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Suzuki K, Kanno M, Koseki S, Kono H. A Structure-Based Gaussian Expansion for Quantum Reaction Dynamics in Molecules: Application to Hydrogen Tunneling in Malonaldehyde. J Phys Chem A 2023; 127:4152-4165. [PMID: 37129441 DOI: 10.1021/acs.jpca.2c09088] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
We developed an approximate method for quantum reaction dynamics simulations, namely, a structure-based Gaussian (SBG) expansion approach, where SBG bases for the expansion of the wave function Ψ, expressed by a product of single-atom Cartesian Gaussians centered at the positions of respective nuclei, are mainly placed around critical structures on reaction pathways such as on the intrinsic reaction coordinate (IRC) through a transition state. In the present approach, the "pseudo-lattice points" at which SBGs are deployed are selected in a perturbative manner so as to make moderate the expansion length. We first applied the SBG idea to a two-dimensional quadruple-well model and obtained accurate tunneling splitting values between the lowest four states. We then applied it to hydrogen tunneling in malonaldehyde and achieved a tunneling splitting of 27.1 cm-1 with only 875 SBGs at the MP2/6-31G(d,p) level of theory, in good agreement with 25 cm-1 by the more elaborate multiconfiguration time-dependent Hartree method. Reasonable results were also obtained for singly and doubly deuterated malonaldehyde. We analyzed the tunneling states by utilizing expansion coefficients of individual SBGs and found that 40-45% of the SBGs in Ψ are nonplanar structures and SBGs away from the IRC contribute a little to hydrogen transfer.
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Affiliation(s)
- Kazuma Suzuki
- Department of Chemistry, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan
| | - Manabu Kanno
- Department of Chemistry, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan
| | - Shiro Koseki
- Department of Chemistry, Graduate School of Science, Osaka Prefecture University, Osaka 599-8531, Japan
| | - Hirohiko Kono
- Department of Chemistry, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan
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2
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Mathea T, Petrenko T, Rauhut G. Advances in vibrational configuration interaction theory - part 2: Fast screening of the correlation space. J Comput Chem 2022; 43:6-18. [PMID: 34651704 DOI: 10.1002/jcc.26764] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2021] [Revised: 09/20/2021] [Accepted: 09/20/2021] [Indexed: 11/11/2022]
Abstract
For larger molecules, the computational demands of configuration selective vibrational configuration interaction theory (cs-VCI) are usually dominated by the configuration selection process, which commonly is based on second order vibrational Møller-Plesset perturbation (VMP2) theory. Here we present two techniques, which lead to substantial accelerations of such calculations while retaining the desired high accuracy of the final results. The first one introduces the concept of configuration classes, which allows for a highly efficient exploitation of the analogs of the Slater-Condon rules in vibrational structure calculations with large correlation spaces. The second approach uses a VMP2 like vector for augmenting the targeted vibrational wavefunction within the selection of configurations and thus avoids any intermediate diagonalization steps. The underlying theory is outlined and benchmark calculations are provided for highly correlated vibrational states of several molecules.
