1
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London N, Bu S, Johnson B, Ananth N. Mean-Field Ring Polymer Rates Using a Population Dividing Surface. J Phys Chem A 2024; 128:5730-5739. [PMID: 38976564 DOI: 10.1021/acs.jpca.4c00005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/10/2024]
Abstract
Mean-field ring polymer molecular dynamics offers a computationally efficient method for the simulation of reaction rates in multilevel systems. Previous work has established that, to model a nonadiabatic state-to-state reaction accurately, it is necessary to ensure reactive trajectories form kinked ring polymer configurations at the dividing surface. Building on this idea, we introduce a population difference coordinate and a reactive flux expression modified to only include contributions from kinked configurations. We test the accuracy of the resulting mean-field rate theory on a series of linear vibronic coupling model systems. We demonstrate that this new kMF-RP rate approach is efficient to implement and quantitatively accurate for models over a wide range of driving forces, coupling strengths, and temperatures.
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Affiliation(s)
- Nathan London
- Department of Chemistry, Cornell University, Ithaca, New York 14853, United States
| | - Siyu Bu
- Department of Chemistry, Cornell University, Ithaca, New York 14853, United States
| | - Britta Johnson
- Department of Chemistry, Cornell University, Ithaca, New York 14853, United States
| | - Nandini Ananth
- Department of Chemistry, Cornell University, Ithaca, New York 14853, United States
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2
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Gay-Balmaz F, Tronci C. Complex Fluid Models of Mixed Quantum-Classical Dynamics. JOURNAL OF NONLINEAR SCIENCE 2024; 34:81. [PMID: 38966687 PMCID: PMC11219418 DOI: 10.1007/s00332-024-10044-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/10/2023] [Accepted: 05/08/2024] [Indexed: 07/06/2024]
Abstract
Several methods in nonadiabatic molecular dynamics are based on Madelung's hydrodynamic description of nuclear motion, while the electronic component is treated as a finite-dimensional quantum system. In this context, the quantum potential leads to severe computational challenges and one often seeks to neglect its contribution, thereby approximating nuclear motion as classical. The resulting model couples classical hydrodynamics for the nuclei to the quantum motion of the electronic component, leading to the structure of a complex fluid system. This type of mixed quantum-classical fluid models has also appeared in solvation dynamics to describe the coupling between liquid solvents and the quantum solute molecule. While these approaches represent a promising direction, their mathematical structure requires a certain care. In some cases, challenging higher-order gradients make these equations hardly tractable. In other cases, these models are based on phase-space formulations that suffer from well-known consistency issues. Here, we present a new complex fluid system that resolves these difficulties. Unlike common approaches, the current system is obtained by applying the fluid closure at the level of the action principle of the original phase-space model. As a result, the system inherits a Hamiltonian structure and retains energy/momentum balance. After discussing some of its structural properties and dynamical invariants, we illustrate the model in the case of pure-dephasing dynamics. We conclude by presenting some invariant planar models.
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Affiliation(s)
- François Gay-Balmaz
- Division of Mathematical Sciences, Nanyang Technological University, Singapore, Singapore
| | - Cesare Tronci
- Department of Mathematics, University of Surrey, Guildford, UK
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3
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Oppenheim J, Sparaciari C, Šoda B, Weller-Davies Z. Gravitationally induced decoherence vs space-time diffusion: testing the quantum nature of gravity. Nat Commun 2023; 14:7910. [PMID: 38049417 PMCID: PMC10696068 DOI: 10.1038/s41467-023-43348-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2023] [Accepted: 11/08/2023] [Indexed: 12/06/2023] Open
Abstract
We consider two interacting systems when one is treated classically while the other system remains quantum. Consistent dynamics of this coupling has been shown to exist, and explored in the context of treating space-time classically. Here, we prove that any such hybrid dynamics necessarily results in decoherence of the quantum system, and a breakdown in predictability in the classical phase space. We further prove that a trade-off between the rate of this decoherence and the degree of diffusion induced in the classical system is a general feature of all classical quantum dynamics; long coherence times require strong diffusion in phase-space relative to the strength of the coupling. Applying the trade-off relation to gravity, we find a relationship between the strength of gravitationally-induced decoherence versus diffusion of the metric and its conjugate momenta. This provides an experimental signature of theories in which gravity is fundamentally classical. Bounds on decoherence rates arising from current interferometry experiments, combined with precision measurements of mass, place significant restrictions on theories where Einstein's classical theory of gravity interacts with quantum matter. We find that part of the parameter space of such theories are already squeezed out, and provide figures of merit which can be used in future mass measurements and interference experiments.
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Affiliation(s)
- Jonathan Oppenheim
- Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT, UK.
| | - Carlo Sparaciari
- Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT, UK
| | - Barbara Šoda
- Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT, UK
- Department of Physics, University of Waterloo, Waterloo, ON, Canada
- Perimeter Institute for Theoretical Physics, Waterloo, ON, Canada
| | - Zachary Weller-Davies
- Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT, UK
- Perimeter Institute for Theoretical Physics, Waterloo, ON, Canada
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4
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Green AT, Martens CC. Zombie cats on the quantum-classical frontier: Wigner-Moyal and semiclassical limit dynamics of quantum coherence in molecules. J Chem Phys 2023; 159:204102. [PMID: 37991156 DOI: 10.1063/5.0177421] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2023] [Accepted: 11/02/2023] [Indexed: 11/23/2023] Open
Abstract
In this paper, we investigate the time evolution of quantum coherence-the off-diagonal elements of the density matrix of a multistate quantum system-from the perspective of the Wigner-Moyal formalism. This approach provides an exact phase space representation of quantum mechanics. We consider the coherent evolution of nuclear wavepackets in a molecule with two electronic states. For harmonic potentials, the problem is analytically soluble for both a fully quantum mechanical description and a semiclassical description. We highlight the serious deficiencies of the semiclassical treatment of coherence for general systems and illustrate how even qualitative accuracy requires higher order terms in the Moyal expansion to be included. The model provides an experimentally relevant example of a molecular Schrödinger's cat state. The alive and dead cats of the exact two-state quantum evolution collapse into a "zombie" cat in the semiclassical limit-an averaged behavior, neither alive nor dead, leading to significant errors. The inclusion of the Moyal correction restores a faithful simultaneously alive and dead representation of the cat that is experimentally observable.
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Affiliation(s)
- Austin T Green
- University of California, Irvine, California 92697-2025, USA
| | - Craig C Martens
- University of California, Irvine, California 92697-2025, USA
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5
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Cook L, Runeson JE, Richardson JO, Hele TJH. Which Algorithm Best Propagates the Meyer-Miller-Stock-Thoss Mapping Hamiltonian for Non-Adiabatic Dynamics? J Chem Theory Comput 2023; 19:6109-6125. [PMID: 37704193 PMCID: PMC10536990 DOI: 10.1021/acs.jctc.3c00709] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2023] [Indexed: 09/15/2023]
Abstract
A common strategy to simulate mixed quantum-classical dynamics is by propagating classical trajectories with mapping variables, often using the Meyer-Miller-Stock-Thoss (MMST) Hamiltonian or the related spin-mapping approach. When mapping the quantum subsystem, the coupled dynamics reduce to a set of equations of motion to integrate. Several numerical algorithms have been proposed, but a thorough performance comparison appears to be lacking. Here, we compare three time-propagation algorithms for the MMST Hamiltonian: the Momentum Integral (MInt) (J. Chem. Phys., 2018, 148, 102326), the Split-Liouvillian (SL) (Chem. Phys., 2017, 482, 124-134), and the algorithm in J. Chem. Phys., 2012, 136, 084101 that we refer to as the Degenerate Eigenvalue (DE) algorithm due to the approximation required during derivation. We analyze the accuracy of individual trajectories, correlation functions, energy conservation, symplecticity, Liouville's theorem, and the computational cost. We find that the MInt algorithm is the only rigorously symplectic algorithm. However, comparable accuracy at a lower computational cost can be obtained with the SL algorithm. The approximation implicitly made within the DE algorithm conserves energy poorly, even for small timesteps, and thus leads to slightly different results. These results should guide future mapping-variable simulations.
