1
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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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2
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Schröder B, Rauhut G. From the Automated Calculation of Potential Energy Surfaces to Accurate Infrared Spectra. J Phys Chem Lett 2024; 15:3159-3169. [PMID: 38478898 PMCID: PMC10961845 DOI: 10.1021/acs.jpclett.4c00186] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2024] [Revised: 02/20/2024] [Accepted: 02/28/2024] [Indexed: 03/22/2024]
Abstract
Advances in the development of quantum chemical methods and progress in multicore architectures in computer science made the simulation of infrared spectra of isolated molecules competitive with respect to established experimental methods. Although it is mainly the multidimensional potential energy surface that controls the accuracy of these calculations, the subsequent vibrational structure calculations need to be carefully converged in order to yield accurate results. As both aspects need to be considered in a balanced way, we focus on approaches for molecules of up to 12-15 atoms with respect to both parts, which have been automated to some extent so that they can be employed in routine applications. Alternatives to machine learning will be discussed, which appear to be attractive, as long as local regions of the potential energy surface are sufficient. The automatization of these methods is still in its infancy, and the generalization to molecules with large amplitude motions or molecular clusters is far from trivial, but many systems relevant for astrophysical studies are already in reach.
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Affiliation(s)
- Benjamin Schröder
- Institute
of Physical Chemistry, University of Goettingen, Tammannstrasse 6, Göttingen 37077, Germany
| | - Guntram Rauhut
- Institute
for Theoretical Chemistry, University of
Stuttgart, Pfaffenwaldring 55, Stuttgart 70569, Germany
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3
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Oenen K, Dinu DF, Liedl KR. Determining internal coordinate sets for optimal representation of molecular vibration. J Chem Phys 2024; 160:014104. [PMID: 38180253 DOI: 10.1063/5.0180657] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2023] [Accepted: 12/10/2023] [Indexed: 01/06/2024] Open
Abstract
Arising from the harmonic approximation in solving the vibrational Schrödinger equation, normal modes dissect molecular vibrations into distinct degrees of freedom. Normal modes are widely used as they give rise to descriptive vibrational notations and are convenient for expanding anharmonic potential energy surfaces as an alternative to higher-order Taylor series representations. Usually, normal modes are expressed in Cartesian coordinates, which bears drawbacks that can be overcome by switching to internal coordinates. Considering vibrational notations, normal modes with delocalized characters are difficult to denote, but internal coordinates offer a route to clearer notations. Based on the Hessian, normal mode decomposition schemes for a given set of internal coordinates can describe a normal mode by its contributions from internal coordinates. However, choosing a set of internal coordinates is not straightforward. While the Hessian provides unique sets of normal modes, various internal coordinate sets are possible for a given system. In the present work, we employ a normal mode decomposition scheme to choose an optimal set. Therefore, we screen reasonable sets based on topology and symmetry considerations and rely on a metric that minimizes coupling between internal coordinates. Ultimately, the Nomodeco toolkit presented here generates internal coordinate sets to find an optimal set for representing molecular vibrations. The resulting contribution tables can be used to clarify vibrational notations. We test our scheme on small to mid-sized molecules, showing how the space of definable internal coordinate sets can significantly be reduced.
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Affiliation(s)
- Kemal Oenen
- Department of General, Inorganic and Theoretical Chemistry, University of Innsbruck, Innrain 80, 6020 Innsbruck, Austria
| | - Dennis F Dinu
- Department of General, Inorganic and Theoretical Chemistry, University of Innsbruck, Innrain 80, 6020 Innsbruck, Austria
| | - Klaus R Liedl
- Department of General, Inorganic and Theoretical Chemistry, University of Innsbruck, Innrain 80, 6020 Innsbruck, Austria
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4
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Tran HK, Berkelbach TC. Vibrational heat-bath configuration interaction with semistochastic perturbation theory using harmonic oscillator or VSCF modals. J Chem Phys 2023; 159:194101. [PMID: 37965997 PMCID: PMC10653875 DOI: 10.1063/5.0172702] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2023] [Accepted: 10/23/2023] [Indexed: 11/16/2023] Open
Abstract
Vibrational heat-bath configuration interaction (VHCI)-a selected configuration interaction technique for vibrational structure theory-has recently been developed in two independent works [J. H. Fetherolf and T. C. Berkelbach, J. Chem. Phys. 154, 074104 (2021); A. U. Bhatty and K. R. Brorsen, Mol. Phys. 119, e1936250 (2021)], where it was shown to provide accuracy on par with the most accurate vibrational structure methods with a low computational cost. Here, we eliminate the memory bottleneck of the second-order perturbation theory correction using the same (semi)stochastic approach developed previously for electronic structure theory. This allows us to treat, in an unbiased manner, much larger perturbative spaces, which are necessary for high accuracy in large systems. Stochastic errors are easily controlled to be less than 1 cm-1. We also report two other developments: (i) we propose a new heat-bath criterion and an associated exact implicit sorting algorithm for potential energy surfaces expressible as a sum of products of one-dimensional potentials; (ii) we formulate VHCI to use a vibrational self-consistent field (VSCF) reference, as opposed to the harmonic oscillator reference configuration used in previous reports. Our tests are done with quartic and sextic force fields, for which we find that with VSCF, the minor improvements to accuracy are outweighed by the higher computational cost associated the matrix element evaluations. We expect VSCF-based VHCI to be important for more general potential representations, for which the harmonic oscillator basis function integrals are no longer analytic.
