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Wodraszka R, Carrington T. Using a pruned basis and a sparse collocation grid with more points than basis functions to do efficient and accurate MCTDH calculations with general potential energy surfaces. J Chem Phys 2024; 160:214121. [PMID: 38836450 DOI: 10.1063/5.0214557] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2024] [Accepted: 05/14/2024] [Indexed: 06/06/2024] Open
Abstract
We propose a new collocation multi-configuration time-dependent Hartree (MCTDH) method. It reduces point-set error by using more points than basis functions. Collocation makes it possible to use MCTDH with a general potential energy surface without computing any integrals. The collocation points are associated with a basis larger than the basis used to represent wavefunctions. Both bases are obtained from a direct product basis built from single-particle functions by imposing a pruning condition. The collocation points are those on a sparse grid. Heretofore, collocation MCTDH calculations with more points than basis functions have only been possible if both the collocation grid and the basis set are direct products. In this paper, we exploit a new pseudo-inverse to use both more points than basis functions and a pruned basis and grid. We demonstrate that, for a calculation of the lowest 50 vibrational states (energy levels and wavefunctions) of CH2NH, errors can be reduced by two orders of magnitude by increasing the number of points, without increasing the basis size. This is true also when unrefined time-independent points are used.
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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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Hino K, Kurashige Y. Encoding a Many-Body Potential Energy Surface into a Grid-Based Matrix Product Operator. J Chem Theory Comput 2024; 20:3839-3849. [PMID: 38647101 DOI: 10.1021/acs.jctc.4c00046] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/25/2024]
Abstract
An efficient algorithm for compressing a given many-body potential energy surface (PES) of molecular systems into a grid-based matrix product operator (MPO) is proposed. The PES is once represented by a full-dimensional or truncated many-body expansion form, which is obtained by ab initio calculations at each grid mesh point, and then all terms in the expansion are compressed and merged into a single MPO while maintaining the bond dimension of the MPO as small as possible. It was shown that the ab initio PES of the H2CO was compressed by more than 2 orders of magnitude in the size of the site operators without loss of accuracy. By the use of grid basis, the tensor rank of the site operators of the MPO is reduced from four to three due to the diagonal nature of the position-dependent operators on grid basis, which significantly reduces the computational cost of the tensor contractions required in the real and imaginary time evolution of the matrix product state (MPS) wave functions with the grid-based MPO (Grid-MPO) Hamiltonian. Similar to other grid-based methods, Grid-MPO is easily applicable to any kinds of potentials of molecular systems, such as analytical empirical model potentials expressed by position operators and ab initio potentials, if the values at the grid points are available. Using the Grid-MPO combined with the MPS, we calculated the time correlation function of the Eigen cation H 3 O + ( H 2 O ) 3 to predict the infrared spectrum and compared with the experimental and the previous theoretical studies. The actual scaling with the size of systems was examined for the multidimensional Henon-Heiles Hamiltonian. It was shown that the method is considerably accelerated by the graphic processing unit (GPU) because the sizes of site operators were kept small and all tensors were able to be stored on the VRAM of a GPU.
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Affiliation(s)
- Kentaro Hino
- Department of Chemistry, Graduate School of Science, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Yuki Kurashige
- Department of Chemistry, Graduate School of Science, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan
- FOREST, JST, Honcho 4-1-8, Kawaguchi, Saitama 332-0012, Japan
- CREST, JST, Honcho 4-1-8, Kawaguchi, Saitama 332-0012, Japan
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Zúñiga J, Bastida A, Requena A. Quantum Dynamics of Oblique Vibrational States in the Hénon-Heiles System. J Phys Chem A 2023; 127:8663-8675. [PMID: 37801706 PMCID: PMC10764095 DOI: 10.1021/acs.jpca.3c03122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2023] [Revised: 09/13/2023] [Indexed: 10/08/2023]
Abstract
In this paper, we study the quantum time evolution of oblique nonstationary vibrational states in a Hénon-Heiles oscillator system with two dissociation channels, which models the stretching vibrational motions of triatomic molecules. The oblique nonstationary states we are interested in are the eigenfunctions of the anharmonic zero-order Hamiltonian operator resulting from the transformation to oblique coordinates, which are defined as those coming from nonorthogonal coordinate rotations that express the matrix representation of the second-order Hamiltonian in a block diagonal form characterized by the polyadic quantum number n = n1 + n2. The survival probabilities calculated show that the oblique nonstationary states evolve within their polyadic group with a high degree of coherence up to the dissociation limits on the short time scale. The degree of coherence is certainly much higher than that exhibited by the local nonstationary states extracted from the conventional orthogonal rotation of the original normal coordinates. We also show that energy exchange between the oblique vibrational modes occurs in a much more regular way than the exchange between the local modes.
