Orbital and Configuration Correlation

The deviation of the CASSCF curve from the FCI curve in Fig. 2 is caused by nonstatic or dynamical correlation [1]. Although dynamical correlation is usually less geometry-dependent than static correlation, it must be included for high accuracy (see Sec. 4). One might think that it is possible to include the effects of dynamical correlation simply by extending the active space. For small molecules, this is, to some extent true, in particular when using the techniques of restricted active space SCF (RASSCF) theory [46]. Nevertheless, because of the enormous number of determinants needed to recover dynamical correlation, the simultaneous optimization of orbitals and configuration coefficients as done in MCSCF theory is not a practical approach to the accurate description of electronic systems. 

The level of electronic structure theory used by Mikkelsen et al. [37] is given by the multiconfigurational (MC) selfconsistent field (SCF) where the wavefunction is fully optimized with respect to all variational parameters these include both orbital and configurations. The main deficiency of standard SCF ab initio procedures, namely, lack of correlation effects, is overcome in this MCSCF approach. The level of solvent-effects theory is the standard spherical cavity immersed in a continuum dielectric an early formalism proposed by Rinaldi and Rivail was used (see Ref. [6] for an extensive analysis). 

Before examining the standard models in any detail, we consider in Section 5.2 the representation of the electronic structure of the hydrogen molecule in a variational space of two orbitals. The purpose of this simple exercise is to familiarize ourselves with the way in which electronic states are represented by Slater determinants, with emphasis on the interplay between orbitals and configurations and on the description of electron correlation by means of superpositions of configurations. 

The mean-field potential and the need to improve it to aohieve reasonably aeourate solutions to the true eleotronio Selirodinger equation introduoe three oonstniots that oharaoterize essentially all ab initio quantum ohemioal methods orbitals, configurations and electron correlation. 

Seetion treats the spatial, angular momentum, and spin symmetries of the many-eleetron wavefunetions that are formed as anti symmetrized produets of atomie or moleeular orbitals. Proper eoupling of angular momenta (orbital and spin) is eovered here, and atomie and moleeular term symbols are treated. The need to inelude Configuration Interaetion to aehieve qualitatively eorreet deseriptions of eertain speeies eleetronie struetures is treated here. The role of the resultant Configuration Correlation Diagrams in the Woodward-Hoffmann theory of ehemieal reaetivity is also developed. 

Lowdin, P.-O., Phys. Rev. 97, 1474, 1490, 1509, Quantum theory of many-particle systems. I. Physical interpretations by means of density matrices, natural spin-orbitals and convergence problems in the method of configuration interaction. II. Study of the ordinary Hartree-Fock approximation. III. Extension of the Har-tree-Fock scheme to include degenerate systems and correlation effects. ... 

Fig. 7. Orbital (a), configuration (b), and state (c, d) correlation diagrams for a typical ground-state symmetry-forbidden pericyclic reaction...

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