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Affiliation(s)
- Lauren
E. Cook
- Department
of Chemistry, University College London, Christopher Ingold Building, London WC1H 0AJ, U.K.
| | - Johan E. Runeson
- Department
of Chemistry and Applied Biosciences, ETH
Zürich, Zürich 8093, Switzerland
| | - Jeremy O. Richardson
- Department
of Chemistry and Applied Biosciences, ETH
Zürich, Zürich 8093, Switzerland
| | - Timothy J. H. Hele
- Department
of Chemistry, University College London, Christopher Ingold Building, London WC1H 0AJ, U.K.
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6
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Meisenheimer P, Zhang H, Raftrey D, Chen X, Shao YT, Chan YT, Yalisove R, Chen R, Yao J, Scott MC, Wu W, Muller DA, Fischer P, Birgeneau RJ, Ramesh R. Ordering of room-temperature magnetic skyrmions in a polar van der Waals magnet. Nat Commun 2023; 14:3744. [PMID: 37353526 DOI: 10.1038/s41467-023-39442-0] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2023] [Accepted: 06/13/2023] [Indexed: 06/25/2023] Open
Abstract
Control and understanding of ensembles of skyrmions is important for realization of future technologies. In particular, the order-disorder transition associated with the 2D lattice of magnetic skyrmions can have significant implications for transport and other dynamic functionalities. To date, skyrmion ensembles have been primarily studied in bulk crystals, or as isolated skyrmions in thin film devices. Here, we investigate the condensation of the skyrmion phase at room temperature and zero field in a polar, van der Waals magnet. We demonstrate that we can engineer an ordered skyrmion crystal through structural confinement on the μm scale, showing control over this order-disorder transition on scales relevant for device applications.
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Affiliation(s)
- Peter Meisenheimer
- Department of Materials Science and Engineering, University of California, Berkeley, CA, USA.
| | - Hongrui Zhang
- Department of Materials Science and Engineering, University of California, Berkeley, CA, USA.
| | - David Raftrey
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
- Department of Physics, University of California, Santa Cruz, CA, USA
| | - Xiang Chen
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
- Department of Physics, University of California, Berkeley, CA, USA
| | - Yu-Tsun Shao
- School of Applied and Engineering Physics, Cornell University, Ithaca, NY, USA
| | - Ying-Ting Chan
- Department of Physics, Rutgers University, New Brunswick, NJ, USA
| | - Reed Yalisove
- Department of Materials Science and Engineering, University of California, Berkeley, CA, USA
| | - Rui Chen
- Department of Materials Science and Engineering, University of California, Berkeley, CA, USA
| | - Jie Yao
- Department of Materials Science and Engineering, University of California, Berkeley, CA, USA
| | - Mary C Scott
- Department of Materials Science and Engineering, University of California, Berkeley, CA, USA
- Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Weida Wu
- Department of Physics, Rutgers University, New Brunswick, NJ, USA
| | - David A Muller
- School of Applied and Engineering Physics, Cornell University, Ithaca, NY, USA
| | - Peter Fischer
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
- Department of Physics, University of California, Santa Cruz, CA, USA
| | - Robert J Birgeneau
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
- Department of Physics, University of California, Berkeley, CA, USA
| | - Ramamoorthy Ramesh
- Department of Materials Science and Engineering, University of California, Berkeley, CA, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
- Department of Physics, University of California, Berkeley, CA, USA
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7
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Hou B, Thoss M, Banin U, Rabani E. Incoherent nonadiabatic to coherent adiabatic transition of electron transfer in colloidal quantum dot molecules. Nat Commun 2023; 14:3073. [PMID: 37244903 PMCID: PMC10224918 DOI: 10.1038/s41467-023-38470-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2022] [Accepted: 04/27/2023] [Indexed: 05/29/2023] Open
Abstract
Electron transfer is a fundamental process in chemistry, biology, and physics. One of the most intriguing questions concerns the realization of the transitions between nonadiabatic and adiabatic regimes of electron transfer. Using colloidal quantum dot molecules, we computationally demonstrate how the hybridization energy (electronic coupling) can be tuned by changing the neck dimensions and/or the quantum dot sizes. This provides a handle to tune the electron transfer from the incoherent nonadiabatic regime to the coherent adiabatic regime in a single system. We develop an atomistic model to account for several states and couplings to the lattice vibrations and utilize the mean-field mixed quantum-classical method to describe the charge transfer dynamics. Here, we show that charge transfer rates increase by several orders of magnitude as the system is driven to the coherent, adiabatic limit, even at elevated temperatures, and delineate the inter-dot and torsional acoustic modes that couple most strongly to the charge transfer dynamics.
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Affiliation(s)
- Bokang Hou
- Department of Chemistry, University of California, Berkeley, CA, 94720, USA
| | - Michael Thoss
- Institute of Physics, University of Freiburg, Hermann-Herder-Straße 3, 79104, Freiburg, Germany
| | - Uri Banin
- Institute of Chemistry and the Center for Nanoscience and Nanotechnology, The Hebrew University of Jerusalem, 91904, Jerusalem, Israel
| | - Eran Rabani
- Department of Chemistry, University of California, Berkeley, CA, 94720, USA.
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA.
- The Raymond and Beverly Sackler Center of Computational Molecular and Materials Science, Tel Aviv University, 69978, Tel Aviv, Israel.
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8
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Athavale V, Teh HH, Shao Y, Subotnik J. Analytical gradients and derivative couplings for the TDDFT-1D method. J Chem Phys 2022; 157:244110. [PMID: 36586994 DOI: 10.1063/5.0130404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022] Open
Abstract
We derive and implement analytic gradients and derivative couplings for time-dependent density functional theory plus one double (TDDFT-1D) which is a semiempirical configuration interaction method whereby the Hamiltonian is diagonalized in a basis of all singly excited configurations and one doubly excited configuration as constructed from a set of reference Kohn-Sham orbitals. We validate the implementation by comparing against finite difference values. Furthermore, we show that our implementation can locate both optimized geometries and minimum-energy crossing points along conical seams of S1/S0 surfaces for a set of test cases.
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Affiliation(s)
- Vishikh Athavale
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Hung-Hsuan Teh
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Yihan Shao
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, Oklahoma 73019, USA
| | - Joseph Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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9
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Gelin MF, Chen L, Domcke W. Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals. Chem Rev 2022; 122:17339-17396. [PMID: 36278801 DOI: 10.1021/acs.chemrev.2c00329] [Citation(s) in RCA: 20] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
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.
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Affiliation(s)
- Maxim F Gelin
- School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Lipeng Chen
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany
| | - Wolfgang Domcke
- Department of Chemistry, Technical University of Munich, D-85747 Garching,Germany
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10
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Malpathak S, Church MS, Ananth N. A Semiclassical Framework for Mixed Quantum Classical Dynamics. J Phys Chem A 2022; 126:6359-6375. [PMID: 36070472 DOI: 10.1021/acs.jpca.2c03467] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
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.
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Affiliation(s)
- Shreyas Malpathak
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University Ithaca, New York 14853, United States
| | - Matthew S Church
- Department of Chemistry, Brown University, Providence, Rhode Island 02906, United States
| | - Nandini Ananth
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University Ithaca, New York 14853, United States
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11
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Pradhan CS, Jain A. Detailed Balance and Independent Electron Surface-Hopping Method: The Importance of Decoherence and Correct Calculation of Diabatic Populations. J Chem Theory Comput 2022; 18:4615-4626. [PMID: 35880817 DOI: 10.1021/acs.jctc.2c00320] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We benchmark and improve the independent electron surface-hopping (IESH) method developed by J. C. Tully's group for nonadiabatic simulations near metal surfaces. We have incorporated decoherence within the IESH method as well as implemented a scheme for the accurate calculation of diabatic populations. We benchmark the original IESH method with the above inclusions for a model system to calculate rate constants and long-time populations. The original IESH method fails to capture the detailed balance for some of the parameters, which is corrected with the inclusion of decoherence and accurate calculation of diabatic populations. Total rate constants are well captured both within the original IESH method as well as within our modified IESH.
