1
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Xu R, Jiang Z, Yang Q, Bloino J, Biczysko M. Harmonic and anharmonic vibrational computations for biomolecular building blocks: Benchmarking DFT and basis sets by theoretical and experimental IR spectrum of glycine conformers. J Comput Chem 2024; 45:1846-1869. [PMID: 38682874 DOI: 10.1002/jcc.27377] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2024] [Revised: 04/01/2024] [Accepted: 04/02/2024] [Indexed: 05/01/2024]
Abstract
Advanced vibrational spectroscopic experiments have reached a level of sophistication that can only be matched by numerical simulations in order to provide an unequivocal analysis, a crucial step to understand the structure-function relationship of biomolecules. While density functional theory (DFT) has become the standard method when targeting medium-size or larger systems, the problem of its reliability and accuracy are well-known and have been abundantly documented. To establish a reliable computational protocol, especially when accuracy is critical, a tailored benchmark is usually required. This is generally done over a short list of known candidates, with the basis set often fixed a priori. In this work, we present a systematic study of the performance of DFT-based hybrid and double-hybrid functionals in the prediction of vibrational energies and infrared intensities at the harmonic level and beyond, considering anharmonic effects through vibrational perturbation theory at the second order. The study is performed for the six-lowest energy glycine conformers, utilizing available "state-of-the-art" accurate theoretical and experimental data as reference. Focusing on the most intense fundamental vibrations in the mid-infrared range of glycine conformers, the role of the basis sets is also investigated considering the balance between computational cost and accuracy. Targeting larger systems, a broad range of hybrid schemes with different computational costs is also tested.
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Affiliation(s)
- Ruiqin Xu
- Department of Physics, College of Sciences, Shanghai University, Shanghai, China
| | | | - Qin Yang
- Institute of Organic Chemistry and Biochemistry, Czech Academy of Science, Prague, Czechia
| | - Julien Bloino
- Classe di Scienze, Scuola Normale Superiore, Pisa, Italy
| | - Malgorzata Biczysko
- Department of Physics, College of Sciences, Shanghai University, Shanghai, China
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2
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Sharma M, Banik S, Roy TK. Performance of Effective Harmonic Oscillator Approach for the Calculations of Vibrational Transition Energies of Large Molecules. J Phys Chem A 2024; 128:5762-5776. [PMID: 38979981 DOI: 10.1021/acs.jpca.4c01583] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/10/2024]
Abstract
The accuracy and performance of the effective harmonic oscillator approximation for the description of anharmonic vibrational structure calculations are tested for large molecular systems and compared with experimental values along with vibrational self-consistent field and second-order perturbation theories. The effective harmonic oscillator approach is an effective single-particle approximation where the variational parameters are the centroids and widths of the multidimensional Gaussian product functions posited as the vibrational wave functions. A comprehensive calculation for 849 transitions that include the fundamentals, two and three quanta overtone transitions, and several combination bands of three polyaromatic hydrocarbons and one DNA nucleobase with a total of 231 normal modes are assessed. A comparison of EHO results with the experimental values is done for the polyaromatic hydrocarbons, and a close agreement is found between the two results. It also offers anharmonic eigenstates and eigenfunctions that are nearly identical with vibrational self-consistent field theory. An extensive analysis on the resultant wave functions of the excited states is performed. The overall root-mean-square deviation (RMSD) between these two methods for 849 transitions understudy is only about 8.3 cm-1, suggesting the effective harmonic oscillator as a viable alternative for the reliable calculations of transition energies of large molecular systems.
