One and Two Dimensional Vibronic Spectra for an Exciton Dimer from Classical Trajectories

Direct All-Atom Nonadiabatic Semiclassical Simulations for Electronic Absorption Spectroscopy of Organic Photovoltaic Non-Fullerene Acceptor in Solution

We investigate the linear absorption spectra of the organic photovoltaic nonfullerene acceptor Y6 in chloroform using perturbative and nonperturbative approaches with atomistic details. Direct nonadiabatic semiclassical mapping dynamics reveal population and coherence evolution during and after ultrafast light pulse, revealing dominant absorption to the S1 state and subsequent oscillatory polarization. The simulated spectra accurately reproduce experimental peak positions and broadening, corresponding to transitions from the ground state to the S1, S2, and S6 excited states. Time-dependent radial distribution functions offer atomistic insights into solvent reorganization in response to charge redistribution. These findings enhance the understanding of nonadiabatic dynamics in Y6 and provide a consistent protocol for simulating electronic spectroscopy in condensed-phase systems.

Nonadiabatic Field: A Conceptually Novel Approach for Nonadiabatic Quantum Molecular Dynamics

Reliable trajectory-based nonadiabatic quantum dynamics methods at the atomic/molecular level are critical for the practical understanding and rational design of many important processes in real large/complex systems, where the quantum dynamical behavior of electrons and that of nuclei are coupled. The paper reports latest progress of nonadiabatic field (NaF), a conceptually novel approach for nonadiabatic quantum dynamics with independent trajectories. Substantially different from the mainstreams of Ehrenfest-like dynamics and surface hopping methods, the nuclear force in NaF involves the nonadiabatic force arising from the nonadiabatic coupling between different electronic states, in addition to the adiabatic force contributed by a single adiabatic electronic state. NaF is capable of faithfully describing the interplay between electronic and nuclear motion in a broad regime, which covers where the relevant electronic states keep coupled in a wide range or all the time and where the bifurcation characteristic of nuclear motion is essential. NaF is derived from the exact generalized phase space formulation with coordinate-momentum variables, where constraint phase space (CPS) is employed for discrete electronic-state degrees of freedom (DOFs) and infinite Wigner phase space is used for continuous nuclear DOFs. We propose efficient integrators for the equations of motion of NaF in both adiabatic and diabatic representations. Since the formalism in the CPS formulation is not unique, NaF can in principle be implemented with various phase space representations of the time correlation function (TCF) for the time-dependent property. They are applied to a suite of representative gas-phase and condensed-phase benchmark models where numerically exact results are available for comparison. It is shown that NaF is relatively insensitive to the phase space representation of the electronic TCF and will be a potential tool for practical and reliable simulations of the quantum mechanical behavior of both electronic and nuclear dynamics of nonadiabatic transition processes in real systems.

Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals

Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.

2D electronic-vibrational spectroscopy with classical trajectories

Two-dimensional electronic-vibrational (2DEV) spectra have the capacity to probe electron–nuclear interactions in molecules by measuring correlations between initial electronic excitations and vibrational transitions at a later time. The trajectory-based semiclassical optimized mean trajectory approach is applied to compute 2DEV spectra for a system with excitonically coupled electronic excited states vibronically coupled to a chromophore vibration. The chromophore mode is in turn coupled to a bath, inducing redistribution of vibrational populations. The lineshapes and delay-time dynamics of the resulting spectra compare well with benchmark calculations, both at the level of the observable and with respect to contributions from distinct spectroscopic processes.

Equilibrium-nonequilibrium ring-polymer molecular dynamics for nonlinear spectroscopy

Two-dimensional Raman and hybrid terahertz-Raman spectroscopic techniques provide invaluable insight into molecular structures and dynamics of condensed-phase systems. However, corroborating experimental results with theory is difficult due to the high computational cost of incorporating quantum-mechanical effects in the simulations. Here, we present the equilibrium-nonequilibrium ring-polymer molecular dynamics (RPMD), a practical computational method that can account for nuclear quantum effects on the two-time response function of nonlinear optical spectroscopy. Unlike a recently developed approach based on the double Kubo transformed (DKT) correlation function, our method is exact in the classical limit, where it reduces to the established equilibrium-nonequilibrium classical molecular dynamics method. Using benchmark model calculations, we demonstrate the advantages of the equilibrium-nonequilibrium RPMD over classical and DKT-based approaches. Importantly, its derivation, which is based on the nonequilibrium RPMD, obviates the need for identifying an appropriate Kubo transformed correlation function and paves the way for applying real-time path-integral techniques to multidimensional spectroscopy.

