Summary
For state-averaged multiconfigurational self consistent field (SA-MCSCF) wave functions, second-order geometrical response equations are derived that allow the determination of first-order configuration amplitude response for equally weighted, energetically degenerate states. The first-order response equations obtained in earlier work do not suffice to determine these particular responses parameters. To formulate such a derivation in a well defined manner, it is found that a specific linear combination of the degenerate states must be formed; this specific combination of states then defines how state energies and wave functions evolve as one passes through the surface intersection. The linear combination among the degenerate states is dependent upon the molecular distortion for which the responses are to be evaluated. Expressions for first- and second-order directional energy derivatives for these energetically degenerate wave functions are also derived. All the equations obtained are computationally tractable and expressed in terms of quantities that result from optimizing the SA-MCSCF wave functions and from solving the first- and part of the second-order geometrical response equations.
Similar content being viewed by others
References
Mead CA, Truhlar DG (1979) J Chem Phys 70:2284
Mead CA (1980) Chem Phys 49:23
Mead CA (1980) Chem Phys 49:33
Mead CA (1983) J Chem Phys 78:807
Davidson ER (1977) J Am Chem Soc 99:397
Davidson ER, Borden WT (1983) J Phys Chem 87:4783
Frey RF, Davidson ER, To be published in Advances in Molecular Electronic Structure Theory, Vol. 1, p. 211–260, (JAI Press Inc., 1990)
Lengsfield BH III, Saxe P, Yarkony DR (1984) J Chem Phys 81:4549
Saxe P, Lengsfield BH III, Yarkony DR (1985) Chem Phys Lett 113:159
Lengsfield BH III, Yarkony DR (1986) J Chem Phys 84:348
Saxe P, Yarkony DR (1987) J Chem Phys 86:321
Bak KL, Boatz J, Simons J (1991) Int J Quantum Chem (to be published)
Nichols J, Taylor H, Schmidt P, Simons J (1990) J Chem Phys 92:340
Jahn HA, Teller E (1937) Proc R Soc London Ser A 161:220
Hernandez R, Simons J (1991) J Chem Phys (submitted)
Xantheas S, Elbert ST, Ruedenberg K (1990) J Chem Phys 93:7519
Teller E (1937) J Phys Chem 41:109
Mead CA (1979) J Chem Phys 70:2276
Herzberg G, Longuet-Higgins HC (1963) Dis Faraday Soc 35:77
Lengsfield BH III (1982) J Chem Phys 77:4073
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bak, K.L., Simons, J. Geometrical linear responses and directional energy derivatives for energetically degenerate MCSCF electronic functions. Theoret. Chim. Acta 82, 7–27 (1992). https://doi.org/10.1007/BF01113127
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01113127