Abstract
A configuration-interaction energy function (Lagrange) which is variational in all variables, including the orbital rotational parameters, is constructed. When this Lagrangian is used for obtaining configuration-interaction derivatives, all the important simplifications which occur for derivatives of variational wave functions carry over in a straightforward way. In particular, the state and orbital rotational response parameters obey the 2n+1 rule and the Lagrange multipliers obey the somewhat stronger 2n+2 rule. The simplifications which are normally obtained by invoking the Handy-Schaefer technique are automatically incorporated to all orders. Simple expressions for energy derivatives up to third order are presented. The relationship between the numerical errors in the variational parameters and the errors in the calculated energy derivatives is discussed.
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References
Pulay P (1977) In: Schaefer III HF (ed) Modern theoretical chemistry, vol. 4. Plenum Press, New York
Pulay P (1987) Adv Chem Phys 69:241
Helgaker T, Jørgensen P (1988) Adv Quantum Chem 19:183
Brooks BR, Laidig WD, Saxe P, Goddard JD, Yamaguchi Y, Schaefer III HF (1980) J Chem Phys 72:4652
Krishnan R, Schlegel HB, Pople JA (1980) J Chem Phys 72:4654
Fox DJ, Osamura Y, Hoffmann MR, Gaw JF, Fitzgerald G, Yamaguchi Y, Schaefer III HF (1983) Chem Phys Lett 102:17
Lee TJ, Handy NC, Rice JE, Scheiner AC, Schaefer III HF (1986) J Chem Phys 85:3930
Jørgensen P, Simons J (1983) J Chem Phys 79:334
Simons J, Jørgensen P, Helgaker TU (1984) Chem Phys 86:413
Handy NC, Schaefer III HF (1984) J Chem Phys 81:5031
Adamowicz L, Laidig WD, Bartlett RJ (1984) Int J Quantum Chem S18:245
Lee TJ, Scuseria GE, Rice JE, Schemer AC, Schaefer III HF (1987) Chem Phys Lett 139:134
Handy NC, Amos RD, Gaw JF, Rice JE, Simandiras ED (1985) Chem Phys Lett 120:151
Amos RD (1987) Adv Chem Phys 67:99
Rice JE, Amos RD (1985) Chem Phys Lett 122:585
Shepard R (1987) Int J Quantum Chem 31:33
Pulay P (1983) J Chem Phys 78:5043
Sellers HL (1986) Int J Quantum Chem 30:433
Sellers HL (1985) Chem Phys Lett 116:153; (1988) Int J Quantum Chem 33:271; King HF, Komornicki A (1986) J Chem Phys 84:5645; (1987) J Chem Phys 86:1076
Epstein ST (1980) Chem Phys Lett 70:311
Dalgaard E, Jørgensen P (1978) J Chem Phys 69:3833
Osamura Y, Yamaguchi Y, Schaefer III HF (1982) J Chem Phys 77:383
Jørgensen P, Simons J (1981) Second quantization-based methods in quantum chemistry. Academic Press, New York
Helgaker TU, Almlöf J (1984) Int J Quantum Chem 26:275
Olsen J, Yeager DL, Jørgensen P (1983) Adv Chem Phys 54:1
Helgaker TU, Almlöf J, Jensen HJAa, Jørgensen P (1986) J Chem Phys 84:6266
Siegbahn PEM, Almlöf J, Heiberg A, Roos BO (1981) J Chem Phys 74:2384
Bacskay GB (1981) Chem Phys 61:385
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Helgaker, T., Jørgensen, P. Configuration-interaction energy derivatives in a fully variational formulation. Theoret. Chim. Acta 75, 111–127 (1989). https://doi.org/10.1007/BF00527713
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DOI: https://doi.org/10.1007/BF00527713