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Affiliation(s)
- Tina Mathea
- Institute for Theoretical Chemistry, University of Stuttgart, Stuttgart, Germany
| | - Taras Petrenko
- Institute for Theoretical Chemistry, University of Stuttgart, Stuttgart, Germany
| | - Guntram Rauhut
- Institute for Theoretical Chemistry, University of Stuttgart, Stuttgart, Germany
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3
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Xie C, Guan Y, Yarkony DR, Guo H. Vibrational energy levels of the S0 and S1 states of formaldehyde using an accurate ab initio based global diabatic potential energy matrix. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1918775] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Changjian Xie
- Institute of Modern Physics, Northwest University, Xi’an, Shaanxi, People’s Republic of China
| | - Yafu Guan
- Department of Chemistry, Johns Hopkins University, Baltimore, MD, USA
| | - David R. Yarkony
- Department of Chemistry, Johns Hopkins University, Baltimore, MD, USA
| | - Hua Guo
- Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, NM, USA
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4
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Harabuchi Y, Tani R, De Silva N, Njegic B, Gordon MS, Taketsugu T. Anharmonic vibrational computations with a quartic force field for curvilinear coordinates. J Chem Phys 2019. [DOI: 10.1063/1.5096167] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yu Harabuchi
- Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo 060-0810, Japan
| | - Ryosuke Tani
- Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo 060-0810, Japan
| | - Nuwan De Silva
- Department of Physical and Biological Sciences, Western New England University, Springfield, Massachusetts 01119, USA
| | - Bosiljka Njegic
- Department of Chemistry, Iowa State University, Ames, Iowa 50011, USA
| | - Mark S. Gordon
- Department of Chemistry, Iowa State University, Ames, Iowa 50011, USA
| | - Tetsuya Taketsugu
- Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo 060-0810, Japan
- Institute for Chemical Reaction Design and Discovery (WPI-ICReDD), Hokkaido University, Sapporo 001-0021, Japan
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5
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Tan JA, Kuo JL. Multilevel Approach for Direct VSCF/VCI MULTIMODE Calculations with Applications to Large “Zundel” Cations. J Chem Theory Comput 2018; 14:6405-6416. [DOI: 10.1021/acs.jctc.8b00679] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jake A. Tan
- Institute of Atomic and Molecular Sciences, Academia Sinica, No. 1 Roosevelt Road, Section 4, Taipei 10617, Taiwan (ROC)
| | - Jer-Lai Kuo
- Institute of Atomic and Molecular Sciences, Academia Sinica, No. 1 Roosevelt Road, Section 4, Taipei 10617, Taiwan (ROC)
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6
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Klinting EL, Thomsen B, Godtliebsen IH, Christiansen O. Employing general fit-bases for construction of potential energy surfaces with an adaptive density-guided approach. J Chem Phys 2018; 148:064113. [DOI: 10.1063/1.5016259] [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)
| | - Bo Thomsen
- Department of Chemistry, Aarhus University, DK-8000 Aarhus C, Denmark
| | | | - Ove Christiansen
- Department of Chemistry, Aarhus University, DK-8000 Aarhus C, Denmark
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7
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Rai P, Sargsyan K, Najm H, Hermes MR, Hirata S. Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1288937] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Prashant Rai
- Sandia National Laboratories, Livermore, CA, USA
| | | | - Habib Najm
- Sandia National Laboratories, Livermore, CA, USA
| | - Matthew R. Hermes
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, IL, USA
| | - So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, IL, USA
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8
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Conte R, Qu C, Bowman JM. Permutationally Invariant Fitting of Many-Body, Non-covalent Interactions with Application to Three-Body Methane–Water–Water. J Chem Theory Comput 2015; 11:1631-8. [DOI: 10.1021/acs.jctc.5b00091] [Citation(s) in RCA: 57] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Riccardo Conte
- Department of Chemistry, Emory University, Atlanta, Georgia 30322, United States
| | - Chen Qu
- Department of Chemistry, Emory University, Atlanta, Georgia 30322, United States
| | - Joel M. Bowman
- Department of Chemistry, Emory University, Atlanta, Georgia 30322, United States
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9
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Yamada T, Aida M. Fundamental frequency from classical molecular dynamics. Phys Chem Chem Phys 2015; 17:3227-40. [PMID: 25519091 DOI: 10.1039/c4cp04068f] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We give a theoretical validation for calculating fundamental frequencies of a molecule from classical molecular dynamics (MD) when its anharmonicity is small enough to be treated by perturbation theory. We specifically give concrete answers to the following questions: (1) What is the appropriate initial condition of classical MD to calculate the fundamental frequency? (2) From that condition, how accurately can we extract fundamental frequencies of a molecule? (3) What is the benefit of using ab initio MD for frequency calculations? Our analytical approaches to those questions are classical and quantum normal form theories. As numerical examples we perform two types of MD to calculate fundamental frequencies of H2O with MP2/aug-cc-pVTZ: one is based on the quartic force field and the other one is direct ab initio MD, where the potential energies and the gradients are calculated on the fly. From those calculations, we show comparisons of the frequencies from MD with the post vibrational self-consistent field calculations, second- and fourth-order perturbation theories, and experiments. We also apply direct ab initio MD to frequency calculations of C-H vibrational modes of tetracene and naphthalene. We conclude that MD can give the same accuracy in fundamental frequency calculation as second-order perturbation theory but the computational cost is lower for large molecules.
