1
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Garashchuk S, Großmann F. Assessing the Accuracy of Quantum Dynamics Performed in the Time-Dependent Basis Representation. J Phys Chem A 2024; 128:8265-8278. [PMID: 39270133 DOI: 10.1021/acs.jpca.4c03657] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/15/2024]
Abstract
A full quantum-mechanical (QM) description of large amplitude nuclear motion, associated with chemical reactions or isomerization of high-dimensional molecular systems, is inherently challenging due to the exponential scaling of the QM complexity with system size. To ameliorate the scaling bottleneck in studies of realistic systems, typically modeled in the configuration space, the nuclear wave functions are represented in terms of time-dependent basis functions. Such bases are expected to give an accurate description with a modest number of basis functions employed, by adapting them to the wave function solving the time-dependent Schrödinger equation. It is not, however, straightforward to estimate the accuracy of the resulting solution: in QM the energy conservation, a convenient such measure for a classical trajectory evolving in a time-independent potential, is not a sufficient criterion of the dynamics' accuracy. In this work, we argue that the expectation value of the Hamiltonian's "variance", quantifying the basis completeness, is a suitable practical measure of the quantum dynamics' accuracy. Illustrations are given for several chemistry-relevant test systems, modeled employing time-independent as well as time-dependent bases, including the coupled and variational coherent states methods and the quantum-trajectory guided adaptable Gaussians (QTAG) as the latter basis type. A novel semilocal definition of the QTAG basis time-evolution for placing the basis functions "in the right place at the right time" is also presented.
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Affiliation(s)
- Sophya Garashchuk
- Department of Chemistry & Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
| | - Frank Großmann
- Institute for Theoretical Physics, Technische Universität Dresden, 01062 Dresden, Germany
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2
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Chan HHS, Meister R, Jones T, Tew DP, Benjamin SC. Grid-based methods for chemistry simulations on a quantum computer. SCIENCE ADVANCES 2023; 9:eabo7484. [PMID: 36857445 PMCID: PMC9977186 DOI: 10.1126/sciadv.abo7484] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/23/2022] [Accepted: 01/30/2023] [Indexed: 06/18/2023]
Abstract
First-quantized, grid-based methods for chemistry modeling are a natural and elegant fit for quantum computers. However, it is infeasible to use today's quantum prototypes to explore the power of this approach because it requires a substantial number of near-perfect qubits. Here, we use exactly emulated quantum computers with up to 36 qubits to execute deep yet resource-frugal algorithms that model 2D and 3D atoms with single and paired particles. A range of tasks is explored, from ground state preparation and energy estimation to the dynamics of scattering and ionization; we evaluate various methods within the split-operator QFT (SO-QFT) Hamiltonian simulation paradigm, including protocols previously described in theoretical papers and our own techniques. While we identify certain restrictions and caveats, generally, the grid-based method is found to perform very well; our results are consistent with the view that first-quantized paradigms will be dominant from the early fault-tolerant quantum computing era onward.
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Affiliation(s)
| | - Richard Meister
- Department of Materials, University of Oxford, Oxford OX1 3PH, UK
| | - Tyson Jones
- Department of Materials, University of Oxford, Oxford OX1 3PH, UK
| | - David P. Tew
- Department of Chemistry, University of Oxford, Oxford OX1 3TA, UK
- Duality Quantum Photonics, 6 Lower Park Row, Bristol BS1 5BJ, UK
| | - Simon C. Benjamin
- Department of Materials, University of Oxford, Oxford OX1 3PH, UK
- Quantum Motion, 9 Sterling Way, London N7 9HJ, UK
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3
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Soley MB, Bergold P, Gorodetsky AA, Batista VS. Functional Tensor-Train Chebyshev Method for Multidimensional Quantum Dynamics Simulations. J Chem Theory Comput 2021; 18:25-36. [PMID: 34898201 DOI: 10.1021/acs.jctc.1c00941] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Methods for efficient simulations of multidimensional quantum dynamics are essential for theoretical studies of chemical systems where quantum effects are important, such as those involving rearrangements of protons or electronic configurations. Here, we introduce the functional tensor-train Chebyshev (FTTC) method for rigorous nuclear quantum dynamics simulations. FTTC is essentially the Chebyshev propagation scheme applied to the initial state represented in a continuous analogue tensor-train format. We demonstrate the capabilities of FTTC as applied to simulations of proton quantum dynamics in a 50-dimensional model of hydrogen-bonded DNA base pairs.