Two-dimensional vibronic spectroscopy with semiclassical thermofield dynamics

Thermofield dynamics is an exactly correct formulation of quantum mechanics at finite temperature in which a wavefunction is governed by an effective temperature-dependent quantum Hamiltonian. The optimized mean trajectory (OMT) approximation allows the calculation of spectroscopic response functions from trajectories produced by the classical limit of a mapping Hamiltonian that includes physical nuclear degrees of freedom and other effective degrees of freedom representing discrete vibronic states. Here, we develop a thermofield OMT (TF-OMT) approach in which the OMT procedure is applied to a temperature-dependent classical Hamiltonian determined from the thermofield-transformed quantum mapping Hamiltonian. Initial conditions for bath nuclear degrees of freedom are sampled from a zero-temperature distribution. Calculations of two-dimensional electronic spectra and two-dimensional vibrational–electronic spectra are performed for models that include excitonically coupled electronic states. The TF-OMT calculations agree very closely with the corresponding OMT results, which, in turn, represent well benchmark calculations with the hierarchical equations of motion method.

Calculating Multidimensional Optical Spectra from Classical Trajectories

Multidimensional optical spectra are measured from the response of a material system to a sequence of laser pulses and have the capacity to elucidate specific molecular interactions and dynamics whose influences are absent or obscured in a conventional linear absorption spectrum. Interpretation of complex spectra is supported by theoretical modeling of the spectroscopic observable, requiring implementation of quantum dynamics for coupled electrons and nuclei. Performing numerically correct quantum dynamics in this context may pose computational challenges, particularly in the condensed phase. Semiclassical methods based on calculating classical trajectories offer a practical alternative. Here I review the recent application of some semiclassical, trajectory-based methods to nonlinear molecular vibrational and electronic spectra.

Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

A partially linearized spin-mapping approach for simulating nonlinear optical spectra

We present a partially linearized method based on spin-mapping for computing both linear and nonlinear optical spectra. As observables are obtained from ensembles of classical trajectories, the approach can be applied to the large condensed-phase systems that undergo photosynthetic light-harvesting processes. In particular, the recently derived spin partially linearized density matrix method has been shown to exhibit superior accuracy in computing population dynamics compared to other related classical-trajectory methods. Such a method should also be ideally suited to describing the quantum coherences generated by interaction with light. We demonstrate that this is, indeed, the case by calculating the nonlinear optical response functions relevant for the pump-probe and 2D photon-echo spectra for a Frenkel biexciton model and the Fenna-Matthews-Olsen light-harvesting complex. One especially desirable feature of our approach is that the full spectrum can be decomposed into its constituent components associated with the various Liouville-space pathways, offering a greater insight beyond what can be directly obtained from experiments.

Analytic and numerical vibronic spectra from quasi-classical trajectory ensembles

The truncated Wigner approximation to quantum dynamics in phase space is explored in the context of computing vibronic line shapes for monomer linear optical spectra. We consider multiple model potential forms including a shifted harmonic oscillator with both equal and unequal frequencies on the ground and excited state potentials as well as a shifted Morse potential model. For the equal-frequency shifted harmonic oscillator model, we derive an analytic expression for the exact vibronic line shape that emphasizes the importance of using a quantum mechanical distribution of phase space initial conditions. For the unequal-frequency shifted harmonic oscillator model, we are no longer able to obtain an exact expression for the vibronic line shape in terms of independent deterministic classical trajectories. We show how one can rigorously account for corrections to the truncated Wigner approximation through nonlinear responses of the line shape function to momentum fluctuations along a classical trajectory and demonstrate the qualitative improvement in the resulting spectrum when the leading-order quantum correction is included. Finally, we numerically simulate absorption spectra of a highly anharmonic shifted Morse potential model. We find that, while finite quantization and the dissociation limit are captured with reasonable accuracy, there is a qualitative breakdown of the quasi-classical trajectory ensemble's ability to describe the vibronic line shape when the relative shift in Morse potentials becomes large. The work presented here provides clarity on the origin of unphysical negative features known to contaminate absorption spectra computed with quasi-classical trajectory ensembles.

Two-dimensional vibrational-electronic spectra with semiclassical mechanics

Two-dimensional vibrational-electronic (2DVE) spectra probe the effects on vibronic spectra of initial vibrational excitation in an electronic ground state. The optimized mean trajectory (OMT) approximation is a semiclassical method for computing nonlinear spectra from response functions. Ensembles of classical trajectories are subject to semiclassical quantization conditions, with the radiation-matter interaction inducing discontinuous transitions. This approach has been previously applied to two-dimensional infrared and electronic spectra and is extended here to 2DVE spectra. For a system including excitonic coupling, vibronic coupling, and interaction of a chromophore vibration with a resonant environment, the OMT method is shown to well approximate exact quantum dynamics.