Ab initio investigation of the Renner-Teller effect in tetra-atomic molecules

Perturbative Handling of the Renner–Teller Effect and Spin–Orbit Coupling in Π Electronic States of Triatomic and Tetra-atomic Molecules

“…However, as shown elsewhere (18,19), in the lowest-order approximation this quantity does not appear directly in the calculations but solely determines the selection rules for the matrix elements of the model Hamiltonian with respect to the nuclear basis functions. After integrating over all electronic coordinates except for θ , the electronic operator H e transforms into the "potential" for bending vibrations.…”

“…The model Hamiltonian we use is of the form [1], but now it involves two doubly degenerate bending modes. To represent them we chose the following four coordinates, introduced in our previous studies (18,19,22,23): (i) ρ T , the displacement (in radian) of the terminal nuclei from the B-B (≡z) axis at the trans-bending vibrations; (ii) φ T , the angle between the instantaneous molecular plane at the trans-bending vibrations and a space-fixed plane with the common z-axis; (iii) ρ C , the cisbending displacement coordinate; (iv) φ C , the angle between the molecular plane and the space-fixed plane at the cis-bending (see Fig. 1).…”

“…The Hamiltonian also incorporates the electronic coordinate θ conjugate to the z-component of the electronic angular momentum operator, L z . Because of the use of the above defined symmetry coordinates the nuclear kinetic energy operator for small-amplitude bending vibrations represents the kinetic energy of two uncoupled twodimensional harmonic oscillators (18,19),…”

“…Perturbative handling of the Renner-Teller effect in and electronic states of triatomic (15)(16)(17) and tetra-atomic (18)(19)(20) molecules has been the subject of considerable interest also in our laboratory. The main motivation for this work has been the attempt to build a bridge between the results of our ab initio studies and the corresponding experimental findings.…”

“…The present authors also prefer variational handling of problems such as the subject of the present study. Such an approach to the RennerTeller effect in tetra-atomic molecules has been developed in our laboratory (18,19,22,23). The range of its applicability has continuously been extended so that it enables us now to tackle also the spin-orbit and magnetic hyperfine effects (24)(25)(26), as well as large-amplitude bending vibrations (27,28).…”