chem Phys 124: 044103 Google Scholar
  77. 77.
    Woon DE and T.H. Dunning J (1993). J Chem Phys 98: 1358 Google Scholar
  78. 78.
    Balabanov NB and Peterson KA (2005). J Chem Phys 123: 064107 Google Scholar
  79. 79.
    Quintal MM, Karton A, Iron MA, Boese AD and Martin JML (2006). J Phys Chem A 110: 709 Google Scholar
  80. 80.
    Truhlar DG, Lynch BJ, Zhao Y, http://comp.chem.umn.edu/ basissets/basis.cgiGoogle Scholar
  81. 81.
    Raghavachari K and Trucks GW (1989). J Chem Phys 91: 1062 Google Scholar
  82. 82.
    Martin RL and Hay PJ (1981). J Chem Phys 75: 4539 Google Scholar
  83. 83.
    Boys SF and Bernardi F (1970). Mol Phys 19: 553 Google Scholar
  84. 84.
    Schwenke DW and Truhlar DG (1985). J Chem Phys 82: 2418 Google Scholar
  85. 85.
    Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Montgomery JA, Jr., 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 G, 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) . Gaussian Inc., PittsburghGoogle Scholar
  86. 86.
    Voorhis TV and Scuseria GE (1997). Mol Phys 92: 601 Google Scholar
  87. 87.
    Perdew JP, Burke K and Ernzerhof M (1996). Phys Rev Lett 77: 3865 Google Scholar
  88. 88.
    Becke AD (1986). J Chem Phys 84: 4524 Google Scholar
  89. 89.
    Kohn W and Sham LJ (1965). Phys Rev 140: 1133 Google Scholar
  90. 90.
    Stoll H, Pavkidou CME and Preuss H (1978). Theor Chim Acta 49: 143 Google Scholar
  91. 91.
    Becke AD (1988). Phys Rev A 38: 3098 Google Scholar
  92. 92.
    Lee C, Yang W and Parr RG (1988). Phys Rev B 37: 785 Google Scholar
  93. 93.
    Becke AD (1993). J Chem Phys 98: 5648 Google Scholar
  94. 94.
    Stephens PJ, Devlin FJ, Chabalowski CF and Frisch MJ (1994).    J Phys Chem 98: 11623 Google Scholar
  95. 95.
    Schmider HL and Becke AD (1998). J Chem Phys 108: 9624 Google Scholar
  96. 96.
    Adamo C and Barone V (1999). J Chem Phys 110: 6158 Google Scholar
  97. 97.
    Valentin CD, Pacchioni G, Bredow T, Dominguez-Ariza D and Illas F (2002). J Chem Phys 117: 2299 Google Scholar
  98. 98.
    Wilson PJ, Bradley TJ and Tozer DJ (2001). J Chem Phys 115: 9233 Google Scholar
  99. 99.
    Curtiss LA, Redfern PC and Raghavachari K (2005). J Chem Phys 123: 124107 Google Scholar
  100. 100.
    Perdew JP, Schmidt K (2001) In: Van-Doren V, Alsenoy CV, Geerlings P (eds) Density functional theory and its applications to materials. American Institute of Physics, New York, p 1Google Scholar
  101. 101.
    Zhao Y, Pu J, Lynch BJ and Truhlar DG (2004). Phys Chem Chem Phys 6: 673 Google Scholar
  102. 102.
    Woodcock HL, Schaefer HF and Schreiner PR (2002). J Phys Chem A 106: 11923 Google Scholar
  103. 103.
    Champagne B, Perpete EA, van Gisbergen SJA, Baerends E-J, Snijders JG, Soubra-Ghaoui C, Robins KA and Kirtman B (1998).   J Chem Phys 109: 10489 Google Scholar
  104. 104.
    Champagne B, Perpete EA, Jacquemin D, Gisbergen SJAV, Baerends E-J, Soubra-Ghaoui C, Robins KA and Kirtman B (2000).   J Phys Chem A 104: 4755 Google Scholar
  105. 105.
    Schreiner PR, Fokin AA, Pascal RA Jr and de Meijere A (2006). Org Lett 8: 3635 Google Scholar
  106. 106.
    Grimme S (2006). Angew Chem Int Ed 45: 4460 Google Scholar
  107. 107.
    Phillips JA and Cramer CJ (2005). J Chem Theory Comput 1: 827 Google Scholar
  108. 108.
    Füsti-Molnár L and Szalay PG (1996). J Phys Chem 100: 6288 Google Scholar
  109. 109.
    Leininger ML and Schaefer HF (1997). J Chem Phys 107: 9059 Google Scholar
  110. 110.
    Ljubic I and Sabljic A (2002). J Phys Chem A 106: 4745 Google Scholar
  111. 111.
    Feller D and Peterson KA (1999). J Chem Phys 110: 8384 Google Scholar
  112. 112.
    Curtiss LA, Raghavachari K, Redfern PC and Pople JA (2000).   J Chem Phys 112: 7374 Google Scholar
  113. 113.
    Grimme S (2005). J Phys Chem A 109: 3067 Google Scholar
  114. 114.
    Cioslowski J, Schimeczek M, Liu G and Stoyanov V (2000). J Chem Phys 113: 9377 Google Scholar
  115. 115.
