Renner-Teller System

We wish to introduce here a very reliable calculation procedure to determine the eigenstates of a general Renner-Teller problem. It is convenient to start writing the matrix representation of the Hamiltonian of a Renner-Teller system on two degenerate p-like electronic states fx, fy and with the interaction part in the form given in Section 2, neglecting at the moment the quartic or higher order terms ... 

Fig. 1. Double interacting chains of orthonormal states, with definite values ofy, representing the Renner-Teller system for orbital p-like functions. N represents the total number of phonons.

As an example for comparison with the results obtained in the literature with different procedures, we have calculated the vibronic levels of Renner-Teller systems with /7-like orbital functions. Notice also that the chain with j = 0 has analytic solution [3,15] 2(n + 1) /1 g, referred to levels A1 A2, while the chains with j and —j (j 0) are degenerate. The vibronic levels are computed through the... 

In the absence of the terms oc these equations represent two uncoupled harmonic oscillators with frequencies (1 2/+), analogous to the zeroth-order pseudo-Renner-Teller system of Section IV,C. The diagonal terms oc distort these potentials, especially near the origin, whereas the corresponding oif-diagonal terms provide a coupling. Both of these terms... 

In Chapter XI, Peric and Peyerimhoff discuss the Renner-Teller coupling in triatomic and tetraatomic molecules. For this purpose, they describe some of their theoretical tools to investigate this subject and use the systems FeH2, CNC, and FICCS as adequate examples. 

Hamiltonian equations, 627-628 perturbative handling, 641-646 II electronic states, 631-633 vibronic coupling, 630-631 ABC bond angle, Renner-Teller effect, triatomic molecules, 611-615 ABCD bond angle, Renner-Teller effect, tetraatomic molecules, 626-628 perturbative handling, 641-646 II electronic states, 634-640 vibronic coupling, 630-631 Abelian theory, molecular systems, Yang-Mills fields ... 

Renner-Teller effect, multiple-state systems, 623... 

EWW Hamiltonian, Renner-Teller effect, triatomic molecules, 610—615 Expanding potential, molecular systems,... 

HCCS radical, Renner-Teller effect, tetraatomic molecules, II electronic states, 633-640 H2D molecule, non-adiabatic coupling, two-state molecular system, 107-109 HD2 molecule, permutational symmetry isotopomers, 713-717 potential energy surfaces, 692-694 Heaviside function ... 

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. 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.

The 0 e Renner-Teller vibronic system describes an orbital doublet ( ) interacting with a two-dimensional vibrational mode of s symmetry. In Section 2 we determine the general formal structure of the electron-phonon interaction matrices with orbital electronic functions of different symmetry (p-like, d-like, /-like, etc.), exploiting their intuitive relation with the Slater-Koster matrices of the two-center integrals. A direct connection with the form obtained through the molecule symmetry is discussed in Section 3. 

MPI-PES and ZEKE-PES will have a major impact on the haloacetylenes. This can be deduced from recent investigations of Renner-Teller interactions in C2H2, the simplest tetraatomic system that can exhibit such an effect118 (i.e. a removal of the double degener-... 

Somewhat paradoxically, symmetry is seen to play an important role in the understanding of the Jahn-Teller effect, the very nature of which is symmetry destruction [52], In a recent review the original paper published by Jahn and Teller [53] was called one of the most seminal papers in chemical physics [54], Only a brief discussion of this effect will be given here for more detail we refer the reader to References [55-59], Bersuker says that all structural instabilities and distortions of high-symmetry configurations of polyatomic systems are of Jahn-Teller origin (here he also refers to other related effects, such as the Renner-Teller effect and the pseudo-Jahn-Teller effect—they will be mentioned later). Bersuker likes to call this the... 

E.I.Dashevskaya and E.E.Nikitin, Correlation of adiabatic states between perturbed rotor and Renner-Teller limits for a closed-shell ion + open shell diatom system, Z. phys. Chem. 214, 1001 (2000)... 

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