Multi configuration self-consistent field

The Multi-Configuration Self-Consistent Field (MCSCF) method can be considered as a Cl where not only are the coefficients in front of the determinants (eq. (4.2)) optimized by the variational principle, but the MOs used for constructing the determinants are also optimized. The MCSCF optimization is iterative 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 functions that can be treated is somewhat smaller than for Cl methods. 

When deriving the HF equations only the variation of the energy with respect to an orbital variation was required to be zero, which is equivalent to the first derivatives of the energy with respect to the MO expansion coefficients being equal to zero. The HF equations can be solved by an iterative SCF method, and there are many techniques for helping the iterative procedure to converge (Section 3.8). There is, however, no 

The full Cl expansion within the active space severely restricts the number of orbitals and electrons that can be treated by CASSCF methods. Table 4.3 shows how many singlet CSFs are generated for an [n/x]-CASSCF wave function (eq. (4.13)), without reductions arising from symmetry. 

It should be noted that CASSCF methods inherently tend to give an unbalanced description, since all the electron correlation recovered is in the active space, with none in the inactive space, or between the active and inactive electrons. This is not a problem if all the valence electrons are included in the active space, but this is only possible for small systems. If only part of the valence electrons are included in the active space, the CASSCF method tends to overestimate the importance of biradical structures. Consider for example acetylene where the hydrogens have been bent 60° away from linearity (this may be considered a model for ortho-benzyne). The in-plane ji-orbital now acquires significant biradical character. The true structure may be described as a linear combination of the following three configurations. 

The structure on the left is biradical, while the two others are ionic, corresponding to both electrons being at the same carbon. The simplest CASSCF wave function that can qualitatively describe this system has two electrons in two orbitals, giving the three 

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A configuration interaction calculation uses molecular orbitals that have been optimized typically with a Hartree-Fock (FIF) calculation. Generalized valence bond (GVB) and multi-configuration self-consistent field (MCSCF) calculations can also be used as a starting point for a configuration interaction calculation. 

The metric term Eq. (2.8) is important for all cases in which the manifold M has non-zero curvature and is thus nonlinear, e.g. in the cases of Time-Dependent Hartree-Fock (TDHF) and Time-Dependent Multi-Configurational Self-Consistent Field (TDMCSCF) c culations. In such situations the metric tensor varies from point to point and has a nontrivial effect on the time evolution. It plays the role of a time-dependent force (somewhat like the location-dependent gravitational force which arises in general relativity from the curvature of space-time). In the case of flat i.e. linear manifolds, as are found in Time-Dependent Configuration Interaction (TDCI) calculations, the metric is constant and does not have a significant effect on the dynamics. 

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... 

By calculating A.U (R) and Al/ (i ) separately, we can straightforwardly calculate the total adiabatic correction V (R) for any isotopes of A and B. The adiabatic corrections are calculated by numerical differentiation of the multi-configurational self-consistent field (MCSCF) wave functions calculated with Dalton [23]. The nurnerical differentiation was performed with the Westa program developed 1986 by Agren, Flores-Riveros and Jensen [22],... 

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

A modification of this scheme has been used for optimizing excited states of multi-configurational self-consistent field wave functions, see H. J. Aa. Jensen and H. Agren, Chem. Phys. 104, 229 (1986). 

MCSCF multi-configuration self-consistent field... 

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. 

Veillard, A., and E. Clementi Complete multi-configuration self-consistent field theory. Theoret. Chim. Acta (Berlin) 7, 133 (1967). 

Linear Combination of Atomic Orbitals Many Body Perturbation Theory Multi-configuration Self Consistent Field Molecules in Molecules... 

Henne Hettema, Hans Jorgen Aa. Jensen, Poul Jorgensen, and Jeppe Olsen (1992). Quadratic response functions for a multi-configurational self-consistent-field wave-function. J. Chem. Phys. 97, 1174-1190. 

MCSCF Multi-Configuration Self-Consistent Field. A means of variationally minimizing the energy of several electron configurations of a given system simultaneously, so as to provide a better description of its electronic structure. 

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