Nonadiabatic quantum Liouville and master equations in the adiabatic basis

Nonadiabatic Derivative Couplings through Multiple Franck-Condon Modes Dictate the Energy Gap Law for Near and Short-Wave Infrared Dye Molecules

Near infrared (NIR, 700-1000 nm) and short-wave infrared (SWIR, 1000-2000 nm) dye molecules exhibit significant nonradiative decay rates from the first singlet excited state to the ground state. While these trends can be empirically explained by a simple energy gap law, detailed mechanisms of nearly universal behavior have remained unsettled for many cases. Theoretical and experimental results for two representative NIR/SWIR dye molecules reported here clarify the key mechanism for the observed energy gap law behavior. It is shown that the first derivative nonadiabatic coupling terms serve as major coupling pathways for nonadiabatic decay processes from the first excited singlet state to the ground state for these NIR and SWIR dye molecules and that vibrational modes other than the highest frequency modes also make significant contributions to the rate. This assessment is corroborated by further theoretical comparison with possible alternative mechanisms of intersystem crossing to triplet states and also by comparison with experimental data for deuterated molecules.

Three-state harmonic models for photoinduced charge transfer

A widely used strategy for simulating the charge transfer between donor and acceptor electronic states in an all-atom anharmonic condensed-phase system is based on invoking linear response theory to describe the system in terms of an effective spin-boson model Hamiltonian. Extending this strategy to photoinduced charge transfer processes requires also taking into consideration the ground electronic state in addition to the excited donor and acceptor electronic states. In this paper, we revisit the problem of describing such nonequilibrium processes in terms of an effective three-state harmonic model. We do so within the framework of nonequilibrium Fermi's golden rule (NE-FGR) in the context of photoinduced charge transfer in the carotenoid-porphyrin-C₆₀ (CPC₆₀) molecular triad dissolved in explicit tetrahydrofuran (THF). To this end, we consider different ways for obtaining a three-state harmonic model from the equilibrium autocorrelation functions of the donor-acceptor, donor-ground, and acceptor-ground energy gaps, as obtained from all-atom molecular dynamics simulations of the CPC₆₀/THF system. The quantum-mechanically exact time-dependent NE-FGR rate coefficients for two different charge transfer processes in two different triad conformations are then calculated using the effective three-state model Hamiltonians as well as a hierarchy of more approximate expressions that lead to the instantaneous Marcus theory limit. Our results show that the photoinduced charge transfer in CPC₆₀/THF can be described accurately by the effective harmonic three-state models and that nuclear quantum effects are small in this system.

Surface Hopping Dynamics beyond Nonadiabatic Couplings for Quantum Coherence

Description of correct electron-nuclear couplings is crucial in modeling of nonadiabatic dynamics. Within traditional semiclassical or mixed quantum-classical dynamics, the coupling between quantum electronic states and classical nuclear trajectories is governed by nonadiabatic coupling vectors coupled to classical nuclear momenta. This enables us to develop a very powerful nonadiabatic dynamics algorithm, namely, surface hopping dynamics, which can describe the splitting of nuclear wave packets and detailed balance. Despite its efficiency and practicality, it suffers from the lack of quantum decoherence due to incorrect accounts for the electron-nuclear coupling. Here we present a new surface hopping algorithm based on the exact electron-nuclear correlation from the exact factorization of molecular wave functions. This algorithm demands comparable computational costs to existing surface hopping methods. Numerical simulations with two-state models and a multidimensional multistate realistic molecule show that the electron-nuclear coupling beyond the nonadiabatic coupling terms can describe the quantum coherence properly.

Ab Initio Nonadiabatic Dynamics with Coupled Trajectories: A Rigorous Approach to Quantum (De)Coherence

We report the first nonadiabatic molecular dynamics study based on the exact factorization of the electron-nuclear wave function. Our approach (a coupled-trajectory mixed quantum-classical, CT-MQC, scheme) is based on the quantum-classical limit derived from systematic and controlled approximations to the full quantum-mechanical problem formulated in the exact-factorization framework. Its strength is the ability to correctly capture quantum (de)coherence effects in a trajectory-based approach to excited-state dynamics. We show this by benchmarking CT-MQC dynamics against a revised version of the popular fewest-switches surface-hopping scheme that is able to fix its well-documented overcoherence issue. The CT-MQC approach is successfully applied to investigation of the photochemistry (ring-opening) of oxirane in the gas phase, analyzing in detail the role of decoherence. This work represents a significant step forward in the establishment of the exact factorization as a powerful tool to study excited-state dynamics, not only for interpretation purposes but mainly for nonadiabatic ab initio molecular dynamics simulations.

Quantum-Classical Nonadiabatic Dynamics: Coupled- vs Independent-Trajectory Methods

Trajectory-based mixed quantum-classical approaches to coupled electron-nuclear dynamics suffer from well-studied problems such as the lack of (or incorrect account for) decoherence in the trajectory surface hopping method and the inability of reproducing the spatial splitting of a nuclear wave packet in Ehrenfest-like dynamics. In the context of electronic nonadiabatic processes, these problems can result in wrong predictions for quantum populations and in unphysical outcomes for the nuclear dynamics. In this paper, we propose a solution to these issues by approximating the coupled electronic and nuclear equations within the framework of the exact factorization of the electron-nuclear wave function. We present a simple quantum-classical scheme based on coupled classical trajectories and test it against the full quantum mechanical solution from wave packet dynamics for some model situations which represent particularly challenging problems for the above-mentioned traditional methods.

The exact forces on classical nuclei in non-adiabatic charge transfer

The decomposition of electronic and nuclear motion presented in Abedi et al. [Phys. Rev. Lett. 105, 123002 (2010)] yields a time-dependent potential that drives the nuclear motion and fully accounts for the coupling to the electronic subsystem. Here, we show that propagation of an ensemble of independent classical nuclear trajectories on this exact potential yields dynamics that are essentially indistinguishable from the exact quantum dynamics for a model non-adiabatic charge transfer problem. We point out the importance of step and bump features in the exact potential that are critical in obtaining the correct splitting of the quasiclassical nuclear wave packet in space after it passes through an avoided crossing between two Born-Oppenheimer surfaces and analyze their structure. Finally, an analysis of the exact potentials in the context of trajectory surface hopping is presented, including preliminary investigations of velocity-adjustment and the force-induced decoherence effect.