Investigating the Photodynamics of trans-Azobenzene with Coupled Trajectories.

In this work, we present the first implementation of coupled-trajectory Tully surface hopping (CT-TSH) suitable for applications to molecular systems. We combine CT-TSH with the semiempirical floating occupation molecular orbital-configuration interaction electronic structure method to investigate the photoisomerization dynamics of trans-azobenzene. Our study shows that CT-TSH can capture correctly decoherence effects in this system, yielding consistent electronic and nuclear dynamics in agreement with (standard) decoherence-corrected TSH. Specifically, CT-TSH is derived from the exact factorization and the electronic coefficients' evolution is directly influenced by the coupling of trajectories, resulting in the improvement of internal consistency if compared to standard TSH.

Effect of Initial Conditions Sampling on Surface Hopping Simulations in the Ultrashort and Picosecond Time Range. Azomethane Photodissociation as a Case Study.

We tested the effect of different ways of sampling the initial conditions in surface hopping simulations, with a focus on the initial energy distributions and on the treatment of the zero point energy (ZPE). As a test case, we chose the gas phase photodynamics of azomethane, which features different processes occurring in overlapping time scales: geometry relaxation in the excited state, internal conversion, photoisomerization, and fast and slow dissociation. The simulations, based on a semiempirical method, had a sufficiently long duration (10 ps) to encompass all of the above processes. We tested several variants of methods based on the quantum mechanical (QM) distributions of the nuclear coordinates q and momenta p, which yield, at least on the average over a large sampling set, the correct QM energy, namely the ZPE when starting from the ground vibrational state. We compared the QM samplings with the classical Boltzmann (CB) distribution obtained by a thermostated trajectory, whereby thermal effects are taken into account, but the ZPE is utterly ignored. We found that most QM and CB approaches yield similar results as to short time dynamics and decay lifetimes, whereas the rate of the ground state dissociation reaction CH3NNCH3 → CH3NN + CH3 is sharply affected by the sampling method. With QM samplings a large fraction of trajectories dissociate promply (<1 ps) after decay to the ground state and with rates of the order of 10-1 ps-1 after the first ps. Instead, the CB samplings yield a much smaller fraction of prompt dissociations and much lower rates at long times. We provided evidence that the ZPE "leaks" from high frequency modes to the reactive ones (N-C bond elongations), therefore unphysically increasing the dissociation rates with QM samplings. We show that an effective way to take into account the ZPE and to avoid the "leaking" problem is to add the ZPE to the potential energy surfaces as a function of the most relevant internal coordinates. Then, Boltzmann sampling can be done as usual, so this approach is suitable also for condensed state dynamics. In the tests we present here, the ZPE correction method yields dissociation rates intermediate between QM and uncorrected Boltzmann samplings.

Nonadiabatic Dynamics with Coupled Trajectories.

In this paper, we discuss coupled-trajectory schemes for molecular-dynamics simulations of excited-state processes. New coupled-trajectory strategies to capture decoherence effects, revival of coherence and nonadiabatic interferences in long-time dynamics are proposed, and compared to independent-trajectory schemes. The working framework is provided by the exact factorization of the electron-nuclear wave function, and it exploits ideas emanating from various surface-hopping schemes. The new coupled-trajectory algorithms are tested on a one-dimensional two-state system using different model parameters which allow one to induce different dynamics. The benchmark is provided by the numerically exact solution of the time-dependent Schrödinger equation.

Relaxation dynamics through a conical intersection: Quantum and quantum-classical studies.

We study the relaxation process through a conical intersection of a photo-excited retinal chromophore model. The analysis is based on a two-electronic-state two-dimensional Hamiltonian developed by Hahn and Stock [J. Phys. Chem. B 104 1146 (2000)] to reproduce, with a minimal model, the main features of the 11-cis to all-trans isomerization of the retinal of rhodopsin. In particular, we focus on the performance of various trajectory-based schemes to nonadiabatic dynamics, and we compare quantum-classical results to the numerically exact quantum vibronic wavepacket dynamics. The purpose of this work is to investigate, by analyzing electronic and nuclear observables, how the sampling of initial conditions for the trajectories affects the subsequent dynamics.

Antiadiabatic View of Fast Environmental Effects on Optical Spectra.

An antiadiabatic approach is proposed to model how the refractive index of the surrounding medium affects optical spectra of molecular systems in condensed phases. The approach solves some of the issues affecting current implementations of continuum solvation models and more generally of effective models where a classical description is adopted for the molecular environment.