Overlap charges

Kreek H and Meath W J 1969 Charge-overlap effects. Dispersion and induction forces J. Chem. Phys. 50 2289... 

Koide A, Meath W J and Allnatt A R 1981 Second-order charge overlap effects and damping functions for isotropic atomic and molecular interactions Chem. Phys. 58 105... 

The relative magnitude of charges, overlap populations and total energies of the geometric isomers of N2H2 as predicted on the basis of each of the three important effects thought to determine molecular structure (see Section 6.0) are shown in Table 42. Comparison of the ab initio data with the various predictions reveals that... 

Table 42. Predicted charges, overlap populations (O. P.), and relative stability of the geometric isomers of N2H2...

Equation (1-92) is very important since in the region of the Van der Waals minimum the charge-overlap contribution to the dispersion energy is always substantial. Additionally, the powerful computational techniques, developed in the 1980 s to obtain accurate polarization propagators118 can be utilized via Eq. (1-92) in the calculations of the dispersion energies at finite distances. 

The electrostatic, induction, and dispersion terms can be expanded in a convergent series closely related to the multipole expansion, but fully accounting for the charge-overlap effects, the so-called bipolar expansion introduced by Buehler and Hirschfelder199,200. In the local coordinate systems with the origins located at the centers of masses of the monomers A and B, separated by the distance R, and with their x and y axes parallel and aligned along the z axes, the distance between two particles in space can be expressed as follows,... 

Koide A, Proctor TR, Allnatt AR, Meath WJ (1986) Charge overlap effects for first-order molecule-molecule interactions, through high partial wave order, using the N2-N2 interaction as a model. Mol Phys 59 491-507... 

Krauss M, Neumann DB (1979) Charge overlap effects in dispersion energies. J Chem Phys 71 107-112... 

Figure 59 Location (xT) and width (w) of the recombination zone for a small space-charge overlap in a plate shaped EL material of thickness d, provided with two injecting ohmic electrodes (anode, cathode), dh and de denote the penetration depths of injected holes and electrons, respectively. We note that xr = dh, d /de = /ih/and dh de = d for w —> 0.

Naturally, the space charge overlap is not the only possible true size effect.37,161,162... 

The Distributed Multipole Analysis (DMA) developed by Stone uses the fact that the electrostatic potential arising from the charge overlap between two basis functions can... 

In cases of LMOs, the charge density. Between localized charge densities the charge-overlap is small, localization... 

N, and OHC—C=CH in terms of the ir-bond order proved unsatisfactory (Fukuyama and Kuchitsu ). Indeed, it appears that the substituent effects on adjacent bond distances do not correlate with any single physical quantity. This is indicated by the ab initio calculations of C=C and C-F distances in CH2=CH2, CHj CHF, CHF=CHF, and CH2=Cp2 by Bak, etal.. Their results do show the observed trend, but neither charge densities due to 7T-overlap nor (a + 7r)-overlap in the C=C and C-F bonds regions account for the computed bond distance changes i.e. larger charge overlap did not always correspond to shorter distance, and vice versa. 

The most important component of the water trimer nonadditive energy is the induction interaction of the second order in V. Its simple mechanism is shown in Fig. 33.3 a permanent multipole moment on monomer A induces multipole moments on monomer B which in turn interact with the permanent multipole moments of monomer C. Higher orders involve interactions between induced moments. The nonadditive induction energy is in general the most important nonadditive component for hydrogen-bonded systems. As already mentioned, it is the only term used—and only in the asymptotic approximation, i.e. neglecting charge-overlap effects—in the polarizable empirical potentials. 

An early computation of a full (i.e. depending on all intermolecular coordinates) PES of two diatomics is the work by Berns and van der Avoird [113] on (N2)2- Their approach is in essence the one sketched above one-cycle SCF to account for first-order exchange and electrostatics (including charge overlap effects) plus multipole-expanded dispersion. The dispersion coefficients were taken from Ref. [114]. 

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