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Rey M, Carrington T. Using nested tensor train contracted basis functions with group theoretical techniques to compute (ro)-vibrational spectra of molecules with non-Abelian groups. J Chem Phys 2024; 161:044102. [PMID: 39037133 DOI: 10.1063/5.0219434] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2024] [Accepted: 06/30/2024] [Indexed: 07/23/2024] Open
Abstract
In this paper, we use nested tensor-train contractions to compute vibrational and ro-vibrational energy levels of molecules with five and six atoms. At each step, we fully exploit symmetry by using symmetry adapted basis functions obtained from an irreducible tensor method. Contracted basis functions are determined by diagonalizing reduced dimensional Hamiltonian matrices. The size of matrices of eigenvectors, used to account for coupling between groups of coordinates, is reduced by discarding rows and columns. The size of the matrices that must be diagonalized is thus substantially reduced, making it possible to use direct eigensolvers, even for molecules with five and six atoms. The symmetry-adapted contracted vibrational basis functions have been used to compute J = 0 energy levels of the CH3CN (C3v) and J > 0 levels of CH4.
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Affiliation(s)
- Michaël Rey
- Groupe de Spectrométrie Moléculaire et Atmosphérique, UMR CNRS 7331, BP 1039, F-51687 Reims Cedex 2, France
| | - Tucker Carrington
- Chemistry Department, Queen's University, Kingston, Ontario K7L 3N6, Canada
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2
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Mátyus E, Martín Santa Daría A, Avila G. Exact quantum dynamics developments for floppy molecular systems and complexes. Chem Commun (Camb) 2023; 59:366-381. [PMID: 36519578 DOI: 10.1039/d2cc05123k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
Molecular rotation, vibration, internal rotation, isomerization, tunneling, intermolecular dynamics of weakly and strongly interacting systems, intra-to-inter-molecular energy transfer, hindered rotation and hindered translation over surfaces are important types of molecular motions. Their fundamentally correct and detailed description can be obtained by solving the nuclear Schrödinger equation on a potential energy surface. Many of the chemically interesting processes involve quantum nuclear motions which are 'delocalized' over multiple potential energy wells. These 'large-amplitude' motions in addition to the high dimensionality of the vibrational problem represent challenges to the current (ro)vibrational methodology. A review of the quantum nuclear motion methodology is provided, current bottlenecks of solving the nuclear Schrödinger equation are identified, and solution strategies are reviewed. Technical details, computational results, and analysis of these results in terms of limiting models and spectroscopically relevant concepts are highlighted for selected numerical examples.
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Affiliation(s)
- Edit Mátyus
- ELTE, Eötvös Loránd University, Institute of Chemistry, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary.
| | - Alberto Martín Santa Daría
- ELTE, Eötvös Loránd University, Institute of Chemistry, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary.
| | - Gustavo Avila
- ELTE, Eötvös Loránd University, Institute of Chemistry, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary.
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3
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Papp D, Tajti V, Avila G, Mátyus E, Czakó G. CH 4·F − revisited: full-dimensional ab initio potential energy surface and variational vibrational states. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2113565] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/15/2022]
Affiliation(s)
- Dóra Papp
- MTA-SZTE Lendület Computational Reaction Dynamics Research Group, Interdisciplinary Excellence Centre and Department of Physical Chemistry and Materials Science, Institute of Chemistry, University of Szeged, Szeged, Hungary
| | - Viktor Tajti
- MTA-SZTE Lendület Computational Reaction Dynamics Research Group, Interdisciplinary Excellence Centre and Department of Physical Chemistry and Materials Science, Institute of Chemistry, University of Szeged, Szeged, Hungary
| | - Gustavo Avila
- ELTE, Eötvös Loránd University, Institute of Chemistry, Budapest, Hungary
| | - Edit Mátyus
- ELTE, Eötvös Loránd University, Institute of Chemistry, Budapest, Hungary
| | - Gábor Czakó
- MTA-SZTE Lendület Computational Reaction Dynamics Research Group, Interdisciplinary Excellence Centre and Department of Physical Chemistry and Materials Science, Institute of Chemistry, University of Szeged, Szeged, Hungary
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4
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Sarka J, Poirier B. Hitting the Trifecta: How to Simultaneously Push the Limits of Schrödinger Solution with Respect to System Size, Convergence Accuracy, and Number of Computed States. J Chem Theory Comput 2021; 17:7732-7744. [PMID: 34761945 DOI: 10.1021/acs.jctc.1c00824] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Methods for solving the Schrödinger equation without approximation are in high demand but are notoriously computationally expensive. In practical terms, there are just three primary factors that currently limit what can be achieved: 1) system size/dimensionality; 2) energy level excitation; and 3) numerical convergence accuracy. Broadly speaking, current methods can deliver on any two of these three goals, but achieving all three at once remains an enormous challenge. In this paper, we shall demonstrate how to "hit the trifecta" in the context of molecular vibrational spectroscopy calculations. In particular, we compute the lowest 1000 vibrational states for the six-atom acetonitrile molecule (CH3CN), to a numerical convergence of accuracy 10-2 cm-1 or better. These calculations encompass all vibrational states throughout most of the dynamically relevant range (i.e., up to ∼4250 cm-1 above the ground state), computed in full quantum dimensionality (12 dimensions), to near spectroscopic accuracy. To our knowledge, no such vibrational spectroscopy calculation has ever previously been performed.
