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Hoppe H, Manthe U. Eigenstate calculation in the state-averaged (multi-layer) multi-configurational time-dependent Hartree approach. J Chem Phys 2024; 160:034104. [PMID: 38230812 DOI: 10.1063/5.0188748] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2023] [Accepted: 12/15/2023] [Indexed: 01/18/2024] Open
Abstract
A new approach for the calculation of eigenstates with the state-averaged (multi-layer) multi-configurational time-dependent Hartree (MCTDH) approach is presented. The approach is inspired by the recent work of Larsson [J. Chem. Phys. 151, 204102 (2019)]. It employs local optimization of the basis sets at each node of the multi-layer MCTDH tree and successive downward and upward sweeps to obtain a globally converged result. At the top node, the Hamiltonian represented in the basis of the single-particle functions (SPFs) of the first layer is diagonalized. Here p wavefunctions corresponding to the p lowest eigenvalues are computed by a block Lanczos approach. At all other nodes, a non-linear operator consisting of the respective mean-field Hamiltonian matrix and a projector onto the space spanned by the respective SPFs is considered. Here, the eigenstate corresponding to the lowest eigenvalue is computed using a short iterative Lanczos scheme. Two different examples are studied to illustrate the new approach: the calculation of the vibrational states of methyl and acetonitrile. The calculations for methyl employ the single-layer MCTDH approach, a general potential energy surface, and the correlation discrete variable representation. A five-layer MCTDH representation and a sum of product-type Hamiltonian are used in the acetonitrile calculations. Very fast convergence and order of magnitude reductions in the numerical effort compared to the previously used block relaxation scheme are found. Furthermore, a detailed comparison with the results of Avila and Carrington [J. Chem. Phys. 134, 054126 (2011)] for acetonitrile highlights the potential problems of convergence tests for high-dimensional systems.
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Affiliation(s)
- Hannes Hoppe
- Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstr. 25, D-33615 Bielefeld, Germany
| | - Uwe Manthe
- Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstr. 25, D-33615 Bielefeld, Germany
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Larsson HR. Computing vibrational eigenstates with tree tensor network states (TTNS). J Chem Phys 2019; 151:204102. [DOI: 10.1063/1.5130390] [Citation(s) in RCA: 29] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Affiliation(s)
- Henrik R. Larsson
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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Schäpers D, Manthe U. Vibronic coupling in the F·CH4 prereactive complex. J Chem Phys 2019; 151:104106. [DOI: 10.1063/1.5110246] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Daniela Schäpers
- Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstr. 25, D-33615 Bielefeld, Germany
| | - Uwe Manthe
- Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstr. 25, D-33615 Bielefeld, Germany
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Wodraszka R, Carrington T. A pruned collocation-based multiconfiguration time-dependent Hartree approach using a Smolyak grid for solving the Schrödinger equation with a general potential energy surface. J Chem Phys 2019; 150:154108. [DOI: 10.1063/1.5093317] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Robert Wodraszka
- 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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Neville SP, Schuurman MS. Efficient Solution of the Electronic Eigenvalue Problem Using Wavepacket Propagation. J Chem Theory Comput 2018; 14:1433-1441. [PMID: 29394052 DOI: 10.1021/acs.jctc.7b01258] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We report how imaginary time wavepacket propagation may be used to efficiently calculate the lowest-lying eigenstates of the electronic Hamiltonian. This approach, known as the relaxation method in the quantum dynamics community, represents a fundamentally different approach to the solution of the electronic eigenvalue problem in comparison to traditional iterative subspace diagonalization schemes such as the Davidson and Lanczos methods. In order to render the relaxation method computationally competitive with existing iterative subspace methods, an extended short iterative Lanczos wavepacket propagation scheme is proposed and implemented. In the examples presented here, we show that by using an efficient wavepacket propagation algorithm the relaxation method is, at worst, as computationally expensive as the commonly used block Davidson-Liu algorithm, and in certain cases, significantly less so.
