Multiconfiguration self-consistent field MCSCF method

The multiconfigurational self-consistent field ( MCSCF) method in whiehthe expeetation value < T H T>/< T T>is treated variationally and simultaneously made stationary with respeet to variations in the Ci and Cy,i eoeffieients subjeet to the eonstraints that the spin-orbitals and the full N-eleetron waveflmetion remain normalized ... 

Nondynamical electron correlation effects are generally important for reaction path calculations, when chemical bonds are broken and new bonds are formed. The multiconfiguration self-consistent field (MCSCF) method provides the appropriate description of these effects [25], In the last decade, the complete active space self-consistent field (CASSCF) method [26] has become the most widely employed MCSCF method. In the CASSCF method, a full configuration interaction (Cl) calculation is performed within a limited orbital space, the so-called active space. Thus all near degeneracy (nondynamical electron correlation) effects and orbital relaxation effects within the active space are treated at the variational level. A full-valence active space CASSCF calculation is expected to yield a qualitatively reliable description of excited-state PE surfaces. For larger systems, however, a full-valence active space CASSCF calculation quickly becomes intractable. 

For the construction of spin eigenfunctions see, for example, Ref. [22], There are obviously many parallels to the multiconfiguration self-consistent field (MCSCF) methods of MO theory, such as the restriction to a relatively small active space describing the chemically most interesting features of the electronic structure. The core wavefunction for the inactive electrons, 4>core, may be taken from prior SCF or complete active space self-consistent field (CASSCF) calculations, or may be optimised simultaneously with the and cat. 

The development of multireference methods represents important progress in electronic stmcture theory in the last decades. The multiconfiguration self-consistent field (MCSCF) method, and configuration interaction (Cl), coupled cluster (CC), and perturbation methods based on the MCSCF functions play a central role in the studies of electronic stmcture of molecules and chemical reaction mechanisms, especially in those concerned with electronic excited states. 

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. 

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