Renner

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

RENNER-TELLER EFFECT AND SPIN-ORBIT COUPLING IN TRIATOMIC AND TETRAATOMIC MOLECULES... 

H. Beyond the Two-State Renner-Teller Effect TV. Tetraatomic Molecules... 

Appendix A Perturbative Handling of the Renner—Teller Effect and Spin-Orbit Coupling in n Electronic States of Tetraatomic Molecules... 

As argued above, it is not Renner who should be blamed for his paper being forgotten for almost 25 years. The reason is that the experimentalists needed this much time to obtain the first spectrum showing the features predicted by him [9,10], The effect that might have looked exotic in the 1930s has become one of... 

In Table I, 3D stands for three dimensional. The symbol symbol in connection with the bending potentials means that the bending potentials are considered in the lowest order approximation as already realized by Renner [7], the splitting of the adiabatic potentials has a p dependence at small distortions of linearity. With exact fomi of the spin-orbit part of the Hamiltonian we mean the microscopic (i.e., nonphenomenological) many-elecbon counterpart of, for example, The Breit-Pauli two-electron operator [22] (see also [23]). 

Figure 3. Low-energy vibronic spectrum in a. 11 electronic state of a linear triatomic molecule, computed for various values of the Renner parameter e and spin-orbit constant Aso (in cm ). The spectrum shown in the center of figure (e = —0.17, A o = —37cm ) corresponds to the A TT state of NCN [28,29]. The zero on the energy scale represents the minimum of the potential energy surface. Solid lines A = 0 vibronic levels dashed lines K = levels dash-dotted lines K = 1 levels dotted lines = 3 levels. Spin-vibronic levels are denoted by the value of the corresponding quantum number P P = Af - - E note that E is in this case spin quantum number),...

In his classical paper, Renner [7] first explained the physical background of the vibronic coupling in triatomic molecules. He concluded that the splitting of the bending potential curves at small distortions of linearity has to depend on p, being thus mostly pronounced in H electronic state. Renner developed the system of two coupled Schrbdinger equations and solved it for H states in the harmonic approximation by means of the perturbation theory. 

The first theoretical handling of the weak R-T combined with the spin-orbit coupling was carried out by Pople [71]. It represents a generalization of the perturbative approaches by Renner and PL-H. The basis functions are assumed as products of (42) with the eigenfunctions of the spin operator conesponding to values E = 1/2. The spin-orbit contribution to the model Hamiltonian was taken in the phenomenological form (16). It was assumed that both interactions are small compared to the bending vibrational frequency and that both the... 

---