Multiconfigurational self-consistent field MCSCF wave functions

Olsen, J., lorgcnsen, P. Time dependent response theory with appUcations in to self consistence field (SCF and multiconfigurational self consistent field (MCSCF) wave functions, l.F.A. PRINT, Aarhus Universitet, 1994... 

As the next standard model of quantum chemisUy, we consider here the generalization of the Hartree-Fock wave function to systems dominated by more than one electronic configuration the multiconfigurational self-consistent field (MCSCF) wave function. This flexible model may be useful for describing the electronic structure of bonded molecular systems, in particular for excited states. Perhaps more important, however, is its ability to describe bond breakings and molecular dissociation processes. 

It is possible to divide electron correlation as dynamic and nondynamic correlations. Dynamic correlation is associated with instant correlation between electrons occupying the same spatial orbitals and the nondynamic correlation is associated with the electrons avoiding each other by occupying different spatial orbitals. Thus, the ground state electronic wave function cannot be described with a single Slater determinant (Figure 3.3) and multiconfiguration self-consistent field (MCSCF) procedures are necessary to include dynamic electron correlation. 

Another class of methods uses more than one Slater determinant as the reference wave function. The methods used to describe electron correlation within these calculations are similar in some ways to the methods listed above. These methods include multiconfigurational self-consistent field (MCSCF), multireference single and double configuration interaction (MRDCI), and /V-clcctron valence state perturbation theory (NEVPT) methods.5... 

Pioneering theoretical work on the formaldehyde -I- OH reaction has been reported by Dupuis and Lester [102] using multiconfiguration self-consistent-field (MCSCF) and configuration interaction (Cl) wave functions. These authors [102] predicted a large positive activation barrier of 5.5 kcal/mol. Using the ab initio Moller-Plesset method up to fourth order (MP4), Francisco [103] determine the barriers and energetic of this reaction. He obtained a small but positive barrier of... 

In this substection we will shortly discuss the computational methods used for calculation of the spin-spin coupling constants. Two main approaches available are ab initio theory from Hartree-Fock (or self-consistent field SCF) technique to its correlated extensions, and density function theory (DFT), where the electron density, instead of the wave function, is the fundamental quantity. The discussion here is limited to the methods actually used for calculation of the intermolecular spin-spin coupling constants, i. e. multiconfigurational self consistent field (MCSCF) theory, coupled cluster (CC) theory and density functional theory (DFT). For example, the second order polarization propagator method (SOPPA) approach is not... 

We have seen that the canonical Hartree-Fock orbitals are not the best choice of orbitals for use in Cl calculations. Let us consider a multideter-minantal wave function containing a relatively small number of configurations. What orbitals should we use in constructing these configurations so as to obtain the best possible result From the variation principle, it is clear that we should vary the orbitals so as to minimize the energy. This is the central idea of the multiconfiguration self-consistent-field (MCSCF) method. Thus the MCSCF wave function is a truncated Cl expansion... 

In Chapter 12, we study the related multiconfigurational self-consistent field (MCSCF) method, in which a simultaneous optimization of orbitals and Cl coefficients is attempted. Although the MCSCF method is incapable of providing accurate energies and wave functions, it is a flexible model, well suited to the study of chemical reactions and excited states. This chapter concentrates on techniques of optimization, a difficult problem in MCSCF theory because of the simultaneous optimization of orbitals and Cl coefficients. 

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... 

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