Electron cloud perturbations

We often refer to Heitler and London s method as the valence bond (VB) model. A comparison between the experimental and the valence bond potential energy curves shows excellent agreement at large 7 ab but poor quantitative agreement in the valence region (Table 4.3). The cause of this lies in the method itself the VB model starts from atomic wavefunctions and adds as a perturbation the fact that the electron clouds of the atoms are polarized when the molecule is formed. 

The electron cloud of an ion subjected to an electric field undergoes deformations that may be translated into displacement of the baricenters of negative charges from the positions held in the absence of external perturbation, which are normally coincident with the centers of nuclear charges (positive). The noncoincidence of the two centers causes a dipole moment, determined by the product of the displaced charge (Z ) and the displacement d. The displacement is also proportional to the intensity of the electrical field (F). The proportionality factor (a) is known as ionic polarizability ... 

The X-rays perturb essentially the electron clouds and the so created defects are cured rather rapidly. All the experiments, particularly those of J, Turkevitch, made in that field led to the conclusion that, whereas very bad catalysts could be slightly improved, the good ones were worsened. 

The first three observed ionization potentials for thieno[3,2-6]thiophene (3) (8.14, 8.66 and 10.02 eV) correlate favorably with those observed for the isoelectronic naphthalene (8.15, 8.80 and 10.00 eV) and benzo[6]thiophene (8.22, 8.77 and 10.05 eV) molecules, in contrast to the corresponding values for thiophene (8.87, 9.49 eV) and benzene (9.24, 9.24 eV) (73JCS(F1)93). This observation is explained by the fact that the delocalized 7r-electron cloud resulting from changing a benzene 7r-bond to a sulfur atom causes greater perturbation in the small framework involved compared to the same interchange in a more extended conjugated system such as naphthalene or benzo[6 jthiophene. 

Not all vibrational transitions can be accessed by Raman scattering. Raman-active transitions are those associated with a change in polarizability of the molecule. In classical terms, this can be viewed as a perturbation of the electron cloud of the molecule. 

Such second-order molecular properties as spin-spin coupling depend upon distortion of electron clouds by additional external perturbations that is, in the NMR experiment they depend upon the electronic motion induced by an applied magnetic field. Theories for such second-order molecular properties require a study of the change in the molecular-orbital wavefunctions, which may be found by using a perturbation method to describe the effects occurring when a magnetic field is applied.8-1065-67... 

We should consider only the effects of extended electronic clouds that could modify the point-dipole-lattice interactions investigated in Section I.B. We assume the isolated-molecule wave function to be valid, neglecting its perturbation by inclusion in the crystal lattice. For all our calculations we neglect the overlap of neighboring molecules wave functions, which is a valid approximation for low-lying excited states, but fails for states near the crystal-lowered ionization threshold for which CT states, or conduction states, appear and invalidate the use of isolated-molecule wave functions. 

If the distance between the interacting systems A and B is sufficiently large to enable the overlap of the respective electronic clouds to be disregarded, then the interaction energy may be calculated from the Rayleigh- Schrodinger perturbation theory, using as a basis of functions to describe the wave function of AB... 

When one is far from resonance, then a further simplification is possible. Kleinman74 showed [15] that energy is simply exchanged among the fields E Ej, and Ek along the three axes i, j, and k, so that the suffixes can be interchanged freely this means that the three fields act independently and can be applied in arbitrary order (at resonance, one field will distort the electronic cloud in such a way that a second field will act on a severely perturbed electron configuration). Thus, when this is not a problem (i.e., when one is far from resonance) for SHG the 27 (or 18) coefficients reduce to 10 ... 

The response of the electrons to a potential perturbation induces oscillations of the electron cloud with a frequency... 

A comprehensive theory of electric polarizabilities and magnetic susceptibilities has been developed [4-6], which accounts for the electromagnetic moments induced in the electron cloud by the switching on of an external time-dependent perturbation. 

The external fields induce forced oscillations in the electron cloud. The interaction is described in terms of the time-dependent Hamiltonian within the framework of propagator methods [3] or, equivalently, introducing time-dependent perturbation theory [22, 23]. Relaxing condition (2) for the free wave, the general form of the Hamiltonian becomes, neglecting electron spin. 

The results we have obtained provide a reinterpretation of IR absorption along the following lines the IR radiation is a dynamic electric field which causes oscillations in the electronic cloud. The perturbed electrons, in turn, induce an additional dynamic electric field at the nuclei via a feedback effect. The latter are hence acted upon by the effective electric field (145), that is, by a frequency-dependent Lorentz force that is responsible for changes of nuclear vibrational motion. Accordingly, the electron distribution of a molecule plays a fundamental role in determining the general features of nuclear vibrations and the magnitude of IR parameters. 

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