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Affiliation(s)
- Micheline B Soley
- Yale Quantum Institute, Yale University, P.O. Box 208334, New Haven, Connecticut 06520-8263, United States.,Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520, United States
| | - Paul Bergold
- Zentrum Mathematik, Technical University of Munich, Boltzmannstr. 3, 85748 Garching, Germany
| | - Alex A Gorodetsky
- Department of Aerospace Engineering, University of Michigan, 1320 Beal Avenue, Ann Arbor, Michigan 48109-2140, United States
| | - Victor S Batista
- Yale Quantum Institute, Yale University, P.O. Box 208334, New Haven, Connecticut 06520-8263, United States.,Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520, United States.,Energy Sciences Institute, Yale University, P.O. Box 27394, West Haven, Connecticut 06516-7394, United States
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4
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Richings GW, Habershon S. Direct Grid-Based Nonadiabatic Dynamics on Machine-Learned Potential Energy Surfaces: Application to Spin-Forbidden Processes. J Phys Chem A 2020; 124:9299-9313. [DOI: 10.1021/acs.jpca.0c06125] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Gareth W. Richings
- Department of Chemistry, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Scott Habershon
- Department of Chemistry, University of Warwick, Coventry CV4 7AL, United Kingdom
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5
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Dutra M, Wickramasinghe S, Garashchuk S. Multidimensional Tunneling Dynamics Employing Quantum-Trajectory Guided Adaptable Gaussian Bases. J Phys Chem A 2020; 124:9314-9325. [PMID: 33090807 DOI: 10.1021/acs.jpca.0c07168] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
An efficient basis representation of time-dependent wavefunctions is essential for theoretical studies of high-dimensional molecular systems exhibiting large-amplitude motion. For fully coupled anharmonic systems, the complexity of a general wavefunction scales exponentially with the system size; therefore, for practical reasons, it is desirable to adapt the basis to the time-dependent wavefunction at hand. Often times on this quest for a minimal basis representation, time-dependent Gaussians are employed, in part because of their localization in both configuration and momentum spaces and also because of their direct connection to classical and semiclassical dynamics, guiding the evolution of the basis function parameters. In this work, the quantum-trajectory guided adaptable Gaussian (QTAG) bases method [ J. Chem. Theory Comput. 2020, 16, 18-34] is generalized to include correlated, i.e., non-factorizable, basis functions, and the performance of the QTAG dynamics is assessed on benchmark system/bath tunneling models of up to 20 dimensions. For the popular choice of initial conditions describing tunneling between the reactant/product wells, the minimal "semiclassical" description of the bath modes using essentially a single multidimensional basis function combined with the multi-Gaussian representation of the tunneling mode is shown to capture the dominant features of dynamics in a highly efficient manner.
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Affiliation(s)
- Matthew Dutra
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
| | - Sachith Wickramasinghe
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
| | - Sophya Garashchuk
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
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6
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Dutra M, Wickramasinghe S, Garashchuk S. Quantum Dynamics with the Quantum Trajectory-Guided Adaptable Gaussian Bases. J Chem Theory Comput 2019; 16:18-34. [DOI: 10.1021/acs.jctc.9b00844] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Matthew Dutra
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
| | - Sachith Wickramasinghe
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
| | - Sophya Garashchuk
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
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7
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Murakami T, Frankcombe TJ. Non-adiabatic quantum molecular dynamics by the basis expansion leaping multi-configuration Gaussian (BEL MCG) method: Multi-set and single-set formalisms. J Chem Phys 2019; 150:144112. [DOI: 10.1063/1.5084749] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Tatsuhiro Murakami
- School of Science, University of New South Wales, Canberra, ACT 2600, Australia
| | - Terry J. Frankcombe
- School of Science, University of New South Wales, Canberra, ACT 2600, Australia
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8
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Murakami T, Frankcombe TJ. Accurate quantum molecular dynamics for multidimensional systems by the basis expansion leaping multi-configuration Gaussian (BEL MCG) method. J Chem Phys 2018; 149:134113. [DOI: 10.1063/1.5046643] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Tatsuhiro Murakami
- School of Physical, Environmental and Mathematical Sciences, University of New South Wales, Canberra, ACT 2600, Australia
| | - Terry J. Frankcombe
- School of Physical, Environmental and Mathematical Sciences, University of New South Wales, Canberra, ACT 2600, Australia
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9
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Kowalewski M, Fingerhut BP, Dorfman KE, Bennett K, Mukamel S. Simulating Coherent Multidimensional Spectroscopy of Nonadiabatic Molecular Processes: From the Infrared to the X-ray Regime. Chem Rev 2017; 117:12165-12226. [DOI: 10.1021/acs.chemrev.7b00081] [Citation(s) in RCA: 81] [Impact Index Per Article: 11.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Affiliation(s)
