Quantum Dynamics of Radiationless Electronic Transitions Including Normal Modes Displacements and Duschinsky Rotations: A Second-Order Cumulant Approach

Abstract

This is the author's final version of the contribution published as:Borrelli, Raffaele; Peluso, Andrea. Quantum dynamics of radiationless electronic transitions including normal modes displacements and duschinsky rotations: A second-order cumulant approach. JOURNAL OF CHEMICAL THEORY AND COMPUTATION. 11 (2) AbstractAn analytical expression for the population dynamics of electronic radiationless transitions has been derived from the second order expansion of the quantum evolution operator in the Liouville space and the cumulant theory. The expression includes the effect of both normal mode displacements and Duschinsky rotations and allows to take into account both equilibrium and non-equilibrium initial conditions. The methodology has been applied to model the electron-transfer process between the accessory bacteriochlorophyll and the bacteriopheophytine in bacterial reactions centers, providing a rate in good agreement with experimental findings.

Behind the scenes of spin-forbidden decay pathways in transition metal complexes

“…Alternatively, analytical solutions are also possible by appropriately modelling the Hamiltonian by analytic functions, which are then evaluated by recursion formulas. 161,[177][178][179] The model Hamiltonian in use is the simple harmonic oscillator. In this case, the calculations are performed in…”

Tunable Redox Potential, Optical Properties, and Enhanced Stability of Modified Ferrocene-Based Complexes

“…16 Normal modes of vibration of Fc, Me 2 Fc, and Me 8 Fc have been computed at the same level of theory. The displacement of normal modes d n have been obtained by projecting the Cartesian displacements onto the direction of normal modes by the relation 17 where ω is the diagonal matrix of the vibrational wavenumbers in γ = 2πω c / ℏ , L is the rectangular matrix of normal modes of the neutral state expressed as linear combinations of Cartesian displacements, and x N/C 0 are the equilibrium coordinates of the molecules in their neutral and cation states, respectively.…”

Finite temperature quantum dynamics of complex systems: Integrating thermo‐field theories and tensor‐train methods

“…The linear vibronic couplings g k can be obtained from the computation of the equilibrium geometry, and of the matrices of normal modes of vibrations of the two electronic states via well‐known relations 92–95 . Our model comprises 267 vibrational modes, and the parameters adopted in here are taken from our previous work 96 …”

“…[92][93][94][95] Our model comprises 267 vibrational modes, and the parameters adopted in here are taken from our previous work. 96 Figure 7 shows the temperature-dependent spectral densities defined in Equation ( 66). As already said, the coupling with the tilde space is negligible for high frequency modes (ω > 2000 cm À1 ) and not reported.…”