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Affiliation(s)
- Tomonori Yamada
- Center for Quantum Life Sciences and Department of Chemistry, Graduate School of Science, Hiroshima University, Higashi-Hiroshima, 739-8526, Japan.
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10
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Rashev S, Moule DC. Variational study on the vibrational level structure and IVR behavior of highly vibrationally excited S0 formaldehyde. SPECTROCHIMICA ACTA. PART A, MOLECULAR AND BIOMOLECULAR SPECTROSCOPY 2012; 87:286-292. [PMID: 22185953 DOI: 10.1016/j.saa.2011.11.055] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2011] [Revised: 11/17/2011] [Accepted: 11/24/2011] [Indexed: 05/31/2023]
Abstract
We perform large scale converged variational vibrational calculations on S(0) formaldehyde up to very high excess vibrational energies (E(v)), E(v)∼17,000cm(-1), using our vibrational method, consisting of a specific search/selection/Lanczos iteration procedure. Using the same method we investigate the vibrational level structure and intramolecular vibrational redistribution (IVR) characteristics for various vibrational levels in this energy range in order to assess the onset of IVR.
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Affiliation(s)
- Svetoslav Rashev
- Institute of Solid State Physics, Bulgarian Academy of Sciences, Tsarigradsko Chaussee 72, 1784 Sofia, Bulgaria.
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11
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Christiansen O. Selected new developments in vibrational structure theory: potential construction and vibrational wave function calculations. Phys Chem Chem Phys 2012; 14:6672-87. [DOI: 10.1039/c2cp40090a] [Citation(s) in RCA: 107] [Impact Index Per Article: 8.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
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12
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Le HA, Bettens RPA. Distributed Multipoles and Energies of Flexible Molecules. J Chem Theory Comput 2011; 7:921-30. [DOI: 10.1021/ct100683u] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Hai-Anh Le
- Department of Chemistry, National University of Singapore, 3 Science Drive 3, Singapore 117543
| | - Ryan P. A. Bettens
- Department of Chemistry, National University of Singapore, 3 Science Drive 3, Singapore 117543
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13
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Sparta M, Hansen MB, Matito E, Toffoli D, Christiansen O. Using Electronic Energy Derivative Information in Automated Potential Energy Surface Construction for Vibrational Calculations. J Chem Theory Comput 2010; 6:3162-75. [DOI: 10.1021/ct100229f] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Manuel Sparta
- The Lundbeck Foundation Center for Theoretical Chemistry, Center for Oxygen Microscopy and Imaging, Department of Chemistry, University of Aarhus, Langelandsgade 140, DK-8000 Aarhus C, Denmark, Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland, and Department of Chemistry, Middle East Technical University, 06531 Ankara, Turkey
| | - Mikkel B. Hansen
- The Lundbeck Foundation Center for Theoretical Chemistry, Center for Oxygen Microscopy and Imaging, Department of Chemistry, University of Aarhus, Langelandsgade 140, DK-8000 Aarhus C, Denmark, Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland, and Department of Chemistry, Middle East Technical University, 06531 Ankara, Turkey
| | - Eduard Matito
- The Lundbeck Foundation Center for Theoretical Chemistry, Center for Oxygen Microscopy and Imaging, Department of Chemistry, University of Aarhus, Langelandsgade 140, DK-8000 Aarhus C, Denmark, Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland, and Department of Chemistry, Middle East Technical University, 06531 Ankara, Turkey
| | - Daniele Toffoli
- The Lundbeck Foundation Center for Theoretical Chemistry, Center for Oxygen Microscopy and Imaging, Department of Chemistry, University of Aarhus, Langelandsgade 140, DK-8000 Aarhus C, Denmark, Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland, and Department of Chemistry, Middle East Technical University, 06531 Ankara, Turkey
| | - Ove Christiansen
- The Lundbeck Foundation Center for Theoretical Chemistry, Center for Oxygen Microscopy and Imaging, Department of Chemistry, University of Aarhus, Langelandsgade 140, DK-8000 Aarhus C, Denmark, Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland, and Department of Chemistry, Middle East Technical University, 06531 Ankara, Turkey
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14
