Outermost core

Hay, P. J. and Wadt, W. R. (1985) Ah initio effective core potentials for molecular calculations. Potentials for K to Au including the outermost core oribitals. 

The Self-Consistent (SfC) (G)RECP version [23, 19, 24, 27] allows one to minimize errors for energies of transitions with the change of the occupation numbers for the OuterMost Core (OMC) shells without extension of space of explicitly treated electrons. It allows one to take account of relaxation of those core shells, which are explicitly excluded from the GRECP calculations, thus going beyond the frozen core approximation. This method is most optimal for studying compounds of transition metals, lanthanides, and actinides. Features of constructing the self-consistent GRECP are ... 

This Hamiltonian is written only for a valence subspace of electrons which are treated explicitly and denoted by indices and jv In practice, this subspace is often extended by inclusion of some outermost core shells for better... 

P. J. Hay and W. R. Wadt, /. Chem. Phys., 82, 299 (1985). Ah Initio Effective Core Potentials for Molecular Calculations. Potentials for K to Au Including the Outermost Core Electrons. 

Generation of the REPs is perhaps the most critical step in the derivation of an ECP/valence basis set scheme. The major question is What core size to use The choice of orbitals to include in the core is fraught with uncertainty. One needs to strike a balance between chemical accuracy and the desire to replace as many core electrons as possible. Replacement of all core electrons by the potential (full-core ECPs) is most prevalent for p-block elements, but not replacing the outermost core electrons (semicore ECPs) is the norm for d- and f-block metals. -i° This issue is discussed in detail in the survey of ECP applications later in this chapter. 

This Hamiltonian is written only for a valence subspace of electrons that are treated explicitly and denoted by indices and j (large-core approximation). As in the case of nonrelativistic pseudopotentials, this subspace is often extended by inclusion of some outermost core shells for better accuracy (smaU-core approximation) but below we consider them as the valence shells if these outermost core and valence shells are not treated using different approximations. In (8.55), h is the one-electron Schrodinger Hamiltonian... 

Most pseudopotentials do not retain the correct nodal structure of the valence orbitals, i.e., the (n — l)s orbital which describes the outermost core electrons is nodeless, the (n)s valence orbital has one node, etc. This approach is termed effective core potential (ECP). The so-called ab initio model potential (AIMP) has the correct nodal structure, i.e., the (n — l)s orbital has n —2 nodes, the (n)s orbital has n — 1 nodes, etc. Comparative studies have shown that the nodeless ECPs, which have the benefit of allowing the basis set to be reduced in size thus offering an additional economic advantage, give equally accurate results as AIMP methods. This is the reason why ECPs are more frequently used for calculating heavy-atom molecules than AIMPs. 

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