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Affiliation(s)
- José Zúñiga
- Departamento de Química
Física, Universidad de Murcia, 30100 Murcia, Spain
| | - Adolfo Bastida
- Departamento de Química
Física, Universidad de Murcia, 30100 Murcia, Spain
| | - Alberto Requena
- Departamento de Química
Física, Universidad de Murcia, 30100 Murcia, Spain
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Choi S, Vaníček J. A time-reversible integrator for the time-dependent Schrödinger equation on an adaptive grid. J Chem Phys 2019; 151:234102. [PMID: 31864241 DOI: 10.1063/1.5127856] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
One of the most accurate methods for solving the time-dependent Schrödinger equation uses a combination of the dynamic Fourier method with the split-operator algorithm on a tensor-product grid. To reduce the number of required grid points, we let the grid move together with the wavepacket but find that the naïve algorithm based on an alternate evolution of the wavefunction and grid destroys the time reversibility of the exact evolution. Yet, we show that the time reversibility is recovered if the wavefunction and grid are evolved simultaneously during each kinetic or potential step; this is achieved by using the Ehrenfest theorem together with the splitting method. The proposed algorithm is conditionally stable, symmetric, and time-reversible and conserves the norm of the wavefunction. The preservation of these geometric properties is shown analytically and demonstrated numerically on a three-dimensional harmonic model and collinear model of He-H2 scattering. We also show that the proposed algorithm can be symmetrically composed to obtain time-reversible integrators of an arbitrary even order. We observed 10 000-fold speedup by using the tenth-order instead of the second-order method to obtain a solution with a time discretization error below 10-9. Moreover, using the adaptive grid instead of the fixed grid resulted in a 64-fold reduction in the required number of grid points in the harmonic system and made it possible to simulate the He-H2 scattering for six times longer while maintaining reasonable accuracy. Applicability of the algorithm to high-dimensional quantum dynamics is demonstrated using the strongly anharmonic eight-dimensional Hénon-Heiles model.
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Affiliation(s)
- Seonghoon Choi
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Jiří Vaníček
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
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Xie W, Sapunar M, Došlić N, Sala M, Domcke W. Assessing the performance of trajectory surface hopping methods: Ultrafast internal conversion in pyrazine. J Chem Phys 2019; 150:154119. [DOI: 10.1063/1.5084961] [Citation(s) in RCA: 35] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Weiwei Xie
- Department of Chemistry, Technical University of Munich, Lichtenbergstr. 4, 85747 Garching, Germany
- Institute of Biological Interfaces (IBG-2), Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
- Institute of Physical Chemistry, Karlsruhe Institute of Technology, Kaiserstr. 12, 76131 Karlsruhe, Germany
| | - Marin Sapunar
- Department of Physical Chemistry, Ruđer Bošković Institute, HR-10000 Zagreb, Croatia
| | - Nađa Došlić
- Department of Physical Chemistry, Ruđer Bošković Institute, HR-10000 Zagreb, Croatia
| | - Matthieu Sala
- Laboratoire Interdisciplinaire Carnot de Bourgogne UMR 6303 CNRS, Université de Bourgogne, BP 47870, F-21078 Dijon, France and Institut für Physikalische Chemie, Christian-Albrechts-Universität zu Kiel, Olshausenstr. 40, D-24098 Kiel, Germany
| | - Wolfgang Domcke
- Department of Chemistry, Technical University of Munich, Lichtenbergstr. 4, 85747 Garching, Germany
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Madsen NK, Hansen MB, Zoccante A, Monrad K, Hansen MB, Christiansen O. Exponential parameterization of wave functions for quantum dynamics: Time-dependent Hartree in second quantization. J Chem Phys 2018; 149:134110. [DOI: 10.1063/1.5049344] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Niels Kristian Madsen
- Department of Chemistry, University of Aarhus, Langelandsgade 140, DK-8000 Aarhus C, Denmark
| | - Mads Bøttger Hansen
- Department of Chemistry, University of Aarhus, Langelandsgade 140, DK-8000 Aarhus C, Denmark
