Time-dependent importance sampling in semiclassical initial value representation calculations for time correlation functions

A Semiclassical Framework for Mixed Quantum Classical Dynamics

Semiclassical (SC) approximations for quantum dynamic simulations in complex chemical systems range from rigorously accurate methods that are computationally expensive to methods that exhibit near-classical scaling with system size but are limited in their ability to describe quantum effects. In practical studies of high-dimensional reactions, neither extreme is the best choice: frequently a high-level quantum mechanical description is only required for a handful of modes, while the majority of environment modes that do not play a key role in the reactive event of interest are well served with a lower level of theory. In this feature, we introduce modified Filinov filtration as a powerful tool to construct mixed quantum-classical SC theories where different subsystems can be quantized to different extents without introducing ad hoc intersubsystem interaction terms. We demonstrate that these Filinov-based SC methods can systematically tune between quantum and classical limit SC behavior, offering a practical way forward to accurate and computationally efficient simulations of high-dimensional quantum processes.

Three-state harmonic models for photoinduced charge transfer

A widely used strategy for simulating the charge transfer between donor and acceptor electronic states in an all-atom anharmonic condensed-phase system is based on invoking linear response theory to describe the system in terms of an effective spin-boson model Hamiltonian. Extending this strategy to photoinduced charge transfer processes requires also taking into consideration the ground electronic state in addition to the excited donor and acceptor electronic states. In this paper, we revisit the problem of describing such nonequilibrium processes in terms of an effective three-state harmonic model. We do so within the framework of nonequilibrium Fermi's golden rule (NE-FGR) in the context of photoinduced charge transfer in the carotenoid-porphyrin-C₆₀ (CPC₆₀) molecular triad dissolved in explicit tetrahydrofuran (THF). To this end, we consider different ways for obtaining a three-state harmonic model from the equilibrium autocorrelation functions of the donor-acceptor, donor-ground, and acceptor-ground energy gaps, as obtained from all-atom molecular dynamics simulations of the CPC₆₀/THF system. The quantum-mechanically exact time-dependent NE-FGR rate coefficients for two different charge transfer processes in two different triad conformations are then calculated using the effective three-state model Hamiltonians as well as a hierarchy of more approximate expressions that lead to the instantaneous Marcus theory limit. Our results show that the photoinduced charge transfer in CPC₆₀/THF can be described accurately by the effective harmonic three-state models and that nuclear quantum effects are small in this system.

Semiclassical vibrational spectroscopy with Hessian databases

We report on a new approach to ease the computational overhead of ab initio "on-the-fly" semiclassical dynamics simulations for vibrational spectroscopy. The well known bottleneck of such computations lies in the necessity to estimate the Hessian matrix for propagating the semiclassical pre-exponential factor at each step along the dynamics. The procedure proposed here is based on the creation of a dynamical database of Hessians and associated molecular geometries able to speed up calculations while preserving the accuracy of results at a satisfactory level. This new approach can be interfaced to both analytical potential energy surfaces and on-the-fly dynamics, allowing one to study even large systems previously not achievable. We present results obtained for semiclassical vibrational power spectra of methane, glycine, and N-acetyl-L-phenylalaninyl-L-methionine-amide, a molecule of biological interest made of 46 atoms.

"Divide and conquer" semiclassical molecular dynamics: A practical method for spectroscopic calculations of high dimensional molecular systems

We extensively describe our recently established "divide-and-conquer" semiclassical method [M. Ceotto, G. Di Liberto, and R. Conte, Phys. Rev. Lett. 119, 010401 (2017)] and propose a new implementation of it to increase the accuracy of results. The technique permits us to perform spectroscopic calculations of high-dimensional systems by dividing the full-dimensional problem into a set of smaller dimensional ones. The partition procedure, originally based on a dynamical analysis of the Hessian matrix, is here more rigorously achieved through a hierarchical subspace-separation criterion based on Liouville's theorem. Comparisons of calculated vibrational frequencies to exact quantum ones for a set of molecules including benzene show that the new implementation performs better than the original one and that, on average, the loss in accuracy with respect to full-dimensional semiclassical calculations is reduced to only 10 wavenumbers. Furthermore, by investigating the challenging Zundel cation, we also demonstrate that the "divide-and-conquer" approach allows us to deal with complex strongly anharmonic molecular systems. Overall the method very much helps the assignment and physical interpretation of experimental IR spectra by providing accurate vibrational fundamentals and overtones decomposed into reduced dimensionality spectra.

