Multiconfiguration self-consistent field MC.SCF

J. Olsen, D.L.Yeager, and P. Jorgensen, Optimization and characterization of a Multiconfigurational Self-Consistent Field (MC-SCF) State", in Adv. Chem. Phys. 54,1 (1983). 

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. 

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. 

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. 

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 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. 

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 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. 

An integral equation formalism (lEF) has been developed as particularly suitable for the description of solvent effects on spectral transition energies within the PCM model. The respective theoretical equations have been applied for the calculation of solvatochromic shifts of several carbonyl-group containing molecules at the self-consistent field (SCF), configuration interaction (Cl) and multiconfiguration self-consistent (MC SCF) field level of theory. The calculated spectral shifts accompanying the transfer of a solvatochromic compound from the gas phase to water were comparable with the experimental data. In Table 11.1.4, the results of calculations are presented for three carbonyl compounds, formaldehyde, acetaldehyde and acetone. 

B. O. Roos, in Lecture Notes in Quantum Chemistry (Lecture Notes in Chemistry, Vol. 58), B. O. Roos, Ed., Springer, Berlin, 1992, pp. 177-254. The Multiconfigurational (MC) Self-Consistent Field (SCF) Theory. 

Roos BO. Multiconfigurational (MC) Self-Consistent-Field (SCF) Theory. In Widmark P-O, editor. European Summer School in Quantum Chemistry, Book II. Lund Lund University 2009. Grein F, Chang TC. Multiconfiguration wavefunctions obtained by application of the generalized Brillouin theorem. Chem Phys Lett. 1971 12 44. 

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