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Affiliation(s)
- Chinmay S Pradhan
- Department of Chemistry, Indian Institute of Technology Bombay, Mumbai 400076, India
| | - Amber Jain
- Department of Chemistry, Indian Institute of Technology Bombay, Mumbai 400076, India
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12
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DECIDE: A Deterministic Mixed Quantum-Classical Dynamics Approach. APPLIED SCIENCES-BASEL 2022. [DOI: 10.3390/app12147022] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Mixed quantum-classical dynamics provides an efficient way of simulating the dynamics of quantum subsystems coupled to many-body environments. Many processes, including proton-transfer reactions, electron-transfer reactions, and vibrational energy transport, for example, take place in such open systems. The most accurate algorithms for performing mixed quantum-classical simulations require very large ensembles of trajectories to obtain converged expectation values, which is computationally prohibitive for quantum subsystems containing even a few degrees of freedom. The recently developed “Deterministic evolution of coordinates with initial decoupled equations” (DECIDE) method has demonstrated high accuracy and low computational cost for a host of model systems; however, these applications relied on representing the equations of motion in subsystem and adiabatic energy bases. While these representations are convenient for certain systems, the position representation is convenient for many other systems, including systems undergoing proton- and electron-transfer reactions. Thus, in this review, we provide a step-by-step derivation of the DECIDE approach and demonstrate how to cast the DECIDE equations in a quantum harmonic oscillator position basis for a simple one-dimensional (1D) hydrogen bond model. After integrating the DECIDE equations of motion on this basis, we show that the total energy of the system is conserved for this model and calculate various quantities of interest. Limitations of casting the equations in an incomplete basis are also discussed.
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13
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Gardner J, Douglas-Gallardo OA, Stark WG, Westermayr J, Janke SM, Habershon S, Maurer RJ. NQCDynamics.jl: A Julia package for nonadiabatic quantum classical molecular dynamics in the condensed phase. J Chem Phys 2022; 156:174801. [PMID: 35525649 DOI: 10.1063/5.0089436] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Abstract
Accurate and efficient methods to simulate nonadiabatic and quantum nuclear effects in high-dimensional and dissipative systems are crucial for the prediction of chemical dynamics in the condensed phase. To facilitate effective development, code sharing, and uptake of newly developed dynamics methods, it is important that software implementations can be easily accessed and built upon. Using the Julia programming language, we have developed the NQCDynamics.jl package, which provides a framework for established and emerging methods for performing semiclassical and mixed quantum-classical dynamics in the condensed phase. The code provides several interfaces to existing atomistic simulation frameworks, electronic structure codes, and machine learning representations. In addition to the existing methods, the package provides infrastructure for developing and deploying new dynamics methods, which we hope will benefit reproducibility and code sharing in the field of condensed phase quantum dynamics. Herein, we present our code design choices and the specific Julia programming features from which they benefit. We further demonstrate the capabilities of the package on two examples of chemical dynamics in the condensed phase: the population dynamics of the spin-boson model as described by a wide variety of semiclassical and mixed quantum-classical nonadiabatic methods and the reactive scattering of H2 on Ag(111) using the molecular dynamics with electronic friction method. Together, they exemplify the broad scope of the package to study effective model Hamiltonians and realistic atomistic systems.
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Affiliation(s)
- James Gardner
- Department of Chemistry, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
| | - Oscar A Douglas-Gallardo
- Department of Chemistry, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
| | - Wojciech G Stark
- Department of Chemistry, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
| | - Julia Westermayr
- Department of Chemistry, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
| | - Svenja M Janke
- Department of Chemistry, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
| | - Scott Habershon
- Department of Chemistry, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
| | - Reinhard J Maurer
- Department of Chemistry, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
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14
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Xie BB, Jia PK, Wang KX, Chen WK, Liu XY, Cui G. Generalized Ab Initio Nonadiabatic Dynamics Simulation Methods from Molecular to Extended Systems. J Phys Chem A 2022; 126:1789-1804. [PMID: 35266391 DOI: 10.1021/acs.jpca.1c10195] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Nonadiabatic dynamics simulation has become a powerful tool to describe nonadiabatic effects involved in photophysical processes and photochemical reactions. In the past decade, our group has developed generalized trajectory-based ab initio surface-hopping (GTSH) dynamics simulation methods, which can be used to describe a series of nonadiabatic processes, such as internal conversion, intersystem crossing, excitation energy transfer and charge transfer of molecular systems, and photoinduced nonadiabatic carrier dynamics of extended systems with and without spin-orbit couplings. In this contribution, we will first give a brief introduction to our recently developed methods and related numerical implementations at different computational levels. Later, we will present some of our latest applications in realistic systems, which cover organic molecules, biological proteins, organometallic compounds, periodic organic and inorganic materials, etc. Final discussion is given to challenges and outlooks of ab initio nonadiabatic dynamics simulations.
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Affiliation(s)
- Bin-Bin Xie
- Hangzhou Institute of Advanced Studies, Zhejiang Normal University, 1108 Gengwen Road, Hangzhou 311231, Zhejiang, P. R. China
| | - Pei-Ke Jia
- Hangzhou Institute of Advanced Studies, Zhejiang Normal University, 1108 Gengwen Road, Hangzhou 311231, Zhejiang, P. R. China
| | - Ke-Xin Wang
- Hangzhou Institute of Advanced Studies, Zhejiang Normal University, 1108 Gengwen Road, Hangzhou 311231, Zhejiang, P. R. China
| | - Wen-Kai Chen
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education College of Chemistry, Beijing Normal University, Beijing 100875, P. R. China
| | - Xiang-Yang Liu
- College of Chemistry and Material Science, Sichuan Normal University, Chengdu 610068, Sichuan, P. R. China
| | - Ganglong Cui
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education College of Chemistry, Beijing Normal University, Beijing 100875, P. R. China
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15
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Ananth N. Path Integrals for Nonadiabatic Dynamics: Multistate Ring Polymer Molecular Dynamics. Annu Rev Phys Chem 2022; 73:299-322. [PMID: 35081325 DOI: 10.1146/annurev-physchem-082620-021809] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
This review focuses on a recent class of path-integral-based methods that simulate nonadiabatic dynamics in the condensed phase using only classical molecular dynamics trajectories in an extended phase space. Specifically, a semiclassical mapping protocol is used to derive an exact, continuous, Cartesian variable path-integral representation for the canonical partition function of a system in which multiple electronic states are coupled to nuclear degrees of freedom. Building on this exact statistical foundation, multistate ring polymer molecular dynamics methods are developed for the approximate calculation of real-time thermal correlation functions. The remarkable promise of these multistate ring polymer methods, their successful applications, and their limitations are discussed in detail.Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
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Affiliation(s)
- Nandini Ananth
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York, USA;
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16
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Mukherjee S, Varganov SA. Intersystem crossing and internal conversion dynamics with GAIMS-TeraChem: Excited state relaxation in 2-cyclopentenone. J Chem Phys 2021; 155:174107. [PMID: 34742200 DOI: 10.1063/5.0068040] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Excited states relaxation in complex molecules often involves two types of nonradiative transitions, internal conversion (IC) and intersystem crossing (ISC). In the situations when the timescales of IC and ISC are comparable, an interplay between these two types of transitions can lead to complex nonadiabatic dynamics on multiple electronic states of different characters and spin multiplicities. We demonstrate that the generalized ab initio multiple spawning (GAIMS) method interfaced with the fast graphics processing unit-based TeraChem electronic structure code can be used to model such nonadiabatic dynamics involving both the IC and ISC transitions in molecules of moderate size. We carried out 1500 fs GAIMS simulations leading to the creation of up to 2500 trajectory basis functions to study the excited states relaxation in 2-cyclopentenone. After a vertical excitation from the ground state to the bright S2 state, the molecule quickly relaxes to the S1 state via conical intersection. The following relaxation proceeds along two competing pathways: one involves IC to the ground state, and the other is dominated by ISC to the low-lying triplet states. The time constants describing the population transfer between the six lowest singlet and triplet states predicted by the GAIMS dynamics are in good agreement with the characteristic times of IC and ISC obtained from the analysis of the time-resolved photoelectron spectrum.
