Time-Sliced Thawed Gaussian Propagation Method for Simulations of Quantum Dynamics

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.

Functional Tensor-Train Chebyshev Method for Multidimensional Quantum Dynamics Simulations

Methods for efficient simulations of multidimensional quantum dynamics are essential for theoretical studies of chemical systems where quantum effects are important, such as those involving rearrangements of protons or electronic configurations. Here, we introduce the functional tensor-train Chebyshev (FTTC) method for rigorous nuclear quantum dynamics simulations. FTTC is essentially the Chebyshev propagation scheme applied to the initial state represented in a continuous analogue tensor-train format. We demonstrate the capabilities of FTTC as applied to simulations of proton quantum dynamics in a 50-dimensional model of hydrogen-bonded DNA base pairs.

Non-adiabatic Excited-State Molecular Dynamics: Theory and Applications for Modeling Photophysics in Extended Molecular Materials

Optically active molecular materials, such as organic conjugated polymers and biological systems, are characterized by strong coupling between electronic and vibrational degrees of freedom. Typically, simulations must go beyond the Born-Oppenheimer approximation to account for non-adiabatic coupling between excited states. Indeed, non-adiabatic dynamics is commonly associated with exciton dynamics and photophysics involving charge and energy transfer, as well as exciton dissociation and charge recombination. Understanding the photoinduced dynamics in such materials is vital to providing an accurate description of exciton formation, evolution, and decay. This interdisciplinary field has matured significantly over the past decades. Formulation of new theoretical frameworks, development of more efficient and accurate computational algorithms, and evolution of high-performance computer hardware has extended these simulations to very large molecular systems with hundreds of atoms, including numerous studies of organic semiconductors and biomolecules. In this Review, we will describe recent theoretical advances including treatment of electronic decoherence in surface-hopping methods, the role of solvent effects, trivial unavoided crossings, analysis of data based on transition densities, and efficient computational implementations of these numerical methods. We also emphasize newly developed semiclassical approaches, based on the Gaussian approximation, which retain phase and width information to account for significant decoherence and interference effects while maintaining the high efficiency of surface-hopping approaches. The above developments have been employed to successfully describe photophysics in a variety of molecular materials.

Improved Ehrenfest Approach to Model Correlated Electron-Nuclear Dynamics

Mixed quantum-classical mechanical descriptions are critical to modeling coupled electron-nuclear dynamics, i.e., nonadiabatic molecular dynamics, relevant to photochemical and photophysical processes. We introduce an efficient description of such dynamics in terms of an effective Hamiltonian that not only properly captures electron-nuclear correlation effects but also helps develop an efficient computational method. In particular, we introduce a coupled Gaussian wavepacket parametrization of the nuclear wave function, which generalizes the Ehrenfest approach to account for electron-nuclei correlations. We test this new approach, Ehrenfest-Plus, on a suite of model problems that probe electron-nuclear correlation in nonadiabatic transitions. The high accuracy of our approach, combined with mixed quantum-classical efficiency, opens a path for improved simulation of nonadiabatic molecular dynamics in realistic molecular systems.

Electronic Delocalization, Vibrational Dynamics, and Energy Transfer in Organic Chromophores

The efficiency of materials developed for solar energy and technological applications depends on the interplay between molecular architecture and light-induced electronic energy redistribution. The spatial localization of electronic excitations is very sensitive to molecular distortions. Vibrational nuclear motions can couple to electronic dynamics driving changes in localization. The electronic energy transfer among multiple chromophores arises from several distinct mechanisms that can give rise to experimentally measured signals. Atomistic simulations of coupled electron-vibrational dynamics can help uncover the nuclear motions directing energy flow. Through careful analysis of excited state wave function evolution and a useful fragmenting of multichromophore systems, through-bond transport and exciton hopping (through-space) mechanisms can be distinguished. Such insights are crucial in the interpretation of fluorescence anisotropy measurements and can aid materials design. This Perspective highlights the interconnected vibrational and electronic motions at the foundation of nonadiabatic dynamics where nuclear motions, including torsional rotations and bond vibrations, drive electronic transitions.

Coupled wave-packets for non-adiabatic molecular dynamics: a generalization of Gaussian wave-packet dynamics to multiple potential energy surfaces

Coupled wave-packets for non-adiabatic dynamics is a new method for simulation of molecular dynamics on coupled potential energy surfaces, which efficiency and correctly accounts for decoherence and interferences effects.

Accurate simulation of the non-adiabatic dynamics of molecules in excited electronic states is key to understanding molecular photo-physical processes. Here we present a novel method, based on a semi-classical approximation, that is as efficient as the commonly used mean field Ehrenfest or ad hoc surface hopping methods and properly accounts for interference and decoherence effects. This novel method is an extension of Heller's thawed Gaussian wave-packet dynamics that includes coupling between potential energy surfaces. By studying several standard test problems we demonstrate that the accuracy of the method can be systematically improved while maintaining high efficiency. The method is suitable for investigating the role of quantum coherence in the non-adiabatic dynamics of many-atom molecules.

Kinetically-constrained ring-polymer molecular dynamics for non-adiabatic chemistries involving solvent and donor–acceptor dynamical effects

We investigate the performance of the recently developed kinetically-constrained ring polymer molecular dynamics (KC-RPMD) method for the description of model condensed-phase electron transfer (ET) reactions in which solvent and donor–acceptor dynamics play an important role. Comparison of KC-RPMD with results from Golden-Rule rate theories and numerically exact quantum dynamics calculations demonstrates that KC-RPMD accurately captures the combination of electronic- and nuclear-dynamical effects throughout the Marcus (intermediate solvent friction) and Zusman (large solvent friction) regimes of ET. It is also demonstrated that KC-RPMD accurately describes systems in which the magnitude of the diabatic coupling depends on the position of a dynamical donor–acceptor mode. In addition to these successes, however, we present an unsurprising failure of KC-RPMD to capture the enhancement of the ET rate in the low solvent friction regime associated with nuclear coherence effects. In this analysis, we re-visit several aspects of the original KC-RPMD formulation, including the form of the kinetic constraint and the choice of the mass of the auxiliary electronic variable. In particular, we introduce a Langevin bath for the auxiliary electronic variable to correct for its unphysically low coupling with the nuclear degrees of freedom. This work demonstrates that the KC-RPMD method is well suited for the direct simulation of non-adiabatic donor–acceptor chemistries associated with many complex systems, including those for which solvent dynamics plays an important role in the reaction mechanism.

Scaling relationships for nonadiabatic energy relaxation times in warm dense matter: toward understanding the equation of state

The dependence of nonadiabatic ion-electron energy transfer rates in warm dense aluminum on the mass density and temperature with decoherence changing this relationship qualitatively.