Long-range corrected double-hybrid density functionals
J. Chem. Phys. 131, 174105 (2009); doi:10.1063/1.3244209
Published 3 November 2009
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We extend the range of applicability of our previous long-range corrected (LC) hybrid functional,
B97X [J.-D. Chai and M. Head-Gordon, J. Chem. Phys. 128, 084106 (2008)], with a nonlocal description of electron correlation, inspired by second-order Møller–Plesset (many-body) perturbation theory. This LC “double-hybrid” density functional, denoted as
B97X-2, is fully optimized both at the complete basis set limit (using 2-point extrapolation from calculations using triple and quadruple zeta basis sets), and also separately using the somewhat less expensive 6-311++G(3df,3pd) basis. On independent test calculations (as well as training set results),
B97X-2 yields high accuracy for thermochemistry, kinetics, and noncovalent interactions. In addition, owing to its high fraction of exact Hartree–Fock exchange,
B97X-2 shows significant improvement for the systems where self-interaction errors are severe, such as symmetric homonuclear radical cations.
©2009 American Institute of Physics
B97X [J.-D. Chai and M. Head-Gordon, J. Chem. Phys. 128, 084106 (2008)], with a nonlocal description of electron correlation, inspired by second-order Møller–Plesset (many-body) perturbation theory. This LC “double-hybrid” density functional, denoted as
B97X-2, is fully optimized both at the complete basis set limit (using 2-point extrapolation from calculations using triple and quadruple zeta basis sets), and also separately using the somewhat less expensive 6-311++G(3df,3pd) basis. On independent test calculations (as well as training set results),
B97X-2 yields high accuracy for thermochemistry, kinetics, and noncovalent interactions. In addition, owing to its high fraction of exact Hartree–Fock exchange,
B97X-2 shows significant improvement for the systems where self-interaction errors are severe, such as symmetric homonuclear radical cations.
©2009 American Institute of Physics
| History: | Received 13 July 2009; accepted 17 September 2009; published 3 November 2009 |
| Permalink: |
http://link.aip.org/link/?JCPSA6/131/174105/1 |
KEYWORDS and PACS
density functional theory,
electron correlations,
free radicals,
HF calculations,
perturbation theory,
positive ions
- 31.15.eg
Exchange-correlation functionals (in current density functional theory) (atoms and molecules) - 31.15.V-
Electron correlation calculations for atoms, ions and molecules - 31.15.xp
Perturbation theory in atomic and molecular physics - 31.15.xr
Self-consistent-field methods in atomic and molecular physics - YEAR: 2009
PUBLICATION DATA
0021-9606 (print)
1089-7690 (online)
REFERENCES (62)
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- P. Hohenberg and W. Kohn,
Phys. Rev. 136, B864 (1964) . - W. Kohn and L. J. Sham,
ibid. 140, A1133 (1965) . - R. G. Parr and W. Yang, Density-Functional Theory of Atoms and Molecules (Oxford University, New York, 1989).
- R. M. Dreizler and E. K. U. Gross, Density Functional Theory: An Approach to the Quantum Many Body Problem (Springer-Verlag, Berlin, 1990).
- W. Kohn, A. D. Becke, and R. G. Parr,
J. Phys. Chem. 100, 12974 (1996) . - A. D. Becke, J. Chem. Phys. 98, 5648 (1993).
- T. Bally and G. N. Sastry,
J. Phys. Chem. A 101, 7923 (1997)
B. Braïda, P. C. Hiberty, and A. Savin, - A. D. Dutoi and M. Head-Gordon,
Chem. Phys. Lett. 422, 230 (2006) . - A. Dreuw, J. L. Weisman, and M. Head-Gordon, J. Chem. Phys. 119, 2943 (2003).
- J. -D. Chai and M. Head-Gordon, J. Chem. Phys. 128, 084106 (2008).
