doi:10.1016/j.cplett.2005.01.116 
Copyright © 2005 Elsevier B.V. All rights reserved.
The role of the cubic and quartic Jahn–Teller coupling in the 
ground electronic state of the methoxy radical CH3O
Aleksandr V. Marenich and James E. Boggs
, 
Institute for Theoretical Chemistry, Department of Chemistry and Biochemistry, The University of Texas at Austin, 1 University Station A5300, Austin, TX 78712-0165, USA
Received 24 September 2004;
revised 15 December 2004.
Available online 22 February 2005.
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Abstract
A spin–vibronic model Hamiltonian accounting for the linear, quadratic, cubic, and quartic Jahn–Teller interactions with the inclusion of spin–orbit coupling and all important anharmonic effects was developed to study electronic and nuclear dynamics in twofold degenerate electron systems and was applied to the 
ground electronic state of the CH3O methoxy radical (C3v). The problem of spin–vibronic eigenvalues and eigenfunctions was solved in a basis set of products of electronic, electron spin, and vibrational functions. The results of calculations show the importance of inclusion of cubic vibronic terms into the model Hamiltonian and the insignificance of quartic terms.
Table 1.
Low spin–vibronic energy (in cm−1) levels of 
CH3O assigned to the normal modes Q5 and Q6
Calculations were performed with Eq. (6) (vibronic coupling of second order), Eqs. Figs. (6) and (7) (third order), Eqs. Figs. (6), (7) and (8) (fourth order) and with the use of −ASOζe = 2d = 134 cm−1 for Eq. (3). Occupation quantum numbers for the rest of vibrational modes were equal to zero. Spin–vibronic eigenstates were approximately correlated to vibronic states with the symmetries of a1, a2, e (e* denotes another component of a doubly degenerate vibronic level).
Table 2.
The fundamental vibronic energy intervals of 
CH3O (in cm−1) calculated with account for the spin–vibronic coupling vs. experimental values
Notations: emission spectroscopy (ES), laser-induced fluorescence (LIF), stimulated emission pumping (SEP). All the entries were counted from the middle of the spin–orbit splitting in the ground vibrational state 00(e), the value of this splitting is −ASOζed. The doubly degenerate (e) vibronic levels undergo the spin–orbit splittings given in parentheses. The energies of these levels are shown as average values over two spin–vibronic components.
a This work: calculations were performed with Eqs. Figs.
(6),
(7) and
(8) (fourth order) and with the use of −
ASOζe = 2
d = 134 cm
−1 for Eq.
(3).
b Our previous work
[1]: calculations were performed with Eqs.
(6) (second order) and with −
ASOζe = 134 cm
−1.
c Calculation
[17] with use of the ab initio based (MRCI–CASSCF) linear and quadratic JT constants from
[3] and the parameter −
ASOζe = 108 cm
−1 deduced from an experimental value of −
ASOζed = 62 cm
−1 [6].
d Assignments were taken from
[3].
Abstract
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