    Ruiz E, Salahub DR and Vela A (1995). J Am Chem Soc 117: 1141 Google Scholar
  116. 116.
    Ruiz E, Salahub DR and Vela A (1996). J Phys Chem 100: 12265 Google Scholar
  117. 117.
    Kool ET, Morales JC and Guckian KM (2000). Angew Chem Int Ed 39: 990 Google Scholar
  118. 118.
    Barthelemy P, Lee SJ and Grinstaff M (2005). Pure Appl Chem 77: 2133 Google Scholar
  119. 119.
    Vondrásek J, Bendová L, Klusák V and Hobza P (2005). J Am Chem Soc 127: 2615 Google Scholar
  120. 120.
    Mansikkamaeki H, Nissinen M and Rissanen K (2004). Angew Chem Int Ed 43: 1243 Google Scholar
  121. 121.
    Vázquez M, Bermejo MR, Licchelli M, González-Noya AM, Pedrido RM, Sangregorio C, Sorace L, García-Deibe AM and Sanmartín J (2005). Eur J Inorg Chem 17: 3479 Google Scholar
  122. 122.
    Hobza P and Sponer J (1999). Chem Rev 99: 3247 Google Scholar
  123. 123.
    Sponer J, Leszczynski J and Hobza P (2001). Biopolymers 61: 3 Google Scholar
  124. 124.
    Birks JB (1970). Photophysics of aromatic molecules. Wiley, New York, p 71Google Scholar
  125. 125.
    Tawada Y, Tsuneda T, Yanagisawa S, Yanai T and Hirao K (2004).    J Chem Phys 120: 8425 Google Scholar
  126. 126.
    Ben-Shlomo SB and Kaldor U (1990). J Chem Phys 92: 3680 Google Scholar
  127. 127.
    Nielsen ES, Jorgensen P and Oddershede J (1980). J Chem Phys 73: 6238 Google Scholar
  128. 128.
    Clouthier DJ and Ramsay DA (1983). Annu Rev Phys Chem 34: 31 Google Scholar
  129. 129.
    Biermann D and Schmidt W (1980). J Am Chem Soc 102: 3163 Google Scholar
  130. 130.
    Grimme S and Parac M (2003). Chem Phys Chem 4: 292 Google Scholar
  131. 131.
    Hautman J and Klein ML (1991). NATO ASI Ser E 205: 395 Google Scholar
  132. 132.
    Karlin KD (1993). Science 261: 701 Google Scholar
  133. 133.
    Crabtree RH (1994). The organometallic chemistry of the transition metals, 2nd ed. Wiley, New York Google Scholar
  134. 134.
    George SM (1995). Chem Rev 95: 475 Google Scholar
  135. 135.
    Somorjai GA (1995). Chem Rev 96: 1223 Google Scholar
  136. 136.
    Ratner MA, Davis B, Kemp M, Mujica V, Roitberg A and Yalirakil S (1998). Ann N Y Acad Sci 852: 22 Google Scholar
  137. 137.
    Truhlar DG, Morokuma K (1999) In: ACS symposium series 721:transition state modeling for catalysis. American Chemical Society, Washington, DCGoogle Scholar
  138. 138.
    Davidson ER (2000). Chem Rev 100: 351 Google Scholar
  139. 139.
    Siegbahn PEM and Blomberg MRA (2000). Chem Rev 100: 421 Google Scholar
  140. 140.
    Gladysz JA (2000). Chem Rev 100: 1167 Google Scholar
  141. 141.
    Rappe AK, Skiff WM and Casewit CJ (2000). Chem Rev 100: 1435 Google Scholar
  142. 142.
    Lovelll T, Stranger R and McGrady JE (2001). Inorg chem, 40: 39 Google Scholar
  143. 143.
    Bertini I, Sigel A and Sigel H (2001). Handbook on Metalloproteins. Marcel Dekker, New York Google Scholar
  144. 144.
    Coperat C, Chabonas M, Saint-Arromon RP and Basset J-M (2003). Angew Chem Int Ed 42: 156 Google Scholar
  145. 145.
    Cavigliasso G and Stranger R (2005). Inorg Chem 44: 5081 Google Scholar
  146. 146.
    Carreón-Macedo J-L and Harvey JN (2006). Phys Chem Chem Phys 8: 93 Google Scholar
  147. 147.
    Tuma C and Sauer J (2006). Phys Chem Chem Phys 8: 3955 Google Scholar
  148. 148.
    Pople JA, Scott AP and Wong MW (1993). Israel J Chem 33: 345 Google Scholar
  149. 149.
    Scott AP and Radom L (1996). J Phys Chem 100: 16502 Google Scholar
  150. 150.
    Fast PL, Corchado J, Sanchez ML and Truhlar DG (1999). J Phys Chem A 103: 3139 Google Scholar
  151. 151.
    Herzberg G (1966). Molecular spectra and molecular structure. III.Electronic spectra and electronic structure of polyatomic molecules. Van Nostrand Reinhold, New York Google Scholar
  152. 152.
    NIST Chemistry Webbook, http://webbook.nist.gov/chemistryGoogle Scholar

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© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of Chemistry and Supercomputing InstituteUniversity of MinnesotaMinneapolisUSA

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