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Nelson PM, Glick ZL, Sherrill CD. Approximating large-basis coupled-cluster theory vibrational frequencies using focal-point approximations. J Chem Phys 2023; 159:094104. [PMID: 37655773 DOI: 10.1063/5.0168608] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2023] [Accepted: 08/09/2023] [Indexed: 09/02/2023] Open
Abstract
The focal-point approximation can be used to estimate a high-accuracy, slow quantum chemistry computation by combining several lower-accuracy, faster computations. We examine the performance of focal-point methods by combining second-order Møller-Plesset perturbation theory (MP2) with coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] for the calculation of harmonic frequencies and that of fundamental frequencies using second-order vibrational perturbation theory (VPT2). In contrast to standard CCSD(T), the focal-point CCSD(T) method approaches the complete basis set (CBS) limit with only triple-ζ basis sets for the coupled-cluster portion of the computation. The predicted harmonic and fundamental frequencies were compared with the experimental values for a set of 20 molecules containing up to six atoms. The focal-point method combining CCSD(T)/aug-cc-pV(T + d)Z with CBS-extrapolated MP2 has mean absolute errors vs experiment of only 7.3 cm-1 for the fundamental frequencies, which are essentially the same as the mean absolute error for CCSD(T) extrapolated to the CBS limit using the aug-cc-pV(Q + d)Z and aug-cc-pV(5 + d)Z basis sets. However, for H2O, the focal-point procedure requires only 3% of the computation time as the extrapolated CCSD(T) result, and the cost savings will grow for larger molecules.
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Affiliation(s)
- Philip M Nelson
- Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, and School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, USA
| | - Zachary L Glick
- Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, and School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, USA
| | - C David Sherrill
- Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, and School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, USA
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Mendolicchio M, Bloino J, Barone V. General Perturb-Then-Diagonalize Model for the Vibrational Frequencies and Intensities of Molecules Belonging to Abelian and Non-Abelian Symmetry Groups. J Chem Theory Comput 2021; 17:4332-4358. [PMID: 34085530 PMCID: PMC8280743 DOI: 10.1021/acs.jctc.1c00240] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2021] [Indexed: 11/29/2022]
Abstract
In this paper, we show that the standard second-order vibrational perturbation theory (VPT2) for Abelian groups can be used also for non-Abelian groups without employing specific equations for two- or threefold degenerate vibrations but rather handling in the proper way all the degeneracy issues and deriving the peculiar spectroscopic signatures of non-Abelian groups (e.g., l -doubling) by a posteriori transformations of the eigenfunctions. Comparison with the results of previous conventional implementations shows a perfect agreement for the vibrational energies of linear and symmetric tops, thus paving the route to the transparent extension of the equations already available for asymmetric tops to the energies of spherical tops and the infrared and Raman intensities of molecules belonging to non-Abelian symmetry groups. The whole procedure has been implemented in our general engine for vibro-rotational computations beyond the rigid rotor/harmonic oscillator model and has been validated on a number of test cases.
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Affiliation(s)
| | - Julien Bloino
- Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy
| | - Vincenzo Barone
- Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy
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Cheng X, Talbot JJ, Steele RP. Tuning vibrational mode localization with frequency windowing. J Chem Phys 2016; 145:124112. [DOI: 10.1063/1.4963109] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Affiliation(s)
- Xiaolu Cheng
- Department of Chemistry and Henry Eyring Center for Theoretical Chemistry, University of Utah, Salt Lake City, Utah 84112, USA
| | - Justin J. Talbot
- Department of Chemistry and Henry Eyring Center for Theoretical Chemistry, University of Utah, Salt Lake City, Utah 84112, USA
| | - Ryan P. Steele
- Department of Chemistry and Henry Eyring Center for Theoretical Chemistry, University of Utah, Salt Lake City, Utah 84112, USA
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Zimmerman PM, Smereka P. Optimizing Vibrational Coordinates To Modulate Intermode Coupling. J Chem Theory Comput 2016; 12:1883-91. [PMID: 26914536 DOI: 10.1021/acs.jctc.5b01168] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The choice of coordinate system strongly affects the convergence properties of vibrational structure computations. Two methods for efficient generation of improved vibrational coordinates are presented and justified by analysis of a model anharmonic two-mode Hessian and numerical computations on polyatomic molecules. To produce optimal coordinates, metrics which quantify off-diagonal couplings over a grid of Hessian matrices are minimized through unitary rotations of the vibrational basis. The first proposed metric minimizes the total squared off-diagonal coupling, and the second minimizes the total squared change in off-diagonal coupling. In this procedure certain anharmonic modes tend to localize, for example X-H stretches. The proposed methods do not rely on prior fitting of the potential energy, vibrational structure computations, or localization metrics, so they are unique from previous vibrational coordinate generation algorithms and are generally applicable to polyatomic molecules. Fitting the potential to the approximate n-mode representation in the optimized bases for all-trans polyenes shows that off-diagonal anharmonic couplings are substantially reduced by the new choices of coordinate system. Convergence of vibrational energies is examined in detail for ethylene, and it is shown that coupling-optimized modes converge in vibrational configuration interaction computations to within 1 cm(-1) using only 3-mode couplings, where normal modes require 4-mode couplings for convergence. Comparison of the vibrational configuration interaction convergence with respect to excitation level for the two proposed metrics shows that minimization of the total off-diagonal coupling is most effective for low-cost vibrational structure computations.