| | - Alberto Zoccante
- Department of Chemistry, University of Aarhus, Langelandsgade 140, DK-8000 Aarhus C, Denmark
| | - Kasper Monrad
- Department of Chemistry, University of Aarhus, Langelandsgade 140, DK-8000 Aarhus C, Denmark
| | - Mikkel Bo Hansen
- Department of Chemistry, University of Aarhus, Langelandsgade 140, DK-8000 Aarhus C, Denmark
| | - Ove Christiansen
- Department of Chemistry, University of Aarhus, Langelandsgade 140, DK-8000 Aarhus C, Denmark
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Kloss B, Burghardt I, Lubich C. Implementation of a novel projector-splitting integrator for the multi-configurational time-dependent Hartree approach. J Chem Phys 2017; 146:174107. [DOI: 10.1063/1.4982065] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
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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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Abstract
Multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) theory is a rigorous and powerful method to simulate quantum dynamics in complex many-body systems. This approach extends the original MCTDH theory of Meyer, Manthe, and Cederbaum to include dynamically contracted layers in a recursive way, within which the equations of motion are determined from the Dirac-Frenkel variational principle. This paper presents the general derivation of the theory and analyzes the important features that make the ML-MCTDH method numerically efficient. Furthermore, we discuss the generalization of the theory to treat many-body identical particles (fermions or bosons) as well as calculating energy eigenstates via the improved relaxation method.
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Affiliation(s)
- Haobin Wang
- Department of Chemistry, University of Colorado Denver, Denver, Colorado 80217-3364, United States
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Keller J, Lasser C. Quasi-classical description of molecular dynamics based on Egorov's theorem. J Chem Phys 2014; 141:054104. [DOI: 10.1063/1.4891517] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Affiliation(s)
- Johannes Keller
- Zentrum Mathematik, Technische Universität München, 80290 München, Germany
| | - Caroline Lasser
- Zentrum Mathematik, Technische Universität München, 80290 München, Germany
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Ronto M, Shalashilin DV. Numerical Implementation and Test of the Modified Variational Multiconfigurational Gaussian Method for High-Dimensional Quantum Dynamics. J Phys Chem A 2013; 117:6948-59. [DOI: 10.1021/jp310976d] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Miklos Ronto
- School of Chemistry, University of Leeds, Leeds LS2 9JT, U.K
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Vendrell O, Meyer HD. Multilayer multiconfiguration time-dependent Hartree method: implementation and applications to a Henon-Heiles hamiltonian and to pyrazine. J Chem Phys 2011; 134:044135. [PMID: 21280715 DOI: 10.1063/1.3535541] [Citation(s) in RCA: 242] [Impact Index Per Article: 18.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method is discussed and a fully general implementation for any number of layers based on the recursive ML-MCTDH algorithm given by Manthe [J. Chem. Phys. 128, 164116 (2008)] is presented. The method is applied first to a generalized Henon-Heiles (HH) hamiltonian. For 6D HH the overhead of ML-MCTDH makes the method slower than MCTDH, but for 18D HH ML-MCTDH starts to be competitive. We report as well 1458D simulations of the HH hamiltonian using a seven-layer scheme. The photoabsorption spectrum of pyrazine computed with the 24D hamiltonian of Raab et al. [J. Chem. Phys. 110, 936 (1999)] provides a realistic molecular test case for the method. Quick and small ML-MCTDH calculations needing a fraction of the time and resources of reference MCTDH calculations provide already spectra with all the correct features. Accepting slightly larger deviations, the calculation can be accelerated to take only 7 min. When pushing the method toward convergence, results of similar quality than the best available MCTDH benchmark, which is based on a wavepacket with 4.6×10(7)time-dependent coefficients, are obtained with a much more compact wavefunction consisting of only 4.5×10(5) coefficients and requiring a shorter computation time.
