Mixed Quantum-Classical Simulations of Transient Absorption Pump–Probe Signals for a Photo-Induced Electron Transfer Reaction Coupled to an Inner-Sphere Vibrational Mode

Abstract

In a previous study (Martinez, F.; Hanna, G. Chem. Phys. Lett. 2013, 573, 77-83), we demonstrated the ability of two approximate solutions of the quantum-classical Liouville equation (QCLE) for qualitatively capturing the electronic dynamics in the pump-probe transient absorption (TA) signal of a model of a condensed phase photoinduced electron transfer reaction whose ground and excited donor states have the same equilibrium geometry. However, the question remained as to the ability of these solutions to treat the more complex situation in which the electronic states are coupled to a low-frequency inner-sphere harmonic vibrational mode (representing an intramolecular mode of the donor-acceptor complex) that shifts their equilibrium geometries with respect to each other and thereby gives rise to signatures of vibrational dynamics in the TA signal. Thus, in this study, we investigated this situation by treating the vibrational mode both quantum mechanically and classically within the context of the approximate Poisson bracket mapping equation (PBME) and forward-backward trajectory solutions (FBTS) of the QCLE. Depending on the definition of the quantum subsystem, both PBME and FBTS are capable of qualitatively capturing several of the main features in the exact TA signal and quantitatively capturing the characteristic time scale of the vibrational dynamics, despite the moderately strong subsystem-bath coupling in this model. Particularly, we found that treating the vibrational mode quantum mechanically using either PBME or FBTS better captures the signatures of the vibrational dynamics, while treating it classically using FBTS better captures the decay in the signal. These findings underscore the utility of the PBME and FBTS approaches for efficiently modeling and interpreting TA signals.

Nonadiabatic Dynamics via the Symmetrical Quasi-Classical Method in the Presence of Anharmonicity

“…A similar approach has been recently applied by Martinez et al to the calculation of transient absorption (TA) pump−probe signals using PBME and FBTS for a model system that involves harmonic PESs. 92 They illustrated that neither FBTS nor PBME was able to produce a quantitative agreement with exact population dynamics and TA signals for multiple simulation parameters irrespective of how the primary mode was treated. We showed that E-SQC is able to produce essentially exact population dynamics for a broad range of parameters.…”

Performance evaluation of the symmetrical quasi-classical dynamics method based on Meyer-Miller mapping Hamiltonian in the treatment of site-exciton models

“…Louiville equation (QCLE) [85][86][87][88][89][90] , path integral [91][92][93][94][95][96][97] , surface hopping [98][99][100][101] , centroid molecular dynamics (CMD) 102 and ring-polymer molecular dynamics (RPMD) [103][104][105][106][107] .…”

“…Thus, this idea can be employed in different dynamics approaches. For instance, it is possible to combine it with semiclassical initial value representation and its extension 38,[73][74][75][76][77][78][79][80][81][82][83][84] quantum classical Louiville equation (QCLE) [85][86][87][88][89][90] , path integral [91][92][93][94][95][96][97] , surface hopping [98][99][100][101] , centroid molecular dynamics (CMD) 102 and ring-polymer molecular dynamics (RPMD) [103][104][105][106][107] .…”

Two‐dimensional electronic spectrum simulation of simple photosynthetic complex models with semi‐classical Poisson bracket mapping equation

“…Among many MQC approaches, we primarily focus on Poisson bracket mapping equation (PBME) 37 as it is a reasonable choice for performing excited state dynamics simulations of complex systems with atomistic resolutions 45 and also for generating nonlinear spectroscopic signals. 48,49 In addition, a PBME variant with a simple modification can yield equilibrium populations in the long-time limit. 44 We find that our scheme with PBME provides 2D electronic spectra in a comparable manner to reference hierarchical equation of motion (HEOM) results when tested for a two-state model with small reorganization energy.…”