Geometrical linear responses and directional energy derivatives for energetically degenerate MCSCF electronic functions
Abstract
For stateaveraged multiconfigurational self consistent field (SAMCSCF) wave functions second order geometrical response equations are derived that allow the determination of firstorder configuration amplitude responses for equally weighted, energetically degenerate states. The firstorder response equations obtained in earlier work do not suffice to determine these particular response 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 secondorder 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 SAMCSCF wavefunctions and from solving the first and part of the secondorder geometrical response equations.
 Publication:

Technical Report
 Pub Date:
 April 1991
 Bibcode:
 1991utah.rept.....B
 Keywords:

 Configuration Interaction;
 Molecular Energy Levels;
 Self Consistent Fields;
 Wave Functions;
 Electron States;
 Ground State;
 Mathematical Models;
 Potential Energy;
 Electronics and Electrical Engineering