Ab initio study of the vibronic and spin–orbit coupling in the X 2Πu state of C2H + 2

Abstract

A variational approach for treating the Renner–Teller effect in tetra-atomic molecules [Perić et al., Mol. Phys. 55, 1159 (1985)] is extended to account for the effect of spin–orbit coupling. The approach is applied to compute the spin–orbit splittings of the vibronic levels in the X 2Πu state of C2H+2. The bending potential curves employed in a previous study [Perić and Peyerimhoff, J. Chem. Phys. (in press)] are improved by carrying out ab initio calculations at a higher level of sophistication. The results of the computations enable a reliable interpretation of recent experimental findings [Pratt et al., J. Chem. Phys., 99, 66 (1993)].

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

“…We do not find it necessary to go into a detailed analysis of the content of Table 2. The reader interested in this subject is referred, e.g., to one of our previous studies (24). It can be seen that the present perturbative formulae enable reliable computation of majority of the levels building the low-lying part of the vibronic spectrum.…”

“…K , vibronic quantum number; g, u, symmetry labeling of vibronic levels; υ T , υ C , vibrational quantum numbers for trans and cis bending respectively (usual spectroscopic notation, υ 4 , υ 5 ); , spin quantum number; var., results of variational calculations; pert., In this section we apply the formulae derived for tetraatomic molecules to compute the vibronic spectrum of the X 2 u state of C 2 H 2 . In these calculations we employ the parameters obtained in a previous ab initio study on this system (24): ω T = 704.4893 cm −1 , ω C = 724.1934 cm −1 , ε T = 0.306485, ε C = 0.013002, and A = − 29.2 cm −1 . Since the spin-orbit coupling constant is in this case much smaller than the vibrational frequencies, we use the formulae presented in Section 3.1.…”

“…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). It has been employed to calculate vibronic spectra of several species in and electronic states, e.g., C 2 H + 2 (23,24), (25,26,29), HCCO (28), and HCCS (30).…”

“…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). It has been employed to calculate vibronic spectra of several species in and electronic states, e.g., C 2 H + 2 (23,24), (25,26,29), HCCO (28), and HCCS (30). However, the availability of such program packages for ab initio handling of the problem considered does not call into question the usefulness of perturbative approaches for interpretation of a usually very restricted sample of experimental findings.…”

An ab initio model for handling the Renner–Teller effect in tetra-atomic molecules. I. Introduction of coordinates and the Hamiltonian

“…The main practical advantage of this method was that it made possible to obtain the term values and the wave functions for all (bending) vibronic levels of interest. It enables also handling the interplay between the vibronic, spin-orbit [29,17], magnetic hyperfine couplings [30,31,[44][45][46][47], and the effects of large-amplitude bending vibrations [32][33][34][35]. Perturbative formulae were derived for a number of cases not handled by PK (particularly those involving the spinorbit coupling) [17,32,34,37,40,41,43].…”