Potential energy surfaces symmetry parameters

Important parameters involved in the Volmer-Butler equation are the transfer coefficients a and (1. They are closely related to the Bronsted relation [Eq. (14.5)] and can be rationalized in terms of the slopes of the potential energy surfaces [Eq. (14.9)]. Due to the latter, the transfer coefficients a and P are also called symmetry factors since they are related to the symmetry of the transitional configuration with respect to the initial and final configurations. 

The computed and fitted potential energy surfaces and their symmetry and resonance assignment are shown in Fig. 3a. Figure 3b shows the parameter geometry dependence that accomplishes the fit of the singlet states. Their semiquantitative relevance is validated by the same reasons discussed in the previous section. 

Obviously, the ground state of the complex must be described by the totally symmetric (nodeless) wave function, so it is of A symmetry. This suggests that both and /J2 are negative. It is, nevertheless, very difficult to estimate the magnitude of the parameters EA and /J, 2 without a prior knowledge of the potential energy surface of the cluster. 

Fig. 12.17. Potential energy surface of a Na cluster containing 12 atoms, plotted in the plane of deformation parameters /3 (giving the quadrupole moment) and 7 (the departure from axial symmetry). By averaging over an ensemble, the actual spectrum is obtained, and is compared with experimental data below the graph (after R.A. Broglia [702]).

Figure 1. Calculated adiabatic potential energy surface of H in PdH, q plotted against the displacement of the whole H sublattice in one of the three symmetry directions, [001], [110] and [111], where 5 is the distance displaced and a is the lattice parameter.

The non-separability of the vibrational modes is illustrated in Fig. 3 through the strong dependence of the JT potential energy surfaces for one of the interacting modes on the coordinates of the other mode (taken as a parameter). Whereas in Fig. 3(a) (zero displacement of the second mode) the potential surface for mode 1 exhibits the familiar Mexican-hat shape, for increasing displacements as in Figs. 3(b) and 3(c) there is an increasing distortion and the rotational symmetry is lost. ... 

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