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Affiliation(s)
- Henry K. Tran
- Department of Chemistry, Columbia University, New York, New York 10027, USA
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5
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Majland M, Berg Jensen R, Greisen Højlund M, Thomas Zinner N, Christiansen O. Optimizing the number of measurements for vibrational structure on quantum computers: coordinates and measurement schemes. Chem Sci 2023; 14:7733-7742. [PMID: 37476724 PMCID: PMC10355095 DOI: 10.1039/d3sc01984e] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2023] [Accepted: 06/07/2023] [Indexed: 07/22/2023] Open
Abstract
One of the primary challenges prohibiting demonstrations of practical quantum advantages for near-term devices amounts to excessive measurement overheads for estimating relevant physical quantities such as ground state energies. However, with major differences between the electronic and vibrational structures of molecules, the question of how the resource requirements of computing anharmonic, vibrational states can be reduced remains relatively unexplored compared to its electronic counterpart. Importantly, bosonic commutation relations, distinguishable Hilbert spaces and vibrational coordinates allow manipulations of the vibrational system that can be exploited to minimize resource requirements. In this work, we investigate the impact of different coordinate systems and measurement schemes on the number of measurements needed to estimate anharmonic, vibrational states for a variety of three-mode (six-mode) molecules. We demonstrate an average of 3-fold (1.5-fold), with up to 7-fold (2.5-fold), reduction in the number of measurements required by employing appropriate coordinate transformations, based on an automized construction of qubit Hamiltonians from a conventional vibrational structure program.
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Affiliation(s)
- Marco Majland
- Kvantify Aps DK-2300 Copenhagen S Denmark
- Department of Physics and Astronomy, Aarhus University DK-8000 Aarhus C Denmark
- Department of Chemistry, Aarhus University DK-8000 Aarhus C Denmark
| | - Rasmus Berg Jensen
- Department of Physics and Astronomy, Aarhus University DK-8000 Aarhus C Denmark
- Department of Chemistry, Aarhus University DK-8000 Aarhus C Denmark
| | | | - Nikolaj Thomas Zinner
- Kvantify Aps DK-2300 Copenhagen S Denmark
- Department of Physics and Astronomy, Aarhus University DK-8000 Aarhus C Denmark
| | - Ove Christiansen
- Kvantify Aps DK-2300 Copenhagen S Denmark
- Department of Chemistry, Aarhus University DK-8000 Aarhus C Denmark
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6
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Hanson-Heine MWD. Static Electron Correlation in Anharmonic Molecular Vibrations: A Hybrid TAO-DFT Study. J Phys Chem A 2022; 126:7273-7282. [PMID: 36164938 PMCID: PMC9574917 DOI: 10.1021/acs.jpca.2c05881] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Abstract
Hybrid thermally-assisted-occupation density functional theory is used to examine the effects of static electron correlation on the prediction of a benchmark set of experimentally observed molecular vibrational frequencies. The B3LYP and B97-1 thermally-assisted-occupation measure of static electron correlation is important for describing the vibrations of many of the molecules that make up several popular test sets of experimental data. Shifts are seen for known multireference systems and for many molecules containing atoms from the second row of the periodic table of elements. Several molecules only show significant shifts in select vibrational modes, and significant improvements are seen for the prediction of hydrogen stretching frequencies throughout the test set.
