Correlation energy non-dynamical

Proton transfer and non-dynamical correlation energy in model molecular... 

The essential part of non dynamical correlation energy for polyatomic molecules is the left-right electron correlation , which is concerned with the ionic-covalent balance within a given two-electron bond. Let us therefore discuss this type of correlation. 

DFT theory even seems to improve the performance of MP2 in cases where there is some small contribution of non dynamic correlation. This is seemingly the case in the BP86 computed first dissociation energies of a variety of metal carbonyls [51]. For instance, in the case of Cr(CO)6, the BP86 value is 192 kJ/mol, in exact (probably fortuitous) agreement with the (computationally most accurate) CCSD(T) value of 192 kJ/mol, but also reasonably close to the experimental value of 154 8 kJ/mol. In this case, the GGA DFT result improves clearly the local DFT SVWN value of 260 kJ/mol, and the MP2 result, wich is 243 kJ/mol. Comparable results can be found for the optimization of the Os-O distance in OsC>4 [52], which is relevant concerning olefin dihydroxylation. 

If we assume that we do not have any problem with non-dynamical correlation, we may assume that there is little need to reoptimize the MOs even if we do not plan to carry out the expansion in Eq. (7.10) to its full CI limit. In that case, the problem is reduced to determining the expansion coefficients for each excited CSF that is included. The energies E of N different CI wave functions (i.e., corresponding to different variationally determined sets of coefficients) can be determined from the N roots of the CI secular equation... 

While fewer data are available, the utility of DFT in computing the bond strengths between transition metals and hydrides, methyl groups, and methylene groups has also been demonstrated (Table 8.2). Because of the non-dynamical correlation problem associated with the partially filled metal d orbitals, such binding energies are usually very poorly predicted by MO theory methods, until quite high levels are used to account for electron correlation. 

A curious effect, prone to appear in near degeneracy situations, is the artifactual symmetry breaking of the electronic wave function [27]. This effect happens when the electronic wave function is unable to reflect the nuclear framework symmetry of the molecule. In principle, an approximate electronic wave function will break symmetry due to the lack of some kind of non-dynamical correlation. A typical example of this case is the allyl radical, which has C2v point group symmetry. If one removes the spatial and spin constraints of its ROHF wave function, a lower energy symmetry broken (Cs) solution is obtained. However, if one performs a simple CASSCF or a SCVB [28] calculation in the valence pi space, the symmetry breaking disappears. On the other hand, from the classical VB point of view, the bonding of the allyl radical is represented as a superposition of two resonant structures. 

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