Quantum Dynamics with Gaussian Bases Defined by the Quantum Trajectories

Assessing the Accuracy of Quantum Dynamics Performed in the Time-Dependent Basis Representation

A full quantum-mechanical (QM) description of large amplitude nuclear motion, associated with chemical reactions or isomerization of high-dimensional molecular systems, is inherently challenging due to the exponential scaling of the QM complexity with system size. To ameliorate the scaling bottleneck in studies of realistic systems, typically modeled in the configuration space, the nuclear wave functions are represented in terms of time-dependent basis functions. Such bases are expected to give an accurate description with a modest number of basis functions employed, by adapting them to the wave function solving the time-dependent Schrödinger equation. It is not, however, straightforward to estimate the accuracy of the resulting solution: in QM the energy conservation, a convenient such measure for a classical trajectory evolving in a time-independent potential, is not a sufficient criterion of the dynamics' accuracy. In this work, we argue that the expectation value of the Hamiltonian's "variance", quantifying the basis completeness, is a suitable practical measure of the quantum dynamics' accuracy. Illustrations are given for several chemistry-relevant test systems, modeled employing time-independent as well as time-dependent bases, including the coupled and variational coherent states methods and the quantum-trajectory guided adaptable Gaussians (QTAG) as the latter basis type. A novel semilocal definition of the QTAG basis time-evolution for placing the basis functions "in the right place at the right time" is also presented.

Nonadiabatic Dynamics with Exact Factorization: Implementation and Assessment

In this work, we report our implementation of several independent-trajectory mixed-quantum-classical (ITMQC) nonadiabatic dynamics methods based on exact factorization (XF) in the Libra package for nonadiabatic and excited-state dynamics. Namely, the exact factorization surface hopping (SHXF), mixed quantum-classical dynamics (MQCXF), and mean-field (MFXF) are introduced. Performance of these methods is compared to that of several traditional surface hopping schemes, such as the fewest-switches surface hopping (FSSH), branching-corrected surface hopping (BCSH), and the simplified decay of mixing (SDM), as well as conventional Ehrenfest (mean-field, MF) method. Based on a comprehensive set of 1D model Hamiltonians, we find the ranking SHXF ≈ MQCXF > BCSH > SDM > FSSH ≫ MF, with the BCSH sometimes outperforming the XF methods in terms of describing coherences. Although the MFXF method can yield reasonable populations and coherences for some cases, it does not conserve the total energy and is therefore not recommended. We also find that the branching correction for auxiliary trajectories is important for the XF methods to yield accurate populations and coherences. However, the branching correction can worsen the quality of the energy conservation in the MQCXF. Finally, we find that using the time-dependent Gaussian width approximation used in the XF methods for computing decoherence correction can improve the quality of energy conservation in the MQCXF dynamics. The parameter-free scheme of Subotnik for computing the Gaussian widths is found to deliver the best performance in situations where such widths are not known a priori.

A Discrete-Variable Local Diabatic Representation of Conical Intersection Dynamics

Conical intersections (CIs) are ubiquitous in polyatomic molecules and are responsible for a wide range of phenomena in photochemistry and photophysics. Modeling the conical intersection dynamics with adiabatic electronic states is hindered by the divergence of the first- and second-order derivative couplings at CIs due to electronic degeneracy. We introduce and implement a novel diabatic representation for exact correlated electron-nuclear wave packet dynamics through conical intersections. It directly employs the adiabatic electronic states but avoids the singular first- and second-order derivative couplings and is robust to different gauge choices of the electronic wave function phases. The reference nuclear geometries defining the adiabatic electronic states are determined by a discrete-variable representation of the nuclear coordinates. The nonadiabatic effects are accounted for by the electronic overlap matrix instead of derivative couplings as in the adiabatic representation. Illustrated by a two-mode conical intersection model, this representation captures all nonadiabatic effects, including electronic transitions, electronic coherence, and geometric phases. Thus, this representation provides a singularity-free framework for modeling ab initio conical intersection wave packet 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.

Multidimensional Tunneling Dynamics Employing Quantum-Trajectory Guided Adaptable Gaussian Bases

An efficient basis representation of time-dependent wavefunctions is essential for theoretical studies of high-dimensional molecular systems exhibiting large-amplitude motion. For fully coupled anharmonic systems, the complexity of a general wavefunction scales exponentially with the system size; therefore, for practical reasons, it is desirable to adapt the basis to the time-dependent wavefunction at hand. Often times on this quest for a minimal basis representation, time-dependent Gaussians are employed, in part because of their localization in both configuration and momentum spaces and also because of their direct connection to classical and semiclassical dynamics, guiding the evolution of the basis function parameters. In this work, the quantum-trajectory guided adaptable Gaussian (QTAG) bases method [ J. Chem. Theory Comput. 2020, 16, 18-34] is generalized to include correlated, i.e., non-factorizable, basis functions, and the performance of the QTAG dynamics is assessed on benchmark system/bath tunneling models of up to 20 dimensions. For the popular choice of initial conditions describing tunneling between the reactant/product wells, the minimal "semiclassical" description of the bath modes using essentially a single multidimensional basis function combined with the multi-Gaussian representation of the tunneling mode is shown to capture the dominant features of dynamics in a highly efficient manner.

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.

"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.

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.

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.