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Affiliation(s)
- Saikat Mukherjee
- Department of Chemistry, University of Nevada, Reno, 1664 N. Virginia Street, Reno, Nevada 89557-0216, USA
| | - Sergey A Varganov
- Department of Chemistry, University of Nevada, Reno, 1664 N. Virginia Street, Reno, Nevada 89557-0216, USA
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17
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Morrow Z, Kwon HY, Kelley CT, Jakubikova E. Reduced-dimensional surface hopping with offline-online computations. Phys Chem Chem Phys 2021; 23:19547-19557. [PMID: 34524324 DOI: 10.1039/d1cp03446d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Molecular dynamics simulations often classically evolve the nuclear geometry on adiabatic potential energy surfaces (PESs), punctuated by random hops between energy levels in regions of strong coupling, in an algorithm known as surface hopping. However, the computational expense of integrating the geometry on a full-dimensional PES and computing the required couplings can quickly become prohibitive as the number of atoms increases. In this work, we describe a method for surface hopping that uses only important reaction coordinates, performs all expensive evaluations of the true PESs and couplings only once before simulating dynamics (offline), and then queries the stored values during the surface hopping simulation (online). Our Python codes are freely available on GitHub. Using photodissociation of azomethane as a test case, this method is able to reproduce experimental results that have thus far eluded ab initio surface hopping studies.
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Affiliation(s)
- Zachary Morrow
- Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC 27695-8205, USA.
| | - Hyuk-Yong Kwon
- Department of Chemistry, North Carolina State University, Box 8204, Raleigh, NC, 27695-8204, USA.
| | - C T Kelley
- Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC 27695-8205, USA.
| | - Elena Jakubikova
- Department of Chemistry, North Carolina State University, Box 8204, Raleigh, NC, 27695-8204, USA.
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18
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Wang Y, Simine L. Solving the Wigner equation with signed particle Monte Carlo for chemically relevant potentials. J Chem Phys 2021; 155:034109. [PMID: 34293875 DOI: 10.1063/5.0055603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Expanding the set of stable, accurate, and scalable methods for simulating molecular quantum dynamics is important for accelerating the computational exploration of molecular processes. In this paper, we adapt the signed particles Monte Carlo algorithm for solving the transient Wigner equation to scenarios of chemical interest. This approach was used in the past to study electronic processes in semi-conductors, but to the best of our knowledge, it had never been applied to molecular modeling. We present the algorithm and demonstrate its excellent performance on harmonic and double well potentials for electronic and nuclear systems. We explore the stability of the algorithm, discuss the choice of hyper-parameters, and cautiously speculate that it may be used in quantum molecular dynamics simulations.
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Affiliation(s)
- Yu Wang
- Department of Chemistry, McGill University, 801 Sherbrooke Street W, Montreal, Quebec H3A 0B8, Canada
| | - Lena Simine
- Department of Chemistry, McGill University, 801 Sherbrooke Street W, Montreal, Quebec H3A 0B8, Canada
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19
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Cho KH, Rhee YM. Cooperation between Excitation Energy Transfer and Antisynchronously Coupled Vibrations. J Phys Chem B 2021; 125:5601-5610. [PMID: 34013724 DOI: 10.1021/acs.jpcb.1c01194] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The effects of the environment in energy transfer systems have been continuously studied for decades. Here, we investigate how the energy transfer and the emergence of vibrational correlations cooperate with each other based on simulations with a few numerically approximate mixed quantum classical (MQC) methods. By adopting a two-state system with locally coupled underdamped vibrations that are resonant with the electronic energy gap, we observe prominent energy dissipations from the electronic system to the vibrations, rehighlighting the role of underdamped vibrations as a temporal electronic energy buffer. More importantly, this energy dissipation generates specific phase relations between the two vibrations. Namely, the vibrations become anticorrelated right after the initiation of the energy transfer but then synchronized as the transfer completes. These phase relations are interpreted as a selective activation of an anticorrelated motion of the vibrations and a subsequent deactivation by thermal energy redistribution. Furthermore, we show that a single vibration simultaneously coupled to the two electronic states with opposite phases induces a completely equivalent energy transfer dynamics as the two localized vibrations. Finally, we discuss how the vibrational energy dissipation dynamics is affected by the adopted MQC approaches and warn about the increased subtlety toward properly treating dissipation effects over having reliable population dynamics.
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Affiliation(s)
- Kwang Hyun Cho
- Department of Chemistry, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Korea
| | - Young Min Rhee
- Department of Chemistry, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Korea
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20
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Lively K, Albareda G, Sato SA, Kelly A, Rubio A. Simulating Vibronic Spectra without Born-Oppenheimer Surfaces. J Phys Chem Lett 2021; 12:3074-3081. [PMID: 33750137 PMCID: PMC8020382 DOI: 10.1021/acs.jpclett.1c00073] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2021] [Accepted: 03/15/2021] [Indexed: 06/12/2023]
Abstract
We show how linear vibronic spectra in molecular systems can be simulated efficiently using first-principles approaches without relying on the explicit use of multiple Born-Oppenheimer potential energy surfaces. We demonstrate and analyze the performance of mean-field and beyond-mean-field dynamics techniques for the H2 molecule in one dimension, in the later case capturing the vibronic structure quite accurately, including quantum Franck-Condon effects. In a practical application of this methodology we simulate the absorption spectrum of benzene in full dimensionality using time-dependent density functional theory at the multitrajectory Ehrenfest level, finding good qualitative agreement with experiment and significant spectral reweighting compared to commonly used single-trajectory Ehrenfest dynamics. These results form the foundation for nonlinear spectral calculations and show promise for future application in capturing phenomena associated with vibronic coupling in more complex molecular and potentially condensed phase systems.
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Affiliation(s)
- Kevin Lively
- Max
Planck Institute for the Structure and Dynamics of Matter and Center
for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Guillermo Albareda
- Max
Planck Institute for the Structure and Dynamics of Matter and Center
for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
- Institute
of Theoretical and Computational Chemistry, University of Barcelona, Martí i Franquès 1-11, 08028 Barcelona, Spain
- Nano-Bio
Spectroscopy Group and ETSF, Universidad
del País Vasco, 20018 San Sebastían, Spain
| | - Shunsuke A. Sato
- Max
Planck Institute for the Structure and Dynamics of Matter and Center
for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
- Center
for Computational Sciences, University of
Tsukuba, Tsukuba 305-8577, Japan
| | - Aaron Kelly
- Max
Planck Institute for the Structure and Dynamics of Matter and Center
for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
- Department
of Chemistry, Dalhousie University, Halifax B3H 4R2, Canada
| | - Angel Rubio
- Max
Planck Institute for the Structure and Dynamics of Matter and Center
for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
- Nano-Bio
Spectroscopy Group and ETSF, Universidad
del País Vasco, 20018 San Sebastían, Spain
- Center
for Computational Quantum Physics (CCQ), Flatiron Institute, 162 Fifth Avenue, New York, New York 10010, United
States
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21
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Chowdhury SN, Huo P. Non-adiabatic Matsubara dynamics and non-adiabatic ring-polymer molecular dynamics. J Chem Phys 2021; 154:124124. [PMID: 33810665 DOI: 10.1063/5.0042136] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Abstract
We present the non-adiabatic Matsubara dynamics, a general framework for computing the time-correlation function (TCF) of electronically non-adiabatic systems. This new formalism is derived based on the generalized Kubo-transformed TCF using the Wigner representation for both the nuclear degrees of freedom and the electronic mapping variables. By dropping the non-Matsubara nuclear normal modes in the quantum Liouvillian and explicitly integrating these modes out from the expression of the TCF, we derived the non-adiabatic Matsubara dynamics approach. Further making the approximation to drop the imaginary part of the Matsubara Liouvillian and enforce the nuclear momentum integral to be real, we arrived at the non-adiabatic ring-polymer molecular dynamics (NRPMD) approach. We have further justified the capability of NRPMD for simulating the non-equilibrium TCF. This work provides the rigorous theoretical foundation for several recently proposed state-dependent RPMD approaches and offers a general framework for developing new non-adiabatic quantum dynamics methods in the future.
