Stochastic and Quasi-Stochastic Hamiltonians for Long-Time Nonadiabatic Molecular Dynamics

Assessing Nonadiabatic Dynamics Methods in Long Timescales

Nonadiabatic dynamics simulations complement time-resolved experiments by revealing ultrafast excited-state mechanistic information in photochemical reactions. Understanding the relaxation mechanisms of photoexcited molecules finds application in energy, material, and medicinal research. However, with substantial computational costs, the nonadiabatic dynamics simulations have been restricted to ultrafast timescales, typically less than a few picoseconds, thus neglecting a wide range of photoactivated processes occurring in much longer timescales. Before developing new methodologies, we must ask: How well do the popular nonadiabatic dynamics methods perform in a long timescale simulation? In this study, we employ the multiconfiguration time-dependent Hartree (MCTDH) and its multilayer variants (ML-MCTDH), ab initio multiple spawning (AIMS), and fewest-switches surface hopping (FSSH) methodologies to simulate the excited-states dynamics of a weakly coupled multidimensional Spin-Boson model Hamiltonian designed for a long timescale decay behavior. Our study assures that despite having very different theoretical backgrounds, all the above methods deliver qualitatively similar results. While quantum dynamics would be very costly for long timescale simulations, the trajectory-based approaches are paving the way for future advancements.

How Good Is the Vibronic Hamiltonian Repetition Approach for Long-Time Nonadiabatic Molecular Dynamics?

Multiple applied studies of slow nonadiabatic processes in nanoscale and condensed matter systems have adopted the "repetition" approximation in which long trajectories for such simulations are obtained by concatenating shorter trajectories, directly available from ab initio calculations, many times. Here, we comprehensively assess this approximation using model Hamiltonians with parameters covering a wide range of regimes. We find that state transition time scales may strongly depend on the length of the repeated data, although the convergence is not monotonic and may be slow. The repetition approach may under- or overestimate the time scales by a factor of ≤7-8, does not directly depend on the dispersion of energy gap and nonadiabatic coupling (NAC) frequencies, but may depend on the magnitude of the NACs. We suggest that the repetition-based nonadiabatic dynamics may be inaccurate in simulations with very small NACs, where intrinsic transition times are on the order of ≥100 ps.

Simulations of molecular photodynamics in long timescales

Nonadiabatic dynamics simulations in the long timescale (much longer than 10 ps) are the next challenge in computational photochemistry. This paper delimits the scope of what we expect from methods to run such simulations: they should work in full nuclear dimensionality, be general enough to tackle any type of molecule and not require unrealistic computational resources. We examine the main methodological challenges we should venture to advance the field, including the computational costs of the electronic structure calculations, stability of the integration methods, accuracy of the nonadiabatic dynamics algorithms and software optimization. Based on simulations designed to shed light on each of these issues, we show how machine learning may be a crucial element for long time-scale dynamics, either as a surrogate for electronic structure calculations or aiding the parameterization of model Hamiltonians. We show that conventional methods for integrating classical equations should be adequate to extended simulations up to 1 ns and that surface hopping agrees semiquantitatively with wave packet propagation in the weak-coupling regime. We also describe our optimization of the Newton-X program to reduce computational overheads in data processing and storage. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.

Interpolating Nonadiabatic Molecular Dynamics Hamiltonian with Inverse Fast Fourier Transform

Nonadiabatic (NA) molecular dynamics (MD) allows one to investigate far-from-equilibrium processes in nanoscale and molecular materials at the atomistic level and in the time domain, mimicking time-resolved spectroscopic experiments. Ab initio NAMD is limited to about 100 atoms and a few picoseconds, due to computational cost of excitation energies and NA couplings. We develop a straightforward methodology that can extend ab initio quality NAMD to nanoseconds and thousands of atoms. The ab initio NAMD Hamiltonian is sampled and interpolated along a trajectory using a Fourier transform, and then, it is used to perform NAMD with known algorithms. The methodology relies on the classical path approximation, which holds for many materials and processes. To achieve a complete ab initio quality description, the trajectory can be obtained using an ab initio trained machine learning force field. The method is demonstrated with charge carrier trapping and relaxation in hybrid organic-inorganic and all-inorganic metal halide perovskites that exhibit complex dynamics and are actively studied for optoelectronic applications.

Extending the Time Scales of Nonadiabatic Molecular Dynamics via Machine Learning in the Time Domain

A novel methodology for direct modeling of long-time scale nonadiabatic dynamics in extended nanoscale and solid-state systems is developed. The presented approach enables forecasting the vibronic Hamiltonians as a direct function of time via machine-learning models trained directly in the time domain. The use of periodic and aperiodic functions that transform time into effective input modes of the artificial neural network is demonstrated to be essential for such an approach to work for both abstract and atomistic models. The best strategies and possible limitations pertaining to the new methodology are explored and discussed. An exemplary direct simulation of unprecedentedly long 20 picosecond trajectories is conducted for a divacancy-containing monolayer black phosphorus system, and the importance of conducting such extended simulations is demonstrated. New insights into the excited states photophysics in this system are presented, including the role of decoherence and model definition.