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7
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Hino K, Kurashige Y. Matrix Product State Formulation of the MCTDH Theory in Local Mode Representations for Anharmonic Potentials. J Chem Theory Comput 2022; 18:3347-3356. [PMID: 35606892 DOI: 10.1021/acs.jctc.2c00243] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The matrix product state formulation of the multiconfiguration time-dependent Hartree theory, MPS-MCTDH, reported previously [Kurashige, J. Chem. Phys. 2018, 19, 194114] is extended to realistic anharmonic potentials with n-mode representations beyond the linear vibronic coupling model. For realistic vibrational potentials, the local mode representation should give a more compact representation of the potentials, i.e., lowering the dimensionality of the entanglements, than the normal coordinates, and the MPS-MCTDH formulation should work more efficiently and maintain the accuracy with a small bond dimension of the MPS ansatz. In fact, it was confirmed that the use of the local coordinates made the interaction matrices diagonal dominant and the number of terms in the n-body expansion of the potentials was significantly reduced. The method was applied to the IR spectrum of the CH2O molecule, the zero-point energies, and the vibrational energy redistribution dynamics of polyenes C2nH2n+2. The results showed that the efficiency of the MPS-MCTDH method is significantly accelerated by the use of local coordinates even if the long-range interactions are included in the potential.
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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
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8
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Inakollu VSS, Yu H. Comparative studies of IR spectra of deprotonated serine with classical and thermostated ring polymer molecular dynamics simulations. STRUCTURAL DYNAMICS (MELVILLE, N.Y.) 2021; 8:054101. [PMID: 34549074 PMCID: PMC8443303 DOI: 10.1063/4.0000124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/17/2021] [Accepted: 08/30/2021] [Indexed: 06/13/2023]
Abstract
Here we report the vibrational spectra of deprotonated serine calculated from the classical molecular dynamics (MD) simulations and thermostated ring-polymer molecular dynamics (TRPMD) simulation with third-order density-functional tight-binding. In our earlier study [Inakollu and Yu, "A systematic benchmarking of computational vibrational spectroscopy with DFTB3: Normal mode analysis and fast Fourier transform dipole autocorrelation function," J. Comput. Chem. 39, 2067 (2018)] of deprotonated serine, we observed a significant difference in the vibrational spectra with the classical MD simulations compared to the infrared multiple photon dissociation spectra. It was postulated that this is due to neglecting the nuclear quantum effects (NQEs). In this work, NQEs are considered in spectral calculation using the TRPMD simulations. With the help of potential of mean force calculations, the conformational space of deprotonated serine is analyzed and used to understand the difference in the spectra of classical MD and TRPMD simulations at 298.15 and 100 K. The high-frequency vibrational bands in the spectra are characterized using Fourier transform localized vibrational mode (FT-νN AC) and interatomic distance histograms. At room temperature, the quantum effects are less significant, and the free energy profiles in the classical MD and the TRPMD simulations are very similar. However, the hydrogen bond between the hydroxyl-carboxyl bond is slightly stronger in TRPMD simulations. At 100 K, the quantum effects are more prominent, especially in the 2600-3600 cm-1, and the free energy profile slightly differs between the classical MD and TRPMD simulations. Using the FT-νN AC and the interatomic distance histograms, the high-frequency vibrational bands are discussed in detail.
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Affiliation(s)
| | - Haibo Yu
- Author to whom correspondence should be addressed:
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9
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Hanson-Heine MWD. Reduced Two-Electron Interactions in Anharmonic Molecular Vibrational Calculations Involving Localized Normal Coordinates. J Chem Theory Comput 2021; 17:4383-4391. [PMID: 34087068 DOI: 10.1021/acs.jctc.1c00314] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Spatially localized vibrational normal mode coordinates are shown to reduce the importance of calculating the full set of two-electron terms in the molecular electronic Schrödinger equation. Electron correlation and dispersion interactions become less significant in (E,E)-1,3,5,7-octatetraene vibrational self-consistent field calculations when displacing remote atoms along multiple coordinates. Electron correlation interactions between spatially remote modes are also found to be less important compared to their corresponding uncorrelated interaction terms. Attenuation of the Coulomb operator indicates that the two-electron terms between remote electrons become less important for accurately describing the strongly contributing mode-coupling terms between sets of localized vibrational modes.
