Multi-configuration self-consistent correlation

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

Werner and co-workers [2, 21, 34] used internally-contracted multi-reference configuration-interaction (IC-MRCI) calculations, based on state-averaged (three-state) multi-configuration, self-consistent-field (MCSCF) calculations with large atomic orbital basis sets, to determine the three electronically adiabatic C1(F)+H2 PESs in the reactant arrangement L4, 2A, and lA. These all correlate with X( P) + H2. These three adiabatic electronic states are the IC-MRCI approximations to the three lowest eigenfunctions of Hgi, namely... 

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. 

A more accurate method which serves as the basis to generate orbitals for higher-order electron-correlation effects is the complete active space multi-configuration self-consistent field (CAS-MCSCF or CASSCF) method. In this method, a set of the most active electrons, usually the valence electrons, are distributed in all possible ways... 

Although the correlation consistent sets were developed to describe correlated wave functions, they also provide a very systematic description of Hartree-Fock as well as simple valence multi-configurational self-consistent field (MCSCF) wave functions for molecules. This should not be too surprising. The radial and angular space spanned by the HF and... 

Core-valence correlation involves the interaction between the inner shell (core) and valence electrons. That this interaction is small is an important axiom of chemistry, as it is well established that the properties of atoms and molecules are largely determined by the valence electrons. This principle underlies the explanation of chemical periodicity and the structure of the periodic table. Conceptually, one considers the inner electrons to be tightly bound and rather inert. Hence, most theoretical studies only consider valence electron correlation with the core electrons frozen at the Hartree-Fock (HF) or multi-configuration self-consistent field (MCSCF) level or replaced with a pseudopotential. The utility and accuracy of the vast body of quantum chemical calculations provide ample evidence justifying this assumption. 

AIMD = ab initio molecular dynamics B-LYP = Becke-Lee-Yang-Parr CVC = core-valence correlation DF = density functional LDA = local density approximation MCLR = multi-configurational linear response MP2 = Mpller-Plesset second order (MRD)CI = multi-reference double-excitation configuration interaction RPA = random phase approximation TD-MCSCF = time-dependent multi-configurational self-consistent field TD-SCF = time-depen-dent self-consistent field. 

A number of types of calculations begin with a HF calculation and then correct for correlation. Some of these methods are Moller-Plesset perturbation theory (MPn, where n is the order of correction), the generalized valence bond (GVB) method, multi-configurational self-consistent field (MCSCF), configuration interaction (Cl), and coupled cluster theory (CC). As a group, these methods are referred to as correlated calculations. 

In order to correlate the solid state and solution phase structures, molecular modelling using the exciton matrix method was used to predict the CD spectrum of 1 from its crystal structure and was compared to the CD spectrum obtained in CHC13 solutions [23]. The matrix parameters for NDI were created using the Franck-Condon data derived from complete-active space self-consistent fields (CASSCF) calculations, combined with multi-configurational second-order perturbation theory (CASPT2). 

Aspects of the relativistic theory of quantum electrodynamics are first reviewed in the context of the electronic structure theory of atoms and molecules. The finite basis set parametrization of this theory is then discussed, and the formulation of the Dirac-Hartree-Fock-Breit procedure presented with additional detail provided which is specific to the treatment of atoms or molecules. Issues concerned with the implementation of relativistic mean-field methods are outlined, including the computational strategies adopted in the BERTHA code. Extensions of the formalism are presented to include open-shell cases, and the accommodation of some electron correlation effects within the multi-configurational Dirac-Hartree-Fock approximation. We conclude with a survey of representative applications of the relativistic self-consistent field method to be found in the literature. 

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