Jahn-Teller-Renner

PERTURBED VIBRATIONAL-ROTATIONAL LEVELS, JAHN-TELLER-RENNER EFFECTS... 

Jahn-Teller, Renner-Teller, and pseudo-Jahn-Teller symmetry breaking 3... 

JAHN-TELLER, RENNER-TELLER, AND PSEUDO-JAHN-TELLER SYMMETRY BREAKING... 

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... 

Higher Order Coupling in Some Jahn-Teller and Renner-Teller Effects... 

Before we continue and in order to avoid confusion, two matters have to be clarified (1) We distinguished between two types of Landau-Zener situations, which form (in two dimensions) the Jahn-Teller conical intersection and the Renner-Teller parabolical intersection. The main difference between the two is... 

There are phenomena such as the Renner and the Jahn-Teller effects where the Bom-Oppenheimer approximation breaks down, hut for the vast majority of chemical applications the Born-Oppenheimer approximation is a vital one. It has a great conceptual importance in chemistry without it we could not speak of a molecular geometry. 

Jahn-Teller effect, 18-20 Linear triatomic molecules, Renner-Teller effect ... 

Potential fluid dynamics, molecular systems, modulus-phase formalism, quantum mechanics and, 265—266 Pragmatic models, Renner-Teller effect, triatomic molecules, 618-621 Probability densities, permutational symmetry, dynamic Jahn-Teller and geometric phase effects, 705-711 Projection operators, geometric phase theory, eigenvector evolution, 16-17 Projective Hilbert space, Berry s phase, 209-210... 

Fig. 1. Conical intersection surface topologies (top), and Renner-Teller surface topologies (bottom). Top left is a generic circular cone, such as is obtained from a Jahn-Teller problem involving only the linear vibronic coupling. Top right is a sloped conical intersection obtained in a general vibronic coupling problem where all three linear vibronic coupling constants are different. Bottom left to right show type-1, -II, -III Renner-Teller surfaces. These are obtained when only second-order vibronic coupling is included.

In fact, as we discuss in section 4 below, pJT coupling gives surfaces resembling the type-II Renner-Teller surfaces shown in Fig. 1, but separated by a finite energy difference. Many theoretical formulations of the pseudo-Jahn-Teller effect have been proposed. The simplest is perhaps the perturbative expansion originally due to Pearson (51)... 

Finally, we note that there are some situations, of which the dynamical Jahn-Teller and Renner-Teller effects are the classic examples, where the nuclear coupling terms are important in any electronic basis 18). Adiabatic potential surfaces may still be defined but the resulting molecular eigenstates cannot be identified with any one surface. 

Fig. 1. The adiabatic potentials (AP) in the Jahn-Teller (a), Renner-Teller (b), and pseudo-Jahn-Teller (c) effects for systems with a double degenerate electronic term interacting with one coordinate Q (E bi problem in the JT case). In all three cases the ground state is unstable in the high-symmetry configuration <2 = 0, while the stable configurations at Q0 are at lower symmetry. The differences between these cases are in the behavior of the AP at Q = 0.

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