Quantum Dynamical Methods Research Articles

Dynamics of high-dimensional quantum systems coupled to a harmonic bath. General theory and implementation via multiconfigurational wave packets and truncated hierarchical equations for the mean-fields.

Modeling the dynamics of a quantum system coupled to a dissipative environment becomes particularly challenging when the system's dimensionality is too high to permit the computation of its eigenstates. This problem is addressed by introducing an eigenstate-free formalism, where the open quantum system is represented as a mixture of high-dimensional, time-dependent wave packets governed by coupled Schrödinger equations, while the environment is described by a multi-component quantum master equation. An efficient computational implementation of this formalism is presented, employing a variational mixed Gaussian/multiconfigurational time-dependent Hartree (G-MCTDH) ansatz for the wave packets and propagating the environment dynamics via hierarchical equations, truncated at the first or second level of the hierarchy. The effectiveness of the proposed methodology is demonstrated on a 61-dimensional model of phonon-driven vibrational relaxation of an adsorbate. G-MCTDH calculations on 4- and 10-dimensional reduced models, combined with truncated hierarchical equations for the mean fields, nearly quantitatively replicate the full-dimensional quantum dynamical results on vibrational relaxation while significantly reducing the computational time. This approach thus offers a promising quantum dynamical method for modeling complex system-bath interactions, where a large number of degrees of freedom must be explicitly considered.

Drag and Thermal Reduction of Spiked Hypersonic Vehicle in Thermochemical Nonequilibrium

This study utilizes the in-house parallel direct simulation Monte Carlo–quantum dynamics method to model the aerodynamic flowfield of a spiked reentry vehicle within a rarefied high-altitude atmosphere. Investigating the flight of spiked aircraft under various flight conditions and spike sizes and considering both the real gas effect and the rarefied gas effect, the aerodynamic characteristic of the aircraft is evaluated. Performance evaluation for effectiveness in drag reduction and thermal protection is based on drag and the maximum stagnation heat flux coefficient at the vehicle’s shoulder. Findings indicate that, in the rarefied atmosphere, the distinction between the characteristic shock intensities of spiked and unspiked vehicles is not pronounced, which results in a drag reduction of approximately 5%, accompanied by a more than 100% increase in thermal effect on the vehicle’s shoulder, obviously poor in effectiveness. Subsequently, this study examines the spiked vehicle equipped with a lateral jet, and this augmented approach achieves a marked reduction in the intensity of the shock wave impacting the vehicle’s shoulder with a drag reduction exceeding 10% and attenuates the thermal impact by over 50% in comparison to the implementation of spiking alone, thereby demonstrating superior performance in terms of effectiveness.

Interfacial Charge Transfer in Photoexcited QD-Molecule Composite of Tetrahedral CdSe Quantum Dot Coupled with Carbazole.

Photoexcited charge transfer dynamics in CdSe quantum dots (QDs) coupled with carbazole were explored to model QD-molecule systems for light-harvesting applications. The absorption spectra of QDs with different sizes, i.e., Cd35Se20X30L30 (T1), Cd56Se35X42L42 (T2), and Cd84Se56X56L56 (T3) were simulated with quantum dynamical methods, which qualitatively match the reported experimental spectra. The carbazole is attached with a 3-amino group at the apex position of T1 (namely T1-3A-Cz), establishing proper electronic communication between T1 and carbazole. The spectra of T1-3A-Cz is 0.22 eV red-shifted compared to T1. A time-dependent perturbation was applied in tune with the lowest energy peak (3.63 eV) of T1-3A-Cz to investigate the charge transfer dynamics, which revealed an ultrafast charge separation within the femtosecond time scale. The electronic structure showed a favorable energy alignment between T1 and carbazole in T1-3A-Cz. The LUMO of carbazole was situated below the conduction band of the QD, while the HOMO of carbazole mixed perfectly with the top of the valence band of the QD, developing the interfacial charge transfer states. These states promoted the photoexcited electron transfer directly from the CdSe core to carbazole. A rapid and enhanced charge separation occurred with the laser field strength increasing from 0.001 to 0.005 V/Å. However, T1 connected to the other positions of carbazole did not show charge separation effectively. The photoinduced charge transfer is negligible in the case of T2-carbazole systems due to poor electronic coupling, and it is not observed in T3-carbazole systems. So, the T1-3A-Cz model acts as a perfect donor-acceptor QD-molecule nanocomposite that can harvest photon energy efficiently. Further enhancement of charge transfer can be achieved by coupling more carbazoles to the T1 QD (e.g., T1-3A-Cz2) due to the extension of hole delocalization between T1 and the carbazoles.