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Affiliation(s)
- Paul M Zimmerman
- Department of Chemistry and ‡Department of Mathematics, University of Michigan , Ann Arbor, Michigan 48109, United States
| | - Peter Smereka
- Department of Chemistry and ‡Department of Mathematics, University of Michigan , Ann Arbor, Michigan 48109, United States
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Piccardo M, Bloino J, Barone V. Generalized Vibrational Perturbation Theory for Rotovibrational Energies of Linear, Symmetric and Asymmetric Tops: Theory, Approximations, and Automated Approaches to Deal with Medium-to-Large Molecular Systems. INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 2015; 115:948-982. [PMID: 26345131 PMCID: PMC4553754 DOI: 10.1002/qua.24931] [Citation(s) in RCA: 72] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/02/2015] [Revised: 04/03/2015] [Accepted: 04/08/2015] [Indexed: 06/05/2023]
Abstract
Models going beyond the rigid-rotor and the harmonic oscillator levels are mandatory for providing accurate theoretical predictions for several spectroscopic properties. Different strategies have been devised for this purpose. Among them, the treatment by perturbation theory of the molecular Hamiltonian after its expansion in power series of products of vibrational and rotational operators, also referred to as vibrational perturbation theory (VPT), is particularly appealing for its computational efficiency to treat medium-to-large systems. Moreover, generalized (GVPT) strategies combining the use of perturbative and variational formalisms can be adopted to further improve the accuracy of the results, with the first approach used for weakly coupled terms, and the second one to handle tightly coupled ones. In this context, the GVPT formulation for asymmetric, symmetric, and linear tops is revisited and fully generalized to both minima and first-order saddle points of the molecular potential energy surface. The computational strategies and approximations that can be adopted in dealing with GVPT computations are pointed out, with a particular attention devoted to the treatment of symmetry and degeneracies. A number of tests and applications are discussed, to show the possibilities of the developments, as regards both the variety of treatable systems and eligible methods.
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Affiliation(s)
- Matteo Piccardo
- Scuola Normale Superiore Piazza dei Cavalieri 7, I-56126, Pisa, Italy E-mail:
| | - Julien Bloino
- Scuola Normale Superiore Piazza dei Cavalieri 7, I-56126, Pisa, Italy E-mail: ; Consiglio Nazionale delle Ricerche, Istituto di Chimica dei Composti Organometallici (CNR-ICCOM) UOS di Pisa Via G. Moruzzi, 1, I-56124, Italy
| | - Vincenzo Barone
- Scuola Normale Superiore Piazza dei Cavalieri 7, I-56126, Pisa, Italy E-mail:
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Zúniga J, Bastida A, Requena A, Halberstadt N, Beswick JA, Janda KC. Vibrational Bound States of the He2Ne+ Cation. J Phys Chem A 2009; 113:14896-903. [DOI: 10.1021/jp905043t] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- José Zúniga
- Departamento de Química Física, Universidad de Murcia, 3010 Murcia, Spain, Laboratoire Collisions, Agrégats, Réactivité, IRSAMC, Université de Toulouse, UPS, and CNRS, UMR5589, F-31062 Toulouse, France, and Department of Chemistry and Institute of Surface and Interface Science, University of California at Irvine, Irvine, California 92697-2025
| | - Adolfo Bastida
- Departamento de Química Física, Universidad de Murcia, 3010 Murcia, Spain, Laboratoire Collisions, Agrégats, Réactivité, IRSAMC, Université de Toulouse, UPS, and CNRS, UMR5589, F-31062 Toulouse, France, and Department of Chemistry and Institute of Surface and Interface Science, University of California at Irvine, Irvine, California 92697-2025
| | - Alberto Requena
- Departamento de Química Física, Universidad de Murcia, 3010 Murcia, Spain, Laboratoire Collisions, Agrégats, Réactivité, IRSAMC, Université de Toulouse, UPS, and CNRS, UMR5589, F-31062 Toulouse, France, and Department of Chemistry and Institute of Surface and Interface Science, University of California at Irvine, Irvine, California 92697-2025
| | - Nadine Halberstadt
- Departamento de Química Física, Universidad de Murcia, 3010 Murcia, Spain, Laboratoire Collisions, Agrégats, Réactivité, IRSAMC, Université de Toulouse, UPS, and CNRS, UMR5589, F-31062 Toulouse, France, and Department of Chemistry and Institute of Surface and Interface Science, University of California at Irvine, Irvine, California 92697-2025
| | - J. Alberto Beswick
