An analysis of model proton-coupled electron transfer reactions via the mixed quantum-classical Liouville approach

Abstract

The nonadiabatic dynamics of model proton-coupled electron transfer (PCET) reactions is investigated for the first time using a surface-hopping algorithm based on the solution of the mixed quantum-classical Liouville equation (QCLE). This method provides a rigorous treatment of quantum coherence/decoherence effects in the dynamics of mixed quantum-classical systems, which is lacking in the molecular dynamics with quantum transitions surface-hopping approach commonly used for simulating PCET reactions. Within this approach, the protonic and electronic coordinates are treated quantum mechanically and the solvent coordinate evolves classically on both single adiabatic surfaces and on coherently coupled pairs of adiabatic surfaces. Both concerted and sequential PCET reactions are studied in detail under various subsystem-bath coupling conditions and insights into the dynamical principles underlying PCET reactions are gained. Notably, an examination of the trajectories reveals that the system spends the majority of its time on the average of two coherently coupled adiabatic surfaces, during which a phase enters into the calculation of an observable. In general, the results of this paper demonstrate the applicability of QCLE-based surface-hopping dynamics to the study of PCET and emphasize the importance of mean surface evolution and decoherence effects in the calculation of PCET rate constants.

Full-dimensional multilayer multiconfigurational time-dependent Hartree study of electron transfer dynamics in the anthracene/C60 complex

“…The HEOM method is regarded as an "exact" method in some sense, but it is computationally very expensive. 22,[45][46][47] Alternatively, several groups advocated the mix-quantum-classical approaches, [39][40][41][42][48][49][50] which seem to be very attractive and practical due to the simplicity of numerical implementation. For instance, the surface hopping method [51][52][53] is very popular in the treatment of the ultrafast ET dynamics, [39][40][41][42] but it suffers from many problems, [54][55][56][57] such as incorrect coherence, internal inconsistency, and frustrated hops.…”

Quasi-Diabatic Propagation Scheme for Direct Simulation of Proton-Coupled Electron Transfer Reaction

“…Note thatĤ sb does not directly couple to the electron or proton, and its presence will not impact the definition of the electronic or vibronic adiabatic states. Following the previous work, 18,19,22,53 here we choose not to includeĤ sb in our calculations. Instead, the solvent fluctuations induced by {R ζ } are modeled with non-zero initial momentum 18 associated with the R. We emphasize that there is no additional theoretical challenge to incorporateĤ sb into the QD propagations outlined in this paper, as it has been done in our previous work.…”

“…where |φ m e and |φ n p are chosen to be the quantum harmonic oscillator bases 18,53 centered at r o e and r o p , respectively. The quantum Hamiltonian operatorV is then expressed in these two-particle basis functions |η ≡ {|φ m e |φ n p }.…”

Quasi Diabatic Propagation Scheme for Direct Simulation of Proton-Coupled Electron Transfer Reaction

“…Note that Ĥsb does not directly couple to the electron or proton, and its presence will not impact the definition of the electronic or vibronic adiabatic states. Following the previous work, 18,19,22,53 here we choose not to include Ĥsb in our calculations. Instead, the solvent fluctuations induced by {R ζ } are modeled with non-zero initial momentum 18 associated with the R. We emphasize that there is no additional theoretical challenge to incorporate Ĥsb into the QD propagations outlined in this paper, as it has been done in our previous work.…”