Slater Coulomb integrals

While in principle all of the methods discussed here are Hartree-Fock, that name is commonly reserved for specific techniques that are based on quantum-chemical approaches and involve a finite cluster of atoms. Typically one uses a standard technique such as GAUSSIAN-82 (Binkley et al., 1982). In its simplest form GAUSSIAN-82 utilizes single Slater determinants. A basis set of LCAO-MOs is used, which for computational purposes is expanded in Gaussian orbitals about each atom. Exchange and Coulomb integrals are treated exactly. In practice the quality of the atomic basis sets may be varied, in some cases even including d-type orbitals. Core states are included explicitly in these calculations. 

Alternatively, these one-center coulomb integrals can be computed from first principles using Slater or Gaussian type orbitals. 

Here, F2 and G1 represent the well known Slater-Condon integrals in terms of which the coulomb and exchange integrals can be expressed ... 

It has been shown in Pariser and Parr s early articles78 82 that the main corrections were (a) a strong reduction of the one-center Coulomb integrals (pp pp) with respect to their value calculated with atomic Slater orbitals. In practice, the value to adopt is the... 

The next fundamental hypothesis in the CNDO procedure concerns the values of the Coulomb integrals which are all approximated as Coulomb integrals over 2s Slater atomic orbitals. If p. and v are on the same atom A ... 

The first of these methods was developed by Hoffmann in 1963 (1) and is known as extended Hiickel theory (EHT). Briefly, the method uses Hiickel formalism however, explicit consideration of non-bonded interactions and all overlap integrals are a refinement. Slater orbitals are used, and the computations require only one parameter, the valence state ionization potential for the Coulomb integral and indirectly for the reso-... 

The extended Hiickel theory calculations, used in this work and discussed below, are based on the approaches of Hoffmann Although VSIP values given by Cusachs, Reynolds and Barnard were explored for use as the Coulomb integrals, the VSIP values obtained from a Hartree-Fock-Slater approximation by Herman and Skillman were consistently used in the present EHT calculations by this author. Both the geometric mean formula due to Mulliken and Cusachs formula ) were considered for the Hamiltonian construction, but the Mulliken-Wolfsberg-Helmholtz arithmetic mean formula was chosen for use. 

The one-center Coulomb integrals (/x/x vv) = F v are calculated analytically while the G integrals are taken as parameters. The IP are taken from atomic spectra. After rearranging Eq. (43), the Uss are obtained. A special feature of INDO/S is the use of distance-dependent Slater exponents for the calculation of two-center integrals [55],... 

Appendix 1 Fitting of 5-type Primitive Gaussian Orbitals that Best Reproduce Two-Electron Coulomb Integrals over 5-Type Slater Orbitals... 

In this appendix, we describe how we found the exponents given in Table 1, which are of x-type primitive Gaussian orbitals such that the two-electron Coulomb integrals over them best reproduce those over s-type Slater orbitals. We construct... 

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