Formula Wolfsberg-Helmholz

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... 

The resonance integrals may be calculated directly from the group overlap integrals either by assuming a proportionality constant k of the order 3 to 7 eV or by using a Wolfsberg-Helmholz formula (Sec. II.A). For simplicity we shall simply consider the one value of k, namely, 3.0 eV. The resonance integrals are then simply three times the values listed above in electron volts. 

The offp), 77ffp), and offs) quantities can be calculated using the Wolfsberg-Helmholz formula [17]... 

Here ( and j span the n atomic orbitals in the basis set of valence orbitals (core electrons are neglected) and the coefficients 7 j- are chosen to diagonalize the Hamiltonian matrix. The quantity S,y is the overlap integral between orbital i and orbital j. EHT approximates the off-diagonal matrix elements Hi - by the Wolfsberg-Helmholz formula/98/... 

In some cases, a distance-dependent exponential factor, KAIS, different from that mentioned above, is also included to correct the off-diagonal EHMO matrix elements and is calculated by the empirical weighted Wolfsberg-Helmholz formula. It considers the Hamiltonian off-diagonal elements, //, , by the following expression ... 

According to the Wolfsberg-Helmholz formula (24), the /3 parameters can be regarded as diagonal terms of the CNDO Fock matrix. 

To start with, the diagonal (on-site) matrix elements are taken as the experimental ionization potentials derived from spectroscopic data of the valence levels. The nondiagonal (off-site) interaction elements H a, however, are approximated as some arithmetic average of the values of the interacting atomic orbitals according to the Wolfsberg-Helmholz formula [112] ... 

The ofif-diagonal elements is determined using the Wolfsberg-Helmholz formula from the extended Hiickel method as ... 

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) ... 

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