Investigating the collective nature of cavity-modified chemical kinetics under vibrational strong coupling

Abstract In this paper, we develop quantum dynamical methods capable of treating the dynamics of chemically reacting systems in an optical cavity in the vibrationally strong-coupling (VSC) limit at finite temperatures and in the presence of a dissipative solvent in both the few and many molecule limits. In the context of two simple models, we demonstrate how reactivity in the collective VSC regime does not exhibit altered rate behavior in equilibrium but may exhibit resonant cavity modification of reactivity when the system is explicitly out of equilibrium. Our results suggest experimental protocols that may be used to modify reactivity in the collective regime and point to features not included in the models studied, which demand further scrutiny.

Strong Laser Field-Driven Coupled Electron-Nuclear Dynamics: Quantum vs Classical Description.

We have performed a coupled electron-nuclear dynamics study of H2+ molecular ions under the influence of an intense few-cycle 4.5 fs laser pulse with an intensity of 4 × 1014 W/cm2 and a central wavelength of 750 nm. Both quantum and classical dynamical methods are employed in the exact similar initial conditions with the aim of head-to-head comparison of two methodologies. A competition between ionization and dissociation channel is explained under the framework of quantum and classical dynamics. The origin of the electron localization phenomena is elucidated by observing the molecular and electronic wave packet evolution pattern. By probing with different carrier envelope phase (CEP) values of the ultrashort pulse, the possibility of electron localization on either of the two nuclei is investigated. The effects of initial vibrational states on final dissociation and ionization probabilities for several CEP values are studied in detail. Finally, asymmetries in the dissociation probabilities are calculated and mutually compared for both quantum and classical dynamical methodologies, whereas Franck-Condon averaging over the initial vibrational states is carried out in order to mimic the existing experimental conditions.