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Affiliation(s)
- Simon P Neville
- Department of Chemistry and Biomolecular Sciences , University of Ottawa , 10 Marie Curie , Ottawa , Ontario K1N 6N5 , Canada
| | - Michael S Schuurman
- Department of Chemistry and Biomolecular Sciences , University of Ottawa , 10 Marie Curie , Ottawa , Ontario K1N 6N5 , Canada.,National Research Council of Canada , 100 Sussex Drive , Ottawa , Ontario K1A 0R6 , Canada
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Wodraszka R, Carrington T. A new collocation-based multi-configuration time-dependent Hartree (MCTDH) approach for solving the Schrödinger equation with a general potential energy surface. J Chem Phys 2018; 148:044115. [DOI: 10.1063/1.5018793] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [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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Manthe U. Wavepacket dynamics and the multi-configurational time-dependent Hartree approach. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:253001. [PMID: 28430111 DOI: 10.1088/1361-648x/aa6e96] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
Multi-configurational time-dependent Hartree (MCTDH) based approaches are efficient, accurate, and versatile methods for high-dimensional quantum dynamics simulations. Applications range from detailed investigations of polyatomic reaction processes in the gas phase to high-dimensional simulations studying the dynamics of condensed phase systems described by typical solid state physics model Hamiltonians. The present article presents an overview of the different areas of application and provides a comprehensive review of the underlying theory. The concepts and guiding ideas underlying the MCTDH approach and its multi-mode and multi-layer extensions are discussed in detail. The general structure of the equations of motion is highlighted. The representation of the Hamiltonian and the correlated discrete variable representation (CDVR), which provides an efficient multi-dimensional quadrature in MCTDH calculations, are discussed. Methods which facilitate the calculation of eigenstates, the evaluation of correlation functions, and the efficient representation of thermal ensembles in MCTDH calculations are described. Different schemes for the treatment of indistinguishable particles in MCTDH calculations and recent developments towards a unified multi-layer MCTDH theory for systems including bosons and fermions are discussed.
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Affiliation(s)
- Uwe Manthe
- Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstr. 25, D-33615 Bielefeld, Germany
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Wang XG, Carrington T. Calculated rotation-bending energy levels of CH5+ and a comparison with experiment. J Chem Phys 2016; 144:204304. [DOI: 10.1063/1.4948549] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Xiao-Gang Wang
- 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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Wodraszka R, Manthe U. CH+5: Symmetry and the Entangled Rovibrational Quantum States of a Fluxional Molecule. J Phys Chem Lett 2015; 6:4229-4232. [PMID: 26538038 DOI: 10.1021/acs.jpclett.5b01869] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Protonated methane, CH5+, is the prototypical example of a fluxional molecular system. The almost unconstrained angular motion of its five hydrogen atoms results in dynamical phenomena not found in rigid or semirigid molecules. Here it is shown that standard concepts to describe rotational quantum states of molecules can not be applied to CH5+ or any other fluxional system of the type ABn or Bn with n > 4 due to fundamental symmetry reasons. Instead, the ro-vibrational states of CH5+ display a unique level scheme, which results from a complex entanglement of rotational and tunneling motions. A detailed analysis of the ro-vibrational quantum states of CH5+ based on full-dimensional quantum dynamics simulations is presented, and the effects of the Pauli principle are considered. The consequences for the interpretation of recent experimental results are highlighted
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Affiliation(s)
- Robert Wodraszka
- Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld , Universitätsstraβe 25, D-33615 Bielefeld, Germany
| | - Uwe Manthe
- Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld , Universitätsstraβe 25, D-33615 Bielefeld, Germany
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Wodraszka R, Manthe U. Iterative Diagonalization in the Multiconfigurational Time-Dependent Hartree Approach: Ro-vibrational Eigenstates. J Phys Chem A 2013; 117:7246-55. [DOI: 10.1021/jp401129t] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Robert Wodraszka
- Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstraße.
25, D-33615 Bielefeld, Germany
| | - Uwe Manthe
- Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstraße.
25, D-33615 Bielefeld, Germany
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Wodraszka R, Palma J, Manthe U. Vibrational Dynamics of the CH4·F–Complex. J Phys Chem A 2012; 116:11249-59. [DOI: 10.1021/jp3052642] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Robert Wodraszka
- Theoretische Chemie, Fakultät
für Chemie, Universität Bielefeld, Universitätsstrasse 25, D-33615 Bielefeld, Germany
| | - Juliana Palma
- Theoretische Chemie, Fakultät
für Chemie, Universität Bielefeld, Universitätsstrasse 25, D-33615 Bielefeld, Germany
| | - Uwe Manthe
- Theoretische Chemie, Fakultät
für Chemie, Universität Bielefeld, Universitätsstrasse 25, D-33615 Bielefeld, Germany
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Mori Y, Takano K. Location of protons in N–H⋯N hydrogen-bonded systems: a theoretical study on intramolecular pyridine–dihydropyridine and pyridine–pyridinium pairs. Phys Chem Chem Phys 2012; 14:11090-8. [DOI: 10.1039/c2cp41425b] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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