Abstract
Using the intermediate hamiltonian theory as a unique conceptual frame and the technique of CI matrix dressing, a wide series of single-reference methods for the treatment of the ground state correlation are reviewed, compared, and sometimes improved. These methods range from independent excitation approximation (the very next step beyond MP2) to coupled cluster, going through the so-called electron pair approximations and the (SC)2CI formalism. A hierarchy of these methods can be established according to two criteria:
-
1.
The physical effects incorporated in the model space, the choice of which is flexible.
-
2.
The quality of the evaluation of the coefficients of the external space determinants. This evaluation, which remains based on a single reference expansion of the wave function, may simply ensure the size consistency or incorporate the linked contributions from the outer space.
These formulations in terms of diagonalizations of dressed CI matrices avoid convergence problems, but their main advantage is their flexibility, since they apply to multi-reference SDCI spaces as well as to SDCI spaces. The use of a common frame allows one to propose consistent combinations of methods of various costs for the treatment of various parts of the correlation energy.
Similar content being viewed by others
References
Hartree DR (1928) Proc Camb Phil Soc 24:89
Hartree DR (1928) Proc Camb Phil Soc 24:111
Hartree DR (1928) Proc Camb Phil Soc 24:426
Fock V (1930) Z Phys 61:126
Harrison RJ, Handy N (1983) Chem Phys Lett 98:97
Olsen J, Roos BD, Jørgensen P, Hensen HJ (1988) J Chem Phys 89:2185
Knowles PJ, Handy NC (1989) J Chem Phys 91:2396
Bauschlicher CW, Langhoff SR, Taylor PR (1990) Adv Chem Phys 77:103
Bendazzoli GL, Evangelisti S (1993) J Chem Phys 98:3141
Evangelisti S, Bendazzoli GL, Gagliardi L (1994) Chem Phys 185:47
Goldstone J (1957) Proc Roy Soc London A 239:267
Brandow BH (1967) Rev Mod Phys 39:771
Langhoff SR, Davidson ER (1974) Int J Quantum Chem 8:61
Ahlrichs R, Scharf P, Ehrhardt C (1985) J Chem Phys 82:890
Kelly HP, Sessler MA (1963) Phys Rev 132:2091
Kelly HP, Sessler MA (1964) Phys Rev A 134:1450
Meyer W (1971) Int J Quantum Chem 5:341
Coester F (1958) Nucl Phys 1:421
Coester F, Kummel H (1960) Nucl Phys 17:477
Čížek J (1966) J Chem Phys 45:4256
Čížek J, Paldus J (1971) Int J Quantum Chem 5:359
Paldus J, Čížek J, Shavitt I (1972) Phys Rev A 5:50
Bartlett RJ (1989) J Phys Chem 93:1697
Daudey JP, Heully JL, Malrieu JP (1993) J Chem Phys 99:1240
Malrieu JP, Nebot-Gil I, Sánchez-Marin J (1994) J Chem Phys 100:1440
Nebot-Gil I, Sánchez-Marin J, Malrieu JP, Heully JL, Maynau D (1995) J Chem Phys 103:2576
Malrieu JP, Durand P, Daudey JP (1985) J Phys A, Math Gen 18:809
Durand P, Malrieu JP (1987) In: Lawley (ed) Ab initio methods in quantum chemistry, Part I. Wiley, Chichester, pp 321–412
Mukhopadhyay D, Datta B, Mukherjee D (1992) Chem Phys Lett 197:236
Zaitsevskii AV, Heully JL (1993) J Phys B 25:603
Meissner L, Nooijen M (1995) J Chem Phys 102:9604
Lepetit MB, Malrieu JP (1993) Chem Phys Lett 208:503
Sinanoglu O (1964) Adv Chem Phys 6:315
Nesbet RK (1965) Adv Chem Phys 9:321
Heully JL, Malrieu JP (1992) Chem Phys Lett 199:545
Nietsche LE, Davidson ER (1978) J Chem Phys 68:3103
Nietsche LE, Davidson ER (1978) J Am Chem Soc 100:7201
Davidson ER, McMurchie LB, Day SJ (1981) J Chem Phys 74:5491
Nebot-Gil I, Sánchez-Marin J, Heully JL, Malrieu JP, Maynau D (1995) Chem Phys Lett 234:45
Adamowicz L, Malrieu JP J Chem Phys, in press
Heully JL, Malrieu JP, Nebot-Gil I, Sánchez-Marin J (1996) Chem Phys Lett 256:589
Szabo A, Ostlund NS (1990) Modern quantum chemistry. Macmillan, New York.
