Propagation with distributed Gaussians as a sparse, adaptive basis for higher-dimensional quantum dynamics

Long-Range Nonequilibrium Coherent Tunneling Induced by Fractional Vibronic Resonances

We study the influence of a linear energy bias on a nonequilibrium excitation on a chain of molecules coupled to local vibrations (a tilted Holstein model) using both a random-walk rate kernel theory and a nonperturbative, massively parallelized adaptive-basis algorithm. We uncover structured and discrete vibronic resonance behavior fundamentally different from both linear response theory and homogeneous polaron dynamics. Remarkably, resonance between the phonon energy ℏω and the bias δ_ϵ occurs not only at integer but also fractional ratios δ_ϵ/(ℏω) = m/n, which effect long-range n-bond m-phonon tunneling. These observations are reproduced in a model calculation of a recently demonstrated Cy3 system, and the effect of dipole-dipole-type non-nearest-neighbor coupling and vibrationally relaxed initial states is also considered. Potential applications range from molecular electronics to optical lattices and artificial light harvesting via vibronic engineering of coherent quantum transport.

Predicting Molecular Photochemistry Using Machine-Learning-Enhanced Quantum Dynamics Simulations

The processes which occur after molecules absorb light underpin an enormous range of fundamental technologies and applications, including photocatalysis to enable new chemical transformations, sunscreens to protect against the harmful effects of UV overexposure, efficient photovoltaics for energy generation from sunlight, and fluorescent probes to image the intricate details of complex biomolecular structures. Reflecting this broad range of applications, an enormously versatile set of experiments are now regularly used to interrogate light-driven chemical dynamics, ranging from the typical ultrafast transient absorption spectroscopy used in many university laboratories to the inspiring central facilities around the world, such as the next-generation of X-ray free-electron lasers.Computer simulations of light-driven molecular and material dynamics are an essential route to analyzing the enormous amount of transient electronic and structural data produced by these experimental sources. However, to date, the direct simulation of molecular photochemistry remains a frontier challenge in computational chemical science, simultaneously demanding the accurate treatment of molecular electronic structure, nuclear dynamics, and the impact of nonadiabatic couplings.To address these important challenges and to enable new computational methods which can be integrated with state-of-the-art experimental capabilities, the past few years have seen a burst of activity in the development of "direct" quantum dynamics methods, merging the machine learning of potential energy surfaces (PESs) and nonadiabatic couplings with accurate quantum propagation schemes such as the multiconfiguration time-dependent Hartree (MCTDH) method. The result of this approach is a new generation of direct quantum dynamics tools in which PESs are generated in tandem with wave function propagation, enabling accurate "on-the-fly" simulations of molecular photochemistry. These simulations offer an alternative route toward gaining quantum dynamics insights, circumventing the challenge of generating ab initio electronic structure data for PES fitting by instead only demanding expensive energy evaluations as and when they are needed.In this Account, we describe the chronological evolution of our own contributions to this field, focusing on describing the algorithmic developments that enable direct MCTDH simulations for complex molecular systems moving on multiple coupled electronic states. Specifically, we highlight active learning strategies for generating PESs during grid-based quantum chemical dynamics simulations, and we discuss the development and impact of novel diabatization schemes to enable direct grid-based simulations of photochemical dynamics; these developments are highlighted in a series of benchmark molecular simulations of systems containing multiple nuclear degrees of freedom moving on multiple coupled electronic states. We hope that the ongoing developments reported here represent a major step forward in tools for modeling excited-state chemistry such as photodissociation, proton and electron transfer, and ultrafast energy dissipation in complex molecular systems.

Moving Boundary Truncated Grid Method: Application to the Time Evolution of Distribution Functions in Phase Space

The moving boundary truncated grid (TG) method, previously developed to integrate the time-dependent Schrödinger equation and the imaginary time Schrödinger equation, is extended to the time evolution of distribution functions in phase space. A variable number of phase space grid points in the Eulerian representation are used to integrate the equation of motion for the distribution function, and the boundaries of the TG are adaptively determined as the distribution function evolves in time. Appropriate grid points are activated and deactivated for propagation of the distribution function, and no advance information concerning the dynamics in phase space is required. The TG method is used to integrate the equations of motion for phase space distribution functions, including the Klein-Kramers, Wigner-Moyal, and modified Caldeira-Leggett equations. Even though the initial distribution function is nonnegative, the solutions to the Wigner-Moyal and modified Caldeira-Leggett equations may develop negative basins in phase space originating from interference effects. Trajectory-based methods for propagation of the distribution function do not permit the formation of negative regions. However, the TG method can correctly capture the negative basins. Comparisons between the computational results obtained from the full grid and TG calculations demonstrate that the TG method not only significantly reduces the computational effort but also permits accurate propagation of various distribution functions in phase space.

A-VCI: A flexible method to efficiently compute vibrational spectra

The adaptive vibrational configuration interaction algorithm has been introduced as a new method to efficiently reduce the dimension of the set of basis functions used in a vibrational configuration interaction process. It is based on the construction of nested bases for the discretization of the Hamiltonian operator according to a theoretical criterion that ensures the convergence of the method. In the present work, the Hamiltonian is written as a sum of products of operators. The purpose of this paper is to study the properties and outline the performance details of the main steps of the algorithm. New parameters have been incorporated to increase flexibility, and their influence has been thoroughly investigated. The robustness and reliability of the method are demonstrated for the computation of the vibrational spectrum up to 3000 cm^-1 of a widely studied 6-atom molecule (acetonitrile). Our results are compared to the most accurate up to date computation; we also give a new reference calculation for future work on this system. The algorithm has also been applied to a more challenging 7-atom molecule (ethylene oxide). The computed spectrum up to 3200 cm^-1 is the most accurate computation that exists today on such systems.

Fingerprints of Delocalized Transition States in Quantum Dynamics

Reactions with delocalized transition states (plateau reactions) can be characterized statically by their energy profile along the reaction path, where they exhibit a broad, flat region instead of one or several well-defined saddle points on the potential energy surface. Employing our new, highly flexible quantum dynamics code to perform two-dimensional and effective four-dimensional quantum wave packet propagations on ab initio based model potentials, we show that plateau reactions can also be discerned from the other standard reaction types by their dynamics.