MLQD: A package for machine learning-based quantum dissipative dynamics

Machine learning has emerged as a promising paradigm to study the quantum dissipative dynamics of open quantum systems. To facilitate the use of our recently published ML-based approaches for quantum dissipative dynamics, here we present an open-source Python package MLQD (https://github.com/Arif-PhyChem/MLQD), which currently supports the three ML-based quantum dynamics approaches: (1) the recursive dynamics with kernel ridge regression (KRR) method, (2) the non-recursive artificial-intelligence-based quantum dynamics (AIQD) approach and (3) the blazingly fast one-shot trajectory learning (OSTL) approach, where both AIQD and OSTL use the convolutional neural networks (CNN). This paper describes the features of the MLQD package, the technical details, optimization of hyperparameters, visualization of results, and the demonstration of the MLQD's applicability for two widely studied systems, namely the spin-boson model and the Fenna–Matthews–Olson (FMO) complex. To make MLQD more user-friendly and accessible, we have made it available on the Python Package Index (PyPi) platform and it can be installed via ▪. In addition, it is also available on the XACS cloud computing platform (https://XACScloud.com) via the interface to the MLatom package (http://MLatom.com). Program summaryProgram Title: MLQDCPC Library link to program files:https://doi.org/10.17632/yxp37csy5x.1Developer's repository link:https://github.com/Arif-PhyChem/MLQDCode Ocean capsule:https://codeocean.com/capsule/5563143/treeLicensing provisions: Apache Software License 2.0Programming language: Python 3.0Supplementary material: Jupyter Notebook-based tutorialsExternal routines/libraries: Tensorflow, Scikit-learn, Hyperopt, Matplotlib, MLatomNature of problem: Fast propagation of quantum dissipative dynamics with machine learning approaches.Solution method: We have developed MLQD as a comprehensive framework that streamlines and supports the implementation of our recently published machine learning-based approaches for efficient propagation of quantum dissipative dynamics. This framework encompasses: (1) the recursive dynamics with kernel ridge regression (KRR) method, as well as the non-recursive approaches utilizing convolutional neural networks (CNN), namely (2) artificial intelligence-based quantum dynamics (AIQD), and (3) one-shot trajectory learning (OSTL).Additional comments including restrictions and unusual features:1.Users can train a machine learning (ML) model following one of the ML-based approaches: KRR, AIQD and OSTL.2.Users have the option to propagate dynamics with the existing trained ML models.3.MLQD also provides the transformation of trajectories into the training data.4.MLQD also supports hyperparameter optimization using MLATOM's grid search functionality for KRR and Bayesian methods with Tree-structured Parzen Estimator (TPE) for CNN models via the HYPEROPT package.5.MLQD also facilitates the visualization of results via auto-plotting.6.MLQD is designed to be user-friendly and easily accessible, with availability on the XACS cloud computing platform (https://XACScloud.com) via the interface to the MLATOM package (http://MLatom.com). In addition, it is also available as a pip package which makes it easy to install. Future outlook: MLQD will be extended to more realistic systems along with the incorporation of other machine learning-based approaches as well as the traditional quantum dynamics methods.

Beyond Conventional Density Functional Theory: Advanced Quantum Dynamical Methods for Understanding Degradation of Per- and Polyfluoroalkyl Substances.

Computational chemistry methods, such as density functional theory (DFT), have now become more common in environmental research, particularly for simulating the degradation of per- and polyfluoroalkyl substances (PFAS). However, the vast majority of PFAS computational studies have focused on conventional DFT approaches that only probe static, time-independent properties of PFAS near stationary points on the potential energy surface. To demonstrate the rich mechanistic information that can be obtained from time-dependent quantum dynamics calculations, we highlight recent studies using these advanced techniques for probing PFAS systems. We briefly discuss recent applications ranging from ab initio molecular dynamics to DFT-based metadynamics and real-time time-dependent DFT for probing PFAS degradation in various reactive environments. These quantum dynamical approaches provide critical mechanistic information that cannot be gleaned from conventional DFT calculations. We conclude with a perspective of promising research directions and recommend that these advanced quantum dynamics simulations be more widely used by the environmental research community to directly probe PFAS degradation dynamics and other environmental processes.

Photoionization Bands of Cyanogen: Multi-Mode Vibronic Coupling and Renner-Teller Effects.

Multi-mode vibronic coupling in the , , and electronic states of Cyanogen radical cation (C N ) is investigated with the aid of ab initio quantum chemistry and first principles quantum dynamics methods. The electronic degenerate states of Π symmetry of C N undergo Renner-Teller (RT) splitting along degenerate vibrational modes of π symmetry. The RT split components form symmetry allowed conical intersections with those from nearby RT split states or with non-degenerate electronic states of Σ symmetry. A parameterized vibronic Hamiltonian is constructed using standard vibronic coupling theory in a diabatic electronic basis and symmetry rules. The parameters of the Hamiltonian are derived from ab initio calculated adiabatic electronic energies. The vibronic spectrum is calculated, assigned and compared with the available experimental data. The impact of various electronic coupling on the vibronic structure of the spectrum is discussed.

An exact imaginary-time path-integral phase-space formulation of multi-time correlation functions.