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Affiliation(s)
- Sutirtha N Chowdhury
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
| | - Pengfei Huo
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
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22
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Brown SE, Shakib FA. Recent progress in approximate quantum dynamics methods for the study of proton-coupled electron transfer reactions. Phys Chem Chem Phys 2021; 23:2535-2556. [PMID: 33367437 DOI: 10.1039/d0cp05166g] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Abstract
Proton-coupled electron transfer (PCET) reactions are ubiquitous natural processes at the heart of energy conversion reactions in photosynthesis and respiration, DNA repair, and diverse enzymatic reactions. Theoretical formulation and computational method developments have eyed modeling of thermal and photoinduced PCET for the last three decades. The accumulation of these studies, collected in dozens of reviews, accounts, and perspectives, has firmly established the influence of quantum effects, including non-adiabatic electronic transitions, vibrational relaxation, zero-point energy, and proton tunneling, on the rate and mechanism of PCET reactions. Here, we focus on some recently-developed methods, spanning the last eight years, that can quantitatively capture these effects in the PCET context and provide efficient means for their qualitative description in complex systems. The theoretical background of each method and their accuracy with respect to exact results are discussed and the results of relevant PCET simulations based on each method are presented.
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Affiliation(s)
- Sandra E Brown
- Department of Chemistry and Biochemistry, University of California, Los Angeles, Los Angeles, CA 90095, USA
| | - Farnaz A Shakib
- Department of Chemistry and Environmental Science, New Jersey Institute of Technology, Newark, NJ 07102, USA.
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23
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Pieroni C, Marsili E, Lauvergnat D, Agostini F. Relaxation dynamics through a conical intersection: Quantum and quantum-classical studies. J Chem Phys 2021; 154:034104. [PMID: 33499611 DOI: 10.1063/5.0036726] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
Abstract
We study the relaxation process through a conical intersection of a photo-excited retinal chromophore model. The analysis is based on a two-electronic-state two-dimensional Hamiltonian developed by Hahn and Stock [J. Phys. Chem. B 104 1146 (2000)] to reproduce, with a minimal model, the main features of the 11-cis to all-trans isomerization of the retinal of rhodopsin. In particular, we focus on the performance of various trajectory-based schemes to nonadiabatic dynamics, and we compare quantum-classical results to the numerically exact quantum vibronic wavepacket dynamics. The purpose of this work is to investigate, by analyzing electronic and nuclear observables, how the sampling of initial conditions for the trajectories affects the subsequent dynamics.
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Affiliation(s)
- Carlotta Pieroni
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405 Orsay, France
| | - Emanuele Marsili
- Department of Chemistry, Durham University, South Road, Durham DH1 3LE, United Kingdom
| | - David Lauvergnat
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405 Orsay, France
| | - Federica Agostini
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405 Orsay, France
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24
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Tang D, Shen L, Fang WH. Evaluation of mixed quantum-classical molecular dynamics on cis-azobenzene photoisomerization. Phys Chem Chem Phys 2021; 23:13951-13964. [PMID: 34142685 DOI: 10.1039/d1cp01374b] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The quantitative prediction of nonadiabatic transitions between different electronic states is important to understand ultrafast processes in photochemistry. A variety of mixed quantum-classical molecular dynamics methods such as surface hopping and Ehrenfest mean-field have been developed. However, how to choose an appropriate one from a wide diversity of dynamics algorithms to study a realistic photochemical process is still unclear. In this work, we implemented 30 combinations of different mixed quantum-classical dynamics methods, including 24 surface hopping models with 8 decoherence corrections and 3 momentum rescaling strategies as well as 6 mean-field models. Then we performed numerical investigations by simulating the photoisomerization of cis-azobenzene combined with on-the-fly electronic structure calculations. Predictions of the S1 lifetime and the quantum yield of the photoproduct using different models are distinct. Surface hopping is more robust than mean-field in our test system. Moreover, the choice of momentum rescaling methods in surface hopping brings more significant changes than decoherence corrections, while a large discrepancy between simulation results with different mean-field algorithms has been observed.
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Affiliation(s)
- Diandong Tang
- Key Laboratory of Theoretical and Computational Photochemistry of Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China.
| | - Lin Shen
- Key Laboratory of Theoretical and Computational Photochemistry of Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China.
| | - Wei-Hai Fang
- Key Laboratory of Theoretical and Computational Photochemistry of Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China.
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25
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Yan Y, Xing T, Shi Q. A new method to improve the numerical stability of the hierarchical equations of motion for discrete harmonic oscillator modes. J Chem Phys 2020; 153:204109. [DOI: 10.1063/5.0027962] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yaming Yan
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100049, China; and Physical Science Laboratory, Huairou National Comprehensive Science Center, Beijing 101407, China
| | - Tao Xing
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100049, China; and Physical Science Laboratory, Huairou National Comprehensive Science Center, Beijing 101407, China
| | - Qiang Shi
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100049, China; and Physical Science Laboratory, Huairou National Comprehensive Science Center, Beijing 101407, China
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26
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Teh HH, Subotnik JE. Analytic gradients and derivative couplings for configuration interaction with all single excitations and one double excitation-En route to nonadiabatic dynamics. J Chem Phys 2020; 153:184106. [PMID: 33187425 DOI: 10.1063/5.0018441] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present analytic gradients and derivative couplings for the simplest possible multireference configuration interaction method, CIS-1D, an electronic structure Ansatz that includes all single excitations and one lone double excitation on top of a Hartree-Fock reference state. We show that the resulting equations are numerically stable and require the evaluation of a similar number of integrals as compared to standard CIS theory; one can easily differentiate the required frontier orbitals (h and l) with minimal cost. The resulting algorithm has been implemented within the Q-Chem electronic structure package and should be immediately useful for understanding photochemistry with S0-S1 crossings.
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Affiliation(s)
- Hung-Hsuan Teh
- University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, USA
| | - Joseph E Subotnik
- University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, USA
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27
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Parker SM, Schiltz CJ. Surface hopping with cumulative probabilities: Even sampling and improved reproducibility. J Chem Phys 2020; 153:174109. [DOI: 10.1063/5.0024372] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Affiliation(s)
- Shane M. Parker
- Department of Chemistry, Case Western Reserve University, 10800 Euclid Ave., Cleveland, Ohio 44106, USA
| | - Colin J. Schiltz
- Department of Chemistry, Case Western Reserve University, 10800 Euclid Ave., Cleveland, Ohio 44106, USA
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28
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Stolyarov EV, White AJ, Mozyrsky D. Mixed quantum-classical approach to model non-adiabatic electron-nuclear dynamics: Detailed balance and improved surface hopping method. J Chem Phys 2020; 153:074116. [PMID: 32828087 DOI: 10.1063/5.0014284] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We develop a density matrix formalism to describe coupled electron-nuclear dynamics. To this end, we introduce an effective Hamiltonian formalism that describes electronic transitions and small (quantum) nuclear fluctuations along a classical trajectory of the nuclei. Using this Hamiltonian, we derive equations of motion for the electronic occupation numbers and for the nuclear coordinates and momenta. We show that, in the limit, when the number of nuclear degrees of freedom coupled to a given electronic transition is sufficiently high (i.e., the strong decoherence limit), the equations of motion for the electronic occupation numbers become Markovian. Furthermore, the transition rates in these (rate) equations are asymmetric with respect to the lower-to-higher energy transitions and vice versa. In thermal equilibrium, such asymmetry corresponds to the detailed balance condition. We also study the equations for the electronic occupations in the non-Markovian regime and develop a surface hopping algorithm based on our formalism. To treat the decoherence effects, we introduce additional "virtual" nuclear wave packets whose interference with the "real" (physical) wave packets leads to the reduction in coupling between the electronic states (i.e., decoherence) as well as to the phase shifts that improve the accuracy of the numerical approach. Remarkably, the same phase shifts lead to the detailed balance condition in the strong decoherence limit.