- Markus Kowalewski
- Department
of Chemistry and Department of Physics and Astronomy, University of California, Irvine, California 92697-2025, United States
| | - Benjamin P. Fingerhut
- Max-Born-Institut für Nichtlineare Optik und Kurzzeitspektroskopie, D-12489 Berlin, Germany
| | - Konstantin E. Dorfman
- State
Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
| | - Kochise Bennett
- Department
of Chemistry and Department of Physics and Astronomy, University of California, Irvine, California 92697-2025, United States
| | - Shaul Mukamel
- Department
of Chemistry and Department of Physics and Astronomy, University of California, Irvine, California 92697-2025, United States
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10
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Greene SM, Batista VS. Tensor-Train Split-Operator Fourier Transform (TT-SOFT) Method: Multidimensional Nonadiabatic Quantum Dynamics. J Chem Theory Comput 2017; 13:4034-4042. [DOI: 10.1021/acs.jctc.7b00608] [Citation(s) in RCA: 61] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Samuel M. Greene
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, United States
- Energy Sciences Institute, Yale University, P.O. Box 27394, West Haven, Connecticut 06516-7394, United States
| | - Victor S. Batista
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, United States
- Energy Sciences Institute, Yale University, P.O. Box 27394, West Haven, Connecticut 06516-7394, United States
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11
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Saller MAC, Habershon S. Quantum Dynamics with Short-Time Trajectories and Minimal Adaptive Basis Sets. J Chem Theory Comput 2017; 13:3085-3096. [DOI: 10.1021/acs.jctc.7b00021] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Maximilian A. C. Saller
- Department of Chemistry and
Centre for Scientific Computing, University of Warwick, Coventry, CV4 7AL, United Kingdom
| | - Scott Habershon
- Department of Chemistry and
Centre for Scientific Computing, University of Warwick, Coventry, CV4 7AL, United Kingdom
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12
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Alborzpour JP, Tew DP, Habershon S. Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression. J Chem Phys 2016; 145:174112. [DOI: 10.1063/1.4964902] [Citation(s) in RCA: 44] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jonathan P. Alborzpour
- Department of Chemistry and Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - David P. Tew
- School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
| | - Scott Habershon
- Department of Chemistry and Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL, United Kingdom
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13
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Heaps CW, Mazziotti DA. Pseudospectral Gaussian quantum dynamics: Efficient sampling of potential energy surfaces. J Chem Phys 2016; 144:164108. [DOI: 10.1063/1.4946807] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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14
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Green JA, Grigolo A, Ronto M, Shalashilin DV. A two-layer approach to the coupled coherent states method. J Chem Phys 2016; 144:024111. [DOI: 10.1063/1.4939205] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- James A. Green
- School of Chemistry, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - Adriano Grigolo
- Instituto de Física “Gleb Wataghin,” Universidade Estadual de Campinas, 13083-859 Campinas, SP, Brazil
| | - Miklos Ronto
- School of Chemistry, University of Leeds, Leeds LS2 9JT, United Kingdom
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15
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Stasyuk AJ, Bultinck P, Gryko DT, Cyrański MK. The effect of hydrogen bond strength on emission properties in 2-(2′-hydroxyphenyl)imidazo[1,2-a]pyridines. J Photochem Photobiol A Chem 2016. [DOI: 10.1016/j.jphotochem.2015.08.013] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
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16
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Green JA, Shalashilin DV. Benchmark calculation for tunnelling through a multidimensional asymmetric double well potential. Chem Phys Lett 2015. [DOI: 10.1016/j.cplett.2015.10.073] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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17
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Alemi M, Loring RF. Two-Dimensional Vibrational Spectroscopy of a Dissipative System with the Optimized Mean-Trajectory Approximation. J Phys Chem B 2015; 119:8950-9. [PMID: 25275943 PMCID: PMC4383732 DOI: 10.1021/jp5076884] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2014] [Revised: 09/10/2014] [Indexed: 11/30/2022]
Abstract
The optimized mean-trajectory (OMT) approximation is a semiclassical method for computing vibrational response functions from action-quantized classical trajectories connected by discrete transitions representing radiation-matter interactions. Here we apply this method to an anharmonic chromophore coupled to a harmonic bath. A forward-backward trajectory implementation of the OMT method is described that addresses the numerical challenges of applying the OMT to large systems with disparate frequency scales. The OMT is shown to well reproduce line shapes and waiting time dynamics in the pure dephasing limit of weak coupling to an off-resonant bath. The OMT is also shown to describe a case where energy transfer is the predominant source of line broadening.