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Affiliation(s)
- János Sarka
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409, United States
| | - Bill Poirier
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409, United States
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5
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Pandey A, Poirier B. An algorithm to find (and plug) “holes” in multi-dimensional surfaces. J Chem Phys 2020; 152:214102. [DOI: 10.1063/5.0005681] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Affiliation(s)
- Ankit Pandey
- Department of Chemistry and Biochemistry, Texas Tech University, P.O. Box 41061, Lubbock, Texas 79409-1061, USA
| | - Bill Poirier
- Department of Chemistry and Biochemistry, Texas Tech University, P.O. Box 41061, Lubbock, Texas 79409-1061, USA
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6
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Le Bris V, Odunlami M, Bégué D, Baraille I, Coulaud O. Using computed infrared intensities for the reduction of vibrational configuration interaction bases. Phys Chem Chem Phys 2020; 22:7021-7030. [PMID: 32191243 DOI: 10.1039/d0cp00593b] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The Adaptive Vibrational Configuration Interaction (A-VCI) algorithm is an iterative process that computes the anharmonic spectrum of a molecule using nested bases to discretize the Hamiltonian operator. For large molecular systems, the size of the discretization space and the computation time quickly become prohibitive. It is therefore necessary to develop new methods to further limit the number of basis functions. Most of the time, the interpretation of an experimental infrared spectrum does not require the calculation of all eigenvalues but only those corresponding to vibrational states with significant intensity. In this paper, a technique that uses infrared intensities is introduced to select a subset of eigenvalues to be precisely calculated. Thus, we build smaller nested bases and reduce both the memory footprint and the computational time. We validate the advantages of this new approach on a well-studied 7-atom molecular system (C2H4O), and we apply it on a larger 10-atom molecule (C4H4N2).
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Affiliation(s)
- Vincent Le Bris
- Universite de Pau et des Pays de l'Adour, E2S UPPA, CNRS, IPREM, Institut des Sciences Analytiques et de Physicochimie pour l'Environnement et les Matériaux, UMR5254, Pau, France.
| | - Marc Odunlami
- Universite de Pau et des Pays de l'Adour, E2S UPPA, CNRS, IPREM, Institut des Sciences Analytiques et de Physicochimie pour l'Environnement et les Matériaux, UMR5254, Pau, France.
| | - Didier Bégué
- Universite de Pau et des Pays de l'Adour, E2S UPPA, CNRS, IPREM, Institut des Sciences Analytiques et de Physicochimie pour l'Environnement et les Matériaux, UMR5254, Pau, France.
| | - Isabelle Baraille
- Universite de Pau et des Pays de l'Adour, E2S UPPA, CNRS, IPREM, Institut des Sciences Analytiques et de Physicochimie pour l'Environnement et les Matériaux, UMR5254, Pau, France.
