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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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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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3
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Lauvergnat D, Nauts A. Smolyak Scheme for solving the Schrödinger equation: Application to Malonaldehyde in Full Dimensionality. Chemphyschem 2023; 24:e202300501. [PMID: 37555577 DOI: 10.1002/cphc.202300501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2023] [Revised: 08/08/2023] [Accepted: 08/09/2023] [Indexed: 08/10/2023]
Abstract
In 1963 Smolyak introduced an approach to overcome the exponential scaling with respect to the number of variables of the direct product size [S. A. Smolyak Soviet Mathematics Doklady, 4, 240 (1963)]. The main idea is to replace a single large direct product by a sum of selected small direct products. It was first used in quantum dynamics in 2009 by Avila and Carrington [G. Avila and T. Carrington, J. Chem. Phys., 131, 174103 (2009)]. Since then, several calculations have been published by Avila and Carrington and by other groups. In the present study, and to push the limit to larger and more complex systems, this scheme is combined with the use of an on-the-fly calculation of the kinetic energy operator and a Block-Davidson procedure to obtain eigenstates in our home-made Fortran codes, ElVibRot and Tnum-Tana. This was applied to compute the tunneling splitting of malonaldehyde in full dimensionality (21D) using the potential of Mizukami et al. [W. Mizukami, S. Habershon, and D.P. Tew, J. Chem. Phys. 141, 1443-10 (2014)]. Our tunneling splitting calculations, 21.7±0.3 cm-1 and 2.9±0.1 cm-1 , show excellent agreement with the experimental values, 21.6 cm-1 and 2.9 cm-1 for the normal isotopologue and the mono-deuterated one, respectively.
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Affiliation(s)
- David Lauvergnat
- Institut de Chimie Physique, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405, Orsay, France
| | - André Nauts
- Institut de Chimie Physique, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405, Orsay, France
- Institute of Condensed Matter and Nanosciences (NAPS), Université Catholique de Louvain, 2 Chemin du Cyclotron, 1348, Louvain-la-Neuve, Belgium
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Rey M. Novel methodology for systematically constructing global effective models from ab initio-based surfaces: A new insight into high-resolution molecular spectra analysis. J Chem Phys 2022; 156:224103. [PMID: 35705402 DOI: 10.1063/5.0089097] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this paper, a novel methodology is presented for the construction of ab initio effective rotation-vibration spectroscopic models from potential energy and dipole moment surfaces. Non-empirical effective Hamiltonians are obtained via the block-diagonalization of selected variationally computed eigenvector matrices. For the first time, the derivation of an effective dipole moment is carried out in a systematic way. This general approach can be implemented quite easily in most of the variational computer codes and turns out to be a clear alternative to the rather involved Van Vleck perturbation method. Symmetry is exploited at all stages to translate first-principles calculations into a set of spectroscopic parameters to be further refined on experiment. We demonstrate on H2CO, PH3, CH4, C2H4, and SF6 that the proposed effective model can provide crucial information to spectroscopists within a very short time compared to empirical spectroscopic models. This approach brings a new insight into high-resolution spectrum analysis of polyatomic molecules and will be also of great help in the modeling of hot atmospheres where completeness is important.
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Affiliation(s)
- Michael Rey
- Groupe de Spectrométrie Moléculaire et Atmosphérique, UMR CNRS 7331, BP 1039, F-51687 Reims Cedex 2, France
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Schröder B, Rauhut G. Comparison of body definitions for incremental vibrational configuration interaction theory (iVCI). J Chem Phys 2022; 156:174103. [DOI: 10.1063/5.0085082] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Within incremental vibrational configuration interaction theory (iVCI), the vibrational state energy is determined by means of a many-body expansion, i.e., it is a sum of terms of increasing order, which allow for an embarrassingly parallel evaluation. The convergence of this expansion depends strongly on the definition of the underlying bodies, which essentially decompose the correlation space into fragments. The different definitions considered here comprise mode-based bodies, excitation level-based bodies, and energy-based bodies. An analysis of the convergence behavior revealed that accounting for resonances within these definitions is mandatory and leads to a substantial improvement of the convergence, that is, the expansions can be truncated at lower orders. Benchmark calculations and systematic comparisons of the different body definitions for a small set of molecules, i.e., ketene, ethene, and diborane, have been conducted to study the overall performance of these iVCI implementations with respect to accuracy and central processing unit time.