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10
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Madsen NK, Jensen RB, Christiansen O. Calculating vibrational excitation energies using tensor-decomposed vibrational coupled-cluster response theory. J Chem Phys 2021; 154:054113. [DOI: 10.1063/5.0037240] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Affiliation(s)
- Niels Kristian Madsen
- Department of Chemistry, University of Aarhus, Langelandsgade 140, DK–8000 Aarhus C, Denmark
| | - Rasmus Berg Jensen
- 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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11
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Mathea T, Petrenko T, Rauhut G. VCI Calculations Based on Canonical and Localized Normal Coordinates for Non-Abelian Molecules: Accurate Assignment of the Vibrational Overtones of Allene. J Phys Chem A 2021; 125:990-998. [DOI: 10.1021/acs.jpca.0c10429] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Tina Mathea
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Taras Petrenko
- 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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12
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Madsen NK, Jensen AB, Hansen MB, Christiansen O. A general implementation of time-dependent vibrational coupled-cluster theory. J Chem Phys 2020; 153:234109. [PMID: 33353317 DOI: 10.1063/5.0034013] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Abstract
The first general excitation level implementation of the time-dependent vibrational coupled cluster (TDVCC) method introduced in a recent publication [J. Chem. Phys. 151, 154116 (2019)] is presented. The general framework developed for time-independent vibrational coupled cluster (VCC) calculations has been extended to the time-dependent context. This results in an efficient implementation of TDVCC with general coupling levels in the cluster operator and Hamiltonian. Thus, the convergence of the TDVCC[k] hierarchy toward the complete-space limit can be studied for any sum-of-product Hamiltonian. Furthermore, a scheme for including selected higher-order excitations for a subset of modes is introduced and studied numerically. Three different definitions of the TDVCC autocorrelation function (ACF) are introduced and analyzed in both theory and numerical experiments. Example calculations are presented for an array of systems including imidazole, formyl fluoride, formaldehyde, and a reduced-dimensionality bithiophene model. The results show that the TDVCC[k] hierarchy converges systematically toward the full-TDVCC limit and that the implementation allows accurate quantum-dynamics simulations of large systems to be performed. Specifically, the intramolecular vibrational-energy redistribution of the 21-dimensional imidazole molecule is studied in terms of the decay of the ACF. Furthermore, the importance of product separability in the definition of the ACF is highlighted when studying non-interacting subsystems.
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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
| | - Ove Christiansen
- Department of Chemistry, University of Aarhus, Langelandsgade 140, DK-8000 Aarhus C, Denmark
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13
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Madsen NK, Hansen MB, Christiansen O, Zoccante A. Time-dependent vibrational coupled cluster with variationally optimized time-dependent basis sets. J Chem Phys 2020; 153:174108. [DOI: 10.1063/5.0024428] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [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
| | - Ove Christiansen
- 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
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14
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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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15
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Mathea T, Rauhut G. Assignment of vibrational states within configuration interaction calculations. J Chem Phys 2020; 152:194112. [DOI: 10.1063/5.0009732] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Tina Mathea
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Guntram Rauhut
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
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16
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Klinting EL, Lauvergnat D, Christiansen O. Vibrational Coupled Cluster Computations in Polyspherical Coordinates with the Exact Analytical Kinetic Energy Operator. J Chem Theory Comput 2020; 16:4505-4520. [DOI: 10.1021/acs.jctc.0c00261] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Affiliation(s)
| | - David Lauvergnat
- Université Paris-Saclay, CNRS, Institut de Chimie Physique, UMR8000, 91405 Orsay, France
| | - Ove Christiansen
- Department of Chemistry, Aarhus University, DK-8000 Aarhus C, Denmark
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17
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Klinting EL, Christiansen O, König C. Toward Accurate Theoretical Vibrational Spectra: A Case Study for Maleimide. J Phys Chem A 2020; 124:2616-2627. [DOI: 10.1021/acs.jpca.9b11915] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Affiliation(s)
| | - Ove Christiansen
- Department of Chemistry, Aarhus University, DK-8000 Aarhus C, Denmark
| | - Carolin König
- Institute of Physical Chemistry, Kiel University, Max-Eyth-Straße 1, D-24118 Kiel, Germany
