Chapter 2 Explicitly Correlated Approaches for Electronic Structure Computations

Annual Reports in Computational Chemistry

Volumn 2, Issue C, 2006, Pages 19-33

  Valeev, Edward F ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77957142126     PISSN: 15741400     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1574-1400(06)02002-0     Document Type: Review

References (73)

1. Schwartz C. Importance of angular correlations between atomic electrons. Phys. Rev. 126 (1962) 1015
2. Kutzelnigg W., and Morgan J.D. Rates of convergence of the partial-wave expansions of atomic correlation energies. J. Chem. Phys. 96 (1992) 4484
3. 2 helium. J. Chem. Phys. 71 (1979) 4142
4. Kato T. On the eigenfunctions of many-particle systems in quantum mechanics. Commun. Pure Appl. Math. 10 (1957) 151
5. Pack R.T., and Brown W.B. Cusp conditions for molecular wavefunctions. J. Chem. Phys. 45 (1966) 556
6. Slater J.C. Central fields and Rydberg formulas in wave mechanics. Phys. Rev. 31 (1928) 333
7. Hylleraas E.A. Neue berechnung der energie des heliums im grundzustande, sowie des tiefsten terms von ortho-helium. Z. Phys. 54 (1929) 347
8. E. F. Valeev, W. D. Allen, H. F. Schaefer, A conventional ci study of the ground state of He using basis functions up to l = 19. Method is described in Ref. [73].
9. Schwartz H.M. Ritz-Hylleraas solutions of the ground state of two-electron atoms involving fractional powers. Phys. Rev. 120 (1960) 483
10. Pekeris C.L. Ground state of two-electron atoms. Phys. Rev. 112 (1958) 1649
11. 10+. Phys. Rev. A 15 (1977) 1-15
12. Sims J.S., and Hagstrom S. High-precision Hy-CI variational calculations for the ground state of neutral helium and helium-like ions. Int. J. Quantum Chem. 90 (2002) 1600-1609
13. James H.M., and Coolidge A.S. The ground state of the hydrogen molecule. J. Chem. Phys. 1 (1933) 825-835
14. u states of the hydrogen molecule. J. Chem. Phys. 43 (1965) 2429-2441
15. Wolniewicz L. Nonadiabatic energies of the ground state of the hydrogen molecule. J. Chem. Phys. 103 (1995) 1792-1799
16. Helgaker T., Klopper W., Koch H., and Noga J. Basis-set convergence of correlated calculation on water. J. Chem. Phys. 106 (1997) 9639
17. 2. J. Chem. Phys. 106 (1997) 8718
18. Klopper W., Bak K.L., Jørgensen P., Olsen J., and Helgaker T. Highly accurate calculations of molecular electronic structure. J. Phys. B: At. Mol. Opt. Phys. 32 (1999) R103-R130
19. Valeev E.F., Allen W.D., Hernandez R., Sherrill C.D., and Schaefer H.F. On the accuracy limits of orbital expansion methods: explicit effects of k-functions on atomic and molecular energies. J. Chem. Phys. 118 (2003) 8594
20. Boys S.F., and Handy N.C. A condition to remove the indeterminacy in interelectronic correlation functions. Proc. Roy. Soc. (London) A 309 (1969) 209
21. Boys S.F., and Handy N.C. The determination of energies and wavefunctions with full electronic correlation. Proc. Roy. Soc. (London) A 310 (1969) 43
22. Nooijen M., and Bartlett R.J. Elimination of coulombic infinities through transformation of the Hamiltonian. J. Chem. Phys. 109 (1998) 8232
23. 2O. Mol. Phys. 23 (1972) 1
24. Ten-no S. A feasible transcorrelated method for treating electronic cusps using a frozen gaussian geminal. Chem. Phys. Lett. 330 (2000) 169-174
25. Handy N.C. Towards an understanding of the form of correlated wavefunctions for atoms. J. Chem. Phys. 58 (1973) 279-287
26. Hino O., Tonimura Y., and Ten-no S. Biorthogonal approach for explicitly correlated calculations using the transcorrelated Hamiltonian. J. Chem. Phys. 115 (2001) 7865-7871
27. Sims J.S., and Hagstrom S. Combined configuration-interaction-Hylleraas-type wave-function study of the ground state of the beryllium atom. Phys. Rev. A 4 (1971) 908