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Braams BJ, Bowman JM. Permutationally invariant potential energy surfaces in high dimensionality. INT REV PHYS CHEM 2009. [DOI: 10.1080/01442350903234923] [Citation(s) in RCA: 535] [Impact Index Per Article: 35.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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15
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Matito E, Toffoli D, Christiansen O. A hierarchy of potential energy surfaces constructed from energies and energy derivatives calculated on grids. J Chem Phys 2009; 130:134104. [DOI: 10.1063/1.3092921] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.0] [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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Shigeta Y, Miyachi H, Matsui T, Hirao K. Dynamic Quantum Isotope Effects on Multiple Proton-Transfer Reactions. BULLETIN OF THE CHEMICAL SOCIETY OF JAPAN 2008. [DOI: 10.1246/bcsj.81.1230] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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17
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Bowman JM, Carrington T, Meyer HD. Variational quantum approaches for computing vibrational energies of polyatomic molecules. Mol Phys 2008. [DOI: 10.1080/00268970802258609] [Citation(s) in RCA: 303] [Impact Index Per Article: 18.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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18
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Evenhuis CR, Manthe U. Calculating vibrational spectra using modified Shepard interpolated potential energy surfaces. J Chem Phys 2008; 129:024104. [DOI: 10.1063/1.2951988] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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19
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Maeda S, Watanabe Y, Ohno K. Finding important anharmonic terms in the sixth-order potential energy function by the scaled hypersphere search method: An application to vibrational analyses of molecules and clusters. J Chem Phys 2008; 128:144111. [DOI: 10.1063/1.2884348] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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20
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Toffoli D, Kongsted J, Christiansen O. Automatic generation of potential energy and property surfaces of polyatomic molecules in normal coordinates. J Chem Phys 2007; 127:204106. [DOI: 10.1063/1.2805085] [Citation(s) in RCA: 51] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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21
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22
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Manzhos S, Carrington T. Using redundant coordinates to represent potential energy surfaces with lower-dimensional functions. J Chem Phys 2007; 127:014103. [PMID: 17627333 DOI: 10.1063/1.2746846] [Citation(s) in RCA: 74] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We propose a method for fitting potential energy surfaces with a sum of component functions of lower dimensionality. This form facilitates quantum dynamics calculations. We show that it is possible to reduce the dimensionality of the component functions by introducing new and redundant coordinates obtained with linear transformations. The transformations are obtained from a neural network. Different coordinates are used for different component functions and the new coordinates are determined as the potential is fitted. The quality of the fits and the generality of the method are illustrated by fitting reference potential surfaces of hydrogen peroxide and of the reaction OH+H(2)-->H(2)O+H.
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Affiliation(s)
- Sergei Manzhos
- Département de Chimie, Université de Montréal, CP 6128, succursale Centre-ville, Montréal (Québec) H3C 3J7, Canada.
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23
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Seidler P, Christiansen O. Vibrational excitation energies from vibrational coupled cluster response theory. J Chem Phys 2007; 126:204101. [PMID: 17552748 DOI: 10.1063/1.2734970] [Citation(s) in RCA: 78] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
Abstract
Response theory in the context of vibrational coupled cluster (VCC) theory is introduced and used to obtain vibrational excitation energies. The relation to the vibrational configuration interaction (VCI) approach is described, and the increase in accuracy of VCC response energies relative to VCI energies is discussed theoretically in terms of a perturbational order expansion and demonstrated numerically. To illustrate the theory, a pilot implementation is used to obtain anharmonic vibrational frequencies for fundamental, first overtone and combination excitations of formaldehyde as well as for the fundamental transitions of ethylene.