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18
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Madsen NK, Hansen MB, Worth GA, Christiansen O. Systematic and variational truncation of the configuration space in the multiconfiguration time-dependent Hartree method: The MCTDH[n] hierarchy. J Chem Phys 2020; 152:084101. [DOI: 10.1063/1.5142459] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [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
| | - 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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19
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Ziegler B, Rauhut G. Localized Normal Coordinates in Accurate Vibrational Structure Calculations: Benchmarks for Small Molecules. J Chem Theory Comput 2019; 15:4187-4196. [DOI: 10.1021/acs.jctc.9b00381] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Benjamin Ziegler
- 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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20
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Panek PT, Hoeske AA, Jacob CR. On the choice of coordinates in anharmonic theoretical vibrational spectroscopy: Harmonic vs. anharmonic coupling in vibrational configuration interaction. J Chem Phys 2019; 150:054107. [PMID: 30736699 DOI: 10.1063/1.5083186] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
Abstract
By a suitable choice of coordinates, the computational effort required for calculations of anharmonic vibrational spectra can be reduced significantly. By using suitable localized-mode coordinates obtained from an orthogonal transformation of the conventionally used normal-mode coordinates, anharmonic couplings between modes can be significantly reduced. However, such a transformation introduces harmonic couplings between the localized modes. To elucidate the role of these harmonic couplings, we consider the vibrational self-consistent field (VSCF)/vibrational configuration interaction (VCI) calculations for both few-mode model systems and for ethene as a molecular test case. We show that large harmonic couplings can result in significant errors in localized-mode L-VSCF/L-VCI calculations and study the convergence with respect to the size of the VCI excitation space. To further elucidate the errors introduced by harmonic couplings, we discuss the connection between L-VSCF/L-VCI and vibrational exciton models. With the help of our results, we propose an algorithm for the localization of normal modes in suitable subsets that are chosen to strictly limit the errors introduced by the harmonic couplings while still leading to maximally localized modes.
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Affiliation(s)
- Paweł T Panek
- Technische Universität Braunschweig, Institute of Physical and Theoretical Chemistry, Gaußstraße 17, 38106 Braunschweig, Germany
| | - Adrian A Hoeske
- Technische Universität Braunschweig, Institute of Physical and Theoretical Chemistry, Gaußstraße 17, 38106 Braunschweig, Germany
| | - Christoph R Jacob
- Technische Universität Braunschweig, Institute of Physical and Theoretical Chemistry, Gaußstraße 17, 38106 Braunschweig, Germany
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21
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Yagi K, Yamada K, Kobayashi C, Sugita Y. Anharmonic Vibrational Analysis of Biomolecules and Solvated Molecules Using Hybrid QM/MM Computations. J Chem Theory Comput 2019; 15:1924-1938. [PMID: 30730746 PMCID: PMC8864611 DOI: 10.1021/acs.jctc.8b01193] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
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Quantum
mechanics/molecular mechanics (QM/MM) calculations are
applied for anharmonic vibrational analyses of biomolecules and solvated
molecules. The QM/MM method is implemented into a molecular dynamics
(MD) program, GENESIS, by interfacing with external electronic structure
programs. Following the geometry optimization and the harmonic normal-mode
analysis based on a partial Hessian, the anharmonic potential energy
surface (PES) is generated from QM/MM energies and gradients calculated
at grid points. The PES is used for vibrational self-consistent field
(VSCF) and post-VSCF calculations to compute the vibrational spectrum.
The method is first applied to a phosphate ion in solution. With both
the ion and neighboring water molecules taken as a QM region, IR spectra
of representative hydration structures are calculated by the second-order
vibrational quasi-degenerate perturbation theory (VQDPT2) at the level
of B3LYP/cc-pVTZ and TIP3P force field. A weight-average of IR spectra
over the structures reproduces the experimental spectrum with a mean
absolute deviation of 16 cm–1. Then, the method
is applied to an enzyme, P450 nitric oxide reductase (P450nor), with
the NO molecule bound to a ferric (FeIII) heme. Starting
from snapshot structures obtained from MD simulations of P450nor in
solution, QM/MM calculations have been carried out at the level of
B3LYP-D3/def2-SVP(D). The spin state of FeIII(NO) is likely
a closed-shell singlet state based on a ratio of N–O and Fe–NO
stretching frequencies (νN–O and νFe–NO) calculated for closed- and open-shell singlet
states. The calculated νN–O and νFe–NO overestimate the experimental ones by 120 and
75 cm–1, respectively. The electronic structure
and solvation of FeIII(NO) affect the structure around
the heme of P450nor leading to an increase in νN–O and νFe–NO.