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Affiliation(s)
- Mallory Alemi
- Department
of Chemistry and
Chemical Biology, Baker Laboratory, Cornell
University, Ithaca, New York 14853, United
States
| | - Roger F. Loring
- Department
of Chemistry and
Chemical Biology, Baker Laboratory, Cornell
University, Ithaca, New York 14853, United
States
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18
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Soley M, Markmann A, Batista VS. Steered quantum dynamics for energy minimization. J Phys Chem B 2015; 119:715-27. [PMID: 25122515 DOI: 10.1021/jp5046723] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We introduce a quantum optimal control algorithm for energy minimization that combines the diffeomorphic modulation under observable response preserving homotopy (D-MORPH) gradient and the Broyden Fletcher Goldfarb Shanno (BFGS) iterative scheme for nonlinear optimization. An extended set of controls defining the time-dependent mass, dipole moment, and external perturbational field are optimized to find an effective Hamiltonian that steers the dynamics of the system into the global minimum without getting trapped into local minima. The algorithm is illustrated as applied to energy minimization on rugged surfaces and golf potentials comparable to those previously explored for testing quantum annealing methodologies.
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Affiliation(s)
- Micheline Soley
- Department of Chemistry, Yale University , P.O. Box 208107, New Haven, Connecticut 06520-8107, United States
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19
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Gerace M, Loring RF. Two-dimensional spectroscopy of coupled vibrations with the optimized mean-trajectory approximation. J Phys Chem B 2013; 117:15452-61. [PMID: 23924378 PMCID: PMC3865215 DOI: 10.1021/jp405225g] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The optimized mean-trajectory (OMT) approximation is a semiclassical representation of the nonlinear vibrational response function used to compute multidimensional infrared spectra. In this method, response functions are calculated from a sequence of classical trajectories linked by discontinuities representing the effects of radiation-matter interactions, thus providing an approximation to quantum dynamics using classical inputs. This approach was previously formulated and assessed numerically for a single anharmonic degree of freedom. Our previous work is generalized here in two respects. First, the derivation of the OMT is extended to any number of coupled anharmonic vibrations by determining semiclassical approximations for pairs of double-sided Feynman diagrams. Second, an efficient numerical procedure is developed for calculating two-dimensional infrared spectra of coupled anharmonic vibrations in the OMT approximation. The OMT approximation is shown to reproduce the fundamental features of the quantum response function including both coherence and population dynamics.
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Affiliation(s)
- Mallory Gerace
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York, 14853, USA
| | - Roger F. Loring
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York, 14853, USA
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20
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Dorfman KE, Fingerhut BP, Mukamel S. Broadband infrared and Raman probes of excited-state vibrational molecular dynamics: simulation protocols based on loop diagrams. Phys Chem Chem Phys 2013; 15:12348-59. [PMID: 23783120 PMCID: PMC3744248 DOI: 10.1039/c3cp51117k] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Vibrational motions in electronically excited states can be observed either by time and frequency resolved infrared absorption or by off resonant stimulated Raman techniques. Multipoint correlation function expressions are derived for both signals. Three representations which suggest different simulation protocols for the signals are developed. These are based on the forward and the backward propagation of the wavefunction, sum over state expansion using an effective vibrational Hamiltonian or a semiclassical treatment of a bath. We show that the effective temporal (Δt) and spectral (Δω) resolution of the techniques is not controlled solely by experimental knobs but also depends on the system dynamics being probed. The Fourier uncertainty ΔωΔt > 1 is never violated.
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Affiliation(s)
- Konstantin E Dorfman
- Department of Chemistry, University of California, Irvine, California 92697-2025, USA.