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Affiliation(s)
- E V Stolyarov
- Institute of Physics of the National Academy of Sciences of Ukraine, pr. Nauky 46, 03028 Kyiv, Ukraine
| | - A J White
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - D Mozyrsky
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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29
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Chen HT, Zhou Z, Subotnik JE. On the proper derivation of the Floquet-based quantum classical Liouville equation and surface hopping describing a molecule or material subject to an external field. J Chem Phys 2020; 153:044116. [PMID: 32752688 DOI: 10.1063/5.0013873] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate different approaches to derive the proper Floquet-based quantum-classical Liouville equation (F-QCLE) for laser-driven electron-nuclear dynamics. The first approach projects the operator form of the standard QCLE onto the diabatic Floquet basis and then transforms to the adiabatic representation. The second approach directly projects the QCLE onto the Floquet adiabatic basis. Both approaches yield a form that is similar to the usual QCLE with two modifications: (1) The electronic degrees of freedom are expanded to infinite dimension and (2) the nuclear motion follows Floquet quasi-energy surfaces. However, the second approach includes an additional cross derivative force due to the dual dependence on time and nuclear motion of the Floquet adiabatic states. Our analysis and numerical tests indicate that this cross derivative force is a fictitious artifact, suggesting that one cannot safely exchange the order of Floquet state projection with adiabatic transformation. Our results are in accord with similar findings by Izmaylov et al., [J. Chem. Phys. 140, 084104 (2014)] who found that transforming to the adiabatic representation must always be the last operation applied, although now we have extended this result to a time-dependent Hamiltonian. This paper and the proper derivation of the F-QCLE should lay the basis for further improvements of Floquet surface hopping.
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Affiliation(s)
- Hsing-Ta Chen
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Zeyu Zhou
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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30
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Malone W, Nebgen B, White A, Zhang Y, Song H, Bjorgaard JA, Sifain AE, Rodriguez-Hernandez B, Freixas VM, Fernandez-Alberti S, Roitberg AE, Nelson TR, Tretiak S. NEXMD Software Package for Nonadiabatic Excited State Molecular Dynamics Simulations. J Chem Theory Comput 2020; 16:5771-5783. [DOI: 10.1021/acs.jctc.0c00248] [Citation(s) in RCA: 33] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- Walter Malone
- Physics and Chemistry of Materials, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Benjamin Nebgen
- Physics and Chemistry of Materials, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Alexander White
- Physics and Chemistry of Materials, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Yu Zhang
- Physics and Chemistry of Materials, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Huajing Song
- Physics and Chemistry of Materials, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Josiah A. Bjorgaard
- Physics and Chemistry of Materials, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Andrew E. Sifain
- U.S. Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, Maryland 21005, United States
| | | | - Victor M. Freixas
- Universidad Nacional de Quilmes/CONICET, Roque Saenz Peña 352, B1876BXD Bernal, Argentina
| | | | - Adrian E. Roitberg
- Department of Chemistry, University of Florida, Gainesville, Florida 32611, United States
| | - Tammie R. Nelson
- Physics and Chemistry of Materials, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
- Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Sergei Tretiak
- Physics and Chemistry of Materials, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
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31
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Nelson TR, White AJ, Bjorgaard JA, Sifain AE, Zhang Y, Nebgen B, Fernandez-Alberti S, Mozyrsky D, Roitberg AE, Tretiak S. Non-adiabatic Excited-State Molecular Dynamics: Theory and Applications for Modeling Photophysics in Extended Molecular Materials. Chem Rev 2020; 120:2215-2287. [PMID: 32040312 DOI: 10.1021/acs.chemrev.9b00447] [Citation(s) in RCA: 220] [Impact Index Per Article: 55.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
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.
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Affiliation(s)
- Tammie R Nelson
- Theoretical Division , Los Alamos National Laboratory , Los Alamos , New Mexico 87545 , United States
| | - Alexander J White
- Theoretical Division , Los Alamos National Laboratory , Los Alamos , New Mexico 87545 , United States
| | - Josiah A Bjorgaard
- Theoretical Division , Los Alamos National Laboratory , Los Alamos , New Mexico 87545 , United States
| | - Andrew E Sifain
- Theoretical Division , Los Alamos National Laboratory , Los Alamos , New Mexico 87545 , United States.,U.S. Army Research Laboratory , Aberdeen Proving Ground , Maryland 21005 , United States
| | - Yu Zhang
- Theoretical Division , Los Alamos National Laboratory , Los Alamos , New Mexico 87545 , United States
| | - Benjamin Nebgen
- Theoretical Division , Los Alamos National Laboratory , Los Alamos , New Mexico 87545 , United States
| | | | - Dmitry Mozyrsky
- Theoretical Division , Los Alamos National Laboratory , Los Alamos , New Mexico 87545 , United States
| | - Adrian E Roitberg
- Department of Chemistry , University of Florida , Gainesville , Florida 32611 , United States
| | - Sergei Tretiak
- Theoretical Division , Los Alamos National Laboratory , Los Alamos , New Mexico 87545 , United States
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32
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Abstract
Dynamics at molecule-metal interfaces are a subject of intense current interest and come in many different flavors of experiments: gas-phase scattering, chemisorption, electrochemistry, nanojunction transport, and heterogeneous catalysis, to name a few. These dynamics involve nuclear degrees of freedom entangled with many electronic degrees of freedom (in the metal), and as such there is always the possibility for nonadiabatic phenomena to appear: the nuclei do not necessarily need to move slower than the electrons to break the Born-Oppenheimer (BO) approximation. In this Feature Article, we review a set of dynamical methods developed recently to deal with such nonadiabatic phenomena at a metal surface, methods that serve as alternatives to Tully's independent electron surface hopping (IESH) model. In the weak molecule-metal coupling regime, a classical master equation (CME) can be derived and a simple surface hopping approach is proposed to propagate nuclear and electronic dynamics stochastically. In the strong molecule-metal interaction regime, a Fokker-Planck equation can be derived for the nuclear dynamics, with electronic DoFs incorporated into the overall friction and random force. Lastly, a broadened classical master equation (BCME) can interpolate between the weak and strong molecule-metal interactions. Here, we briefly review these methods and the relevant benchmarking data, showing in particular how the methods can be used to calculate nonequilibrium transport properties. We highlight several open questions and pose several avenues for future study.