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Affiliation(s)
- Peter Seidler
- The Lundbeck Foundation Center for Theoretical Chemistry, Department of Chemistry, University of Aarhus, Langelandsgade 140, DK-8000 Aarhus C, Denmark.
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Seidler P, Kongsted J, Christiansen O. Calculation of Vibrational Infrared Intensities and Raman Activities Using Explicit Anharmonic Wave Functions. J Phys Chem A 2007; 111:11205-13. [PMID: 17474728 DOI: 10.1021/jp070327n] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Methods for automatic computation of IR intensities and Raman activities are described using vibrational self-consistent field (VSCF) and vibrational configuration interaction (VCI) wave functions. Inclusion of effects due to anharmonicity in the potential energy and property surfaces are found to improve the results substantially as compared to experimental data. Sample calculations employing water and formaldehyde are presented, allowing for comparison between different vibrational methods. The convergence with respect to excitation level in VCI and the extent of mode coupling in the potential and property expansions is investigated. In addition, different electronic methods used for generating the potential and property surfaces, namely CCSD, CCSD(T), DFT/B3LYP, and DFT/CAM-B3LYP have been compared. Details of the potential and property surfaces may have significant effects on the IR and Raman intensities.
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Affiliation(s)
- Peter Seidler
- The Lundbeck Foundation Center for Theoretical Chemistry, Department of Chemistry, University of Aarhus, Langelandsgade 140, DK-8000 Aarhus C, Denmark.
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25
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Kongsted J, Christiansen O. Automatic generation of force fields and property surfaces for use in variational vibrational calculations of anharmonic vibrational energies and zero-point vibrational averaged properties. J Chem Phys 2006; 125:124108. [PMID: 17014167 DOI: 10.1063/1.2352734] [Citation(s) in RCA: 65] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An automatic and general procedure for the calculation of geometrical derivatives of the energy and general property surfaces for molecular systems is developed and implemented. General expressions for an n-mode representation are derived, where the n-mode representation includes only the couplings between n or less degrees of freedom. The general expressions are specialized to derivative force fields and property surfaces, and a scheme for calculation of the numerical derivatives is implemented. The implementation is interfaced to electronic structure programs and may be used for both ground and excited electronic states. The implementation is done in the context of a vibrational structure program and can be used in combination with vibrational self-consistent field (VSCF), vibrational configuration interaction (VCI), vibrational Moller-Plesset, and vibrational coupled cluster calculations of anharmonic wave functions and calculation of vibrational averaged properties at the VSCF and VCI levels. Sample calculations are presented for fundamental vibrational energies and vibrationally averaged dipole moments and frequency dependent polarizabilities and hyperpolarizabilities of water and formaldehyde.
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Affiliation(s)
- Jacob Kongsted
- Department of Chemistry, University of Aarhus, DK-8000 Aarhus C, Denmark.
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26
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Mil'nikov GV, Yagi K, Taketsugu T, Nakamura H, Hirao K. Simple and accurate method to evaluate tunneling splitting in polyatomic molecules. J Chem Phys 2006; 120:5036-45. [PMID: 15267369 DOI: 10.1063/1.1647052] [Citation(s) in RCA: 56] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
A practical and accurate semiclassical method for calculating the tunneling splitting of the ground state in polyatomic molecules is presented based on a recent version of the instanton theory [J. Chem. Phys. 115, 6881 (2001)]. The method uses ab initio quantum chemical data for the potential energy surface without any concomitant extrapolation and requires only a small number of ab initio data points to get convergence even for large molecules. This enables one to use an advanced level of electronic structure theory and achieve a high accuracy of the result. The method is applied to the 9-atomic malonaldehyde molecule by making use of the potential energy surface at the level of CCSD(T) with the hybrid basis set of aug-cc-pVTZ (for oxygen atoms and the transferred hydrogen atom) and cc-pVTZ (for other atoms).
