State-averaged multiconfiguration

State-Averaged Multiconfigurational Self-Consistent Field Method... 

Initially only state-averaged multiconfigurational self-consistent field (SA-MCSCF) wave functions could be treated but subsequently the algorithm was extended to treat general multireference configuration interaction (MRCI) wave functions. Here x(X) denotes the space fixed frame coordinates of the A electrons nuclei) and < >/ is one of A electronic... 

Cl = configuration interaction SA-MCSCF = state averaged multiconfigurational self-consistent field. 

Multiconfigurational quasi-degenerate perturbation theory (MC-QDPT) [5,6] We have also proposed a multistate multireference perturbation theory, the QDPT with MCSCF reference functions (MC-QDPT). In this PT, state-averaged CASSCF is first performed to set reference functions, and then an elfective Hamiltonian is constructed, which is finally diagonalized to obtain the energies of interest. 

A more balanced description thus requires multiconfiguration self-consistent field (MCSCF)-based methods, where the orbitals are optimized for each particular state or optimized for a suitable average of the desired states (state-averaged MCSCF). In semiempirical methods, however, an MCSCF procedure is normally not required due to the limited flexibility of the minimal valence atomic orbital basis commonly used in these methods. Instead, a multireference Cl method including a limited number of suitably chosen configurations will be appropriate. 

The time dependence of the molecular wave function is carried by the wave function parameters, which assume the role of dynamical variables [19,20]. Therefore the choice of parameterization of the wave functions for electronic and nuclear degrees of freedom becomes important. Parameter sets that exhibit continuity and nonredundancy are sought and in this connection the theory of generalized coherent states has proven useful [21]. Typical parameters include molecular orbital coefficients, expansion coefficients of a multiconfigurational wave function, and average nuclear positions and momenta. We write... 

Fig. 11.12. The experimental and theoretical branching ratios for the 1000 eV ionisation of lead to the 6ps/2 and 6pi/2 states of Pb+, plotted against recoil momentum p (Frost et al, 1986). The calculations with target-state correlations in the plane wave impulse approximation are indicated by MCDF, multiconfiguration Dirac—Fock EAL, extended average level OL, optimal level. Cl indicates ion-state configuration interaction.

Figure 13. Valence spinors of the Db atom in the 6d 7s ground state configuration from average-level all-electron (AE, dashed lines) multiconfiguration Dirac-Hartree-Fock calculations and corresponding valence-only calculations using a relativistic energy-consistent 13-valence-electron pseudopotential (PP, solid lines). A logarithmic scale for the distance r from the (point) nucleus is us in order to resolve the nodal structure of the all-electron spinors. The innermost parts have been truncated.

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