- J. -D. Chai and M. Head-Gordon,
Phys. Chem. Chem. Phys. 10, 6615 (2008) . - J. -D. Chai and M. Head-Gordon,
Chem. Phys. Lett. 467, 176 (2008) . - H. Iikura, T. Tsuneda, T. Yanai, and K. Hirao, J. Chem. Phys. 115, 3540 (2001).
- O. A. Vydrov, J. Heyd, A. V. Krukau, and G. E. Scuseria, J. Chem. Phys. 125, 074106 (2006)
- H. Stoll and A. Savin, in Density Functional Methods in Physics, edited by R. M. Dreizler and J. D. Providencia (Plenum, New York, 1985), p. 177
- J. G. Ángyán, I. C. Gerber, A. Savin, and J. Toulouse, Phys. Rev. A 72, 012510 (2005).
- E. Goll, H. -J. Werner, and H. Stoll,
Chem. Phys. 346, 257 (2008)
E. Goll, T. Leininger, F. R. Manby, A. Mitrushchenkov, H. -J. Werner, and H. Stoll, - J. A. Parkhill, J. -D. Chai, A. D. Dutoi, and M. Head-Gordon,
Chem. Phys. Lett. 478, 283 (2009) . - P. J. Stephens, F. J. Devlin, C. F. Chabalowski, and M. J. Frisch,
J. Phys. Chem. 98, 11623 (1994) . - A. D. Becke, J. Chem. Phys. 107, 8554 (1997).
- T. M. Henderson, A. F. Izmaylov, G. E. Scuseria, and A. Savin, J. Chem. Phys. 127, 221103 (2007)
- J. F. Dobson, K. McLennan, A. Rubio, J. Wang, T. Gould, H. M. Le, and B. P. Dinte,
Aust. J. Chem. 54, 513 (2001) . - S. Kristyan and P. Pulay,
Chem. Phys. Lett. 229, 175 (1994) . - X. Wu, M. C. Vargas, S. Nayak, V. Lotrich, and G. Scoles, J. Chem. Phys. 115, 8748 (2001)
- H. Rydberg, B. I. Lundqvist, D. C. Langreth, and M. Dion, Phys. Rev. B 62, 6997 (2000)
- O. A. Vydrov and T. Van Voorhis, J. Chem. Phys. 130, 104105 (2009).
- A. D. Becke and E. R. Johnson, J. Chem. Phys. 122, 154104 (2005)
- B. G. Janesko, T. M. Henderson, and G. E. Scuseria, J. Chem. Phys. 130, 081105 (2009).
- S. Grimme, J. Chem. Phys. 124, 034108 (2006).
- T. Schwabe and S. Grimme,
Phys. Chem. Chem. Phys. 9, 3397 (2007) . - A. Tarnopolsky, A. Karton, R. Sertchook, D. Vuzman, and J. M. L. Martin,
J. Phys. Chem. A 112, 3 (2008) . - T. Benighaus, R. A. DiStasio, Jr., R. C. Lochan, J. -D. Chai, and M. Head-Gordon,
J. Phys. Chem. A 112, 2702 (2008) . - Y. Zhang, X. Xu, and W. A. Goddard III,
Proc. Natl. Acad. Sci. U.S.A. 106, 4963 (2009) . - C. Møller and M. S. Plesset,
Phys. Rev. 46, 618 (1934) . - S. Paziani, S. Moroni, P. Gori-Giorgi, and G. B. Bachelet, Phys. Rev. B 73, 155111 (2006)
- S. J. Chakravorty, S. R. Gwaltney, E. R. Davidson, F. A. Parpia, and C. F. Fischer, Phys. Rev. A 47, 3649 (1993).
- L. A. Curtiss, K. Raghavachari, P. C. Redfern, and J. A. Pople, J. Chem. Phys. 106, 1063 (1997).
- L. A. Curtiss, P. C. Redfern, K. Raghavachari, and J. A. Pople, J. Chem. Phys. 109, 42 (1998).
- L. A. Curtiss, K. Raghavachari, P. C. Redfern, and J. A. Pople, J. Chem. Phys. 112, 7374 (2000).
