Valence-bond charge transfer model

Apart from purely electronic effects, an asymmetric nuclear relaxation in the electric field can also contribute to the first hyperpolarizability in processes that are partly induced by a static field, such as the Pockels effect [55, 56], and much attention is currently devoted to the study of the vibrational hyperpolarizability, can be deduced from experimental data in two different ways [57, 58], and a review of the theoretical calculations of p, is given in Refs. [59] and [60]. The numerical value of the static P is often similar to that of static electronic hyperpolarizabilities, and this was rationalized with a two-state valence-bond charge transfer model. Recent ab-initio computational tests have shown, however, that this model is not always adequate and that a direct correlation between static electronic and vibrational hyperpolarizabilities does not exist [61]. 

Suitieri97 has also evaluated the anharmonic contributions to the nuclear relaxation y for some push-pull polyenes using analytical methods in a valence bond charge transfer model. Saal and Ouamerali98 have investigated the vibrational ft of N-fluorophemyl-2,5-dimethypyrrole in the double harmonic... 

Bishop, D.M., Champagne, B., Kirtman, B. Relationship between static vibrational and electronic hyperpolarizabilities of rr-conjugated push-pull molecules within the two-state valence-bond charge-transfer model. J. Chem. Phys. 109, 9987-9994 (1998)... 

Lu, D., Chen, G., Perry, J.W., Goddard, III, W.A. Valence-bond charge-transfer model for nonlinear optical properties of charge-transfer organic molecules. J. Am. Chem. Soc. 116. 10679-10685 (1994)... 

The two-form model has its roots in the valence-bond charge-transfer (VB-CT) model derived by Mulliken [84] and used with minor modifications by Warshel et al. for studying reactions in solutions [114]. Goddard et al. applied this VB-CT model to study the nonlinear optical properties of tire charge-transfer systems. [27, 59]. The analysis of the relationship between electronic and vibrational components of the hyperpolarizabilities within the two-state valence-bond approach was presented by Bishop et al. [17]. Despite the limitations of the VB-CT model, it is very simple and gives some insight into mutual relationships between nonlinear optical responses through the various orders. 

In such models, the bonding is considered to be partially ionic with a charge transfer from A1 to the Ni 3d valence band. To explain the properties of /J NiAl at a more sophisticated level, Fox and Tabernor (1991) measured four low-angle structure factors by the HEED critical-voltage technique. The deformation density based on these four reflections shows a depletion of density around both the Ni and A1 atoms, and a buildup of about 0.13 eA-3 along the [111] direction halfway between Ni and A1 nearest neighbors. 

Given the quality of data described above, it is possible to go beyond the neutral spherical atom model, and to determine the redistribution of valence electrons due to chemical bonding. In other words, we can develop a description of the electron density distribution that includes charge transfer and non-spherical atoms. 

The predicted course of reaction between a heteronuclear pair of atoms is shown in Figure 7.2. Promotion is once more modeled with isotropic compression of both types of atom. The more electropositive atom (at the lower quantum potential) reaches its valence state first and valence density starts to migrate from the parent core and transfers to an atom of the second kind, still below its valence state. The partially charged atom is more readily compressible to its promotion state, as shown by the dotted line. When this modified atom of the second kind reaches its valence state two-way delocalization occurs and an electron-pair bond is established as before. It is notable how the effective activation barrier is lowered with respect to both homonuclear (2Vq)i barriers to reaction. The effective reaction profile is the sum of the two promotion curves of atoms 1 and 2, with charge transfer. 

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