Multi-configuration self-consistent field method

Spin-restricted and multi-configuration self-consistent-field methods differ in the assumed func-... 

A conceptually straightforward improvement on the CI approximation is to reoptimize the molecular orbitals for a truncated CI expansion. This approach is called multi-configuration self-consistent field method (MCSCF) and its most prominent variant is the complete active space SCF method (CASSCF) [64]. In the first generation of MCSCF methods [65, 66], the CI coefficients C/ in Eq. 

However, although, starting from this point, many sophisticated methods for wave function expansion, for example, the coupled cluster approach, multi-configuration self-consistent-field method or multi-reference Cl methods, have been developed, the correlation problem faced many computational limitation, some of them almost insurmountable, due to the immense number of integrals to be evaluated. 

Configuration Interaction and Multi-configuration Self-consistent Field Methods... 

The Multi-Configuration Self-Consistent Field method combines the ideas of orbital optimization through a SCF technique as in the Hartree-Fock method, and a multiconfiguration expansion of the electronic wavefunction as in the configuration interaction method. In other words, the electronic wavefunction is still expressed as a linear combination of Slater determinants but now both the coeffi-... 

Multi-configurational self-consistent field methods involving only the valence atomic orbitals, such as the generalized valence bond (GVB see Spin-coupled Theory)... 

The Multi-configuration Self-consistent Field (MCSCF) method can be considered as a Cl where not only the coefficients in front of the determinants are optimized by the variational principle, but also the MOs used for constructing the determinants are made optimum. The MCSCF optimization is iterative just like the SCF procedure (if the multi-configuration is only one, it is simply HF). Since the number of MCSCF iterations required for achieving convergence tends to increase with the number of configurations included, the size of MCSCF wave function that can be treated is somewhat smaller than for Cl methods. 

The Multi-Configuration Self-Consistent Field (MCSCF) method includes configurations created by excitations of electrons within an active space. Both the coefficients ca of the expansion in terms of CSFs and the expansion coefficients of the... 

The accurate calculation of these molecular properties requires the use of ab initio methods, which have increased enormously in accuracy and efficiency in the last three decades. Ab initio methods have developed in two directions first, the level of approximation has become increasingly sophisticated and, hence, accurate. The earliest ab initio calculations used the Hartree-Fock/self-consistent field (HF/SCF) methodology, which is the simplest to implement. Subsequently, such methods as Mpller-Plesset perturbation theory, multi-configuration self-consistent field theory (MCSCF) and coupled-cluster (CC) theory have been developed and implemented. Relatively recently, density functional theory (DFT) has become the method of choice since it yields an accuracy much greater than that of HF/SCF while requiring relatively little additional computational effort. 

ELECTRON CORRELATION METHODS 4.6 MULTI-CONFIGURATION SELF-CONSISTENT FIELD 121... 

For variational methods, such as Hartree-Fock (HF), multi-configurational self-consistent field (MCSCF), and Kohn-Sham density functional theory (KS-DFT), the initial values of the parameters are equal to zero and 0) thus corresponds to the reference state in the absence of the perturbation. The A operators are the non-redundant state-transfer or orbital-transfer operators, and carries no time-dependence (the sole time-dependence lies in the complex A parameters). Furthermore, the operator A (t)A is anti-Hermitian, and tlie exponential operator is thus explicitly unitary so that the norm of the reference state is preserved. Perturbation theory is invoked in order to solve for the time-dependence of the parameters, and we expand the parameters in orders of the perturbation... 

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