- J. A. Pople, M. Head-Gordon, D. J. Fox, K. Raghavachari, and L. A. Curtiss, J. Chem. Phys. 90, 5622 (1989).
- Y. Zhao, B. J. Lynch, and D. G. Truhlar,
J. Phys. Chem. A 108, 2715 (2004) . - Y. Zhao, N. González-García, and D. G. Truhlar,
J. Phys. Chem. A 109, 2012 (2005) - P. Jurečka, J. Šponer, J. Černý, and P. Hobza,
Phys. Chem. Chem. Phys. 8, 1985 (2006) . - A. Halkier, T. Helgaker, P. Jørgensen, W. Klopper, H. Koch, J. Olsen, and A. K. Wilson,
Chem. Phys. Lett. 286, 243 (1998) . - C. W. Murray, N. C. Handy, and G. J. Laming,
Mol. Phys. 78, 997 (1993) . - V. I. Lebedev and D. N. Laikov, Dokl. Math 59, 477 (1999), and references therein.
- R. A. Kendall and H. A. Früchtl,
Theor. Chem. Acc. 97, 158 (1997) . - P. M. W. Gill, B. G. Johnson, and J. A. Pople,
Chem. Phys. Lett. 209, 506 (1993) . - S. Grimme, J. Chem. Phys. 118, 9095 (2003).
- Y. Shao, L. Fusti-Molnar, Y. Jung, J. Kussmann, C. Ochsenfeld, S. T. Brown, A. T. B. Gilbert, L. V. Slipchenko, S. V. Levchenko, D. P. O'Neill, R. A. DiStasio, Jr., R. C. Lochan, T. Wang, G. J. O. Beran, N. A. Besley, J. M. Herbert, C. Y. Lin, T. Van Voorhis, S. H. Chien, A. Sodt, R. P. Steele, V. A. Rassolov, P. E. Maslen, P. P. Korambath, R. D. Adamson, B. Austin, J. Baker, E. F. C. Byrd, H. Dachsel, R. J. Doerksen, A. Dreuw, B. D. Dunietz, A. D. Dutoi, T. R. Furlani, S. R. Gwaltney, A. Heyden, S. Hirata, C. -P. Hsu, G. Kedziora, R. Z. Khalliulin, P. Klunzinger, A. M. Lee, M. S. Lee, W. Liang, I. Lotan, N. Nair, B. Peters, E. I. Proynov, P. A. Pieniazek, Y. M. Rhee, J. Ritchie, E. Rosta, C. D. Sherrill, A. C. Simmonett, J. E. Subotnik, H. L. Woodcock III, W. Zhang, A. T. Bell, A. K. Chakraborty, D. M. Chipman, F. J. Keil, A. Warshel, W. J. Hehre, H. F. Schaefer III, J. Kong, A. I. Krylov, P. M. W. Gill, and M. Head-Gordon,
Phys. Chem. Chem. Phys. 8, 3172 (2006) . - S. F. Boys and F. Bernardi,
Mol. Phys. 19, 553 (1970) . - L. A. Curtiss, P. C. Redfern, and K. Raghavachari, J. Chem. Phys. 123, 124107 (2005).
- Y. Zhao and D. G. Truhlar,
J. Phys. Chem. A 109, 5656 (2005) . - T. Van Mourik, A. K. Wilson, and T. H. Dunning,
Mol. Phys. 96, 529 (1999) . - G. D. Purvis and R. J. Bartlett, J. Chem. Phys. 76, 1910 (1982).
- K. Raghavachari, G. W. Trucks, J. A. Pople, and M. Head-Gordon,
Chem. Phys. Lett. 157, 479 (1989) . - W. Kurlancheek and M. Head-Gordon,
Mol. Phys. 107, 1223 (2009) . - R. C. Lochan and M. Head-Gordon, J. Chem. Phys. 126, 164101 (2007).
- R. P. Steele, R. A. DiStasio, Y. Shao, J. Kong, and M. Head-Gordon, J. Chem. Phys. 125, 074108 (2006).