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Affiliation(s)
- Wenjie Dou
- Department of Chemistry , University of California, Berkeley , Berkeley , California 94720 , United States
| | - Joseph E Subotnik
- Department of Chemistry , University of Pennsylvania , Philadelphia , Pennsylvania 19104 , United States
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33
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Gong Z, Wu J. Absorption matrix of multi-site systems calculated by a hybrid quantum-classical Liouville equation. J Chem Phys 2019; 151:224109. [DOI: 10.1063/1.5138217] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Zhihao Gong
- Physics Department, Zhejiang University, 38 ZheDa Road, Hangzhou, Zhejiang 310027, China
| | - Jianlan Wu
- Physics Department, Zhejiang University, 38 ZheDa Road, Hangzhou, Zhejiang 310027, China
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34
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Zheng J, Xie Y, Jiang S, Long Y, Ning X, Lan Z. Initial sampling in symmetrical quasiclassical dynamics based on Li-Miller mapping Hamiltonian. Phys Chem Chem Phys 2019; 21:26502-26514. [PMID: 31777888 DOI: 10.1039/c9cp03975a] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Abstract
A symmetrical quasiclassical (SQC) dynamics approach based on the Li-Miller (LM) mapping Hamiltonian (SQC-LM) was employed to describe nonadiabatic dynamics. In principle, the different initial sampling procedures may be applied in the SQC-LM dynamics, and the results may be dependent on different initial sampling. We provided various initial sampling approaches and checked their influence. We selected two groups of models including site-exciton models for exciton dynamics and linear vibronic coupling models for conical intersections to test the performance of SQC-LM dynamics with the different initial sampling methods. The results were examined with respect to those of the accurate multiconfigurational time-dependent Hartree (MCTDH) quantum dynamics. For both the models, the SQC-LM method more-or-less gives a reasonable description of the population dynamics, while the influence of the initial sampling approaches on the final results is noticeable. It seems that the suitable initial sampling methods should be determined by the system under study. This indicates that the combination of the SQC-LM method with a suitable sampling approach may be a potential method in the description of nonadiabatic dynamics.
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Affiliation(s)
- Jie Zheng
- Industrial Research Institute of Nonwovens & Technical Textiles, College of Textiles Clothing, Qingdao University, Qingdao 266071, China.
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35
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Church MS, Ananth N. Semiclassical dynamics in the mixed quantum-classical limit. J Chem Phys 2019; 151:134109. [PMID: 31594341 DOI: 10.1063/1.5117160] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The semiclassical double Herman-Kluk initial value representation is an accurate approach to computing quantum real time correlation functions, but its applications are limited by the need to evaluate an oscillatory integral. In previous work, we have shown that this "sign problem" can be mitigated using the modified Filinov filtration technique to control the extent to which individual modes of the system contribute to the overall phase of the integrand. Here, we follow this idea to a logical conclusion: we analytically derive a general expression for the mixed quantum-classical limit of the semiclassical correlation function-analytical mixed quantum-classical-initial value representation (AMQC-IVR), where the phase contributions from the "classical" modes of the system are filtered while the "quantum" modes are treated in the full semiclassical limit. We numerically demonstrate the accuracy and efficiency of the AMQC-IVR formulation in calculations of quantum correlation functions and reaction rates using three model systems with varied coupling strengths between the classical and quantum subsystems. We also introduce a separable prefactor approximation that further reduces computational cost but is only accurate in the limit of weak coupling between the quantum and classical subsystems.
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Affiliation(s)
- Matthew S Church
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
| | - Nandini Ananth
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
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36
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Bondar DI, Gay-Balmaz F, Tronci C. Koopman wavefunctions and classical-quantum correlation dynamics. Proc Math Phys Eng Sci 2019; 475:20180879. [PMID: 31611710 PMCID: PMC6784396 DOI: 10.1098/rspa.2018.0879] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2018] [Accepted: 07/29/2019] [Indexed: 11/12/2022] Open
Abstract
Upon revisiting the Hamiltonian structure of classical wavefunctions in Koopman–von Neumann theory, this paper addresses the long-standing problem of formulating a dynamical theory of classical–quantum coupling. The proposed model not only describes the influence of a classical system onto a quantum one, but also the reverse effect—the quantum backreaction. These interactions are described by a new Hamiltonian wave equation overcoming shortcomings of currently employed models. For example, the density matrix of the quantum subsystem is always positive definite. While the Liouville density of the classical subsystem is generally allowed to be unsigned, its sign is shown to be preserved in time for a specific infinite family of hybrid classical–quantum systems. The proposed description is illustrated and compared with previous theories using the exactly solvable model of a degenerate two-level quantum system coupled to a classical harmonic oscillator.
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Affiliation(s)
- Denys I Bondar
- Department of Physics and Engineering Physics, Tulane University, New Orleans, LA, USA
| | - François Gay-Balmaz
- CNRS and École Normale Supérieure, Laboratoire de Météorologie Dynamique, Paris, France
| | - Cesare Tronci
- Department of Mathematics, University of Surrey, Guildford, UK.,Mathematical Sciences Research Institute, Berkeley, CA, USA
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37
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Shen L, Tang D, Xie B, Fang WH. Quantum Trajectory Mean-Field Method for Nonadiabatic Dynamics in Photochemistry. J Phys Chem A 2019; 123:7337-7350. [PMID: 31373814 DOI: 10.1021/acs.jpca.9b03480] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
The mixed quantum-classical dynamical approaches have been widely used to study nonadiabatic phenomena in photochemistry and photobiology, in which the time evolutions of the electronic and nuclear subsystems are treated based on quantum and classical mechanics, respectively. The key issue is how to deal with coherence and decoherence during the propagation of the two subsystems, which has been the subject of numerous investigations for a few decades. A brief description on Ehrenfest mean-field and surface-hopping (SH) methods is first provided, and then different algorithms for treatment of quantum decoherence are reviewed in the present paper. More attentions were paid to quantum trajectory mean-field (QTMF) method under the picture of quantum measurements, which is able to overcome the overcoherence problem. Furthermore, the combined QTMF and SH algorithm is proposed in the present work, which takes advantages of the QTMF and SH methods. The potential to extend the applicability of the QTMF method was briefly discussed, such as the generalization to other type of nonadiabatic transitions, the combination with multiscale computational models, and possible improvements on its accuracy and efficiency by using machine-learning techniques.
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Affiliation(s)
- Lin Shen
- Key Laboratory of Theoretical and Computational Photochemistry of Ministry of Education, College of Chemistry , Beijing Normal University , Beijing 100875 , P. R. China
| | - Diandong Tang
- Key Laboratory of Theoretical and Computational Photochemistry of Ministry of Education, College of Chemistry , Beijing Normal University , Beijing 100875 , P. R. China
| | - Binbin Xie
- Hangzhou Institute of Advanced Studies , Zhejiang Normal University , 1108 Gengwen Road , Hangzhou 311231 , Zhejiang P. R. China
| | - Wei-Hai Fang
- Key Laboratory of Theoretical and Computational Photochemistry of Ministry of Education, College of Chemistry , Beijing Normal University , Beijing 100875 , P. R. China
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38
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Wang L, Qiu J, Bai X, Xu J. Surface hopping methods for nonadiabatic dynamics in extended systems. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2019. [DOI: 10.1002/wcms.1435] [Citation(s) in RCA: 31] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Linjun Wang
- Center for Chemistry of Novel & High‐Performance Materials, Department of Chemistry Zhejiang University Hangzhou China
| | - Jing Qiu
- Center for Chemistry of Novel & High‐Performance Materials, Department of Chemistry Zhejiang University Hangzhou China
| | - Xin Bai
- Center for Chemistry of Novel & High‐Performance Materials, Department of Chemistry Zhejiang University Hangzhou China
| | - Jiabo Xu
- Center for Chemistry of Novel & High‐Performance Materials, Department of Chemistry Zhejiang University Hangzhou China
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39
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Runeson JE, Richardson JO. Spin-mapping approach for nonadiabatic molecular dynamics. J Chem Phys 2019; 151:044119. [DOI: 10.1063/1.5100506] [Citation(s) in RCA: 33] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Johan E. Runeson
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
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40
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Schile AJ, Limmer DT. Simulating conical intersection dynamics in the condensed phase with hybrid quantum master equations. J Chem Phys 2019; 151:014106. [DOI: 10.1063/1.5106379] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Addison J. Schile
- Department of Chemistry, University of California, Berkeley, California 94720-1460, USA
- Lawrence Berkeley National Laboratory, University of California, Berkeley, California 94720-1460, USA
| | - David T. Limmer
- Department of Chemistry, University of California, Berkeley, California 94720-1460, USA
- Lawrence Berkeley National Laboratory, University of California, Berkeley, California 94720-1460, USA
- Kavli Energy NanoSciences Institute, University of California, Berkeley, California 94720-1460, USA
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41
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Teh HH, Jin BY, Cheng YC. Frozen-mode small polaron quantum master equation with variational bound for excitation energy transfer in molecular aggregates. J Chem Phys 2019; 150:224110. [DOI: 10.1063/1.5096287] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Hung-Hsuan Teh
- Department of Chemistry, National Taiwan University, Taipei City 10617, Taiwan
| | - Bih-Yaw Jin
- Department of Chemistry, National Taiwan University, Taipei City 10617, Taiwan
| | - Yuan-Chung Cheng
- Department of Chemistry, National Taiwan University, Taipei City 10617, Taiwan
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42
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Agostini F, Curchod BFE. Different flavors of nonadiabatic molecular dynamics. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2019. [DOI: 10.1002/wcms.1417] [Citation(s) in RCA: 42] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Affiliation(s)
- Federica Agostini
- Laboratoire de Chimie Physique UMR 8000 CNRS/University Paris‐Sud Orsay France
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43
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Baskov R, White AJ, Mozyrsky D. Improved Ehrenfest Approach to Model Correlated Electron-Nuclear Dynamics. J Phys Chem Lett 2019; 10:433-440. [PMID: 30621396 DOI: 10.1021/acs.jpclett.8b03061] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
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.
