Wolfsberg-Helmholtz formula

The tight-binding band structure calculations were based upon the effective one-electron Hamiltonian of the extended Huckel method. [5] The off-diagonal matrix elements of the Hamiltonian were calculated acording to the modified Wolfsberg-Helmholtz formula. All valence electrons were explicitly taken into account in the calculations and the basis set consisted of double- Slater-type orbitals for C, O and S and a single- Slater-type orbitals for H. The exponents, contraction coefficients and atomic parameters were taken from previous work [6],... 

The off-diagonal elements are calculated by the Wolfsberg-Helmholtz formula... 

The origin of the difficulty with the numerical scale factor k in the Wolfsberg-Helmholtz formula (5) lies chiefly in the variation of kinetic-energy matrix elements with distance apart of the two atoms involved. 

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. 

Our conclusions in this paper would not be significantly altered if, instead of the arithmetic mean in (5), we used the Wolfsberg-Helmholtz-Mulliken geometrical-mean formula recently advocated by Allen and Russell. ... 

This formula is often called the Wolfsberg-Helmholtz relation. 

Equation (3.43) resembles the formula [equation (3.44)] adopted by Wolfsberg and Helmholtz [59] for the interaction matrix elements. This form, with the empirical factor — 1.75, was adopted by Hoffmann in his derivation of extended Hiickel theory [60], namely... 

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