28. Clary D.C., and Handy N.C. CI-Hylleraas variational calculations on the ground state of the neon atom. Phys. Rev. A 14 (1976) 1607
29. 2S states of the lithium atom. Int. J. Quantum Chem. 51 (1994) 211-224
30. Busse G., Kleindienst H., and Luchow A. Nonrelativistic energies for the be atom: Double-linked Hylleraas-CI calculation. Int. J. Quantum Chem. 66 (1998) 241-247
31. Frye D., Preiskorn A., and Clementi E. The Hylleraas-CI method in molecular calculations. iii. Implementation and numerical verification of a three-electron many-center theory. J. Comput. Chem. 12 (1991) 560-564
32. Boys S.F. The integral formulae for the variational solution of the molecular many-electron wave equation in terms of gaussian functions with direct electron correlation. Proc. Roy. Soc. (London) A 258 (1960) 402
33. Singer K. The use of Gaussian (exponential quadratic) wave functions in molecular problems. i. general formulae for the evaluation of integrals. Proc. Roy. Soc. (London) A 258 (1960) 412
34. Karunakaran K.M., and Christoffersen R.E. Explicitly correlated configuration interaction wavefunctions using spherical gaussians. Formulation and initial application to lih. J. Chem. Phys. 62 (1975) 1972-1973
35. Cencek W., and Rychlewski J. Many-electron explicitly correlated gaussian functions. i. General theory and test results. J. Chem. Phys. 98 (1993) 1252
36. Kozlowski P.M., and Adamowicz L. An effective method for generating nonadiabatic many-body wave function using explicitly correlated Gaussian-type functions. J. Chem. Phys. 95 (1991) 6681-6698
37. Szalewicz K., Zabolitzki J.G., Jeziorski B., and Monkhorst H.J. Atomic and molecular correlation energies with explicitly correlated gaussian geminals. iv. a simplified treatment of strong orthogonality in MBPT and coupled cluster calculations. J. Chem. Phys. 81 (1984) 2723-2731
38. Handy N.C. Correlated Gaussian wavefunctions. Mol. Phys. 26 (1973) 169
39. Jeziorski B., and Szalewicz K. High-accuracy compton profile of molecular hydrogen from explicitly correlated Gaussian wave function. Phys. Rev. A 19 (1979) 2360-2365
40. Cencek W., and Kutzelnigg W. Accurate relativistic energies of one- and two-electron systems using Gaussian wave functions. J. Chem. Phys. 105 (1996) 5878-5885
41. Bukowski R., Jeziorski B., and Szalewicz K. Gaussian geminals in explicitly correlated coupled cluster theory including single and double excitations. J. Chem. Phys. 110 (1999) 4165
42. 2O using explicitly correlated Gaussian geminals. J. Chem. Phys. 102 (1995) 888
43. Adamowicz L., and Sadlej A.J. Perturbation calculation of molecular correlation energy using gaussian-type geminals. Second-order pair energies of LiH and BH. J. Chem. Phys. 69 (1978) 3992-4000
44. 12-dependent terms in the wave function as closed sums of partial wave amplitudes for large l. Theor. Chim. Acta 68 (1985) 445
45. Klopper W., and Röhse R. Computation of some new two-electron Gaussian integrals. Theor. Chim. Acta 83 (1992) 441
46. 12 theories. J. Chem. Phys. 113 (2000) 3990
47. 12 Møller-Plesset perturbation theory. J. Chem. Phys. 119 (2003) 4607-4613
48. Ten-no S., and Manby F.R. Density fitting for the decomposition of three-electron integrals in explicitly correlated electronic structure theory. J. Chem. Phys. 119 (2003) 5358-5363
49. Klopper W., and Kutzelnigg W. Møller-Plesset calculations taking care of the correlation cusp. Chem. Phys. Lett. 134 (1987) 17
50. Kutzelnigg W., and Klopper W. Wave functions with terms linear in the interelectronic coordinates to take care of the correlation cusp. i. general theory. J. Chem. Phys. 94 (1991) 1985
51. Gdanitz R.J. A formulation of multiple-reference CI with terms linear in the interelectronic distances. Chem. Phys. Lett. 210 (1993) 253
52. J. Noga, W. Klopper and W. Kutzelnigg, Recent Advances in Coupled-Cluster Methods, World Scientific, Singapore, 1997, p. 1.