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Affiliation(s)
- Gennady V Mil'nikov
- Department of Theoretical Studies, Institute for Molecular Science, Myodaiji, Okazaki 444-8585, Japan.
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27
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Oyanagi C, Yagi K, Taketsugu T, Hirao K. Highly accurate potential-energy and dipole moment surfaces for vibrational state calculations of methane. J Chem Phys 2006; 124:64311. [PMID: 16483211 DOI: 10.1063/1.2162891] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
Full-dimensional ab initio potential-energy surface (PES) and dipole moment surface are constructed for a methane molecule at the CCSD(T)/cc-pVTZ and MP2/cc-pVTZ levels of theory, respectively, by the modified Shepard interpolation method based on the fourth-order Taylor expansion [MSI(4th)]. The reference points for the interpolation have been set in the coupling region of CH symmetric and antisymmetric stretching modes so as to reproduce the vibrational energy levels related to CH stretching vibrations. The vibrational configuration-interaction calculations have been performed to obtain the energy levels and the absorption intensities up to 9000 cm(-1) with the use of MSI(4th)-PES. The calculated fundamental frequencies and low-lying vibrational energy levels show that MSI(4th) is superior to the widely employed quartic force field, giving a better agreement with the experimental values. The absorption bands of overtones as well as combination bands, which are caused by purely anharmonic effects, have been obtained up to 9000 cm(-1). Strongly coupled states with visible intensity have been found in the 6500-9000 cm(-1) region where the experimental data are still lacking.
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Affiliation(s)
- Chikako Oyanagi
- Department of Chemistry, Ochanomizu University, Tokyo, Japan
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28
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Kowal AT. First-principles calculation of geometry and anharmonic vibrational spectra of thioformamide and thioformamide-d2. J Chem Phys 2006; 124:14304. [PMID: 16409033 DOI: 10.1063/1.2139995] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The equilibrium geometry of thioformamide HCSNH2 has been determined at the MP2 and CCSD(T) electron correlation levels under C(s) symmetry constraints using triple-zeta basis sets up to cc-pVTZ. All optimized planar structures are true minima on the potential-energy surface and are characterized by the C-N bond length within 1.353-1.343 A, C-S distances of 1.656-1.628 A, and NCS angle between 125.7 degrees and 125.9 degrees . The wave number of the NH2 out-of-plane wagging mode computed in the harmonic approximation shows stronger dependence on the basis set rather than the electron correlation level and varies from 85.9 cm(-1) at CCSD(T)cc-pVDZ level to 335 cm(-1) at MP2/aug-cc-pVTZ level. Anharmonic vibrational spectra of HCSNH2 and HCSND2 have been determined directly from the potential-energy surfaces computed at MP2 level in triple-zeta valence (TZV)(2df,2p) and TZV+(2df,2p) basis sets using vibrational self-consistent-field (VSCF) and correlation-corrected VSCF (CC-VSCF) methods. CC-VSCF wave numbers of fundamental, first overtone, and most intense combination transitions are reported for thioformamide and those of fundamentals for thioformamide-d2. The NH2 wagging (nu12) mode is strongly anharmonic and its fundamentals have been computed at 406.9 cm(-1) [TZV(2df,2p)] and 399.5 cm(-1) [TZV+(2df,2p)], which is remarkably close to the experimental energy of 393 cm(-1). Anharmonically computed fundamentals of this mode in thioformamide-d2, 299.7 cm(-1) [TZV(2df,2p)] and 299.6 cm(-1) [TZV+(2df,2p)], are only approximately 7 cm(-1) higher than the transition energy (293 cm(-1)) observed in the gas phase spectrum of HCSND2. The first overtone of the NH2 wagging mode of thioformamide (nu12 (02)) has been calculated by CC-VSCF procedure at 830.8 cm(-1) [TZV(2df,2p)] and 880.0 cm(-1) [TZV+(2df,2p)], which implies "negative" (nu12 (02)>2*nu12 (01)) anharmonicity of this mode.
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Affiliation(s)
- Andrzej T Kowal
- Department of Chemistry, Wrocław University of Technology, Wyb. St. Wyspiańskiego 27, 50-370 Wrocław, Poland.
