Correlation energy origin

For all results in this paper, spin-orbit coupling corrections have been added to open-shell calculations from a compendium given elsewhere I0) we note that this consistent treatment sometimes differs from the original methods employed by other workers, e.g., standard G3 calculations include spin-orbit contributions only for atoms. In the SAC and MCCM calculations presented here, core correlation energy and relativistic effects are not explicitly included but are implicit in the parameters (i.e., we use parameters called versions 2s and 3s in the notation of previous papers 11,16,18)). 

With an appropriate /(r12) function, e.g., in the original linear form f(r-[2) — C12, the operator product r firu) is no longer singular. Such cancellation is not possible with Slater determinants alone and this is what allows explicitly correlated wave functions to achieve accurate correlation energies with relatively small basis sets. With the single explicitly correlated term, therefore, we effectively include a linear combination of an infinite set of Slater determinants, but without the need to solve an infinite set of equations to determine the corresponding amplitudes. The R12 method constructs wave functions that are more compact and computationally tractable than naive Slater-determinant-based counterparts. 

In this section we shall discuss an approach which is neither variational nor perturba-tional. This approach also has its origin in nuclear physics and was introduced to quantum chemistry by Sinanoglu47, It is based on a cluster expansion of the wave function. A systematic method for the calculation of cluster expansion components of the exact wave function was developed by C ek48 The characteristic feature of this approach is the expansion of the wave function as a linear combination of Slater determinants. Formally, this expansion is similar to the ordinary Cl expansion. The cluster expansion, however, gives us not only the physical insight of the correlation energy but it also shows the connections between the variational approaches (Cl) and the perturbational approaches (e.g. MB-RSPT). 

For the details and derivation of the physical interpretation we refer the reader to the original literature14,15. Since the Coulomb self-energy component of the KS electron-interaction energy functional and its derivative, the Hartree potential, are known functionals of the density, we provide in Section HA the expressions governing the interpretation of the KS exchange-correlation energy... 

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