| | - Olivier Coulaud
- HiePACS project-team, Inria Bordeaux Sud-Ouest, 200, avenue de la Vieille Tour, F-33405 Talence Cedex, France
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7
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Lesko E, Ardiansyah M, Brorsen KR. Vibrational adaptive sampling configuration interaction. J Chem Phys 2019; 151:164103. [DOI: 10.1063/1.5126510] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ethan Lesko
- Department of Chemistry, University of Missouri, Columbia, Missouri 65203, USA
| | - Muhammad Ardiansyah
- Department of Chemistry, University of Missouri, Columbia, Missouri 65203, USA
| | - Kurt R. Brorsen
- Department of Chemistry, University of Missouri, Columbia, Missouri 65203, USA
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8
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Pandey A, Poirier B. Using phase-space Gaussians to compute the vibrational states of OCHCO+. J Chem Phys 2019; 151:014114. [DOI: 10.1063/1.5096770] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ankit Pandey
- Department of Chemistry and Biochemistry, Texas Tech University, P.O. Box 41061, Lubbock, Texas 79409-1061, USA
| | - Bill Poirier
- Department of Chemistry and Biochemistry, Texas Tech University, P.O. Box 41061, Lubbock, Texas 79409-1061, USA
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9
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Jasper AW, Harding LB, Knight C, Georgievskii Y. Anharmonic Rovibrational Partition Functions at High Temperatures: Tests of Reduced-Dimensional Models for Systems with up to Three Fluxional Modes. J Phys Chem A 2019; 123:6210-6228. [DOI: 10.1021/acs.jpca.9b03592] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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10
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Jerke J, Karwowski J, Poirier B. Exact matrix elements for general two-body central-force interactions, expressed as sums of products. Mol Phys 2019. [DOI: 10.1080/00268976.2018.1538541] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Affiliation(s)
- Jonathan Jerke
- Department of Chemistry and Biochemistry, and Department of Physics, Texas Tech University, Lubbock, TX, USA
| | - Jacek Karwowski
- Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University, Toruń, Poland
| | - Bill Poirier
- Department of Chemistry and Biochemistry, and Department of Physics, Texas Tech University, Lubbock, TX, USA
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11
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Garashchuk S, Rassolov V. Quantum Trajectory Dynamics Based on Local Approximations to the Quantum Potential and Force. J Chem Theory Comput 2019; 15:3906-3916. [DOI: 10.1021/acs.jctc.9b00027] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Sophya Garashchuk
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
| | - Vitaly Rassolov
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
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12
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Scheit S, Goswami S, Meyer HD, Köppel H. Fully quantal treatment of nonadiabatic molecular photodynamics: General considerations and application to the benzene cation. COMPUT THEOR CHEM 2019. [DOI: 10.1016/j.comptc.2019.01.011] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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13
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Odunlami M, Le Bris V, Bégué D, Baraille I, Coulaud O. A-VCI: A flexible method to efficiently compute vibrational spectra. J Chem Phys 2018; 146:214108. [PMID: 28595393 DOI: 10.1063/1.4984266] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The adaptive vibrational configuration interaction algorithm has been introduced as a new method to efficiently reduce the dimension of the set of basis functions used in a vibrational configuration interaction process. It is based on the construction of nested bases for the discretization of the Hamiltonian operator according to a theoretical criterion that ensures the convergence of the method. In the present work, the Hamiltonian is written as a sum of products of operators. The purpose of this paper is to study the properties and outline the performance details of the main steps of the algorithm. New parameters have been incorporated to increase flexibility, and their influence has been thoroughly investigated. The robustness and reliability of the method are demonstrated for the computation of the vibrational spectrum up to 3000 cm-1 of a widely studied 6-atom molecule (acetonitrile). Our results are compared to the most accurate up to date computation; we also give a new reference calculation for future work on this system. The algorithm has also been applied to a more challenging 7-atom molecule (ethylene oxide). The computed spectrum up to 3200 cm-1 is the most accurate computation that exists today on such systems.
