Penetration integral

D. J., Jeffrey, P. Improving the in vitro prediction of in vivo centtal nervous system penetration Integrating permeability, P-glycoprotein efflux, and free fractions in blood and brain. 

Core-electron attraction integrals are calculated using the Goeppert-Mayer-Sklar approximation with neglect of penetration integrals. 

In the CNDO/1 method the penetration terms (Zb-Tab—Vab) were evaluated by approximating all coulomb penetration integrals i>ab as... 

Yonezawa et al. in their CNDO level method approximate the penetration integral vab = (B ii) be setting them equal to the negative of the corresponding repulsion integral, thus... 

Dewar and Klopman (PNDO) approximate the penetration integral v[Pg.32]

Here W is the ionization potential of an electron in the p-AO of an isolated atom i, (/3M)0 is the one-electron exchange integral between the AO s of atoms i, j, and (ii, jj) and (it, j) are the usual electron repulsion and penetration integrals. In practice the penetration integrals are usually disregarded this should certainly be justifiable in the present connection where we are concerned only with differences in energy between closely related systems. Equation (31) then becomes—... 

As in CNDO, in MNDO the penetration integrals are neglected (Section 6.2.3, CNDO/2). A consequence of this is that the core-core repulsions (Vcc in Eq. 6.2) cannot be realistically calculated simply as the sum of pairs of classical electrostatic interactions between point charges centered on the nuclei. Instead, Dewar and coworkers chose [38] the expression... 

For the parabolic barrier arising from the quadratic expansion about the saddle point, the barrier penetration integral is given by... 

This purely parametric method can easily be converted into a Parr-Pariser scheme, as done for paraffins 46>, by selecting appropriate values for the penetration integrals (U, ] pp) and electron repulsion integrals pp qq) between hybrid orbitals. 

In the Pariser-Parr-Pople scheme, the so-called zero differential overlap approximation is used, and the u-electron system is treated as a nonpolarizable core. The interelectronic repulsions are explicitly taken into account in the total Hamiltonian. Resonance integrals, core integrals, and electronic repulsion integrals are given empirically, and Coulomb penetration integrals are neglected. ... 

The effect of neglecting the Coulomb penetration integrals is considered in detail by J. R. Hoyland and L. Goodman. ... 

Assumption of the penetration integrals to be zero is equivalent to the assumption that the interatomic electron-electron interactions are canceled by the nuclear attraction. Using these approximations one finds for the Fock matrix elements ... 

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