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Affiliation(s)
- Kiyoshi Yagi
- Theoretical Molecular Science Laboratory, RIKEN Cluster for Pioneering Research, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - Kenta Yamada
- Theoretical Molecular Science Laboratory, RIKEN Cluster for Pioneering Research, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - Chigusa Kobayashi
- Computational Biophysics Research Team, RIKEN Center for Computational Science, 7-1-26 Minatojima-Minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan
| | - Yuji Sugita
- Theoretical Molecular Science Laboratory, RIKEN Cluster for Pioneering Research, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
- Computational Biophysics Research Team, RIKEN Center for Computational Science, 7-1-26 Minatojima-Minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan
- Laboratory for Biomolecular Function Simulation, RIKEN Center for Biosystems Dynamics Research, 1-6-5 Minatojima-Minamimachi,
Chuo-ku, Kobe, Hyogo 650-0047, Japan
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22
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Qu C, Bowman JM. Quantum approaches to vibrational dynamics and spectroscopy: is ease of interpretation sacrificed as rigor increases? Phys Chem Chem Phys 2019; 21:3397-3413. [DOI: 10.1039/c8cp04990d] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
The subject of this Perspective is quantum approaches, beyond the harmonic approximation, to vibrational dynamics and IR spectroscopy.
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Affiliation(s)
- Chen Qu
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University
- Atlanta
- USA
| | - Joel M. Bowman
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University
- Atlanta
- USA
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23
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Ziegler B, Rauhut G. Rigorous use of symmetry within the construction of multidimensional potential energy surfaces. J Chem Phys 2018; 149:164110. [DOI: 10.1063/1.5047912] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Affiliation(s)
- Benjamin Ziegler
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Guntram Rauhut
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
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24
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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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25
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Hanson-Heine MWD. Reduced Basis Set Dependence in Anharmonic Frequency Calculations Involving Localized Coordinates. J Chem Theory Comput 2018; 14:1277-1285. [PMID: 29385338 DOI: 10.1021/acs.jctc.7b01075] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Localized normal coordinates are known to be effective in speeding up anharmonic frequency calculations by reducing the complexity of the nuclear Hamiltonian and wave function. Displacing atoms in localized coordinates can also cause relatively small changes in the electronic structure, which can be exploited for further computational efficiency improvements during ab initio electronic structure calculations of the potential energy surface by reducing the electronic basis set dependence. Three different schemes for reducing the basis set dependence have been investigated in this work. These include combining localized coordinate schemes with general mixed basis sets, distance based force-field reductions, and using coordinate specific basis sets. The importance of accurately describing electronic interactions is found to diminish both for multicoordinate terms involving the displacement of remote atoms and when describing the interactions between more remote atoms within specific coordinates.
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26
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Madsen NK, Godtliebsen IH, Losilla SA, Christiansen O. Tensor-decomposed vibrational coupled-cluster theory: Enabling large-scale, highly accurate vibrational-structure calculations. J Chem Phys 2018; 148:024103. [DOI: 10.1063/1.5001569] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | | | | | - Ove Christiansen
- Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark
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27
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Baiardi A, Stein CJ, Barone V, Reiher M. Vibrational Density Matrix Renormalization Group. J Chem Theory Comput 2017; 13:3764-3777. [DOI: 10.1021/acs.jctc.7b00329] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Alberto Baiardi
- Scuola Normale
Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - Christopher J. Stein
- Laboratorium
für Physikalische Chemie, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Vincenzo Barone
- Scuola Normale
Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - Markus Reiher
- Laboratorium
für Physikalische Chemie, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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28
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Madsen NK, Godtliebsen IH, Christiansen O. Efficient algorithms for solving the non-linear vibrational coupled-cluster equations using full and decomposed tensors. J Chem Phys 2017; 146:134110. [DOI: 10.1063/1.4979498] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Niels K. Madsen
- Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark
| | | | - Ove Christiansen
- Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark
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29
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Hanson-Heine MWD. Intermediate vibrational coordinate localization with harmonic coupling constraints. J Chem Phys 2017; 144:204116. [PMID: 27250288 DOI: 10.1063/1.4951011] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Optimized normal coordinates can significantly improve the speed and accuracy of vibrational frequency calculations. However, over-localization can occur when using unconstrained spatial localization techniques. The unintuitive mixtures of stretching and bending coordinates that result can make interpreting spectra more difficult and also cause artificial increases in mode-coupling during anharmonic calculations. Combining spatial localization with a constraint on the coupling between modes can be used to generate coordinates with properties in-between the normal and fully localized schemes. These modes preserve the diagonal nature of the mass-weighted Hessian matrix to within a specified tolerance and are found to prevent contamination between the stretching and bending vibrations of the molecules studied without a priori classification of the different types of vibration present. Relaxing the constraint can also be used to identify which normal modes form specific groups of localized modes. The new coordinates are found to center on more spatially delocalized functional groups than their fully localized counterparts and can be used to tune the degree of vibrational correlation energy during anharmonic calculations.
