Five Electronic State Beyond Born–Oppenheimer Equations and Their Applications to Nitrate and Benzene Radical Cation

Abstract

We present explicit form of Adiabatic to Diabatic Transformation (ADT) equations and expressions of non-adiabatic coupling terms (NACTs) for a coupled five-state electronic manifold in terms of ADT angles between electronic wave functions. ADT matrices eliminate the numerical instability arising from singularity of NACTs and transform the adiabatic Schrödinger equation to its diabatic form. Two real molecular systems NO and CH (Bz) are selectively chosen for the demonstration of workability of those equations. We examine the NACTs among the lowest five electronic states of the NO radical [X̃A (1B), ÃE″ (1A and 1B) and B̃E' (1A and 2B)], in which all types of non-adiabatic interactions, that is, Jahn-Teller (JT) interactions, Pseudo Jahn-Teller (PJT) interactions, and accidental conical intersections (CIs) are present. On the other hand, lowest five electronic states of Bz [X̃E (1B and 1B), B̃E (1A and 1B), and C̃A (1B)] depict similar kind of complex feature of non-adiabatic effects. For NO radical, the two components of degenerate in-plane asymmetric stretching mode are taken as a plane of nuclear configuration space (CS), whereas in case of Bz, two pairs are chosen: One is the pair of components of degenerate in-plane asymmetric stretching mode, and the other one is constituted with one of the components each from out-of-plane degenerate bend and in-plane degenerate asymmetric stretching modes. We calculate ab initio adiabatic potential energy surfaces (PESs) and NACTs among the lowest five electronic states at the CASSCF level using MOLPRO quantum chemistry package. Subsequently, the ADT is performed using those newly developed equations to validate the positions of the CIs, evaluate the ADT angles and construct smooth, symmetric, and continuous diabatic PESs for both the molecular systems.

Topological Effects in Vibronically Coupled Degenerate Electronic States: A Case Study on Nitrate and Benzene Radical Cation

“…This radical has been optimized employing UCCSD(T) (a spin unrestricted coupled cluster method with all single and double excitations and perturbative accounts of triple excitations) level of calculation, and the optimized parameters are presented in Table 1. 37 Adiabatic PESs for five lowest electronic states 19 have been already constructed using state-averaged complete active space self-consistent field (CASSCF) calculations employing 6-31g** basis set and (9e, 8o) configuration active space (CAS). On the other hand, analytic NACTs 19 between the five low-lying electronic states have been obtained by implementing coupled-perturbed multi configuration space self-consistent field (CP-MCSCF) theory.…”

“…37 Adiabatic PESs for five lowest electronic states 19 have been already constructed using state-averaged complete active space self-consistent field (CASSCF) calculations employing 6-31g** basis set and (9e, 8o) configuration active space (CAS). On the other hand, analytic NACTs 19 between the five low-lying electronic states have been obtained by implementing coupled-perturbed multi configuration space self-consistent field (CP-MCSCF) theory. In this nuclear plane, strong JT interactions are present within E″ as well as E′ states, forming “2–3” and “4–5” JT CIs at the equilibrium D 3 h point.…”

“…In order to exploit the inherent symmetry of the molecule ( D 3 h ), ADT equations are solved for the chosen pair of normal modes ( Q 3 x – Q 3 y ) along the ρ coordinate for each ϕ grid. 19 Our aim is to construct dressed adiabatic, dressed diabatic, and adiabatic-via-dressed diabatic potentials along Q 3 x and Q 3 y normal mode coordinates. Dressed adiabatic and dressed diabatic PECs are plotted as functions of Q i by taking average over the other normal mode coordinate ( Q j ), whereas adiabatic-via-dressed diabatic potentials can be generated by diagonalizing the dressed diabatic energy matrix ( W Q j ( Q i )).…”

“…39 We have investigated the JT interactions of the ground ( X̃ 2 E 1g ) and excited states (B ~ 2 E 2g ) as well as accidental CIs within the higher excited states (B ~ 2 E 2g – C̃ 2 A 2u ) using the ADT equations by employing the BBO formalism. 19…”

Nonadiabatic coupling and diabatic electronic population dynamics on 11A2 and 11B1 states of ozone molecule

“…The extended BO equations in terms of ADT angles have been formulated for the two, three, and four electronic‐state sub‐Hilbert space using curl condition . The ADT equations have been formulated in five and six electronic‐state sub‐Hilbert space to evaluate adiabatic PESs, components of nonadiabatic coupling terms, validity of curl conditions, and the nature of curl/divergence equations. Generally, in polyatomic molecules, nonadiabatic processes occur essentially around CIs .…”