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

A study of the Raman spectrum of CO2 using an algebraic approach

“…The local-mode description is introduced via a canonical transformation which, after an anharmonization procedure, cases where the Born-Oppenheimer approximation is broken, our approach is not expected to provide a good description of the system. In such cases, ab initio calculations play a fundamental role [7,8].…”

Renner–Teller effect in six-atomic molecules: Ab initio investigation of the vibronic spectrum of

“…The matrix elements of our model Hamiltonian in the basis (24) are subject to very restrictive selection rules being direct consequence of the conservation laws (40) and (42) (for details, see Refs. [22,25]). First, they always vanish if R 0 6 ¼ R. The matrix element diagonal with respect to the electronic part of the basis functions,…”

“…Ref. [22]) we have introduced the convention that the sign of the quantity E i is positive if the potential curve corresponding to the adiabatic wave function symmetric with respect to reflection in the instantaneous molecular plane lies above its antisymmetric counterpart. The cross-parameters k T12 , k C12 , E T12 , and E C12 may be obtained most easily employing the potential energy points calculated at q C = 0 (q T = 0), at the planar geometries corresponding to / C2 À / C1 (/ T2 À / T1 ) = 0 and p:…”

“…Perturbative formulae were derived for a number of cases not considered by PK (particularly those involving the spinorbit coupling) [21]. In two recent studies, [22,23], it was shown that the RT effect in tetra-atomic molecules can be considered as a superposition of three most important mechanisms that violate the BO approximation, namely the vibronic coupling caused by distortion of linearity, conical intersections (like in the case of the Jahn-Teller effect [24]), and avoided crossings of potential surfaces. Finally, the model for handling the RT effect was generalized to linear molecules with arbitrary number of atoms [25] and applied to the concrete case of a five-atomic species (X 2 P u state of the C À 5 ion) [26].…”

“…Employing the procedure analogous to that described in detail in Refs. [20,22] we introduce a set of polar coordinates, Q T1 , u T1 , Q T2 , u T2 , Q C1 , u C1 , Q C2 , u C2 , corresponding to the (Cartesian) normal coordinates, Q T1x , Q T1y , Q T2x , Q T2y , Q C1x , Q C1y , Q C2x , Q C2y , the last ones diagonalizing the kinetic and potential energy operators given by Eqs. (20) and (21).…”