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Affiliation(s)
- Magnus W D Hanson-Heine
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
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30
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Panek PT, Jacob CR. On the benefits of localized modes in anharmonic vibrational calculations for small molecules. J Chem Phys 2017; 144:164111. [PMID: 27131535 DOI: 10.1063/1.4947213] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Anharmonic vibrational calculations can already be computationally demanding for relatively small molecules. The main bottlenecks lie in the construction of the potential energy surface and in the size of the excitation space in the vibrational configuration interaction (VCI) calculations. To address these challenges, we use localized-mode coordinates to construct potential energy surfaces and perform vibrational self-consistent field and L-VCI calculations [P. T. Panek and C. R. Jacob, ChemPhysChem 15, 3365 (2014)] for all vibrational modes of two prototypical test cases, the ethene and furan molecules. We find that the mutual coupling between modes is reduced when switching from normal-mode coordinates to localized-mode coordinates. When using such localized-mode coordinates, we observe a faster convergence of the n-mode expansion of the potential energy surface. This makes it possible to neglect higher-order contributions in the n-mode expansion of the potential energy surface or to approximate higher-order contributions in hybrid potential energy surfaces, which reduced the computational effort for the construction of the anharmonic potential energy surface significantly. Moreover, we find that when using localized-mode coordinates, the convergence with respect to the VCI excitation space proceeds more smoothly and that the error at low orders is reduced significantly. This makes it possible to devise low-cost models for obtaining a first approximation of anharmonic corrections. This demonstrates that the use of localized-mode coordinates can be beneficial already in anharmonic vibrational calculations of small molecules and provides a possible avenue for enabling such accurate calculations also for larger molecules.
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Affiliation(s)
- Paweł T Panek
- TU Braunschweig, Institute of Physical and Theoretical Chemistry, Hans-Sommer-Str. 10, 38106 Braunschweig, Germany
| | - Christoph R Jacob
- TU Braunschweig, Institute of Physical and Theoretical Chemistry, Hans-Sommer-Str. 10, 38106 Braunschweig, Germany
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31
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Battocchio G, Madsen NK, Christiansen O. Density matrices and iterative natural modals in vibrational structure theory. Mol Phys 2016. [DOI: 10.1080/00268976.2016.1243263] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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32
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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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33
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Abstract
Because of the size of polypeptides and proteins, the quantum-chemical prediction of their vibrational spectra presents an exceptionally challenging task. Here, we address one of these challenges, namely, the inclusion of anharmonicities. By performing the expansion of the potential energy surface in localized-mode coordinates instead of the normal-mode coordinates, it becomes possible to calculate anharmonic vibrational spectra of polypeptides efficiently and reliably. We apply this approach to calculate the infrared, Raman, and Raman optical activity spectra of helical alanine polypeptides consisting of up to 20 amino acids. We find that while anharmonicities do not alter the band shapes, simple scaling procedures cannot account for the different shifts found for the individual bands. This closes an important gap in theoretical vibrational spectroscopy by making it possible to quantify the anharmonic contributions and opens the door to a first-principles calculation of multidimensional vibrational spectra.
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Affiliation(s)
- Paweł T Panek
- Institute of Physical and Theoretical Chemistry, TU Braunschweig , Hans-Sommer-Str. 10, 38106 Braunschweig, Germany
| | - Christoph R Jacob
- Institute of Physical and Theoretical Chemistry, TU Braunschweig , Hans-Sommer-Str. 10, 38106 Braunschweig, Germany
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