Multiconfigurational Self-Consistent Field method MC SCF

In the configuration interaction method, it is sometimes obvious that certain determinants of the Cl expansion must contribute to the wave function, if the latter is to correctly describe the system. For example, if we want to describe the system in which a bond is being broken (or is being formed), for its description we need several determinants for sure (cf. description of the dissociation of the hydrogen molecule on p. 371). 

Each of the determinants is constructed from molecular spinorbitals which are not fixed (as in the Cl method) but are modified in such a way as to have the total energy as low as possible. 

The MC SCF method is the most general scheme of the methods that use a linear combination of Slater determinants as an approximation to the wave function. In the limiting case of the MC SCF, when the number of determinants is equal to 1, we have, of course, the Hartree-Fock method. 

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The MC SCF (Multiconfiguration Self Consistent Field) method is similar to the Cl scheme, but we vary not only the coefficients in front of the Slater determinants, but also the Slater determinants themselves (changing the analytical form of the orbitals in them). We have learnt about two versions the classic one (we optimize alternatively coefficients of Slater determinants and the orbitals) and a unitary one (we optimize simultaneously the determinantal coefficients and orbitals). 

J. Hinze. MC-SCF. 1. The multiconfiguration self-consistent-field method. /. Chem. Phys., 59(12) (1973) 6424-6432. 

In order to make up for those imperfections one needs to turn to post-Hartree-Fock methods. Two variational techniques are worth discussing due to their popularity the configuration-interaction (SCF Cl) method and the multiconfiguration self-consistent-field (MC SCF) method. 

Complete multiconfiguration-self consistent-field (CMC-SCF) technique designates the method where a given occupied molecular orbital of the set is excited to all unoccupied molecular orbitals. If an occupied orbital is excited to one or more, but not all, of the unoccupied orbitals, the technique is described as incomplete MC-SCF (IMC-SCF). The reader is referred to refs. 13 and 14 for details of the derivation. The CMC-SCF formalism differs from most many body techniques presented to date insofar as the Hartree-Fock energy is not assumed to be the zero order energy. 

In the multiconfigurational self-consistent field (MC SCF) method, as in Cl, it is up to us to decide which set of determinants we consider sufficient for the description of the system. 

The calculations are not all at exactly the same bond length R. The basis set is indicated after the slash in the method. R, L, C, and T are basis sets of Slater-type functions. The aug-cc-pVDZ and aug-cc-pVTZ basis sets [360] are composed of Gaussian functions. SCF stands for self-consistent-field MC, for multiconfiguration FO, for first-order Cl, for configuration interaction MR, for multireference MPn, for nth-order Mpller-Plesset perturbation theory and SDQ, for singles, doubles, and quadruples. 

The standard method for selecting the 4>j is to ask for the <)>i which maximize the importance of one or more terms in the sum. This gives the self-consistent-field (SCF) or multiconfiguration SCF (MC-SCF) equations. If each < >. is expanded as a linear combination of some fixed set of basis functions f - the coefficients can be found by an extension of the Roothaan SCF equations. 

C. Froese Fischer, Self-Consistent-Field (SCF) euid Multiconfiguration (MC) Hartree-Fock (HF) Methods in Atomic Calculations Numerical Integration Approaches, Comput. Phys. Rep. 3 (1986) 273-325. 

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