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Affiliation(s)
- Oriol Vendrell
- Center for Free-Electron Laser Science, DESY, Notkestrasse 85, D-22607 Hamburg, Germany.
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Bhattacharya S, Panda AN, Meyer HD. Multiconfiguration time-dependent Hartree approach to study the OH+H2 reaction. J Chem Phys 2010; 132:214304. [DOI: 10.1063/1.3429609] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [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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Manthe U. The state averaged multiconfigurational time-dependent Hartree approach: Vibrational state and reaction rate calculations. J Chem Phys 2008; 128:064108. [DOI: 10.1063/1.2829404] [Citation(s) in RCA: 83] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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15
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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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16
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Koh YW, Takatsuka K. Finding periodic orbits of higher-dimensional flows by including tangential components of trajectory motion. Phys Rev E 2008; 76:066205. [PMID: 18233902 DOI: 10.1103/physreve.76.066205] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2007] [Revised: 08/22/2007] [Indexed: 11/07/2022]
Abstract
Methods to search for periodic orbits are usually implemented with the Newton-Raphson type algorithms that extract the orbits as fixed points. When used to find periodic orbits in flows, however, many such approaches have focused on using mappings defined on the Poincaré surfaces of section, neglecting components perpendicular to the surface of section. We propose a Newton-Raphson based method for Hamiltonian flows that incorporates these perpendicular components by using the full monodromy matrix. We investigated and found that inclusion of these components is crucial to yield an efficient process for converging upon periodic orbits in high dimensional flows. Numerical examples with as many as nine degrees of freedom are provided to demonstrate the effectiveness of our method.
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Affiliation(s)
- Yang Wei Koh
- Department of Basic Sciences, Graduate School of Arts and Sciences, The University of Tokyo, Komaba, 153-8902, Tokyo, Japan.
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Schröder M, Carreón-Macedo JL, Brown A. Implementation of an iterative algorithm for optimal control of molecular dynamics into MCTDH. Phys Chem Chem Phys 2008; 10:850-6. [DOI: 10.1039/b714821f] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Wang H, Skinner DE, Thoss M. Calculation of reactive flux correlation functions for systems in a condensed phase environment: A multilayer multiconfiguration time-dependent Hartree approach. J Chem Phys 2006; 125:174502. [PMID: 17100449 DOI: 10.1063/1.2363195] [Citation(s) in RCA: 60] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
A numerically exact quantum mechanical approach is proposed to evaluate thermal rate constants for systems in a model condensed phase environment. Employing the reactive flux correlation function formalism, the approach efficiently combines the multilayer multiconfiguration time-dependent Hartree theory with an importance sampling scheme for thermal distribution of the initial states. The performance of the method is illustrated by applications to two models of condensed phase dynamics: the donor-acceptor electron transfer model also known as the spin-boson model and a model for proton transfer reactions in the condensed phase.
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Affiliation(s)
- Haobin Wang
- Department of Chemistry and Biochemistry, New Mexico State University, Las Cruces, NM 88003, USA.
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Manthe U. On the integration of the multi-configurational time-dependent Hartree (MCTDH) equations of motion. Chem Phys 2006. [DOI: 10.1016/j.chemphys.2006.05.028] [Citation(s) in RCA: 54] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Dawes R, Carrington T. Using simultaneous diagonalization and trace minimization to make an efficient and simple multidimensional basis for solving the vibrational Schrödinger equation. J Chem Phys 2006; 124:054102. [PMID: 16468846 DOI: 10.1063/1.2162168] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this paper we improve the product simultaneous diagonalization (SD) basis method we previously proposed [J. Chem. Phys. 122, 134101 (2005)] and applied to solve the Schrodinger equation for the motion of nuclei on a potential surface. The improved method is tested using coupled complicated Hamiltonians with as many as 16 coordinates for which we can easily find numerically exact solutions. In a basis of sorted products of one-dimensional (1D) SD functions the Hamiltonian matrix is nearly diagonal. The localization of the 1D SD functions for coordinate qc depends on a parameter we denote alphac. In this paper we present a trace minimization scheme for choosing alphac to nearly block diagonalize the Hamiltonian matrix. Near-block diagonality makes it possible to truncate the matrix without degrading the accuracy of the lowest energy levels. We show that in the sorted product SD basis perturbation theory works extremely well. The trace minimization scheme is general and easy to implement.