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Affiliation(s)
- Mokshi Sharma
- Department of Chemistry and Chemical Sciences, Central University of Jammu, Rahya-Suchani (Bagla), Jammu, Jammu and Kashmir 181143, India
| | - Subrata Banik
- Department of Chemistry, School of Chemical and Biotechnology, SASTRA Deemed University, Thanjavur, Tamil Nadu 613401, India
| | - Tapta Kanchan Roy
- Department of Chemistry and Chemical Sciences, Central University of Jammu, Rahya-Suchani (Bagla), Jammu, Jammu and Kashmir 181143, India
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3
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Suda K, Yokogawa D. Vibrational Self-Consistent Field (VSCF) and Post-VSCF Method Calculations Combined with the Reference Interaction Site Model Self-Consistent Field Method Coupled with the Constrained Spatial Electron Density Distribution: Applications to NaHCOO in Aqueous Phase. J Chem Theory Comput 2024; 20:4885-4892. [PMID: 38815984 DOI: 10.1021/acs.jctc.4c00360] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/01/2024]
Abstract
Investigating vibrational behavior in solution is crucial for understanding molecular dynamics within a solvent environment. Notably, the analysis of Raman spectra for molecules in solution is important owing to its ability to unveil intricate solute-solvent interactions. Previous studies have effectively employed frequency calculations utilizing the reference interaction site model self-consistent field method in conjunction with constrained spatial electron density distribution (RISM-SCF-cSED) to understand molecular vibrations in solution, primarily focusing on fundamental vibrational modes. However, the oversight of overtones and combination tones in these studies prompted us to combine the vibrational self-consistent field (VSCF) and vibrational second-order Mo̷ller-Plesset perturbation (VMP2) methods with RISM-SCF-cSED to address these aspects theoretically. Illustrating the efficacy of this integrated approach, we computed the Raman spectra of sodium formate (NaHCOO) in water, revealing the necessity of accounting for molecular anharmonicity in solution vibrational analysis. Our findings underscore the potency of VSCF and VMP2 in conjunction with RISM-SCF-cSED as a robust theoretical framework for such calculations.
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Affiliation(s)
- Kayo Suda
- Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan
| | - Daisuke Yokogawa
- Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan
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4
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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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5
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Gleeson R, Aggelund PA, Østergaard FC, Schaltz KF, Sauer SPA. Exploring Alternate Methods for the Calculation of High-Level Vibrational Corrections of NMR Spin-Spin Coupling Constants. J Chem Theory Comput 2024. [PMID: 38299500 DOI: 10.1021/acs.jctc.3c01223] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2024]
Abstract
Traditional nuclear magnetic resonance (NMR) calculations typically treat systems with a Born-Oppenheimer-derived electronic wave function that is solved for a fixed nuclear geometry. One can numerically account for this neglected nuclear motion by averaging over property values for all nuclear geometries with a vibrational wave function and adding this expectation value as a correction to an equilibrium geometry property value. Presented are benchmark coupled-cluster singles and doubles (CCSD) vibrational corrections to spin-spin coupling constants (SSCCs) computed at the level of vibrational second-order perturbation theory (VPT2) using the vibrational averaging driver of the CFOUR program. As CCSD calculations of vibrational corrections are very costly, cheaper electronic structure methods are explored via a newly developed Python vibrational averaging program within the Dalton Project. Namely, results obtained with the second-order polarization propagator approximation (SOPPA) and density functional theory (DFT) with the B3LYP and PBE0 exchange-correlation functionals are compared to the benchmark CCSD//CCSD(T) and experimental values. CCSD//CCSD(T) corrections are also combined with literature CC3 equilibrium geometry values to form the highest-order vibrationally corrected values available (i.e., CC3//CCSD(T) + CCSD//CCSD(T)). CCSD//CCSD(T) statistics showed favorable statistics in comparison to experimental values, albeit at an unfavorably high computational cost. A cheaper CCSD//CCSD(T) + B3LYP method showed quite similar mean absolute deviation (MAD) values as CCSD//CCSD(T), concluding that CCSD//CCSD(T) + B3LYP is optimal in terms of cost and accuracy. With reference to experimental values, a vibrational correction was not worth the cost for all of the other methods tested. Finally, deviation statistics showed that CC3//CCSD(T) + CCSD//CCSD(T) vibrational-corrected equilibrium values deteriorated in comparison to CCSD//CCSD(T) attributed to the use of a smaller basis set or lack of solvation effects for the CC3 equilibrium calculations.