Semiclassical treatment of quantum propagation with nonlinear classical dynamics: A third-order thawed Gaussian approximation

The time-dependent WKB approximation for a coherent state is expanded to third order around a guiding real trajectory, allowing for the novel treatment of nonlinearity in its semiclassical dynamics, which is generally present in all physical systems far from the classical regime. The result is a closed-form solution consisting of a linear combination of Airy functions and their derivatives multiplied by an exponential. The expression's ability to capture nonlinearity is demonstrated by examining the autocorrelation of initial coherent states in anharmonic systems with few to many contributing periodic orbits. Its accuracy is compared to the quadratic expansion and found to be superior in regimes of ℏ where the curvature begins to be significant, as expected. Moreover, the expression is shown to be a real-trajectory uniformization over two coalescing saddle points that are emblematic of significant curvature. This extends real-trajectory time-dependent wave-packet semiclassical methods to highly anharmonic systems for the first time and establishes their regime of validity.

A journey through chemical dynamics

The charge with the invitation to write this autobiographical article was to describe what led me to a career in science and to choose the specific topics and scientific directions I have pursued. This is thus a very personal story and by no means a scientific review of the work that is mentioned. As will be clear, this journey was not an orderly, well-thought-out plan, but just "happened," one step after the other.

Semiclassical Monte-Carlo approach for modelling non-adiabatic dynamics in extended molecules

Modelling of non-adiabatic dynamics in extended molecular systems and solids is a next frontier of atomistic electronic structure theory. The underlying numerical algorithms should operate only with a few quantities (that can be efficiently obtained from quantum chemistry), provide a controlled approximation (which can be systematically improved) and capture important phenomena such as branching (multiple products), detailed balance and evolution of electronic coherences. Here we propose a new algorithm based on Monte-Carlo sampling of classical trajectories, which satisfies the above requirements and provides a general framework for existing surface hopping methods for non-adiabatic dynamics simulations. In particular, our algorithm can be viewed as a post-processing technique for analysing numerical results obtained from the conventional surface hopping approaches. Presented numerical tests for several model problems demonstrate efficiency and accuracy of the new method.

Many interesting chemical problems like photosynthesis and photovoltaics involve non-adiabatic dynamical phenomena, which are difficult to predict theoretically. Here, the authors develop a new numerical method capable of recovering quantum interferences that are neglected by conventional methods.

Electronically nonadiabatic dynamics in complex molecular systems: an efficient and accurate semiclassical solution

Chemical reaction dynamics is always a central theme in chemistry research. In many important chemical processes, reaction dynamics is electronically nonadiabatic, i.e., dynamics involves coupled multiple electronic states. We demonstrate in this paper that a semiclassical (SC) treatment based on an initial value representation methodology and a classical mapping formalism for the electronic degrees of freedom is now able to provide a rigorous and practical solution to electronically nonadiabatic dynamics in complex molecular systems. The key component of this treatment is to incorporate a correlated importance sampling protocol in nonadiabatic SC calculations, which results in a speedup factor of 100 or more in comparison with that using the standard sampling approach. This is illustrated by application to a two-state model coupled with up to 10 nuclear bath modes for a benchmark nonadiabatic excitation energy transfer problem. This work provides great opportunities for the effectively theoretical investigations on reaction mechanisms in complex molecular systems, in which electronically nonadiabatic dynamics plays an importance role.

Communication: importance sampling including path correlation in semiclassical initial value representation calculations for time correlation functions

Full semiclassical (SC) initial value representation (IVR) for time correlation functions involves a double phase space average over a set of two phase points, each of which evolves along a classical path. Conventionally, the two initial phase points are sampled independently for all degrees of freedom (DOF) in the Monte Carlo procedure. Here, we present an efficient importance sampling scheme by including the path correlation between the two initial phase points for the bath DOF, which greatly improves the performance of the SC-IVR calculations for large molecular systems. Satisfactory convergence in the study of quantum coherence in vibrational relaxation has been achieved for a benchmark system-bath model with up to 21 DOF.

Beating the efficiency of both quantum and classical simulations with a semiclassical method

While rigorous quantum dynamical simulations of many-body systems are extremely difficult (or impossible) due to exponential scaling with dimensionality, the corresponding classical simulations ignore quantum effects. Semiclassical methods are generally more efficient but less accurate than quantum methods and more accurate but less efficient than classical methods. We find a remarkable exception to this rule by showing that a semiclassical method can be both more accurate and faster than a classical simulation. Specifically, we prove that for the semiclassical dephasing representation the number of trajectories needed to simulate quantum fidelity is independent of dimensionality and also that this semiclassical method is even faster than the most efficient corresponding classical algorithm. Analytical results are confirmed with simulations of fidelity in up to 100 dimensions with 2(1700)-dimensional Hilbert space.