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Affiliation(s)
- Richard Dawes
- Département de chimie, Université de Montréal, C.P. 6128, succursale Centre-ville, Montréal (Québec) H3C 3J7, Canada.
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Wang H, Thoss M. Quantum-mechanical evaluation of the Boltzmann operator in correlation functions for large molecular systems: A multilayer multiconfiguration time-dependent Hartree approach. J Chem Phys 2006; 124:034114. [PMID: 16438574 DOI: 10.1063/1.2161178] [Citation(s) in RCA: 70] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
It is shown that the Boltzmann operator in time correlation functions for complex molecular systems can be evaluated in a numerically exact way employing the multilayer formulation of the multiconfiguration time-dependent Hartree theory in combination with Monte Carlo importance sampling techniques. The performance of the method is illustrated by selected applications to photoinduced intervalence electron transfer reactions in the condensed phase. Furthermore, the validity of approximate schemes to evaluate the Boltzmann is discussed.
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Affiliation(s)
- Haobin Wang
- Department of Chemistry and Biochemistry, MSC 3C, New Mexico State University, Las Cruces, New Mexico 88003, USA.
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Markmann A, Worth GA, Mahapatra S, Meyer HD, Köppel H, Cederbaum LS. Simulation of a complex spectrum: Interplay of five electronic states and 21 vibrational degrees of freedom in C5H4+. J Chem Phys 2005; 123:204310. [PMID: 16351259 DOI: 10.1063/1.2104531] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Using a five-state, all-mode vibronic coupling model Hamiltonian derived in a previous publication [A. Markmann et al., J. Chem. Phys. 122, 144320 (2005)], we have calculated the photoelectron spectrum of the pentatetraene cation in the neighborhood of the B (2)E state, which can be represented with charge-localized components. To this end, quantum nuclear dynamics calculations were performed using the multiconfiguration time-dependent Hartree method, taking all 21 vibrational normal modes into account. Compared to experiment, the main features are reproduced but higher accuracy experiments are necessary to gauge the accuracy of the predictions for the vibronic progressions at the rising flank of the spectrum.
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Affiliation(s)
- Andreas Markmann
- Theoretische Chemie, Technische Universität München, Lichtenbergstrasse 4, 85 747 Garching, Germany.
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van Harrevelt R, Manthe U. Multidimensional time-dependent discrete variable representations in multiconfiguration Hartree calculations. J Chem Phys 2005; 123:64106. [PMID: 16122299 DOI: 10.1063/1.1995692] [Citation(s) in RCA: 54] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In the multiconfiguration time-dependent Hartree (MCTDH) approach, the wave function is expanded in time-dependent basis functions, called single-particle functions, to increase the efficiency of the wave-packet propagation. The correlation discrete variable representation (CDVR) approach, which is based on a time-dependent discrete variable representation (DVR), can be employed to evaluate matrix elements of the potential energy. The efficiency of the MCTDH method can be further enhanced by using multidimensional single-particle functions. However, up to now the CDVR approach could not be used in MCTDH calculations employing multidimensional single-particle functions, since this would require a general multidimensional non-direct-product DVR scheme. Recently, Dawes and Carrington presented a practical scheme to implement general non-direct-product multidimensional DVRs [R. Dawes and T. Carrington, Jr., J. Chem. Phys. 121, 726 (2004)]. The present work utilizes their scheme in the MCTDH/CDVR approach. The accuracy is tested using the photodissociation of NOCl as example. The results show that the CDVR scheme based on multidimensional time-dependent DVRs allows for an accurate evaluation of the potential in MCTDH calculations with multidimensional single-particle functions.
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Affiliation(s)
- Rob van Harrevelt
- Theoretische Chemie, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany.
