Multi-configuration

Kosloff R and Hammerich A D 1991 Nonadiabatic reactive routes and the applicability of multi configuration time dependent self consistent field approximations Feredey Discuss. Chem. Soc. 91 239-47... 

Levy B 1969 Multi-configuration self-consistent wavefunctions for formaldehyde Chem. Phys. Lett. 4 17... 

The wave function for the elechonic structure can in principle be any of the constructions employed in electronic structure theoiy. The prefened choice in this context is a wave funchons that can be classified as single and multi-configurational, and for the latter type only complete active space (CAS) wave... 

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 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 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. 

Figgen, D., Rauhut, G., Dolg, M. and StoD, H. (2005) Energy-consistent pseudopotentials for group 11 and 12 atoms adjustment to multi-configuration Dirac-Hartree-Fock data. Chemical Physics, 311, 227-244. 

Grafenstein, J., Cremer, D., 2000, The Combination of Density Functional Theory with Multi-Configuration Methods - CAS-DFT , Chem. Phys. Lett., 316, 569. 

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... 

Such a wave function is represented by a linear combination of wave functions for more than one electron configuration, and is called a "multi-configurational" wave function. The consideration of more than one configuration can reduce the correlation error. Such an approach is referred to as the method of configuration interaction (Cl) . 

Within the SCF-CI method a fixed set of molecular orbitals is used. This means that during the calculation (leading to slow convergence) the individual molecular orbitals remain unchanged. A method where the linear expansion coefficients and the LCAO coefficients are optimized simultaneously is the multi-configuration SCF (MCSCF). 

In recent years density-functional methods32 have made it possible to obtain orbitals that mimic correlated natural orbitals directly from one-electron eigenvalue equations such as Eq. (1.13a), bypassing the calculation of multi-configurational MP or Cl wavefunctions. These methods are based on a modified Kohn-Sham33 form (Tks) of the one-electron effective Hamiltonian in Eq. (1.13a), differing from the HF operator (1.13b) by inclusion of a correlation potential (as well as other possible modifications of (Fee(av))-... 

Nevertheless, the one-electron approach does have its deHciencies, and we believe that a major theoretical effort must now be devoted to improving on it. This is not only in order to obtain better quantitative results but, perhaps more importantly, to develop a framework which can encompass all types of charge-transfer processes, including Auger and quasi-resonant ones. To do so is likely to require the use of many-electron multi-configurational wavefunctions. There have been some attempts along these lines and we have indicated, in detail, how such a theory might be developed. The few many-electron calculations which have been made do differ qualitatively from the one-electron results for the same systems and, clearly, further calculations on other systems are required. 

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],... 

There are two approaches to map crystal charge density from the measured structure factors by inverse Fourier transform or by the multipole method [32]. Direct Fourier transform of experimental structure factors was not useful due to the missing reflections in the collected data set, so a multipole refinement is a better approach to map charge density from the measured structure factors. In the multipole method, the crystal charge density is expanded as a sum of non-spherical pseudo-atomic densities. These consist of a spherical-atom (or ion) charge density obtained from multi-configuration Dirac-Fock (MCDF) calculations [33] with variable orbital occupation factors to allow for charge transfer, and a small non-spherical part in which local symmetry-adapted spherical harmonic functions were used. 

---