Pseudo-harmonic approximation

Fig. 12.10 The dependence of [u 2 exp(Uj)/(exp(Uj) — l)2], and thence the contribution to the isotope effect on the thermal pressure, pseudo-harmonic approximation. For purposes of illustration the graph was constructed assuming u /u = v /v = 21/2, approximately the ratio for CH/CD stretching frequencies...

This approximate expression is similar to the response function (5.138) which we wrote down by analogy with the expressions (5.136,137) for e(o)), except that the harmonic frequency o).(q) has been replaced by the pseudo-harmonic frequency o)-(q) and r.(q) has been replaced by r.(q). From the ex-perimental point of view, we see that o)j(q) and Fj(q) are to be determined from the measured positions and half-widths of the infrared absorption bands, the Raman lines, or the peaks of inelastic neutron scattering spectra. Examples of infrared experimental data are shown in Fig.5.14. The pseudoharmonic frequencies d).(q) defined by (5.144) should not be confused with... 

In this section, we will examine the role of interelectronic repulsion in the perspective of the internal symmetries of the shell. The key observation is that in a d-only approximation — i.e. if the t2g-orbital functions can be written as products of a common radial part and a spherical harmonic angular function of rank two - the interelectronic repulsion operator and the pseudo-angular momentum operators commute [2]. This implies that the dominant part of the... 

Totally symmetric modes are not subject to symmetry restrictions. Their potentials may contain odd and even terms in Q so that the harmonic-oscillator approximation imposes unwarranted symmetry restrictions. Similarly, the corresponding vibronic coupling operator may contain both odd and even terms so that the distinction between pseudo-Jahn-Teller and pseudo-Renner-Teller coupling disappears. Since the potential energy minimum of a totally symmetric mode is different in different electronic states, the pseudo-Jahn Teller/Renner-Teller limit is quite different from the limiting cases discussed in Section I V,B,C. Finally, the transition moments... 

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