An exact representation of quantum mechanics using the language of phase-space variables provides a natural starting point to introduce and develop semiclassical approximations for the calculation of time correlation functions. Here, we introduce an exact path-integral formalism for calculations of multi-time quantum correlation functions as canonical averages over ring-polymer dynamics in imaginary time. The formulation provides a general formalism that exploits the symmetry of path integrals with respect to permutations in imaginary time, expressing correlations as products of imaginary-time-translation-invariant phase-space functions coupled through Poisson bracket operators. The method naturally recovers the classical limit of multi-time correlation functions and provides an interpretation of quantum dynamics in terms of "interfering trajectories" of the ring-polymer in phase space. The introduced phase-space formulation provides a rigorous framework for the future development of quantum dynamics methods that exploit the invariance of imaginary time path integrals to cyclic permutations.

Quasi-diabatic propagation scheme for simulating polariton chemistry.

We generalize the quasi-diabatic (QD) propagation scheme to simulate the non-adiabatic polariton dynamics in molecule-cavity hybrid systems. The adiabatic-Fock states, which are the tensor product states of the adiabatic electronic states of the molecule and photon Fock states, are used as the locally well-defined diabatic states for the dynamics propagation. These locally well-defined diabatic states allow using any diabatic quantum dynamics methods for dynamics propagation, and the definition of these states will be updated at every nuclear time step. We use several recently developed non-adiabatic mapping approaches as the diabatic dynamics methods to simulate polariton quantum dynamics in a Shin-Metiu model coupled to an optical cavity. The results obtained from the mapping approaches provide very accurate population dynamics compared to the numerically exact method and outperform the widely used mixed quantum-classical approaches, such as the Ehrenfest dynamics and the fewest switches surface hopping approach. We envision that the generalized QD scheme developed in this work will provide a powerful tool to perform the non-adiabatic polariton simulations by allowing a direct interface between the diabatic dynamics methods and ab initio polariton information.

Adiabatic and Nonadiabatic Dynamics with Interacting Quantum Trajectories.

We present a quantum dynamics method based on the propagation of interacting quantum trajectories to describe both adiabatic and nonadiabatic processes within the same formalism. The idea originates from the work of Poirier [Chem. Phys.2010,370, 4-14] and Schiff and Poirier [J. Chem. Phys.2012,136, 031102] on quantum dynamics without wavefunctions. It consists of determining the quantum force arising in the Bohmian hydrodynamic formulation of quantum dynamics using only information about quantum trajectories. The particular time-dependent propagation scheme proposed here results in very stable dynamics. Its performance is discussed by applying the method to analytical potentials in the adiabatic regime, and by combining it with the exact factorization method in the nonadiabatic regime.

Perturbation theory under the truncated Wigner approximation: How system-environment entanglement formation drives quantum decoherence

Quantum decoherence is the disappearance of simple phase relations within a discrete quantum system as a result of interactions with an environment. For many applications, the question is not necessarily how to avoid (inevitable) system-environment interactions, but rather how to design environments that optimally preserve a system's phase relations in spite of such interactions. The formation of system-environment entanglement is a major driving mechanism for decoherence, and a detailed understanding of this process could inform strategies for conserving coherence optimally. This requires scalable, flexible, and systematically improvable quantum dynamical methods that retain detailed information about the entanglement properties of the environment, yet very few current methods offer this combination of features. Here, we address this need by introducing a theoretical framework wherein we combine the truncated Wigner approximation with standard time-dependent perturbation theory allowing for computing expectation values of operators in the combined system-environment Hilbert space. We demonstrate the utility of this framework by applying it to the spin-boson model, representative of qubits and simple donor-acceptor systems. For this model, our framework provides an analytical description of perturbative contributions to expectation values. We monitor how quantum decoherence at zero temperature is accompanied by entanglement formation with individual environmental degrees of freedom. Based on this entanglement behavior, we find that the selective suppression of low-frequency environmental modes is particularly effective for mitigating quantum decoherence.