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Pouilly B, Monnerville M, Gatti F, Meyer HD. Wave packet study of the UV photodissociation of the Ar2HBr complex. J Chem Phys 2005; 122:184313. [PMID: 15918710 DOI: 10.1063/1.1891725] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The photodissociation dynamics of the Ar2HBr van der Waals molecule is studied using the multiconfiguration time-dependent Hartree method. Standard Jacobian coordinates are used to describe the molecule. Two four-dimensional calculations are carried out where the rotation of the Ar2 molecule and, in addition, either the vibration of Ar2-Br or that of Ar2 are frozen. The time-evolution of the probability density in the different modes and the calculation of the dissociative flux show that the dissociating hydrogen atom preferentially moves out of the plane defined by Ar2 and Br. A comprehensive study of the cage effect in the process is presented.
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Affiliation(s)
- B Pouilly
- Unité Mixte de Recherche (UMR) 8523, Centre d'Etudes et de Recherches Lasers et Applications, Université des Sciences et Technologies de Lille, Villeneuve d'Ascq Cédex, France.
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Abstract
This review describes some developments in the theory and application of the semiclassical initial representation for the treatment of the dynamical and static properties of atoms and molecules. The theoretical basis of initial value treatments for the propagator is discussed. A variety of useful alternative initial value expressions for the propagator and other quantities are presented as generalizations of the well-known Herman-Kluk approximation. Special emphasis is given to treatments that involve integration over only half the phase space variables. The recent development of semiclassical initial value expressions that are exact for specific, desired systems is reviewed and some of the implications are described.
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Affiliation(s)
- Kenneth G Kay
- Department of Chemistry, Bar-Ilan University, Ramat-Gan, Israel.
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28
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Shalashilin DV, Child MS. The phase space CCS approach to quantum and semiclassical molecular dynamics for high-dimensional systems. Chem Phys 2004. [DOI: 10.1016/j.chemphys.2004.06.013] [Citation(s) in RCA: 116] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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van Harrevelt R, Manthe U. Multiconfigurational time-dependent Hartree calculations for dissociative adsorption of H2 on Cu(100). J Chem Phys 2004; 121:3829-35. [PMID: 15303951 DOI: 10.1063/1.1775785] [Citation(s) in RCA: 22] [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 efficiency of the multiconfigurational time-dependent Hartree (MCTDH) method for calculating the initial-state selected dissociation probability of H(2)(v=0,j=0) on Cu(100) is investigated. The MCTDH method is shown to be significantly more efficient than standard wave packet methods. A large number of single-particle functions is required to converge the initial-state selected reaction probability for dissociative adsorption. Employing multidimensional coordinates in the MCTDH ansatz (mode combination) is found to be crucial for the efficiency of these MCTDH calculations. Perspectives towards the application of the MCTDH approach to study dissociative adsorption of polyatomic molecules on surfaces are discussed.
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Affiliation(s)
- Rob van Harrevelt
- Theoretische Chemie, Technische Universitat Munchen, Lichtenbergstrasse 4, 85747 Garching, Germany
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Lasorne B, Gatti F, Baloitcha E, Meyer HD, Desouter-Lecomte M. Cumulative isomerization probability studied by various transition state wave packet methods including the MCTDH algorithm. Benchmark: HCN→CNH isomerization. J Chem Phys 2004; 121:644-54. [PMID: 15260590 DOI: 10.1063/1.1760713] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
Abstract
The 3D cumulative isomerization probability N(E) for the transfer of a light particle between two atoms is computed by one time-independent and two time-dependent versions of the transition state wave packet (TSWP) method. The time-independent method is based on the direct expansion of the microcanonical projection operator on Chebyshev polynomials. In the time-dependent TSWP methods, the propagations are carried out by the split operator scheme and the multiconfiguration time-dependent Hartree (MCTDH) algorithm. This is the very first implementation of the TSWP method in the Heidelberg MCTDH package [G. W. Worth, M. H. Beck, A. Jackle, and H.-D. Meyer, The MCDTH package, Version 8.2 (2000); H.-D Meyer, Version 8.3 (2002). See http://www.pci.uni-heidelberg.de/tc/usr/mctdh/]. The benchmark is the HCN-->CNH isomerization for zero total angular momentum. Particular insights are given into the tunneling region. In larger systems, the time-dependent version of TSWP making use of the MCTDH algorithm will permit to treat more and more modes quantum mechanically, for very accurate results. Therefore, it was important to calibrate the implementation. Besides, we also assess the efficiency of a reduced dimensionality approach by comparing the new exact 3D calculations of N(E) for the HCN-->CNH isomerization with results obtained via 1D or 2D active subspaces. This suggests that, it should be possible to take directly benefit of the present 3D approaches, adapted for triatomic Jacobi coordinates to compute N(E) for H-transfer in larger systems, via three active coordinates. The prerequisite is then the simplification of the reduced 3D kinetic energy operator with rigid constraint to take the form corresponding to a pseudo triatomic system in Jacobi coordinates with effective masses. This last step is checked in the methoxy radical and malonaldehyde. Finally, different ways to obtain reliable eigenvectors of the flux operator associated with a dividing surface are revisited.
