Effective vibrational potential

This is the Schrodinger equation for vibrational motion, with eigenstates S R) representing vibrational wave functions in electronic state k, under the effective vibrational potential... 

Most of our discussion of vibrational eigenstates and selection rules has been centered on the harmonic approximation. Of course, the effective vibrational potential Uj R) is not well approximated by a parabola for energies corresponding to large vibrational quantum numbers v (cf. Fig. 3.7), and considerable work has been expended to find alternative expressions for either l7kk(K) or the vibrational energy levels which are both compact and accurate. It has become conventional to fit experimentally determined vibrational levels Gp(cm ) to expressions of the form [6]... 

Hay, P. J., Martin, R. L., 1998, Theoretical Studies of the Structures and Vibrational Frequencies of Actinide Compounds Using Relativistic Effective Core Potentials With Hartree-Fock and Density Functional Methods ... 

The most extensive potential obtained so far with experimental confirmation is that of Le Roy and Van Kranendonk for the Hj — rare gas complexes 134). These systems have been found to be very amenable to an adiabatic model in which there is an effective X—Hj potential for each vibrational-rotational state of (c.f. the Born Oppenheimer approximation of a vibrational potential for each electronic state). The situation for Ar—Hj is shown in Fig. 14, and it appears that although the levels with = 1) are in the dissociation continuum they nevertheless are quasi bound and give spectroscopically sharp lines. 

Kaupert, Heydtmann and Thiel"2 calculated the vibrational spectrum of monohalo-genated 1 at the HF level using the 6-31 G(d) basis set and effective core potentials with DZ + P basis sets for Cl, Br and I. Reduction from Z)3h to Cs symmetry leads to considerable coupling between modes (exceptions C—H stretching and CH2-deformation modes) of 1. Vibrational frequencies that are influenced by the halogen substituent are shifted to lower values with increasing mass of the halogen. 

The optical centrifuge is capable of imparting so much rotational energy to a diatomic molecule that the bond breaks. To see how this happens, note that the effective radial potential seen by a diatomic molecule is a sum.of its real potential V(R) and a centrifugal one associated with its angular motion. That is, the vibrational motion sees the effective potential... 

It will be noticed that two contributions to the vibrational potential energy, of the general form V(R ) and independent of the rotational and spin quantum numbers, have also been included in equation (7.124). These are corrections to Vn(R), the zeroth-order contribution to the electronic energy defined in equation (7.76). The first term, Vr d)(R), is the adiabatic contribution to the electronic energy, which we have discussed in section 2.7. It describes the first-order effect of the nuclear kinetic energy within the... 

Electroacoustics — Ultrasound passing through a colloidal dispersion forces the colloidal particles to move back and forth, which leads to a displacement of the double layer around the particles with respect to their centers, and thus induces small electric dipoles. The sum of these dipoles creates a macroscopic AC voltage with the frequency of the sound waves. The latter is called the Colloid Vibration Potential (CVP) [i]. The reverse effect is called Electrokinetic Sonic Amplitude (ESA) effect [ii]. See also Debye effect. 

The diffraction effect has two causes In a collision, two molecules form short-lived dimers, which have discrete vibrational and rotational energy levels. This vibration effect should be observable for light gases (helium, hydrogen) at low densities. However, de Boer and Michels showed even in 1939 that the influence of the vibration effect on the second virial coefficient is rather small [1], and can be accounted for by using effective pair potentials [2]. 

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