Multiconfiguration SCF Theory

The black box situation of SCF applications has not yet been reached for the multiconfigurational SCF theory. This constitutes a major problem, since MCSCF is a much better starting point for quantum chemical calculations on many interesting chemical problems (a good example is studies of transition states for chemical reactions). A development towards more automatized procedures can consequently be expectedto take place in MCSCF theory too. 

Pack and Hirschfelder (133) discuss the energy corrections to the Bom-Oppenheimer approximation, while Bunker (134) discusses the partial breakdown of the Bom-Oppenheimer approximation. The Hell-mann-Feynman theorem is also discussed by Tuan (135) with reference to multiconfiguration SCF-theory, while Loeb and Rasiel (136) discuss constraints upon the LiH molecule with reference to the Hellmann-Fe5mman theorem. King (137) developed a theory of effective Cartesian force constants which relate to the sum of the squares of the normal frequencies these effective force constants are independent of the inter-nuclear repulsion of the nuclei in a molecule, and thus removes one of the indeterminacy of the Hellmann-Feynman method described above. 

The various response tensors are identified as terms in these series and are calculated using numerical derivatives of the energy. This method is easily implemented at any level of theory. Analytic derivative methods have been implemented using self-consistent-field (SCF) methods for a, ft and y, using multiconfiguration SCF (MCSCF) methods for ft and using second-order perturbation theory (MP2) for y". The response properties can also be determined in terms of sum-over-states formulation, which is derived from a perturbation theory treatment of the field operator — [iE, which in the static limit is equivalent to the results obtained by SCF finite field or analytic derivative methods. 

Roos, B. J. (1992) The multiconfigurational (MC) self-consistent field (SCF) theory,in Roos, B. J.(eds.), Lecture notes in quantum chemistry, Springer-Verlag, Berlin,pp. 179-254. 

The Section on More Quantitive Aspects of Electronic Structure Calculations introduces many of the computational chemistry methods that are used to quantitatively evaluate molecular orbital and configuration mixing amplitudes. The Hartree-Fock self-consistent field (SCF), configuration interaction (Cl), multiconfigurational SCF (MCSCF), many-body and Mpller-Plesset perturbation theories,... 

Multiconfiguration SCF (MCSCF) Theory and Complete Active Space SCF (CASSCF) Theory... 

Efficient techniques for optimizing orbitals have been elaborated in multiconfiguration SCF (MCSCF) theory (see e.g. the book by McWeeny [134] and refs, therein). Since the APSG wave function represents a special class among MCSCF functions, these procedures can be applied to determine the optimal Arai-subspaces [65],... 

The integral-driven procedure indicated above is practicable only if the elements of the two-particle density matrix can be rapidly accessed. In the closed-shell Hartree-Fock case, the two-particle density matrix can be easily constructed from the one-particle density. The situation is similar for open-shell and small multiconfigurational SCF wavefunctions the two-particle density matrix can be built up from a few compact matrices. In most open-shell Hartree Fock theories (Roothaan, 1960), the energy expression (Eq. (23))... 

Configuration Interaction Density Functional Theory Equation of Motion CCSD Multiconfiguration-SCF Moller Plesset 2nd Order Multireference Cl Multistate CASPT2 Restricted Active Space SCF Restricted Hartree Fock Symmetry Adapted Cluster-CI Self Consistent Field Singlestate CASPT2... 

A b initio quantum chemical studies of hyperfine structures (hfs) were initiated some 25 years ago, with the pioneering work of Meyer and others [127]. However, results from the early Hartee-Fock-based methods deviated considerably from experimentally determined hf parameters. It was not until the configuration interaction (Cl) techniques were fully developed for hfs calculations, that theoretical predictions of high accuracy were possible for atomic and molecular radicals [20]. This is mainly associated with the importance of electron correlation and with the development of new and fax larger basis sets. In later years, hfs calculations have also been carried out with great success using various levels of multiconfiguration SCF (MCSCF) [21], multireference Cl (MRCI) [22] and coupled cluster (CC) theory [23]. 

T. Helgaker, P. Jprgensen, J. Olsen, Molecular electronic structure theory, Wiley, Chichester, 2000. B.O. Roos, Multiconfigurational (MC) self-consistent (SCF) theory, in B.O. Roos, P.-O. Widmark (Eds.), European summer school in quantum chemistry, book II, Lund University, Lund, Sweden, 2000. 

---