The Renner effect in four‐atomic molecules

Abstract

AbstractsThe theory of the Renner effect in X2Y2 and X2YZ linear molecules is considered.The Renner equations are obtained with the help of the Born-Oppenheimer method. It is shown that these equations contain two Renner parameters for an X2Y2 molecule and three Renner parameters for an X,YZ molecules. Assuming these parameters to be small enough, an approximate solution of the Renner equations is obtained with the help of perturbation theory. Some general qualitative results are obtained in the first order of the perturbation theory; the second order calculations are made for some specific cases. The theoretical results are used to consider experimental data concerning the vibrational structure of the lIT, -' C t electronic transition in C,H2 and C,D2 molecules.

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

“…The functions R(ρ T ) and R(ρ C ) appearing in [29] are the eigenfunctions of the first and the second part of this Hamiltonian respectively. They are of the form [13]. l T and l C are the quantum numbers for the nuclear angular momentum caused by the two-dimensional trans and cis bending vibrations, respectively.…”

“…The A = 0 limits of the formulae presented in this section cover all particular cases (including υ T = 1, υ C = 1 and υ T = 2, υ C = 1) handled in the previous works (13,18,19).…”

“…A consequence is that the perturbative formulae cannot be derived for a general case, because the level of degeneracy of zeroth-order vibronic levels increases rapidly with increasing values for the bending quantum numbers (in the case of triatomics all zeroth-order vibronic levels are either nondegenerate or twofold degenerate). A perturbative approach for handling several particular coupling cases in 1 electronic states of tetra-atomics was developed by Petelin and Kiselev (13). The combined effect of vibronic and spin-orbit coupling in the lowest-lying vibronic species was considered by Tang and Saito (14).…”

Ab Initio Investigation of the Vibronic and Magnetic Hyperfine Effects in theX2ΠuState of[formula]

“…As discussed above the lowest lying level with K Å 1 (P u ) represents a socalled unique character, e.g., it has nearly equal contributions from all four electronic species in question. Therefore the contribution of the 2 ). Another important class of cases (one of them being the subject of the present study), where the electronic hfcc's (as well as a number of other properties) calculated for the equilibrium geometry cannot be directly compared with the experimental findings, represent those characterized by strong coupling between the electronic and nuclear motions.…”

“…In the first paper of this series, published 10 years ago (1), a variational approach for handling the vibronic effects in tetraatomics possessing linear equilibrium geometry was proposed. It was based on an earlier work by Petelin and Kiselev (2), who had derived perturbative formulae covering some special coupling cases. Unfortunately, for a long time the experimental information concerning the Renner-Teller effect in tetraatomic molecules has been very scarce (3,4) so that it has not been possible to demonstrate the utility of our theoretical approach for explaining and predicting the structure of vibronic spectra.…”