Wolfsberg-Helmholz relation

In general, the semiempirical approach has been widely adopted in inorganic systems, and the most common approximation is either to assume that Hu is directly proportional to the overlap integral Sij9 or related to it by a Wolfsberg-Helmholz type of formula (43) ... 

The next step is to evaluate the coulomb and resonance integrals. Direct calculation of the latter requires specification of the Hamiltonian and hence explicit account of electron-repulsion terms, which is very difficult for these complex molecules. Accordingly, it is usual to make the earlier assumptions that is, either the resonance integral is directly proportional to the overlap integral or is related to it by a Wolfsberg-Helmholz formula... 

It may hence be pertinent to draw the attention to two kinds of development of ligand field theory which have taken place since 1962. They are both related to the Wolfsberg-Helmholz model (27) where it is assumed that the non-diagonal elements between orbitals centered on afferent atoms are proportional to the product of their overlap integral and their average energy with a proportionality constant k usually assumed to have values between 1.6 and 2. Thus, the secular determinant for two interacting orbitals is ... 

Both Hartree-Fock and Wolfsberg-Helmholz and related methods have been applied to metal carbonyl compounds. The Hartree-Fock method 90) treats each electron as moving in a potential field due to the nuclei and to the charge-density of all the other electrons. The interelectronic repulsion potential takes account of the tendency of electrons of parallel spin to avoid each other (exclusion), but not of correlation due to electron-electron repulsion independent of spin ). The field due to some assumed electron distribution is evaluated, and wave-functions calculated for motion in that field. When sufficiently close agreement between assumed and calculated wave-functions is finally obtained, the solution is said to be self-consistent . 

It is necessary to evaluate (3 in Equation (5.9) by fitting to some experimental data. One method has been to use the Mulliken criteria relating (3 to / and S. This was first done by Wolfsberg and Helmholz. It requires separate consideration of s and p orbitals, however. 

---