2D spectroscopies from condensed phase dynamics: Accessing third-order response properties from equilibrium multi-time correlation functions

The third-order response lies at the heart of simulating and interpreting nonlinear spectroscopies ranging from two-dimensional infrared (2D-IR) to 2D electronic (2D-ES), and 2D sum frequency generation (2D-SFG). The extra time and frequency dimensions in these spectroscopic techniques provide access to rich information on the electronic and vibrational states present, the coupling between them, and the resulting rates at which they exchange energy that are obscured in linear spectroscopy, particularly for condensed phase systems that usually contain many overlapping features. While the exact quantum expression for the third-order response is well established, it is incompatible with the methods that are practical for calculating the atomistic dynamics of large condensed phase systems. These methods, which include both classical mechanics and quantum dynamics methods that retain quantum statistical properties while obeying the symmetries of classical dynamics, such as LSC-IVR, centroid molecular dynamics, and Ring Polymer Molecular Dynamics (RPMD), naturally provide short-time approximations to the multi-time symmetrized Kubo transformed correlation function. Here, we show how the third-order response can be formulated in terms of equilibrium symmetrized Kubo transformed correlation functions. We demonstrate the utility and accuracy of our approach by showing how it can be used to obtain the third-order response of a series of model systems using both classical dynamics and RPMD. In particular, we show that this approach captures features such as anharmonically induced vertical splittings and peak shifts while providing a physically transparent framework for understanding multidimensional spectroscopies.

Influence of various scattering mechanisms on thermal conductivity of doped Pr1.3−xLa0.7CexCuO4 high-temperature superconductor

A theoretical analysis of thermal conductivity of high-temperature superconductor cuprates, Pr1.3−xLa0.7CexCuO4 (PLCCO), has been successfully investigated. In this formulation, the idea of relaxation times and other scattering processes has been developed from frequency (energy) line widths using a quantum dynamical method. The major emphasis of this study is on the influence of phonon-dopant atom scattering on the thermal conductivity of Ce-doped PLCCO, as well as other prominent scattering processes such as electron-phonon, cubic and quartic anharmonic phonon, cubic and quartic phonon interference, and so on. The proposed theory has achieved a satisfactory agreement between theory and experiment.

Artificial neural network-based path integral simulations of hydrogen isotope diffusion in palladium

The contribution of nuclear quantum effects (NQEs) to the kinetics and dynamics of interstitial H isotopes in face-centered cubic Pd was intensively investigated using several path-integral techniques, along with a newly developed machine-learning interatomic potential based on artificial neural networks for Pd–H alloys. The diffusion coefficients (D) of protium, deuterium, and tritium in Pd were predicted over a wide temperature range (50–1500 K) based on quantum transition-state theory (QTST) combined with path-integral molecular-dynamics simulations. The importance of NQEs even at high temperatures was illustrated in terms of the characteristic temperature dependence of the activation free energies for H-isotope migration in Pd. This illuminates the overall picture of anomalous D crossovers among the three H isotopes in Pd. In addition, the D of protium in Pd was directly computed using two approximate quantum-dynamics methods based on Feynman’s path-integral theory, i.e. centroid molecular dynamics (CMD) and ring-polymer molecular dynamics (RPMD), in the temperature range 370–1500 K. The D values obtained from the CMD and RPMD simulations were very similar and agreed better with the reported experimental values than the QTST results in this temperature range. Our machine learning-based path-integral calculations elucidate the underlying quantum nature of the ‘reversed S’-type nonlinear behavior of D for the three H isotopes in Pd on the Arrhenius plots.

Applicability of the Thawed Gaussian Wavepacket Dynamics to the Calculation of Vibronic Spectra of Molecules with Double-Well Potential Energy Surfaces.

