Semilocalized atomic orbitals

Mueller, C. R., J. Chem. Phys. 19, 1498, Scmilocalized orbitals. II. A comparison of atomic, molecular and semilocalized orbital methods for diatomic hydrogenfluoride. ... 

Here, a and b are purely localized AOs, while Coulson—Fischer orbitals energy minimization, are generally not very delocalized (e < 1), and as such they can be viewed as distorted orbitals that remain atomic-like in nature. However, minor as this may look, the slight delocalization renders the Coulson—Fischer wave function equivalent to the VB-full wave function (Eq. 3.4a) with the three classical structures. A straightforward expansion of the Coulson—Fischer wave function leads to the linear combination of the classical structures in Equation 3.6. 

The analytical forms of the modern PPs used today have little in common with the formulas we obtain by a strict derivation of the theory (Dolg 2000). Formally, the pseudo-orbital transformation leads to nodeless pseudovalence orbitals for the lowest atomic valence orbitals of a given angular quantum number l (one-component) or Ij (two-component). The simplest and historically the first choice is the local ansatz for A VCy in Equation (3.4). However, this ansatz turned out to be too inaccurate and therefore was soon replaced by a so-called semilocal form, which in two-component form may be written as... 

Compact one- and two-Gaussian expansions for the components of the effective potentials of atoms in the first two rows are presented by Stevens-Basch-Krauss [485]. Later, the list of ECP was extended to the third-, fourth- and fifth-row atoms [486] and includes relativistic ECP (RECP). The pseudo-orbital basis-set expansions for the first two rows of atoms consist of four Gaussian primitives using a common set of exponents for the s and p functions. Analytic SBK RECP are generated in order to reproduce POs and eigenvalues as closely as possible. The semilocal SBK ECP are given by... 

Spin-orbit effects can be incorporated using a two-component relativistic method for the atom such as the Wood-Boring method. In this case, the usual representation is a semilocal form as is used in the pseudopotential method. 

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