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Affiliation(s)
- B Lasorne
- Laboratoire de Chimie Physique (UMR 8000), Centre Scientifique d'Orsay, Universite Paris-Sud, F-91405 Orsay Cedex, France
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Thoss M, Wang H. SEMICLASSICAL DESCRIPTION OF MOLECULAR DYNAMICS BASED ON INITIAL-VALUE REPRESENTATION METHODS. Annu Rev Phys Chem 2004; 55:299-332. [PMID: 15117255 DOI: 10.1146/annurev.physchem.55.091602.094429] [Citation(s) in RCA: 137] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Recent progress in the development of semiclassical methods to describe quantum effects in molecular dynamics is reviewed. Focusing on rigorous semiclassical methods that are based on the initial-value representation of the semiclassical propagator, we discuss several promising schemes that have been developed in the past few years to extend the applicability of semiclassical approaches to complex molecular systems. In particular, integral-filtering techniques and forward-backward methods are surveyed. Furthermore, recently proposed approaches that allow the semiclassical description of nonadiabatic molecular dynamics are discussed. The potential and efficiency of these methods is illustrated by selected applications.
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Affiliation(s)
- Michael Thoss
- Theoretische Chemie, Technische Universitat Munchen, D-85747 Garching, Germany.
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Sklarz T, Kay KG. Semiclassical initial value treatment of correlation functions. J Chem Phys 2004; 120:2606-17. [PMID: 15268404 DOI: 10.1063/1.1637342] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Two semiclassical, initial value representation (IVR) treatments are presented for the correlation function psi(f) e-iHt/h psi(i), where psi(i) and psi(f), are energy eigenfunctions of a "zero-order" Hamiltonian describing an arbitrary, integrable, vibrational system. These wave functions are treated semiclassically so that quantum calculations and numerical integrations over these states are unnecessary. While one of the new approximations describes the correlation function as an integral over all phase space variables of the system, in a manner similar to most existing IVR treatments, the second approximation describes the correlation function as an integral over only half of the phase space variables (i.e., the angle variables for the initial system). The relationship of these treatments to the conventional Herman-Kluk approximation for correlation functions is discussed. The accuracy and convergence of these treatments are tested by calculations of absorption spectra for model systems having up to 18 degrees of freedom, using Monte Carlo techniques to perform the multidimensional phase space integrations. Both treatments are found to be capable of producing spectra of excited, anharmonic states that agree well with quantum results. Although generally less accurate than full phase space or Herman-Kluk treatments, the half phase space method is found to require far fewer trajectories to achieve convergence. In addition, this number is observed to increase much more slowly with the system size than it does for the former methods, making the half-phase space technique a very promising method for the treatment of large systems.
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Affiliation(s)
- Temira Sklarz
- Department of Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel
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Christiansen O. Møller–Plesset perturbation theory for vibrational wave functions. J Chem Phys 2003. [DOI: 10.1063/1.1601593] [Citation(s) in RCA: 170] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
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Wang H, Thoss M. Multilayer formulation of the multiconfiguration time-dependent Hartree theory. J Chem Phys 2003. [DOI: 10.1063/1.1580111] [Citation(s) in RCA: 625] [Impact Index Per Article: 29.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
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Trin J, Monnerville M, Pouilly B, Meyer HD. Photodissociation of the ArHBr complex investigated with the multiconfiguration time-dependent Hartree approach. J Chem Phys 2003. [DOI: 10.1063/1.1523013] [Citation(s) in RCA: 17] [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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