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Affiliation(s)
- Roman Baskov
- Institute of Physics of the National Academy of Sciences of Ukraine , Pr. Nauky 46 , Kyiv-28 MSP 03028 , Ukraine
| | - Alexander J White
- Theoretical Division , Los Alamos National Laboratory , Los Alamos , New Mexico 87545 , United States
| | - Dmitry Mozyrsky
- Theoretical Division , Los Alamos National Laboratory , Los Alamos , New Mexico 87545 , United States
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44
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Tang D, Fang WH, Shen L, Cui G. Combining Meyer–Miller Hamiltonian with electronic structure methods for on-the-fly nonadiabatic dynamics simulations: implementation and application. Phys Chem Chem Phys 2019; 21:17109-17117. [DOI: 10.1039/c9cp02682g] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The MM/SQC method combined with electronic structure calculations at the level of OM2/MRCI and on-the-fly nonadiabatic dynamics simulations.
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Affiliation(s)
- Diandong Tang
- Key Laboratory of Theoretical and Computational Photochemistry of Ministry of Education
- College of Chemistry
- Beijing Normal University
- Beijing 100875
- China
| | - Wei-Hai Fang
- Key Laboratory of Theoretical and Computational Photochemistry of Ministry of Education
- College of Chemistry
- Beijing Normal University
- Beijing 100875
- China
| | - Lin Shen
- Key Laboratory of Theoretical and Computational Photochemistry of Ministry of Education
- College of Chemistry
- Beijing Normal University
- Beijing 100875
- China
| | - Ganglong Cui
- Key Laboratory of Theoretical and Computational Photochemistry of Ministry of Education
- College of Chemistry
- Beijing Normal University
- Beijing 100875
- China
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45
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Affiliation(s)
- Yifan Shen
- Department of Chemistry, Zhejiang University, Hangzhou 310027, China
| | - Linjun Wang
- Department of Chemistry, Zhejiang University, Hangzhou 310027, China
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46
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47
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Quasi-Lie Brackets and the Breaking of Time-Translation Symmetry for Quantum Systems Embedded in Classical Baths. Symmetry (Basel) 2018. [DOI: 10.3390/sym10100518] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Many open quantum systems encountered in both natural and synthetic situations are embedded in classical-like baths. Often, the bath degrees of freedom may be represented in terms of canonically conjugate coordinates, but in some cases they may require a non-canonical or non-Hamiltonian representation. Herein, we review an approach to the dynamics and statistical mechanics of quantum subsystems embedded in either non-canonical or non-Hamiltonian classical-like baths which is based on operator-valued quasi-probability functions. These functions typically evolve through the action of quasi-Lie brackets and their associated Quantum-Classical Liouville Equations, or through quasi-Lie brackets augmented by dissipative terms. Quasi-Lie brackets possess the unique feature that, while conserving the energy (which the Noether theorem links to time-translation symmetry), they violate the time-translation symmetry of their algebra. This fact can be heuristically understood in terms of the dynamics of the open quantum subsystem. We then describe an example in which a quantum subsystem is embedded in a bath of classical spins, which are described by non-canonical coordinates. In this case, it has been shown that an off-diagonal open-bath geometric phase enters into the propagation of the quantum-classical dynamics. Next, we discuss how non-Hamiltonian dynamics may be employed to generate the constant-temperature evolution of phase space degrees of freedom coupled to the quantum subsystem. Constant-temperature dynamics may be generated by either a classical Langevin stochastic process or a Nosé–Hoover deterministic thermostat. These two approaches are not equivalent but have different advantages and drawbacks. In all cases, the calculation of the operator-valued quasi-probability function allows one to compute time-dependent statistical averages of observables. This may be accomplished in practice using a hybrid Molecular Dynamics/Monte Carlo algorithms, which we outline herein.
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48
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Abstract
Electronic friction is a correction to the Born-Oppenheimer approximation, whereby nuclei in motion experience a drag in the presence of a manifold of electronic states. The notion of electronic friction has a long history and has been (re-)discovered in the context of a wide variety of different chemical and physical systems including, but not limited to, surface scattering events, surface reactions or chemisorption, electrochemistry, and conduction through molecular-(or nano-) junctions. Over the years, quite a few different forms of electronic friction have been offered in the literature. In this perspective, we briefly review these developments of electronic friction, highlighting the fact that we can now isolate a single, unifying form for (Markovian) electronic friction. We also focus on the role of electron-electron interactions for understanding frictional effects and offer our thoughts on the strengths and weaknesses of using electronic friction to model dynamics in general.
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Affiliation(s)
- Wenjie Dou
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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49
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Gong Z, Wu J. Quantum kinetic expansion in the spin-boson model: Implemented by the quantum-classical Liouville equation in an anharmonic bath. J Chem Phys 2018; 148:234107. [DOI: 10.1063/1.5028306] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Affiliation(s)
- Zhihao Gong
- Physics Department, Zhejiang University, 38 ZheDa Road, Hangzhou, Zhejiang 310027, China
| | - Jianlan Wu
- Physics Department, Zhejiang University, 38 ZheDa Road, Hangzhou, Zhejiang 310027, China
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50
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Mignolet B, Curchod BFE. A walk through the approximations of ab initio multiple spawning. J Chem Phys 2018; 148:134110. [PMID: 29626896 DOI: 10.1063/1.5022877] [Citation(s) in RCA: 41] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Full multiple spawning offers an in principle exact framework for excited-state dynamics, where nuclear wavefunctions in different electronic states are represented by a set of coupled trajectory basis functions that follow classical trajectories. The couplings between trajectory basis functions can be approximated to treat molecular systems, leading to the ab initio multiple spawning method which has been successfully employed to study the photochemistry and photophysics of several molecules. However, a detailed investigation of its approximations and their consequences is currently missing in the literature. In this work, we simulate the explicit photoexcitation and subsequent excited-state dynamics of a simple system, LiH, and we analyze (i) the effect of the ab initio multiple spawning approximations on different observables and (ii) the convergence of the ab initio multiple spawning results towards numerically exact quantum dynamics upon a progressive relaxation of these approximations. We show that, despite the crude character of the approximations underlying ab initio multiple spawning for this low-dimensional system, the qualitative excited-state dynamics is adequately captured, and affordable corrections can further be applied to ameliorate the coupling between trajectory basis functions.
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Affiliation(s)
- Benoit Mignolet
- Theoretical Physical Chemistry, UR MolSYS, B6c, University of Liège, B4000 Liège, Belgium
| | - Basile F E Curchod
- Department of Chemistry, Durham University, South Road, Durham DH1 3LE, United Kingdom
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