Non-dynamic correlation

However, if this is not the case, the perturbations are large and perturbation theory is no longer appropriate. In other words, perturbation methods based on single-determinant wavefunctions cannot be used to recover non-dynamic correlation effects in cases where more than one configuration is needed to obtain a reasonable approximation to the true many-electron wavefunction. This represents a serious impediment to the calculation of well-correlated wavefunctions for excited states which is only possible by means of cumbersome and computationally expensive multi-reference Cl methods. 

Luckily, this impasse was removed through the recent introduction of the CASPT2 model, which combines a powerful procedure for treating cases of strong non-dynamic correlation (CASSCF) with a very economical one for treating dynamic correlation296. As will be shown below, the CASPT2 method works very well for polyene radical cations. 

The treatment of systems where non-dynamic correlation is critical is quite more complicated from a methodological point of view. As mentioned above, non-dynamic correlation is associated to the presence of neardegeneracies in the electronic ground state of the system, which means that there are Slater determinants with a weight similar to that of the HF solution in equation 4. The problem of non-dynamic correlation is usually treated successfully by the CASSCF method [43] for organic systems. This method introduces with high accuracy the correlation in the orbitals involved in the near degeneracy, which constitute the so called active space. The problem in... 

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. 

Breaking the Curse of the Non-Dynamical Correlation Problem The Spin-Flip Method... 

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. 

It is, however, for the transition metals themselves that DFT has proven to be a tremendous improvement over HF and post-HF methods, particularly for cases where tlie metal atom is coordinatively unsaturated. The narrow separation between filled and empty d-block orbitals typically leads to enormous non-dynamical correlation problems with an HF treatment, and DFT is much less prone to analogous problems. Even in cases of a saturated coordination sphere, DFT methods typically significantly ouqierform HF or MP2. Jonas and Thiel (1995) used the BP86 functional to compute geometries for the neutral hexacarbonyl complexes of Cr, Mo, and W, the pentacarbonyl complexes of Fe, Ru, and Os, and the tetracarbonyl... 

The use of computed spectra to bolster structural assignments has seen heavy use in matrix isolation experiments. This is a slightly atypical example, insofar as the species involved actually require some careful attention to non-dynamical correlation, but represents an excellent example of how theory can aid experiment in the identification of short-lived reactive species. 

Krylov, A. I., Slipchenko, L. V., and Levchenko, S. V. Breaking the Curse of the Non-dynamical Correlation Problem the Spin-Flip Method , ACS Symp. Ser., in press. 

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