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Affiliation(s)
- Marc Odunlami
- Université de Pau et des Pays de l'Adour, CNRS, Institut des Sciences Analytiques et de Physico-Chimie pour l'Environnement et les Matériaux, UMR5254, 64000 Pau, France
| | - Vincent Le Bris
- Université de Pau et des Pays de l'Adour, CNRS, Institut des Sciences Analytiques et de Physico-Chimie pour l'Environnement et les Matériaux, UMR5254, 64000 Pau, France
| | - Didier Bégué
- Université de Pau et des Pays de l'Adour, CNRS, Institut des Sciences Analytiques et de Physico-Chimie pour l'Environnement et les Matériaux, UMR5254, 64000 Pau, France
| | - Isabelle Baraille
- Université de Pau et des Pays de l'Adour, CNRS, Institut des Sciences Analytiques et de Physico-Chimie pour l'Environnement et les Matériaux, UMR5254, 64000 Pau, France
| | - Olivier Coulaud
- HiePACS Project-Team, Inria Bordeaux Sud-Ouest, 200, Avenue de la Vieille Tour, 33405 Talence Cedex, France
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14
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Large Scale Exact Quantum Dynamics Calculations: Using Phase Space to Truncate the Basis Effectively. ADVANCES IN CHEMICAL PHYSICS 2018. [DOI: 10.1002/9781119374978.ch9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register]
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15
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Halverson T, Iouchtchenko D, Roy PN. Quantifying entanglement of rotor chains using basis truncation: Application to dipolar endofullerene peapods. J Chem Phys 2018; 148:074112. [DOI: 10.1063/1.5011769] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Affiliation(s)
- Tom Halverson
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Dmitri Iouchtchenko
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Pierre-Nicholas Roy
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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16
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Jasper AW, Gruey ZB, Harding LB, Georgievskii Y, Klippenstein SJ, Wagner AF. Anharmonic Rovibrational Partition Functions for Fluxional Species at High Temperatures via Monte Carlo Phase Space Integrals. J Phys Chem A 2018; 122:1727-1740. [DOI: 10.1021/acs.jpca.7b11722] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Ahren W. Jasper
- Chemical Sciences and Engineering
Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - Zackery B. Gruey
- Chemical Sciences and Engineering
Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - Lawrence B. Harding
- Chemical Sciences and Engineering
Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - Yuri Georgievskii
- Chemical Sciences and Engineering
Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - Stephen J. Klippenstein
- Chemical Sciences and Engineering
Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - Albert F. Wagner
- Chemical Sciences and Engineering
Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
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17
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Larsson HR, Tannor DJ. Dynamical pruning of the multiconfiguration time-dependent Hartree (DP-MCTDH) method: An efficient approach for multidimensional quantum dynamics. J Chem Phys 2017; 147:044103. [DOI: 10.1063/1.4993219] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- H. R. Larsson
- Institut für Physikalische Chemie, Christian-Albrechts-Universität zu Kiel, 24098 Kiel, Germany
- Department of Chemical Physics, Weizmann Institute of Science, 76100 Rehovot, Israel
| | - D. J. Tannor
- Department of Chemical Physics, Weizmann Institute of Science, 76100 Rehovot, Israel
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18
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Carrington T. Perspective: Computing (ro-)vibrational spectra of molecules with more than four atoms. J Chem Phys 2017; 146:120902. [DOI: 10.1063/1.4979117] [Citation(s) in RCA: 67] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Tucker Carrington
- Chemistry Department, Queen’s University, Kingston, Ontario
K7L 3N6, Canada
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19
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Larsson HR, Hartke B, Tannor DJ. Efficient molecular quantum dynamics in coordinate and phase space using pruned bases. J Chem Phys 2016; 145:204108. [DOI: 10.1063/1.4967432] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- H. R. Larsson
- Institut für Physikalische Chemie, Christian-Albrechts-Universität zu Kiel, 24098 Kiel, Germany
| | - B. Hartke
- Institut für Physikalische Chemie, Christian-Albrechts-Universität zu Kiel, 24098 Kiel, Germany
| | - D. J. Tannor
- Department of Chemical Physics, Weizmann Institute of Science, 76100 Rehovot, Israel
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20
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Leclerc A, Thomas PS, Carrington T. Comparison of different eigensolvers for calculating vibrational spectra using low-rank, sum-of-product basis functions. Mol Phys 2016. [DOI: 10.1080/00268976.2016.1249980] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Arnaud Leclerc
- Université de Lorraine , UMR CNRS 7565 SRSMC, Metz, France
| | - Phillip S. Thomas
- Chemistry Department, Queen's University , Kingston, Ontario, Canada
| | - Tucker Carrington
