Wave operators, multiconfigurational

Similar iterative schemes were used to determine the MO s for multiconfigurational wave functions, in the early implementations. Fock-like operators were constructed and diagonalized iteratively. The convergence problems with these methods are, however, even more severe in the MCSCF case, and modem methods are not based on this approach. The electronic energy is instead considered to be a function of the variational parameters of the wave function - the Cl coefficients and the molecular orbital coefficients. Second order (or approximate second order) iterative methods are then used to find a stationary point on the energy surface. 

Ab initio determinations of SOC in carbene (1) have been carried out for three bond angles (0 = 90, 112 and 135°) by McKellar et al. [27J using SCI and SDCI wave functions and by Vahtras et al. [19] for the equilibrium geometry employing a multiconfiguration linear response (MCLR) approach. Both sets of calculations are based on the full coupling operator with the... 

With this brief discussion of the three basic steps (a)-(c) from Subsecfion 4.1, we have arrived at our original destination to represent all physical quantities of interest as sum (of products) of one- and two-parficle amplifudes. In practice, each of these expansions are often lengthy and the complexity of fhese expansions increases rapidly if the number of particle and holes is increased in the valence shells. The latter can be seen easily from the fact that each (valence-shell) particle of hole introduces an additional creation or annihilation operator into the operator strings a)a and (a ), respectively. In contrast to other, e.g. multiconfigurational, expansions of the wave functions, however, the explicit form of the approximate states IV a) cannot be derived so easily in MBPT or the CCA. For this reason also, a straightforward and simply handling of the perturbation expansions decides how successfully the theory can be applied to open-shell atoms and molecules in the future. 

The most popular way of including dynamic correlation upon a CASSCF reference wave function [54-57] is the second-order perturbation theory (CASPT2) developed by Roos and coworkers [58]. However, in contrast to the single-configurational case, where the definition of the zeroth-order Hamiltonian is universal and taken as the sum of the one-electron Fock operators, the generalization of the zeroth-order Hamiltonian to the multiconfigurational case is not straightforward [59, 60]. A different, theoretically more justified approach is to... 

Meyer, H.D. and Worth, G.A., Quantum molecular dynamics propagating wave-packets and density operators using the multiconfiguration time-dependent Hartree method, Theor. Chem. Acc., 109, 251-267, 2003. 

Secticm 14.2.1. Extending the Fock curator in the orbital basis (10.4.2) to multiconfigurational CASSCF wave fiinctions 0), we obtain the CASSCF Fock operator [26]... 

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