Simulating vibrationally resolved electronic spectra of anharmonic systems, especially those involving double-well potential energy surfaces, often requires expensive quantum dynamics methods. Here, we explore the applicability and limitations of the recently proposed single-Hessian thawed Gaussian approximation for the simulation of spectra of systems with double-well potentials, including 1,2,4,5-tetrafluorobenzene, ammonia, phosphine, and arsine. This semiclassical wavepacket approach is shown to be more robust and to provide more accurate spectra than the conventional harmonic approximation. Specifically, we identify two cases in which the Gaussian wavepacket method is especially useful due to the breakdown of the harmonic approximation: (i) when the nuclear wavepacket is initially at the top of the potential barrier but delocalized over both wells, e.g., along a low-frequency mode, and (ii) when the wavepacket has enough energy to classically go over the low potential energy barrier connecting the two wells. The method is efficient and requires only a single classical ab initio molecular dynamics trajectory, in addition to the data required to compute the harmonic spectra. We also present an improved algorithm for computing the wavepacket autocorrelation function, which guarantees that the evaluated correlation function is continuous for arbitrary size of the time step.

Time‐dependent density matrix renormalization group method for quantum dynamics in complex systems

AbstractThe simulations of spectroscopy and quantum dynamics are of vital importance to the understanding of the electronic processes in complex systems, including the radiative/radiationless electronic relaxation relevant for optical emission, charge/energy transfer in molecular aggregates related to carrier mobility in organic materials, as well as photovoltaic and thermoelectric conversion, light‐harvesting and spin transport, and so forth. In recent years, time‐dependent density matrix renormalization group (TD‐DMRG) has emerged as a general, numerically accurate and efficient method for high‐dimensional full‐quantum dynamics. This review will cover the fundamental algorithms of TD‐DMRG in the modern framework of matrix product states (MPS) and matrix product operators (MPO), including the basic algebra with respect to MPS and MPO, the novel time evolution schemes to propagate MPS, and the automated MPO construction algorithm to encode generic Hamiltonian. Most importantly, the proposed method can handle the mixed state density matrix at finite temperature, enabling quantum statistical description for molecular aggregates. We demonstrate the performance of TD‐DMRG by benchmarking with the current state‐of‐the‐art methods for simulating quantum dynamics of the spin‐boson model and the Frenkel–Holstein(–Peierls) model. As applications of TD‐DMRG to real‐world problems, we present theoretical investigations of carrier mobility and spectral function of rubrene crystal, and the radiationless decay rate of azulene with an anharmonic potential energy surface.This article is categorized under: Theoretical and Physical Chemistry > Statistical Mechanics Theoretical and Physical Chemistry > Reaction Dynamics and Kinetics Software > Simulation Methods

Multidimensional stochastic dissipative quantum dynamics using a Lindblad operator.

In this paper, multidimensional dissipative quantum dynamics is studied within a system-bath approach in the Markovian regime using a model Lindblad operator. We report on the implementation of a Monte Carlo wave packet algorithm in the Heidelberg version of the Multi-Configuration Time-Dependent Hartree (MCTDH) program package, which is henceforth extended to treat stochastic dissipative dynamics. The Lindblad operator is represented as a sum of products of one-dimensional operators. The new form of the operator is not restricted to the MCTDH formalism and could be used with other multidimensional quantum dynamical methods. As a benchmark system, a two-dimensional coupled oscillators model representing the internal stretch and the surface-molecule distance in the O2/Pt(111) system coupled to a Markovian bath of electron-hole-pairs is used. The simulations reveal the interplay between coherent intramolecular coupling due to anharmonic terms in the potential and incoherent relaxation due to coupling to an environment. It is found that thermalization of the system can be approximately achieved when the intramolecular coupling is weak.

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.

Complex Time Method for Quantum Dynamics When an Exceptional Point is Encircled in the Parameter Space

Complex Time Method for Quantum Dynamics When an Exceptional Point is Encircled in the Parameter Space