53. Klopper W., and Lüthi H.P. Towards the accurate computation of properties of transition metal compounds: the binding energy of ferrocene. Chem. Phys. Lett. 262 (1996) 546
54. Sinnokrot M.O., Valeev E.F., and Sherrill C.D. Estimates of the ab initio limit for pi-pi interactions: the benzene dimer. J. Am. Chem. Soc. 124 (2002) 10887
55. Klopper W., Quack M., and Suhm M.A. A new ab initio based six-dimensional semi-empirical pair interaction potential for HF. Chem. Phys. Lett. 261 (1996) 35
56. Valeev E.F., Allen W.D., Schaefer H.F., and Császár A.G. The second-order Møller-Plesset limit for the barrier to linearity of water. J. Chem. Phys. 114 (2001) 2875
57. 3 ground state in the neighborhood of the minimum with microhartree accuracy and vibrational frequencies derived from it. J. Chem. Phys. 101 (1994) 2231-2243
58. Noga J., Valiron P., and Klopper W. The accuracy of atomization energies from explicitly correlated coupled-cluster calculations. J. Chem. Phys. 115 (2001) 2022-2032
59. Klopper W., and Samson C.C.M. Explicitly correlated second-order Møller-Plesset methods with auxiliary basis sets. J. Chem. Phys. 116 (2002) 6397
60. Valeev E.F. Improving on the resolution of the identity in linear r12 ab initio theories. Chem. Phys. Lett. 395 4-6 (2004) 190-195
61. Ten-no S. Explicitly correlated second order perturbation theory: introduction of a rational generator and numerical quadratures. J. Chem. Phys. 121 (2004) 117-129
62. C. L. Janssen, I. B. Nielsen, M. L. Leininger, E. F. Valeev and E. T. Seidl, The Massively Parallel Quantum Chemistry Program (MPQC): Version 2.2, Sandia National Laboratories, Livermore, CA USA, http://www.mpqc.org/(2003).
63. J. Noga, P. Valiron, W. Klopper and T. Helgaker, DIRCCR12-OS is a direct CCSD(T)-R12 program, 2003.
64. Gdanitz R.J., Black G.D., Lansing C.S., Palmer B.J., and Schuchardt K.L. Registering the amica electronic structure code in the extensible computational chemistry environment. J. Comp. Chem. 26 (2005) 214-225
65. T. D. Crawford, C. D. Sherrill, E. F. Valeev, J. T. Fermann, R. A. King, M. L. Leininger, S. T. Brown, C. L. Janssen, E. T. Seidl, J. P. Kenny and W. D. Allen, PSI 3.2, http://www.psicode.org/(2003).
66. H. -J. Werner, P. J. Knowles, R. Lindh, M. Schütz, P. Celani, T. Korona, F. R. Manby, G. Rauhut, R. D. Amos, A. Bernhardsson, A. Berning, D. L. Cooper, M. J. O. Deegan, A. J. Dobbyn, F. Eckert, C. Hampel, G. Hetzer, A. W. Lloyd, S. J. McNicholas, W. Meyer, M. E. Mura, A. Nicklass, P. Palmieri, R. Pitzer, U. Schumann, H. Stoll, A. J. Stone, R. Tarroni and T. Thorsteinsson, Molpro, developmental version 2002.9, a package of ab initio programs, see http://www.molpro.net/(2005).
67. Persson B.J., and Taylor P.R. Accurate quantum-chemical calculation: the use of Gaussian-type geminal functions in the treatment of electron correlation. J. Chem. Phys. 105 (1996) 5915
68. Gilbert T.L. Interpretation of the rapid convergence of correlated wave functions. Rev. Mod. Phys. 35 (1963) 491
69. Ten-no S. Initiation of explicitly correlated Slater-type germinal theory. Chem. Phys. Lett. 398 (2004) 56-61
70. May A.J., Valeev E., Polly R., and Manby F.R. Analysis of the errors in explicitly correlated electronic structure theory. Phys. Chem. Chem. Phys. 7 (2005) 2710-2713
71. Tew D.P., and Klopper W. New correlation factors for explicitly correlated electronic wavefunctions. J. Chem. Phys. 123 (2005) 074101
72. J. Rychlewski (ed.), Explicitly correlated wave functions in chemistry and physics. Theory and applications. In Progress in Theoretical Chemistry and Physics, Springer, New York, 2003, Vol. 13.
73. Brown R.T., and Fontana P.R. Configuration interaction in two- and three-electron atoms. J. Chem. Phys. 45 (1966) 4248