- R. A. DiStasio, R. P. Steele, Y. M. Rhee, Y. Shao, and M. Head-Gordon,
J. Comput. Chem. 28, 839 (2007) . - R. P. Steele, R. A. DiStasio, and M. Head-Gordon,
J. Chem. Theory Comput. 5, 1560 (2009) . - For a recent review, W. Klopper, F. R. Manby, S. Ten-No, and E. F. Valeev,
Int. Rev. Phys. Chem. 25, 427 (2006) .
P. Mori-Sánchez, A. J. Cohen, and W. Yang, J. Chem. Phys. 125, 201102 (2006)
A. Ruzsinszky, J. P. Perdew, G. I. Csonka, O. A. Vydrov, and G. E. Scuseria, ibid. 126, 104102 (2007)
A. J. Cohen, P. Mori-Sánchez, and W. Yang,
P. M. W. Gill, R. D. Adamson and J. A. Pople,
T. Leininger, H. Stoll, H. -J. Werner, and A. Savin,
J. Toulouse, F. Colonna, and A. Savin, J. Chem. Phys. 122, 014110 (2005)
I. C. Gerber and J. G. Ángyán,
R. Baer and D. Neuhauser, Phys. Rev. Lett. 94, 043002 (2005)
E. Goll, H. -J. Werner, and H. Stoll,
E. Goll, H. -J. Werner, H. Stoll, T. Leininger, P. Gori-Giorgi, and A. Savin,
I. C. Gerber, J. G. Ángyán, M. Marsman, and G. Kresse, J. Chem. Phys. 127, 054101 (2007)
E. Livshits and R. Baer,
J. -W. Song, T. Hirosawa, T. Tsuneda, and K. Hirao, J. Chem. Phys. 126, 154105 (2007)
M. A. Rohrdanz and J. M. Herbert, ibid. 129, 034107 (2008).
U. Zimmerli, M. Parrinello, and P. Koumoutsakos, ibid. 120, 2693 (2004)
S. Grimme,
S. Grimme,
J. Antony and S. Grimme,
P. Jurečka, J. Černý, P. Hobza, and D. R. Salahub,
A. Goursot, T. Mineva, R. Kevorkyants, and D. Talbi,
S. Grimme, J. Antony, T. Schwabe, and C. Mück-Lichtenfeld,
J. Černý, P. Jurečka, P. Hobza, and H. Valdés,
C. Morgado, M. A. Vincent, I. H. Hillier, and X. Shan,
M. Kabeláč, H. Valdés, E. C. Sherer, C. J. Cramer, and P. Hobza,
J. Černý and P. Hobza,
M. Dion, H. Rydberg, E. Schröder, D. C. Langreth, and B. I. Lundqvist, ibid. 92, 246401 (2004)
D. C. Langreth, M. Dion, H. Rydberg, E. Schröder, P. Hyldgaard, and B. I. Lundqvist,
S. D. Chakarova-Käck, E. Schröder, B. I. Lundqvist, and D. C. Langreth, Phys. Rev. Lett. 96, 146107 (2006)
A. Puzder, M. Dion, and D. C. Langreth, J. Chem. Phys. 124, 164105 (2006)
T. Thonhauser, A. Puzder, and D. C. Langreth, ibid. 124, 164106 (2006)
T. Thonhauser, V. R. Cooper, S. Li, A. Puzder, P. Hyldgaard, and D. C. Langreth, Phys. Rev. B 76, 125112 (2007).
A. D. Becke and E. R. Johnson, ibid. 123, 154101 (2005)
124, 014104 (2006)
E. R. Johnson and A. D. Becke, ibid. 124, 174104 (2006)
A. D. Becke and E. R. Johnson, J. Chem. Phys. 127, 124108 (2007)
127, 154108 (2007)
E. R. Johnson and A. D. Becke, ibid. 128, 124105 (2008).
E. Goll, M. Ernst, F. Moegle-Hofacker, and H. Stoll, ibid. 130, 234112 (2009).








