Valence state ionization potentials

I means the valence state ionization potential for the atomic orbital n, stands for the core charge, and Cj, and Xm are coefficients and atomic orbitals in the LCAO expansion... 

For example, the ir-eiectron energy change in the dimerization of benzyl is taken as a twofold difference in the rr-electron energies of benzene and benzyl. With the SCF data, a double value of the valence state ionization potential of carbon [I in eq. (25)] has to be added to this difference. The entries of Table XII show that in all equilibria considered, a dimer is favored. 

H is the one-electron operator and i is the Slater basis set function (2s, 2p). The diagonal elements of Htj (Hit) are approximated as the valence state ionization potentials and the off-diagonal elements Htj are estimated using the Wolfsberg-Helmholtz approximation,... 

The valence state ionization potential —the resonance integrals and the one-center electron repulsion integrals can be considered as basic parameters of the semiempirical method and can be adjusted to give optimal agreement. The core charges Z, indicate the number of 71 electrons the center M contributes to the n system, and the two-center electron repulsion integrals are obtained from an empirical relationship such as the Mataga-Nishimoto formula ... 

Using the corrected w-SCF MO procedure (an empirical diminution of the values of the atomic valence-state ionization potentials). 

The parameter a is evaluated from valence state ionization potentials Ii and electron affinity At in the same valence state. Two distinct cases may arise ... 

Here It and I) are the valence-state ionization potentials of the atomic orbitals and xpj, calculated for the appropriate barycenters. I ab is the intemuclear distance between the atoms of which y>i and y>) are atomic orbitals. Sy is calculated using Slater orbitals. The quantity [2 1b + (qi + pf)]-1/2 is essentially equal to 7y (Eq. 62). 

This expression is generally used as such with or without neglect of the second term and using as Ip the negative of the valence-state ionization potential of atom P. Although such a simplification may be of little importance in hydrocarbons, where it seems to influence merely the absolute values of the molecular ionization potentials and where the atomic -electron populations are close to unity, this is not the case for heteromolecules. Here, an empirical choice of Up values in place of the first two terms in Eq. (24) is better.84... 

The diagonal elements are set equal to the effective valence-state ionization potentials of the orbitals in question. The off-diagonal elements, Hr can be evaluated in several ways. The two expressions in most common usage are the original Wolfsberg-Helmholz expression,... 

Since the valence state ionization potentials are known to be functions of the electron population at that atom, we have introduced iterative schemes for calculating Hrr such as Equations 11 and 12 ... 

The Hamiltonian matrix, H, is approximated in the following way. The diagonal elements are effective valence-state ionization potentials... 

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-... 

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