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Affiliation(s)
- Benjamin Schröder
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Guntram Rauhut
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
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Bhatty AU, Brorsen KR. An alternative formulation of vibrational heat-bath configuration interaction. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1936250] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Abuzar U. Bhatty
- Department of Chemistry, University of Missouri, Columbia, MO, USA
| | - Kurt R. Brorsen
- Department of Chemistry, University of Missouri, Columbia, MO, USA
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Schröder B, Rauhut G. Incremental vibrational configuration interaction theory, iVCI: Implementation and benchmark calculations. J Chem Phys 2021; 154:124114. [DOI: 10.1063/5.0045305] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023] Open
Affiliation(s)
- Benjamin Schröder
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Guntram Rauhut
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
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Madsen NK, Hansen MB, Worth GA, Christiansen O. MR-MCTDH[n]: Flexible Configuration Spaces and Nonadiabatic Dynamics within the MCTDH[n] Framework. J Chem Theory Comput 2020; 16:4087-4097. [DOI: 10.1021/acs.jctc.0c00379] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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
| | - Graham A. Worth
- Department of Chemistry, University College London, 20, Gordon St., WC1H 0AJ London, United Kingdom
| | - Ove Christiansen
- Department of Chemistry, University of Aarhus, Langelandsgade 140, DK−8000 Aarhus C, Denmark
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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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Zak EJ, Carrington T. Using collocation and a hierarchical basis to solve the vibrational Schrödinger equation. J Chem Phys 2019; 150:204108. [PMID: 31153182 DOI: 10.1063/1.5096169] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We show that it is possible to compute vibrational energy levels of polyatomic molecules with a collocation method and a basis of products of one-dimensional harmonic oscillator functions pruned so that it does not include functions for which the indices of many of the one-dimensional functions are nonzero. Functions with many nonzero indices are coupled only by terms that depend simultaneously on many coordinates, and they are typically small. The collocation equation is derived without invoking differences of interpolation operators, which simplifies implementation of the method. This, however, requires inverting a matrix whose elements are values of the pruned basis functions at the collocation points. The collocation points are the points on a Smolyak grid whose size is equal to the size of the pruned basis set. The Smolyak grid is built from symmetrized Leja points. Because both the basis and the grid are not tensor products, the inverse is not straightforward. It can be done by using so-called hierarchical 1-D basis functions. They are defined so that the matrix whose elements are the 1-D hierarchical basis functions evaluated at points is lower triangular. We test the method by applying it to compute 100 energy levels of CH2NH with an iterative eigensolver.
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Affiliation(s)
- Emil J Zak
- 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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Baiardi A, Stein CJ, Barone V, Reiher M. Optimization of highly excited matrix product states with an application to vibrational spectroscopy. J Chem Phys 2019; 150:094113. [DOI: 10.1063/1.5068747] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Alberto Baiardi
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Christopher J. Stein
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Vincenzo Barone
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - Markus Reiher
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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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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Nauts A, Lauvergnat D. Numerical on-the-fly implementation of the action of the kinetic energy operator on a vibrational wave function: application to methanol. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1473652] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
Affiliation(s)
- André Nauts
- Institute of Condensed Matter and Nanosciences (NAPS), Université Catholique de Louvain, Louvain-la-Neuve, Belgium
- Laboratoire de Chimie Physique, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Orsay, France
| | - David Lauvergnat
- Laboratoire de Chimie Physique, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Orsay, France
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15
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Avila G, Carrington T. Computing vibrational energy levels of CH4with a Smolyak collocation method. J Chem Phys 2017; 147:144102. [DOI: 10.1063/1.4999153] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Gustavo Avila
- 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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Avila G, Carrington T. Reducing the cost of using collocation to compute vibrational energy levels: Results for CH2NH. J Chem Phys 2017; 147:064103. [DOI: 10.1063/1.4994920] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Gustavo Avila
- 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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17
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Wodraszka R, Carrington T. Systematically expanding nondirect product bases within the pruned multi-configuration time-dependent Hartree (MCTDH) method: A comparison with multi-layer MCTDH. J Chem Phys 2017; 146:194105. [PMID: 28527461 DOI: 10.1063/1.4983281] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We propose a pruned multi-configuration time-dependent Hartree (MCTDH) method with systematically expanding nondirect product bases and use it to solve the time-independent Schrödinger equation. No pre-determined pruning condition is required to select the basis functions. Using about 65 000 basis functions, we calculate the first 69 vibrational eigenpairs of acetonitrile, CH3CN, to an accuracy better than that achieved in a previous pruned MCTDH calculation which required more than 100 000 basis functions. In addition, we compare the new pruned MCTDH method with the established multi-layer MCTDH (ML-MCTDH) scheme and determine that although ML-MCTDH is somewhat more efficient when low or intermediate accuracy is desired, pruned MCTDH is more efficient when high accuracy is required. In our largest calculation, the vast majority of the energies have errors smaller than 0.01 cm-1.
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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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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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Castro E, Avila G, Manzhos S, Agarwal J, Schaefer HF, Carrington T. Applying a Smolyak collocation method to Cl2CO. Mol Phys 2016. [DOI: 10.1080/00268976.2016.1271153] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Eduardo Castro
- Chemistry Department, Queen's University , Kingston, Canada
| | - Gustavo Avila
- Chemistry Department, Queen's University , Kingston, Canada
| | - Sergei Manzhos
- Department of Mechanical Engineering, National University of Singapore , Singapore, Singapore
| | - Jay Agarwal
- Center for Computational Quantum Chemistry, University of Georgia , Athens, GA, USA
| | - Henry F. Schaefer
- Center for Computational Quantum Chemistry, University of Georgia , Athens, GA, USA
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