- Chemistry Department, Queen's University , Kingston, Ontario, Canada
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21
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Brown J, Carrington T. Using an expanding nondirect product harmonic basis with an iterative eigensolver to compute vibrational energy levels with as many as seven atoms. J Chem Phys 2016; 145:144104. [DOI: 10.1063/1.4963916] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- James Brown
- Chemistry Department, Queen’s University, Kingston, Ontario K7L 3N6, Canada
| | - Tucker Carrington
- Chemistry Department, Queen’s University, Kingston, Ontario K7L 3N6, Canada
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22
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Wu F, Ren Y, Bian W. The hydrogen tunneling splitting in malonaldehyde: A full-dimensional time-independent quantum mechanical method. J Chem Phys 2016; 145:074309. [DOI: 10.1063/1.4960789] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Feng Wu
- Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yinghui Ren
- Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Wensheng Bian
- Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
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23
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Wodraszka R, Carrington T. Using a pruned, nondirect product basis in conjunction with the multi-configuration time-dependent Hartree (MCTDH) method. J Chem Phys 2016; 145:044110. [DOI: 10.1063/1.4959228] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Robert Wodraszka
- Department of Chemistry, Queen’s University, Kingston, Ontario K7L 3N6, Canada
| | - Tucker Carrington
- Department of Chemistry, Queen’s University, Kingston, Ontario K7L 3N6, Canada
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24
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Brown J, Carrington T. Assessing the utility of phase-space-localized basis functions: Exploiting direct product structure and a new basis function selection procedure. J Chem Phys 2016; 144:244115. [DOI: 10.1063/1.4954721] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- James Brown
- Chemistry Department, Queen’s University, Kingston, Ontario K7L 3N6, Canada
| | - Tucker Carrington
- Chemistry Department, Queen’s University, Kingston, Ontario K7L 3N6, Canada
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25
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Machnes S, Assémat E, Larsson HR, Tannor DJ. Quantum Dynamics in Phase Space using Projected von Neumann Bases. J Phys Chem A 2016; 120:3296-308. [PMID: 26977715 DOI: 10.1021/acs.jpca.5b12370] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We describe the mathematical underpinnings of the biorthogonal von Neumann method for quantum mechanical simulations (PvB). In particular, we present a detailed discussion of the important issue of nonorthogonal projection onto subspaces of biorthogonal bases, and how this differs from orthogonal projection. We present various representations of the Schrödinger equation in the reduced basis and discuss their relative merits. We conclude with illustrative examples and a discussion of the outlook and challenges ahead for the PvB representation.
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Affiliation(s)
- Shai Machnes
- Department of Chemical Physics, Weizmann Institute of Science , 76100 Rehovot, Israel
| | - Elie Assémat
- Department of Chemical Physics, Weizmann Institute of Science , 76100 Rehovot, Israel
| | - Henrik R Larsson
- Institut für Physikalische Chemie, Christian-Albrechts-Universität zu Kiel , Olshausenstraße 40, D-24098 Kiel, Germany
| | - David J Tannor
- Department of Chemical Physics, Weizmann Institute of Science , 76100 Rehovot, Israel
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26
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Gu B, Garashchuk S. Quantum Dynamics with Gaussian Bases Defined by the Quantum Trajectories. J Phys Chem A 2016; 120:3023-31. [DOI: 10.1021/acs.jpca.5b10029] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Bing Gu
- Department of Chemistry & Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
| | - Sophya Garashchuk
- Department of Chemistry & Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
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27
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Affiliation(s)
- Thomas Halverson
- Department of Chemistry and
Biochemistry, and Department of Physics, Texas Tech University, P.O. Box 41061, Lubbock, Texas 79409-1061, United States
| | - Bill Poirier
- Department of Chemistry and
Biochemistry, and Department of Physics, Texas Tech University, P.O. Box 41061, Lubbock, Texas 79409-1061, United States
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28
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Brown J, Carrington T. Using an iterative eigensolver to compute vibrational energies with phase-spaced localized basis functions. J Chem Phys 2015; 143:044104. [DOI: 10.1063/1.4926805] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- James Brown
- Chemistry Department, Queen’s University, Kingston, Ontario K7L 3N6, Canada
| | - Tucker Carrington
- Chemistry Department, Queen’s University, Kingston, Ontario K7L 3N6, Canada
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