Investigating the Photodynamics of trans-Azobenzene with Coupled Trajectories

Nonadiabatic Dynamics with Exact Factorization: Implementation and Assessment

In this work, we report our implementation of several independent-trajectory mixed-quantum-classical (ITMQC) nonadiabatic dynamics methods based on exact factorization (XF) in the Libra package for nonadiabatic and excited-state dynamics. Namely, the exact factorization surface hopping (SHXF), mixed quantum-classical dynamics (MQCXF), and mean-field (MFXF) are introduced. Performance of these methods is compared to that of several traditional surface hopping schemes, such as the fewest-switches surface hopping (FSSH), branching-corrected surface hopping (BCSH), and the simplified decay of mixing (SDM), as well as conventional Ehrenfest (mean-field, MF) method. Based on a comprehensive set of 1D model Hamiltonians, we find the ranking SHXF ≈ MQCXF > BCSH > SDM > FSSH ≫ MF, with the BCSH sometimes outperforming the XF methods in terms of describing coherences. Although the MFXF method can yield reasonable populations and coherences for some cases, it does not conserve the total energy and is therefore not recommended. We also find that the branching correction for auxiliary trajectories is important for the XF methods to yield accurate populations and coherences. However, the branching correction can worsen the quality of the energy conservation in the MQCXF. Finally, we find that using the time-dependent Gaussian width approximation used in the XF methods for computing decoherence correction can improve the quality of energy conservation in the MQCXF dynamics. The parameter-free scheme of Subotnik for computing the Gaussian widths is found to deliver the best performance in situations where such widths are not known a priori.

Exploring Exact-Factorization-Based Trajectories for Low-Energy Dynamics near a Conical Intersection

We study low-energy dynamics generated by a two-dimensional two-state Jahn-Teller Hamiltonian in the vicinity of a conical intersection using quantum wave packet and trajectory dynamics. Recently, these dynamics were studied by comparing the adiabatic representation and the exact factorization, with the purpose to highlight the different nature of topological-phase and geometric-phase effects arising in the two theoretical representations of the same problem. Here, we employ the exact factorization to understand how to accurately model low-energy dynamics in the vicinity of a conical intersection using an approximate description of the nuclear motion that uses trajectories. We find that since nonadiabatic effects are weak but non-negligible, the trajectory-based description that invokes the classical approximation struggles to capture the correct behavior.

On-the-fly simulation of time-resolved fluorescence spectra and anisotropy

We combine on-the-fly trajectory surface hopping simulations and the doorway-window representation of nonlinear optical response functions to create an efficient protocol for the evaluation of time- and frequency-resolved fluorescence (TFRF) spectra and anisotropies of the realistic polyatomic systems. This approach gives the effective description of the proper (e.g., experimental) pulse envelopes, laser field polarizations, and the proper orientational averaging of TFRF signals directly from the well-established on-the-fly nonadiabatic dynamic simulations without extra computational cost. To discuss the implementation details of the developed protocol, we chose cis-azobenzene as a prototype to simulate the time evolution of the TFRF spectra governed by its nonadiabatic dynamics. The results show that the TFRF is determined by the interplay of several key factors, i.e., decays of excited-state populations, evolution of the transition dipole moments along with the dynamic propagation, and scaling factor of the TFRF signals associated with the cube of emission frequency. This work not only provides an efficient and effective approach to simulate the TFRF and anisotropies of realistic polyatomic systems but also discusses the important relationship between the TFRF signals and the underlining nonadiabatic dynamics.

Nonadiabatic dynamics with classical trajectories: The problem of an initial coherent superposition of electronic states

Advances in coherent light sources and development of pump-probe techniques in recent decades have opened the way to study electronic motion in its natural time scale. When an ultrashort laser pulse interacts with a molecular target, a coherent superposition of electronic states is created and the triggered electron dynamics is coupled to the nuclear motion. A natural and computationally efficient choice to simulate this correlated dynamics is a trajectory-based method where the quantum-mechanical electronic evolution is coupled to a classical-like nuclear dynamics. These methods must approximate the initial correlated electron-nuclear state by associating an initial electronic wavefunction to each classical trajectory in the ensemble. Different possibilities exist that reproduce the initial populations of the exact molecular wavefunction when represented in a basis. We show that different choices yield different dynamics and explore the effect of this choice in Ehrenfest, surface hopping, and exact-factorization-based coupled-trajectory schemes in a one-dimensional two-electronic-state model system that can be solved numerically exactly. This work aims to clarify the problems that standard trajectory-based techniques might have when a coherent superposition of electronic states is created to initialize the dynamics, to discuss what properties and observables are affected by different choices of electronic initial conditions and to point out the importance of quantum-momentum-induced electronic transitions in coupled-trajectory schemes.