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21
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Gerace M, Loring RF. An optimized semiclassical approximation for vibrational response functions. J Chem Phys 2013; 138:124104. [PMID: 23556706 DOI: 10.1063/1.4795941] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The observables of multidimensional infrared spectroscopy may be calculated from nonlinear vibrational response functions. Fully quantum dynamical calculations of vibrational response functions are generally impractical, while completely classical calculations are qualitatively incorrect at long times. These challenges motivate the development of semiclassical approximations to quantum mechanics, which use classical mechanical information to reconstruct quantum effects. The mean-trajectory (MT) approximation is a semiclassical approach to quantum vibrational response functions employing classical trajectories linked by deterministic transitions representing the effects of the radiation-matter interaction. Previous application of the MT approximation to the third-order response function R(3)(t3, t2, t1) demonstrated that the method quantitatively describes the coherence dynamics of the t3 and t1 evolution times, but is qualitatively incorrect for the waiting-time t2 period. Here we develop an optimized version of the MT approximation by elucidating the connection between this semiclassical approach and the double-sided Feynman diagrams (2FD) that represent the quantum response. Establishing the direct connection between 2FD and semiclassical paths motivates a systematic derivation of an optimized MT approximation (OMT). The OMT uses classical mechanical inputs to accurately reproduce quantum dynamics associated with all three propagation times of the third-order vibrational response function.
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Affiliation(s)
- Mallory Gerace
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
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22
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Igumenshchev K, Ovchinnikov M, Maniadis P, Prezhdo O. Signatures of discrete breathers in coherent state quantum dynamics. J Chem Phys 2013; 138:054104. [PMID: 23406095 DOI: 10.1063/1.4788618] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
In classical mechanics, discrete breathers (DBs) - a spatial time-periodic localization of energy - are predicted in a large variety of nonlinear systems. Motivated by a conceptual bridging of the DB phenomena in classical and quantum mechanical representations, we study their signatures in the dynamics of a quantum equivalent of a classical mechanical point in phase space - a coherent state. In contrast to the classical point that exhibits either delocalized or localized motion, the coherent state shows signatures of both localized and delocalized behavior. The transition from normal to local modes have different characteristics in quantum and classical perspectives. Here, we get an insight into the connection between classical and quantum perspectives by analyzing the decomposition of the coherent state into system's eigenstates, and analyzing the spacial distribution of the wave-function density within these eigenstates. We find that the delocalized and localized eigenvalue components of the coherent state are separated by a mixed region, where both kinds of behavior can be observed. Further analysis leads to the following observations. Considered as a function of coupling, energy eigenstates go through avoided crossings between tunneling and non-tunneling modes. The dominance of tunneling modes in the high nonlinearity region is compromised by the appearance of new types of modes - high order tunneling modes - that are similar to the tunneling modes but have attributes of non-tunneling modes. Certain types of excitations preferentially excite higher order tunneling modes, allowing one to study their properties. Since auto-correlation functions decrease quickly in highly nonlinear systems, short-time dynamics are sufficient for modeling quantum DBs. This work provides a foundation for implementing modern semi-classical methods to model quantum DBs, bridging classical and quantum mechanical signatures of DBs, and understanding spectroscopic experiments that involve a coherent state.
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Affiliation(s)
- Kirill Igumenshchev
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA.
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23
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Igumenshchev K, Ovchinnikov M, Prezhdo OV. Herman–Kluk allows analysis of quantum discrete breathers in higher dimensional systems. Mol Phys 2012. [DOI: 10.1080/00268976.2012.680513] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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24
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Saha R, Markmann A, Batista VS. Tunneling through Coulombic barriers: quantum control of nuclear fusion. Mol Phys 2012. [DOI: 10.1080/00268976.2012.679635] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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25
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Habershon S. Trajectory-guided configuration interaction simulations of multidimensional quantum dynamics. J Chem Phys 2012; 136:054109. [DOI: 10.1063/1.3681167] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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26
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Habershon S. Linear dependence and energy conservation in Gaussian wavepacket basis sets. J Chem Phys 2012; 136:014109. [DOI: 10.1063/1.3671978] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
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27
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Igumenshchev K, Prezhdo O. Quantized Hamilton dynamics describes quantum discrete breathers in a simple way. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:026616. [PMID: 21929137 DOI: 10.1103/physreve.84.026616] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2011] [Revised: 06/17/2011] [Indexed: 05/31/2023]
Abstract
We study the localization of energy in a nonlinear coupled system, exhibiting so-called breather modes, using quantized Hamilton dynamics (QHD). Already at the lowest order, which is only twice as complex as classical mechanics, this simple semiclassical method incorporates quantum-mechanical effects. The transition between the localized and delocalized regimes is instantaneous in classical mechanics, while it is gradual due to tunneling in both quantum mechanics and QHD. In contrast to classical mechanics, which predicts an abrupt appearance of breathers, quantum mechanics and QHD show an alternation of localized and delocalized behavior in the transient region. QHD includes zero-point energy that is reflected in a shifted energy asymptote for the localized states, providing another improvement on the classical perspective. By detailed analysis of the distribution and transfer of energy within classical mechanics, QHD, and quantum dynamics, we conclude that QHD is an efficient approach that accounts for moderate quantum effects and can be used to identify quantum breathers in large nonlinear systems.
