Jahn-Teller stabilization energies

The CPF approach gives quantitative reement with the experimental spectroscopic constants (24-25) for the ground state of Cu2 when large one-particle basis sets are used, provided that relativistic effects are included and the 3d electrons are correlated. In addition, CPF calculations have given (26) a potential surface for Cus that confirms the Jahn-Teller stabilization energy and pseudorotational barrier deduced (27-28) from the Cus fluorescence spectra (29). The CPF method has been used (9) to study clusters of up to six aluminum atoms. 

Fig. 12. Schematic energy level diagram illustrating the Jahn-Teller stabilization energy accompanying a tetragonal elongation of an octahedral Cu(II) complex.

Fig. 13. Top Schematic representation of the two components of the Jahn-Teller-active vibrational mode for the E e Jahn-Teller coupling problem for octahedral d9 Cu(II) complexes. Bottom Resulting first-order Mexican hat potential energy surface for showing the Jahn-Teller radius, p, and the first-order Jahn-Teller stabilization energy, Ejt.

A general approach for predicting Jahn-Teller distortions of copper(II) hexa-amines has recently been published, and it has the potential to be applied to donor atoms other than nitrogen, metal centers other than copper(II), and various types of coordination polyhedra11641. The method is based on a harmonic first-order model11651 where the Jahn-Teller stabilization energy is the result of the Qg distortion mode (Fig. 11.1, Eqs. 11.3, 11.4). 

This distortion leads to a gain of electronic energy, i.e. the Jahn-Teller stabilization energy En as defined by Eqs. 11.5, 11.6,... 

Fig. 11.2. Total energy as a function of the strain energy ESt and the Jahn-Teller stabilization energy jt.

Consequently the Jahn-Teller stabilization energy, Ejt, is reduced in the E O component to one-quarter of the (t ) Oh value. In an exactly similar fashion it can also be shown that for the Tj and T20 components the coupling constants, B and C, are both reduced to one-half of their values in the parent 1 (t2g) Oh state so that once again the value of Ejt will in each case be only one-quarter of the Oh value. 

Table 2 Vibronic coupling and Jahn-Teller stabilization energy in Cso anions (10 a.u.). The...

An inverse to the (26) transformation should be used to analyze dependence of the potential energy on the changes of the interionic distances. The contour plot of the potential energy surface in the state can be also used to estimate from it the value of the Jahn-Teller stabilization energy, as will be shown below. 

Example of Estimations of the Jahn-Teller Stabilization Energy Using the Excited State Geometry Analysis... 

Qr > 0 (compression)] with the Jahn-Teller stabilization energy ( jt ) and the energy of the vertical electronic transition from the minimum of the non-degenerate... 

Note that ctf = pEjjiT), where jx(r) is the Jahn-Teller stabilization energy for the coupling with T-type vibrations. If aE, a 2< l, appropriate to the case of either weak vibronic coupling, or high temperatures and arbitrary values of aE and aTl, then the reduction parameters can be expanded in a series with respect to the small aE and a 2 value, and with the accuracy up to the linear in JT(0 terms they can be represented by the relations... 

Similar estimations can be carried out for octahedral molecules ReF6 and IrF6. For them the data taken from the works of Meredith et al. (1977), Webb and Bernstein (1979), and Bernstein and Webb (1979) about the Jahn-Teller stabilization energies and appropriate values of the deviation of the reduction parameters from unity at room temperatures calculated by Eq. (100) are given in Table I. It can be seen from these data that the predicted corrections are between 10 and 40%. Note that by changing the temperature by several tens of degrees the change of these corrections may be essential. 

The parameters employed in the calculation of the spectrum shown in Figure 4 imply a Jahn-Teller stabilization energy of 1073 cm . This number is comparable with vibrational frequencies. Consequently, already the lowest vibronic levels have energies near to or above that of the conical intersection of the Jahn-Teller-split potential-energy surfaces. Therefore they are subject to strong nonadiabatic interactions and cannot be ascribed to one of the two surfaces alone. 

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