Multiconfigurational wave function electron correlation

The difficulties are mainly caused by two problems (1) the fact that even a qualitatively correct description of excited states often requires multiconfigurational wave functions and (2) that dynamic electron correlation effects in excited states are often significantly greater than in the electronic ground states of molecules, and may also vary greatly between different excited states. For explanations of the concepts invoked in this section, see Section 3.2.3 of Chapter 22 in this volume. Therefore, an accurate modeling of electronic spectra requires methods that account for both effects simultaneously. 

The major difficulty in wave function based calculations is that, starting from an independent-particle model, correlation between electrons of opposite spin must somehow be introduced into T. Inclusion of this type of electron correlation is essential if energies are to be computed with any degree of accuracy. How, through the use of multiconfigurational wave functions, correlation between electrons of opposite spin is incorporated into is the subject of Section 3.2.3. 

Malcolm NOJ, McDouall JJW (1996) Combining multiconfigurational wave functions with density functional estimates of dynamic electron correlation, J Phys Chem, 100 10131-10134... 

Ab initio MO methods based on HF or small multiconfigurational wave-functions have been the method of choice, up to the present, for studies of organic systems and other molecules with light nuclei. The properties of stable species on the PES are often reproduced very well by calculations with just HF wavefunctions. Studies of reactions usually require the more sophisticated and expensive techniques, such as Cl or MP perturbation theory, that take into account the effects of the correlation between the electrons that is omitted from the HF approximation. The additional energy lowering computed with these methods with respect to that obtained with an HF calculation is called the correlation energy. A detailed and up-to-date discussion of the accuracy of state-of-the-art MO methods when applied to a variety of problems may be found in the book by Hehre et al. 

When the HF wave function gives a very poor description of the system, i.e. when nondynamical electron correlation is important, the multiconfigurational SCF (MCSCF) method is used. This method is based on a Cl expansion of the wave function in which both the coefficients of the Cl and those of the molecular orbitals are variationally determined. The most common approach is the Complete Active Space SCF (CASSCF) scheme, where the user selects the chemically important molecular orbitals (active space), within which a full Cl is done. 

It is possible to divide electron correlation as dynamic and nondynamic correlations. Dynamic correlation is associated with instant correlation between electrons occupying the same spatial orbitals and the nondynamic correlation is associated with the electrons avoiding each other by occupying different spatial orbitals. Thus, the ground state electronic wave function cannot be described with a single Slater determinant (Figure 3.3) and multiconfiguration self-consistent field (MCSCF) procedures are necessary to include dynamic electron correlation. 

Another class of methods uses more than one Slater determinant as the reference wave function. The methods used to describe electron correlation within these calculations are similar in some ways to the methods listed above. These methods include multiconfigurational self-consistent field (MCSCF), multireference single and double configuration interaction (MRDCI), and /V-clcctron valence state perturbation theory (NEVPT) methods.5... 

Inclusion of Electron Correlation. HF calculations, performed with basis sets so large that the calculations approach the HF limit for a particular molecule, still calculate total energies rather poorly. The reason is that, as already discussed, HF wave functions include no correlation between electrons of opposite spins. In order to include this type of correlation, multiconfigurational (MC) wave functions, like that in Eq. 5, must be used. 

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