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Affiliation(s)
- Kirill Igumenshchev
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA.
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28
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Gelman D, Schwartz SD. Modeling vibrational resonance in linear hydrocarbon chain with a mixed quantum-classical method. J Chem Phys 2009; 130:134110. [PMID: 19355720 DOI: 10.1063/1.3110063] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The quantum dynamics of a vibrational excitation in a linear hydrocarbon model system is studied with a new mixed quantum-classical method. The method is suited to treat many-body systems consisting of a low dimensional quantum primary part coupled to a classical bath. The dynamics of the primary part is governed by the quantum corrected propagator, with the corrections defined in terms of matrix elements of zeroth order propagators. The corrections are taken to the classical limit by introducing the frozen Gaussian approximation for the bath degrees of freedom. The ability of the method to describe dynamics of multidimensional systems has been tested. The results obtained by the method have been compared to previous quantum simulations performed with the quasiadiabatic path integral method.
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Affiliation(s)
- David Gelman
- Department of Biophysics, Albert Einstein College of Medicine, 1300 Morris Park Ave., Bronx, New York 10461, USA
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29
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Kim J, Wu Y, Brédas JL, Batista VS. Quantum Dynamics of the Excited-State Intramolecular Proton Transfer in 2-(2′-Hydroxyphenyl)benzothiazole. Isr J Chem 2009. [DOI: 10.1560/ijc.49.2.187] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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30
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Wu Y, Brédas JL. Simulations of the emission spectra of fac-tris(2-phenylpyridine) iridium and Duschinsky rotation effects using the Herman–Kluk semiclassical initial value representation method. J Chem Phys 2008; 129:214305. [DOI: 10.1063/1.3027514] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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31
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Gelman D, Schwartz SD. Tunneling dynamics with a mixed quantum-classical method: Quantum corrected propagator combined with frozen Gaussian wave packets. J Chem Phys 2008; 129:024504. [DOI: 10.1063/1.2949818] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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32
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Shalashilin DV, Child MS. Basis set sampling in the method of coupled coherent states: Coherent state swarms, trains, and pancakes. J Chem Phys 2008; 128:054102. [DOI: 10.1063/1.2828509] [Citation(s) in RCA: 64] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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33
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Jie Q. Approximating the ground state of fermion systems by multiple determinant states: matching pursuit approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:026705. [PMID: 18352146 DOI: 10.1103/physreve.77.026705] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/22/2007] [Revised: 01/22/2008] [Indexed: 05/26/2023]
Abstract
We present a simple and stable numerical method to approximate the ground state of a quantum many-body system by multiple determinant states. This method searches these determinant states one by one according to the matching pursuit algorithm. The first determinant state is identical to that of the Hartree-Fock theory. Calculations for a two-dimensional Hubbard model serve as a demonstration.
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Affiliation(s)
- Quanlin Jie
- Department of Physics, Wuhan University, Wuhan 430072, People's Republic of China.
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34
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Chen X, Batista VS. The MP/SOFT methodology for simulations of quantum dynamics: Model study of the photoisomerization of the retinyl chromophore in visual rhodopsin. J Photochem Photobiol A Chem 2007. [DOI: 10.1016/j.jphotochem.2007.05.015] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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35
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Wu Y, Herman MF. On the properties of a primitive semiclassical surface hopping propagator for nonadiabatic quantum dynamics. J Chem Phys 2007; 127:044109. [PMID: 17672683 DOI: 10.1063/1.2756532] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A previously developed nonadiabatic semiclassical surface hopping propagator [M. F. Herman J. Chem. Phys. 103, 8081 (1995)] is further studied. The propagator has been shown to satisfy the time-dependent Schrodinger equation (TDSE) through order h, and the O(h2) terms are treated as small errors, consistent with standard semiclassical analysis. Energy is conserved at each hopping point and the change in momentum accompanying each hop is parallel to the direction of the nonadiabatic coupling vector resulting in both transmission and reflection types of hops. Quantum mechanical analysis and numerical calculations presented in this paper show that the h2 terms involving the interstate coupling functions have significant effects on the quantum transition probabilities. Motivated by these data, the h2 terms are analyzed for the nonadiabatic semiclassical propagator. It is shown that the propagator can satisfy the TDSE for multidimensional systems by including another type of nonclassical trajectories that reflect on the same surfaces. This h2 analysis gives three conditions for these three types of trajectories so that their coefficients are uniquely determined. Besides the nonadiabatic semiclassical propagator, a numerically useful quantum propagator in the adiabatic representation is developed to describe nonadiabatic transitions.