Ab initio nonadiabatic molecular dynamics of charge carriers in metal halide perovskites

Photoinduced nonequilibrium processes in nanoscale materials play key roles in photovoltaic and photocatalytic applications. This review summarizes recent theoretical investigations of excited state dynamics in metal halide perovskites (MHPs), carried out using a state-of-the-art methodology combining nonadiabatic molecular dynamics with real-time time-dependent density functional theory. The simulations allow one to study evolution of charge carriers at the ab initio level and in the time-domain, in direct connection with time-resolved spectroscopy experiments. Eliminating the need for the common approximations, such as harmonic phonons, a choice of the reaction coordinate, weak electron-phonon coupling, a particular kinetic mechanism, and perturbative calculation of rate constants, we model full-dimensional quantum dynamics of electrons coupled to semiclassical vibrations. We study realistic aspects of material composition and structure and their influence on various nonequilibrium processes, including nonradiative trapping and relaxation of charge carriers, hot carrier cooling and luminescence, Auger-type charge-charge scattering, multiple excitons generation and recombination, charge and energy transfer between donor and acceptor materials, and charge recombination inside individual materials and across donor/acceptor interfaces. These phenomena are illustrated with representative materials and interfaces. Focus is placed on response to external perturbations, formation of point defects and their passivation, mixed stoichiometries, dopants, grain boundaries, and interfaces of MHPs with charge transport layers, and quantum confinement. In addition to bulk materials, perovskite quantum dots and 2D perovskites with different layer and spacer cation structures, edge passivation, and dielectric screening are discussed. The atomistic insights into excited state dynamics under realistic conditions provide the fundamental understanding needed for design of advanced solar energy and optoelectronic devices.

Modeling nonlocal electron-phonon coupling in organic crystals using interpolative maps: The spectroscopy of crystalline pentacene and 7,8,15,16-tetraazaterrylene

Electron-phonon coupling plays a central role in the transport properties and photophysics of organic crystals. Successful models describing charge- and energy-transport in these systems routinely include these effects. Most models for describing photophysics, on the other hand, only incorporate local electron-phonon coupling to intramolecular vibrational modes, while nonlocal electron-phonon coupling is neglected. One might expect nonlocal coupling to have an important effect on the photophysics of organic crystals because it gives rise to large fluctuation in the charge-transfer couplings, and charge-transfer couplings play an important role in the spectroscopy of many organic crystals. Here, we study the effects of nonlocal coupling on the absorption spectrum of crystalline pentacene and 7,8,15,16-tetraazaterrylene. To this end, we develop a new mixed quantum-classical approach for including nonlocal coupling into spectroscopic and transport models for organic crystals. Importantly, our approach does not assume that the nonlocal coupling is linear, in contrast to most modern charge-transport models. We find that the nonlocal coupling broadens the absorption spectrum non-uniformly across the absorption line shape. In pentacene, for example, our model predicts that the lower Davydov component broadens considerably more than the upper Davydov component, explaining the origin of this experimental observation for the first time. By studying a simple dimer model, we are able to attribute this selective broadening to correlations between the fluctuations of the charge-transfer couplings. Overall, our method incorporates nonlocal electron-phonon coupling into spectroscopic and transport models with computational efficiency, generalizability to a wide range of organic crystals, and without any assumption of linearity.

Influence of Defects on Excited-State Dynamics in Lead Halide Perovskites: Time-Domain ab Initio Studies

This Perspective summarizes recent research into the excited-state dynamics in lead halide perovskites that are of paramount importance for photovoltaic and photocatalytic applications. Nonadiabatic molecular dynamics combined with time-domain ab initio density functional theory allows one to mimic time-resolved spectroscopy experiments at the atomistic level of detail. The focus is placed on realistic aspects of perovskite materials, including point defects, surfaces, grain boundaries, mixed stoichiometries, dopants, and interfaces. The atomistic description of the quantum dynamics of electron and hole trapping and recombination, provided by the time-domain ab initio simulations, generates important insights into the mechanisms of charge and energy losses and guides the development of high-performance perovskite solar cell devices.

Development of effective stochastic potential method using random matrix theory for efficient conformational sampling of semiconductor nanoparticles at non-zero temperatures

The relationship between structure and property is central to chemistry and enables the understanding of chemical phenomena and processes. Need for an efficient conformational sampling of chemical systems arises from the presence of solvents and the existence of non-zero temperatures. However, conformational sampling of structures to compute molecular quantum mechanical properties is computationally expensive because a large number of electronic structure calculations are required. In this work, the development and implementation of the effective stochastic potential (ESP) method is presented to perform efficient conformational sampling of molecules. The overarching goal of this work is to alleviate the computational bottleneck associated with performing a large number of electronic structure calculations required for conformational sampling. We introduce the concept of a deformation potential and demonstrate its existence by the proof-by-construction approach. A statistical description of the fluctuations in the deformation potential due to non-zero temperature was obtained using infinite-order moment expansion of the distribution. The formal mathematical definition of the ESP was derived using the functional minimization approach to match the infinite-order moment expansion for the deformation potential. Practical implementation of the ESP was obtained using the random-matrix theory method. The developed method was applied to two proof-of-concept calculations of the distribution of HOMO-LUMO gaps in water molecules and solvated CdSe clusters at 300 K. The need for large sample size to obtain statistically meaningful results was demonstrated by performing 10⁵ ESP calculations. The results from these prototype calculations demonstrated the efficacy of the ESP method for performing efficient conformational sampling. We envision that the fundamental nature of this work will not only extend our knowledge of chemical systems at non-zero temperatures but also generate new insights for innovative technological applications.

Charge transfer dynamics at the boron subphthalocyanine chloride/C60 interface: non-adiabatic dynamics study with Libra-X

The Libra-X software for non-adiabatic molecular dynamics is reported. It is used to comprehensively study the charge transfer dynamics at the boron subphtalocyanine chloride (SubPc)/fullerene (C₆₀) interface.