NON-HARTREE-FOCK SEMIEMPIRICAL QUANTUM CHEMISTRY

In the previous section we described existing HFR-based semiempirical methods and demonstrated their hybrid nature in a wide sense. We have also shown that for certain physical situations the semiempirical methods may become invalid due to the necessity to explicitly address nontrivial electronic correlations manifesting themselves either in numerous Slater determinants to be included in the consideration or in nonvanishing matrix elements of the cumulant of two-electron density matrix whose presence must be somehow reproduced in the calculation. 

The standard prescription in this situation would be to apply the ab initio methods and to attempt to take into account missing correlations in their framework. This is, however, possible only for the systems of very modest size due to the M5 -=-M7 scalability of the correlated ab initio methods already mentioned. Using DFT methods in the situation when explicit correlations are necessary may be completely wrong, due to the structural deficiency of this class of methods, which precludes any treatment of nontrivial parts of correlations, requiring multiconfigurational wave function. 

Our account of the cumulant properties indicates, however, another possibility to develop a local correlated theory such that the correlations are taken into account only for some specific electronic groups of the entire system (chromophores) while the rest is treated on a noncorrelated level. The cumulant being a local quantity restricted to only one group can be then economically estimated by some appropriate method. Of course such an approach would require parametrization of the semiempirical method 

A semiempirical method can be developed for the arbitrary form of the trial wave function of electrons, which is predefined by the specific class of molecules to be described and by the physical properties and/or effects which have to be reproduced within its framework. Two characteristic examples will be considered in this section. One is the strictly local geminal (SLG) wave function the other is the somewhat less specified wave function of the GF form selected to describe transition metal complexes. 

One more achievement along the geminal way may be that the HFR based semiempirics scales as N3 with the increase of the size of the system. Working in the basis of strictly local HOs in the SLG framework opens up the prospect of obtaining the linearly scaling semiempirical method. 

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