Electron correlation static

The Slater—Condon integrals Ft(ff), Ft(fd), and Gj-(fd), which represent the static electron correlation within the 4f" and 4f 15d1 configurations. They are obtained from the radial wave functions R, of the 4f and 5d Kohn—Sham orbitals of the lanthanide ions.23,31... 

Accounting for Static Electron Correlation within CASSCF... 

As an example, the results for formation of the donor-acceptor bond in MejN-BMCj are shown in Figure 16.4. Such bonds (and their strengthening by dispersion and weakening by EXR effects) play an important role in the so-called frustrated Lewis pairs (FLP), which have attracted enormous attention recently because of their ability to activate small molecules such as H2 [35-37]. Because the bond dissociates heterolyticaUy into closed-shell fragments, static electron correlation effects play no important role and a standard restricted DFT treatment... 

All molecules with more than one electron experience dynamic electron correlation the choice of the term is self-evident each electron sees each other electron as a moving particle to be avoided. Some molecules have highest-occupied MOs of equal or nearly equal energy, each with one electron, and so require a computational approach in which the electrons are not taken to be paired in spatial MOs these molecules experience static electron correlation, so-called possibly... 

The MCSCF provides a good first-order description covering the static electron correlation due to degeneracy problems. Dynamic electron correlation should be addressed with the MCSCF wave function as a reference. The multireference configuration interaction, or MRCI, generates excited determinants from all (or selected) determinants included in the MCSCF. The complete active space perturbation theory, second order (CASPT2) is a more economical approach. Both methods can be applied to compute excited states. 

A natural starting point is to combine a multiconfigurational SCF approach to treat the static electron correlation and DFT for the remaining (mainly dynamic) electron correlation. It is, however, not easy to design functionals that only take into account this latter part of the electron correlation and do not consider (part of) the static correlation. Despite many efforts, there seems no deflnitive solution to the double counting problem. 

Usually, two different types of electronic correlation are distinguished, the static electronic correlation and the dynamic electronic correlation. Although this distinction is by no means strict, it is useful because the two types of electronic correlation have different physical origins and different methods can be used to recover one or the other type of correlation. 

MC approaches [30] involve the optimization of molecular orbitals within a restricted subspace of electronic occupations provided such active space is appropriately chosen, they allow for an accurate description of static electron correlation effects. Dynamical correlation effects can also be introduced either at the perturbation theory level [complete active space with second-order perturbation theory (CASPT2), and multireference Mpller-Plesset (MR-MP2) methods] [31] or via configuration interaction (MR-CI). 

State averaged MCSCF, 147 State correlation diagram, 356 St4te selected CI/MCSCF, 123 Static electron correlation, 118 Static properties, 235 Statistical error, 375... 

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