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Affiliation(s)
- Yinghua Wu
- Department of Chemistry, Tulane University, New Orleans, Louisiana 70118, USA
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36
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Miller WH. Including quantum effects in the dynamics of complex (i.e., large) molecular systems. J Chem Phys 2006; 125:132305. [PMID: 17029424 DOI: 10.1063/1.2211608] [Citation(s) in RCA: 75] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The development in the 1950s and 1960s of crossed molecular beam methods for studying chemical reactions at the single-collision molecular level stimulated the need and desire for theoretical methods to describe these and other dynamical processes in molecular systems. Chemical dynamics theory has made great strides in the ensuing decades, so that methods are now available for treating the quantum dynamics of small molecular systems essentially completely. For the large molecular systems that are of so much interest nowadays (e.g., chemical reactions in solution, in clusters, in nanostructures, in biological systems, etc.), however, the only generally available theoretical approach is classical molecular dynamics (MD) simulations. Much effort is currently being devoted to the development of approaches for describing the quantum dynamics of these complex systems. This paper reviews some of these approaches, especially the use of semiclassical approximations for adding quantum effects to classical MD simulations, also showing some new versions that should make these semiclassical approaches even more practical and accurate.
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Affiliation(s)
- William H Miller
- Department of Chemistry and K. S. Pitzer Center for Theoretical Chemistry, University of California, Berkeley, California 94720-1460, USA.
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37
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Chen X, Batista VS. Matching-pursuit/split-operator-Fourier-transform simulations of excited-state nonadiabatic quantum dynamics in pyrazine. J Chem Phys 2006; 125:124313. [PMID: 17014180 DOI: 10.1063/1.2356477] [Citation(s) in RCA: 55] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A simple approach for numerically exact simulations of nonadiabatic quantum dynamics in multidimensional systems is introduced and applied to the description of the photoabsorption spectroscopy of pyrazine. The propagation scheme generalizes the recently developed matching-pursuit/split-operator-Fourier-transform (MP/SOFT) method [Y. Wu and V. S. Batista, J. Chem. Phys. 121, 1676 (2004)] to simulations of nonadiabatic quantum dynamics. The time-evolution operator is applied, as defined by the Trotter expansion to second order accuracy, in dynamically adaptive coherent-state expansions. These representations are obtained by combining the matching-pursuit algorithm with a gradient-based optimization method. The accuracy and efficiency of the resulting computational approach are demonstrated in calculations of time-dependent survival amplitudes and photoabsorption cross sections, using a model Hamiltonian that allows for direct comparisons with benchmark calculations. Simulations in full-dimensional potential energy surfaces involve the propagation of a 24-dimensional wave packet to describe the S(1)S(2) interconversion of pyrazine after S(0)-->S(2) photoexcitation. The reported results show that the generalized MP/SOFT method is a practical and accurate approach to model nonadiabatic reaction dynamics in polyatomic systems.
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Affiliation(s)
- Xin Chen
- Department of Chemistry, Yale University, New Haven, CT 06520-8107, USA
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38
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Wu Y, Batista VS. Matching-pursuit split-operator Fourier-transform simulations of excited-state intramolecular proton transfer in 2-(2′-hydroxyphenyl)-oxazole. J Chem Phys 2006; 124:224305. [PMID: 16784272 DOI: 10.1063/1.2202847] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The excited-state intramolecular proton-transfer dynamics associated with the keto-enolic tautomerization reaction in 2-(2(')-hydroxyphenyl)-oxazole is simulated according to a numerically exact quantum-dynamics propagation method and a full-dimensional excited-state potential energy surface, based on an ab initio reaction surface Hamiltonian. The reported simulations involve the propagation of 35-dimensional wave packets according to the recently developed matching-pursuit/split-operator-Fourier-transform (MP/SOFT) method by Wu and Batista. The underlying propagation scheme recursively applies the time-evolution operator as defined by the Trotter expansion to second order accuracy in dynamically adaptive coherent-state expansions. Computations of time-dependent survival amplitudes, photoabsorption cross sections, and time-dependent reactant(product) populations are compared to the corresponding calculations based on semiclassical approaches, including the Herman-Kluk semiclassical initial value representation method. The reported results demonstrate the capabilities of the MP/SOFT method as a valuble computational tool to study ultrafast reaction dynamics in polyatomic systems as well as to validate semiclassical simulations of complex (nonintegrable) quantum dynamics in multidimensional model systems.
