Extended Born-Oppenheimer Equations for Non-Abelian Situations: A Study on NO3 Radical and 1,3,5-C6H3F3+ Radical Cation

Publication date: Available online 14 March 2019Source: Computational and Theoretical ChemistryAuthor(s): Soumya Mukherjee, Bijit Mukherjee, Subhankar Sardar, Satrajit AdhikariAbstractFormulation of single-surface extended Born-Oppenheimer (EBO) equation is a long-standing problem for three or higher dimensional sub-Hilbert space mainly due to the difficulty to include the contribution of off-diagonal elements of anti-symmetric nonadiabatic coupling matrix (τ→) as the diagonal ones. Diagonalization of a vector matrix is possible only when its components commute with each other (i.e. curl τ→=0→) and thereby, that vector matrix (τ→) can be expressed as a product of a vector function and an antisymmetric scalar matrix. For two electronic state sub-Hilbert space (Abelian case), since curl τ→=0→ naturally, such factorization is readily obtained. In non-Abelian cases, for systems with three or more than three sub-Hilbert space, such factorization of nonadiabatic coupling matrix (NACM) may be achievable approximately, [J. Chem. Phys. 124 (2006) 074101/1-18; J. Phys. Chem. A 112 (2008) 9868-9885] which will be explored further both theoretically and numerically. In this article, we take an attempt to generalize the single-surface EBO equations for higher dimensional sub-Hilbert space by selecting two realistic molecular systems containing Jahn-Teller (JT) conical intersections (CIs). The curl equations and gauge invariance (GI) of the eigenvalues of the NACM for NO3 r...

Source: Computational and Theoretical Chemistry - March 14, 2019 Category: Chemistry Source Type: research