Raghavachari K (1991) Ann Rev Phys Chem 42:615
Meyer W (1973) J Chem Phys 58:1017
Ahlrichs R, Scharf P (1987) In: Lawley(ed) Ab initio methods in quantum chemistry, Part I. Wiley, Chichester, pp 501–537
Purvis GD, Bartlett RJ (1982) J Chem Phys 76:1910
Lee YS, Kucharski SA, Bartlett RJ (1984) J Chem Phys 81:5906
Assfeld X, Almlöf JE, Truhlar DG (1995) Chem Phys Lett 241:438
Lepetit MB, Malrieu JP (1987) J Chem Phys 87:5937
Meyer W (1974) Theor Chim Acta 35:277
Malrieu JP, Daudey JP, Caballol R (1994) J Chem Phys 101:8908
Meller J, Malrieu JP, Heully JL (1995) Chem Phys Lett 244:440
Practical applications (see Refs. [25,26]) have revealed that numerical stability advises to select a first column dressing (cf. Eq. (19)), in order to avoid the occurrence of some very small denominatorsc i in Eq. (18). However, this would result in a non-HermitianH + Δ operator. A first-row + first-column dressing, which is Hermitian and good for numerical purposes, is then recommended (see Ref. [26])
Epstein PS (1926) Phys Rev 28:690
Nesbet RK (1955) Proc R Soc London, Ser A 230:312
Nesbet RK (1955) Proc Roy Soc London, Ser A 230:912
Arrighini P (1981) Intermolecular forces, their evaluation by perturbation theory. In: Berthier, Dewar, Fischer, Fukui, Hall, Hartmann, Jaffé, Jortner, Kutzelnigg, Ruedenberg, Scrocco (eds) Lecture Notes in Chemistry, Vol 25. Springer-Verlag, Berlin Heidelberg New York
Lindgren I, Morrison J (1986) Atomic many-body theory. Springer-Verlag, Berlin Heidelberg New York London Paris Tokyo
Gershgorn Z, Shavitt T (1968) Int J Quantum Chem 2:751
Bachrach SM, Chiles RA, Dykstra CE (1981) J Chem Phys 75:2270
Čížek J, Paldus J (1971) Phys Rev A 3:525
Paldus J (1992) In: Wilson, Diercksen (eds) Methods in Computational Molecular Physics, NATO ASI Series, Series B, Physics, Vol 293. Plenum Press, New York, pp 99–194
Kutzelnigg W (1977) In: Schaefer (ed) Methods of electronic structure theory, modern theoretical chemistry, Vol 3. Plenum Press, New York, pp 129–188
See Ref. [43] and references therein in relation with comparing QCI and CC formalisms
Pople JA, Head-Gordon M, Raghavachari K (1987) J Chem Phys 87:5968
Raghavachari K, Trucks GW, Pople JA, Head-Gordon M (1989) Chem Phys Lett 157:479
Lee TJ, Scuseria GE (1990) J Chem Phys 93:489
Watts JD, Cernusák I, Noga J, Bartlett RJ, Bauschlicher CW, Lee TJ, Rendell AP, Taylor PR (1990) J Chem Phys 93:8875
Sánchez-Marin J, Nebot-Gil I, Maynau D, Malrieu JP (1995) Theor Chim Acta 92:241
Bartlett RJ, Watts JD, Kucharski SA, Noga J (1990) Chem Phys Lett 165:513
Bartlett RJ, Watts JD, Kucharski SA, Noga J (1990) Chem Phys Lett 167:609
Noga J, Bartlett RJ (1987) J Chem Phys 86:7041
Urban M, Noga J, Cole SJ, Bartlett RJ (1985) J Chem Phys 83:4041
Sánchez-Marin J, Maynau D, Malrieu JP (1993) Theor Chim Acta 87:107
Meller J, Caballol R, Malrieu JP (1996) J Chem Phys 104:4068
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sánchez-Marín, J., Nebot-Gil, I., Malrieu, J.P. et al. Size-consistent single-reference methods for electronic correlation: a unified formulation through intermediate hamiltonian theory. Theoret. Chim. Acta 95, 215–241 (1996). https://doi.org/10.1007/BF02335465
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02335465