Explicitly correlated wave function theory

Explicitly correlated wave function fheory [14] is anofher imporfanf approach in quantum chemistry. One introduces inter-electron distances together with the nuclear-electron distances and set up some presumably accurate wave function and applies the variation principle. The Hylleraas wave function reported in 1929 [15] was the first of this theory and gave accurate results for the helium atom. Many important studies have been published since then even when we limit ourselves to the helium atom [16-28]. They clarified the natures and important aspects of very accurate wave functions. However, the explicitly correlated wave function theory has not been very popularly used in the studies of chemical problems in comparison with the Hartree-Fock and electron correlation approach. One reason was that it was generally difficult to formulate very accurate wave functions of general molecules with intuitions alone and another reason was that this approach was rather computationally demanding. 

J. Rychlewski (ed.) Explicitly Correlated Wave Functions in Chemistry and Physics. Theory and Applications. 2003 ISBN 1-4020-1674-3... 

Rychlewski J (2003) Explicitly correlated wave functions in chemistry and physics — theory and applications. Kluwer Academic, Dordrecht... 

The common feature of the explicitly correlated approaches discussed so far is that the whole wave function is expanded in explicitly correlated basis functions. Kutzelnigg and Klopper proposed a different approach, initially at the MP2 level of theory ]16]. The general idea of Kuztelnigg and Klopper was to supplement the conventional Cl expansion with the explicitly correlated part in the following way... 

Finally, algorithms have been developed which incorporate electron correlation effects explicitly in wave function based band theory for crystalline solids [16, 17]. These algorithms construct the many-electron Hamiltonian matrix for a periodic system by extracting the matrix elements from calculations on finite embedded clusters. In this way the incorporation of correlation effects leads to many-electron energy bands, not only associated with hole states and added-electron states but also with excited states. More recently, Pisani and co-workers [18] introduced a post-Hartree-Fock program based on periodic local second order Mpller-Plesset perturbation theory. 

However, the introduction of the RI approximation led to the need for large basis sets. In old R12 method, only one single basis was used for both the electronic wave function and the RI approximation. The new formulation of R12 theory presented here uses an independent basis set denoted auxiliary basis set for the RI approximation while we employ a (much) smaller basis set for the MP2 wave function (7). This auxiliary basis set makes it possible to employ standard basis sets in explicitly correlated MP2-R12 calculations. 

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