- Departamento de Química Física, Universidad de Murcia, 3010 Murcia, Spain, Laboratoire Collisions, Agrégats, Réactivité, IRSAMC, Université de Toulouse, UPS, and CNRS, UMR5589, F-31062 Toulouse, France, and Department of Chemistry and Institute of Surface and Interface Science, University of California at Irvine, Irvine, California 92697-2025
| | - Kenneth C. Janda
- Departamento de Química Física, Universidad de Murcia, 3010 Murcia, Spain, Laboratoire Collisions, Agrégats, Réactivité, IRSAMC, Université de Toulouse, UPS, and CNRS, UMR5589, F-31062 Toulouse, France, and Department of Chemistry and Institute of Surface and Interface Science, University of California at Irvine, Irvine, California 92697-2025
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Rauhut G, Knizia G, Werner HJ. Accurate calculation of vibrational frequencies using explicitly correlated coupled-cluster theory. J Chem Phys 2009; 130:054105. [DOI: 10.1063/1.3070236] [Citation(s) in RCA: 157] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Czakó G, Furtenbacher T, Császár * AG, Szalay V. Variational vibrational calculations using high-order anharmonic force fields. Mol Phys 2004. [DOI: 10.1080/0026897042000274991] [Citation(s) in RCA: 51] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Zúñiga J, Bastida A, Requena A, Sibert EL. A theoretical study of the vibrational spectrum of the CS2 molecule. J Chem Phys 2002. [DOI: 10.1063/1.1465413] [Citation(s) in RCA: 13] [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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Reimers JR. A practical method for the use of curvilinear coordinates in calculations of normal-mode-projected displacements and Duschinsky rotation matrices for large molecules. J Chem Phys 2001. [DOI: 10.1063/1.1412875] [Citation(s) in RCA: 444] [Impact Index Per Article: 19.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Zúñiga J, Bastida A, Alacid M, Requena A. Global potential energy surfaces for the CO2 and CS2 molecules. Chem Phys Lett 1999. [DOI: 10.1016/s0009-2614(99)01080-5] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Zúñiga J, Alacid M, Bastida A, Carvajal FJ, Requena A. Determination of a Potential Energy Surface for CO2 Using Generalized Internal Vibrational Coordinates. JOURNAL OF MOLECULAR SPECTROSCOPY 1999; 195:137-146. [PMID: 10191158 DOI: 10.1006/jmsp.1999.7816] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
A potential energy surface for CO2 is determined from experimental data using generalized internal vibrational coordinates. These coordinates are defined as two arbitrary distances and the angle between them and depend on two external parameters, which can be properly optimized. An optimal generalized internal coordinate system is obtained for CO2 by minimizing unconverged vibrational energies with respect to the external parameters. The optimal coordinates are shown to be superior to previously derived normal hyperspherical coordinates for this molecule. A nonlinear least-squares fit of the potential energy surface of CO2 to observed vibrational frequencies is made by using the optimal internal coordinates and fully variational calculations. The potential function is represented by a fourth-order Morse-cosine expansion and its quality is checked by computing highly excited vibrational transition frequencies which were not included in the fit. Copyright 1999 Academic Press.
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Affiliation(s)
- J Zúñiga
- Departamento de Química Física, Universidad de Murcia, Murcia, 30100, Spain
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Zúñiga J, Alacid M, Bastida A, Carvajal FJ, Requena A. Determination of highly excited rovibrational states for N2O using generalized internal coordinates. J Chem Phys 1999. [DOI: 10.1063/1.478538] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.0] [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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Zúñiga J, Bastida A, Alacid M, Requena A. Optimal generalized internal vibrational coordinates for symmetrical linear triatomic molecules. Chem Phys Lett 1998. [DOI: 10.1016/s0009-2614(98)01175-0] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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15
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Zùñiga J, Alacid M, Bastida A, Requena A. Variational calculations of vibrational states of N2O using hyperspherical normal coordinates. J Chem Phys 1996. [DOI: 10.1063/1.472469] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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