Vibronic coupling in cyclopentadienyl radical: A method for calculation of vibronic coupling constant and vibronic coupling density analysis

Abstract

A method of calculation of vibronic or electron-phonon coupling constant is presented for a Jahn-Teller molecule, cyclopentadienyl radical. It is pointed out that symmetry breaking at degenerate point and violation of Hellmann-Feynman theorem occur in the calculations based on a single Slater determinant. In order to overcome these difficulties, the electronic wave functions are calculated using generalized restricted Hartree-Fock and complete active space self-consistent-field method and the couplings are computed as matrix elements of the electronic operator of the vibronic coupling. Our result agrees well with the experimental and theoretical values. A concept of vibronic coupling density is proposed in order to explain the order of magnitude of the coupling constant from view of the electronic and vibrational structures. It illustrates the local properties of the coupling and enables us to control the interaction. It could open a way to the engineering of vibronic interactions.

Graph theory and the Jahn–Teller theorem

“…The coupling of electronic states with vibrational distortion modes has recently been analysed by Sato et al (2006Sato et al ( , 2010 in terms of a vibronic coupling density, which separately identifies bond (inter-site) and atom (on-site) contributions to the vibronic coupling parameters. For many examples, this scheme reveals the dominant role of the underlying molecular graph in the JT effect.…”

Charge and Magnetic Orderings in the Triangular-Lattice Antiferromagnet InFe2O4

“…Vibronic coupling density analysis is shown to be intuitive and useful for the explanation of the order of magnitude of the coupling constant of C 5 H 5 [3], C 6 H 6 + , and C 6 H 6 - [4]. Moreover, this analysis is applied to the explanation of the effect of deuterium substitution and halogen substitution on the vibronic coupling.…”

“…A concept of vibronic coupling density η (r) [3], which illustrates the local property of the coupling, is proposed to explain the magnitude of the coupling from the view of the frontier electron density ρ  (r) and potential derivative along normal modes v (r).…”

“…On the other hand, the interaction of electro deficient aromatic rings with anion or electronegative atom is quite rare in molecule-based crystals. Herein, we synthesized the novel host compound, {[Cu 3 (CN) 3 {HAT-(CN) 3 (OEt) 3 }] ·3THF}} n (1· THF) (HAT = hexaaza triphenyrene) , and observed the interaction of electro deficient π plane of HAT and electronegative atoms of guest molecules. [1] Crystal structural analyses of 1·THF reveal that the THF is included in cavity of 1 and the oxygen atom of THF interact with the π plane of HAT.…”

Hydrogenation of Fullerene C60: Material Design of Organic Semiconductors by Computation

“…The reorganization energy is a stabilization energy by geometrical relaxation originating from the change in electronic structure [64][65][66]. The strong forces on the nuclei generally result in large λ and geometrical relaxation.…”