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A scaled hypersphere interpolation technique for efficient construction of multidimensional potential energy surfaces. Chem Phys Lett 2005. [DOI: 10.1016/j.cplett.2005.08.063] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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30
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Yagi K, Hirao K, Taketsugu T, Schmidt MW, Gordon MS. Ab initiovibrational state calculations with a quartic force field: Applications to H2CO, C2H4, CH3OH, CH3CCH, and C6H6. J Chem Phys 2004; 121:1383-9. [PMID: 15260682 DOI: 10.1063/1.1764501] [Citation(s) in RCA: 158] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
For polyatomic molecules, n-mode coupling representations of the quartic force field (nMR-QFF) are presented, which include terms up to n normal coordinate couplings in a fourth-order polynomial potential energy function. The computational scheme to evaluate third-and fourth-order derivatives by finite differentiations of the energy is fully described. The code to generate the nMR-QFF has been implemented into GAMESS program package and interfaced with the vibrational self-consistent field (VSCF) and correlation corrected VSCF (cc-VSCF) methods. As a demonstration, fundamental frequencies have been calculated by the cc-VSCF method based on 2MR-QFF for formaldehyde, ethylene, methanol, propyne, and benzene. The applications show that 2MR-QFF is a highly accurate potential energy function, with errors of 1.0-1.9% relative to the experimental value in fundamental frequencies. This approach will help quantitative evaluations of vibrational energies of a general molecule with a reasonable computational cost.
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Affiliation(s)
- Kiyoshi Yagi
- Department of Applied Chemistry, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
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Carbonniere P, Begue D, Dargelos A, Pouchan C. Construction of an accurate quartic force field by using generalised least-squares fitting and experimental design. Chem Phys 2004. [DOI: 10.1016/j.chemphys.2004.01.007] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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32
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Lee HS, Light JC. Iterative solutions with energy selected bases for highly excited vibrations of tetra-atomic molecules. J Chem Phys 2004; 120:4626-37. [PMID: 15267322 DOI: 10.1063/1.1646370] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The use of energy selected bases (ESB) with iterative diagonalization of the Hamiltonian matrix is described for vibrations of tetra-atomic systems. The performance of the method is tested by computing vibrational states of HOOH below 10,000 cm(-1) (1296 A+ symmetry states) and H(2)CO below 13,500 cm(-1) (729 A(1) symmetry states). For iterative solutions, we tested both the implicitly restarted Lanczos method (IRLM) and the standard (nonreorthogonalizing) Lanczos approach. Comparison with other contracted basis approach as well as direct product grid representation shows superior performance of the ESB/IRLM approach. Of the two systems, H(2)CO is found to be more challenging than HOOH since it has much stronger couplings among vibrational modes, which leads to a drastically larger primitive basis set. For H(2)CO we also discuss some interesting behavior of the molecule in the high internal energy regime.
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Affiliation(s)
- Hee-Seung Lee
- Department of Chemistry and James Franck-Institute, University of Chicago, Chicago, Illinois 60637, USA
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Abstract
The theory and first implementation of a vibrational coupled cluster (VCC) method for calculations of the vibrational structure of molecules is presented. Different methods for introducing approximate VCC methods are discussed including truncation according to a maximum number of simultaneous mode excitations as well as an interaction space order concept is introduced. The theory is tested on calculation of anharmonic frequencies for a three-mode model system and a formaldehyde quartic force field. The VCC method is compared to vibrational self-consistent-field, vibrational Møller-Plesset perturbation theory, and vibrational configuration interaction (VCI). A VCC calculation typically gives higher accuracy than a corresponding VCI calculation with the same number of parameters and the same formal operation count.
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Affiliation(s)
- Ove Christiansen
- Department of Chemistry, University of Arhus, DK-8000 Arhus C, Denmark
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A new method for constructing multidimensional potential energy surfaces by a polar coordinate interpolation technique. Chem Phys Lett 2003. [DOI: 10.1016/j.cplett.2003.08.129] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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35
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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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