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Affiliation(s)
- Yinghua Wu
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, USA
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39
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Sherratt PA, Shalashillin DV, Child MS. Description of multidimensional tunnelling with the help of coupled coherent states guided by classical Hamiltonians with quantum corrections. Chem Phys 2006. [DOI: 10.1016/j.chemphys.2005.06.050] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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40
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Shalashilin DV, Child MS. A version of diffusion Monte Carlo method based on random grids of coherent states. II. Six-dimensional simulation of electronic states of H2. J Chem Phys 2005; 122:224109. [PMID: 15974653 DOI: 10.1063/1.1926269] [Citation(s) in RCA: 10] [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 report a new version of the diffusion Monte Carlo (DMC) method, based on coherent-state quantum mechanics. Randomly selected grids of coherent states in phase space are used to obtain numerical imaginary time solutions of the Schrodinger equation, with an iterative refinement technique to improve the quality of the Monte Carlo grid. Accurate results were obtained, for the appropriately symmetrized two lowest states of the hydrogen molecule, by Monte Carlo sampling and six-dimensional propagation in the full phase space.
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Affiliation(s)
- Dmitrii V Shalashilin
- Physical and Theoretical Chemistry Laboratory, Oxford University, South Parks Road, Oxford OX1 3QZ, United Kingdom.
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41
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Abstract
This Perspective presents a broad overview of the present status of theoretical capabilities for describing quantum dynamics in molecular systems with many degrees of freedom, e.g., chemical reactions in solution, clusters, solids, or biomolecular environments.
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Affiliation(s)
- William H Miller
- Department of Chemistry and K. S. Pitzer Center for Theoretical Chemistry, University of California, and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720-1460, USA.
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42
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Wu Y, Herman MF, Batista VS. Matching-pursuit∕split-operator Fourier-transform simulations of nonadiabatic quantum dynamics. J Chem Phys 2005; 122:114114. [PMID: 15836208 DOI: 10.1063/1.1881132] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A rigorous and practical approach for simulations of nonadiabatic quantum dynamics is introduced. The algorithm involves a natural extension of the matching-pursuitsplit-operator Fourier-transform (MPSOFT) method [Y. Wu and V. S. Batista, J. Chem. Phys. 121, 1676 (2004)] recently developed for simulations of adiabatic quantum dynamics in multidimensional systems. The MPSOFT propagation scheme, extended to nonadiabatic dynamics, recursively applies the time-evolution operator as defined by the standard perturbation expansion to first-, or second-order, accuracy. The expansion is implemented in dynamically adaptive coherent-state representations, generated by an approach that combines the matching-pursuit algorithm with a gradient-based optimization method. The accuracy and efficiency of the resulting propagation method are demonstrated as applied to the canonical model systems introduced by Tully for testing simulations of dual curve-crossing nonadiabatic dynamics.
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Affiliation(s)
- Yinghua Wu
- Department of Chemistry, Tulane University, New Orleans, Louisiana 70118, USA
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43
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Chen X, Wu Y, Batista VS. Matching-pursuit/split-operator-Fourier-transform computations of thermal correlation functions. J Chem Phys 2005; 122:064102. [PMID: 15740362 DOI: 10.1063/1.1848513] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A rigorous and practical methodology for evaluating thermal-equilibrium density matrices, finite-temperature time-dependent expectation values, and time-correlation functions is described. The method involves an extension of the matching-pursuit/split-operator-Fourier-transform method to the solution of the Bloch equation via imaginary-time propagation of the density matrix and the evaluation of Heisenberg time-evolution operators through real-time propagation in dynamically adaptive coherent-state representations.
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Affiliation(s)
- Xin Chen
- Department of Chemistry, Yale University, New Haven, Connecticut 06520-8107, USA
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