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Affiliation(s)
- Ronan Gleeson
- Department of Chemistry, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Patrick A Aggelund
- Department of Chemistry, University of Copenhagen, 2100 Copenhagen, Denmark
| | | | - Kasper F Schaltz
- Department of Chemistry, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Stephan P A Sauer
- Department of Chemistry, University of Copenhagen, 2100 Copenhagen, Denmark
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6
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Hoffman AJ, Temmerman W, Campbell E, Damin AA, Lezcano-Gonzalez I, Beale AM, Bordiga S, Hofkens J, Van Speybroeck V. A Critical Assessment on Calculating Vibrational Spectra in Nanostructured Materials. J Chem Theory Comput 2024; 20:513-531. [PMID: 38157404 PMCID: PMC10809426 DOI: 10.1021/acs.jctc.3c00942] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2023] [Revised: 11/30/2023] [Accepted: 12/05/2023] [Indexed: 01/03/2024]
Abstract
Vibrational spectroscopy is an omnipresent spectroscopic technique to characterize functional nanostructured materials such as zeolites, metal-organic frameworks (MOFs), and metal-halide perovskites (MHPs). The resulting experimental spectra are usually complex, with both low-frequency framework modes and high-frequency functional group vibrations. Therefore, theoretically calculated spectra are often an essential element to elucidate the vibrational fingerprint. In principle, there are two possible approaches to calculate vibrational spectra: (i) a static approach that approximates the potential energy surface (PES) as a set of independent harmonic oscillators and (ii) a dynamic approach that explicitly samples the PES around equilibrium by integrating Newton's equations of motions. The dynamic approach considers anharmonic and temperature effects and provides a more genuine representation of materials at true operating conditions; however, such simulations come at a substantially increased computational cost. This is certainly true when forces and energy evaluations are performed at the quantum mechanical level. Molecular dynamics (MD) techniques have become more established within the field of computational chemistry. Yet, for the prediction of infrared (IR) and Raman spectra of nanostructured materials, their usage has been less explored and remain restricted to some isolated successes. Therefore, it is currently not a priori clear which methodology should be used to accurately predict vibrational spectra for a given system. A comprehensive comparative study between various theoretical methods and experimental spectra for a broad set of nanostructured materials is so far lacking. To fill this gap, we herein present a concise overview on which methodology is suited to accurately predict vibrational spectra for a broad range of nanostructured materials and formulate a series of theoretical guidelines to this purpose. To this end, four different case studies are considered, each treating a particular material aspect, namely breathing in flexible MOFs, characterization of defects in the rigid MOF UiO-66, anharmonic vibrations in the metal-halide perovskite CsPbBr3, and guest adsorption on the pores of the zeolite H-SSZ-13. For all four materials, in their guest- and defect-free state and at sufficiently low temperatures, both the static and dynamic approach yield qualitatively similar spectra in agreement with experimental results. When the temperature is increased, the harmonic approximation starts to fail for CsPbBr3 due to the presence of anharmonic phonon modes. Also, the spectroscopic fingerprints of defects and guest species are insufficiently well predicted by a simple harmonic model. Both phenomena flatten the potential energy surface (PES), which facilitates the transitions between metastable states, necessitating dynamic sampling. On the basis of the four case studies treated in this Review, we can propose the following theoretical guidelines to simulate accurate vibrational spectra of functional solid-state materials: (i) For nanostructured crystalline framework materials at low temperature, insights into the lattice dynamics can be obtained using a static approach relying on a few points on the PES and an independent set of harmonic oscillators. (ii) When the material is evaluated at higher temperatures or when additional complexity enters the system, e.g., strong anharmonicity, defects, or guest species, the harmonic regime breaks down and dynamic sampling is required for a correct prediction of the phonon spectrum. These guidelines and their illustrations for prototype material classes can help experimental and theoretical researchers to enhance the knowledge obtained from a lattice dynamics study.
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Affiliation(s)
| | - Wim Temmerman
- Center
for Molecular Modeling, Ghent University, 9000 Ghent, Belgium
| | - Emma Campbell
- Cardiff
Catalysis Institute, Cardiff University, Cardiff CF10 3AT, United Kingdom
- Research
Complex at Harwell, Didcot OX11 0FA, United
Kingdom
| | | | - Ines Lezcano-Gonzalez
- Research
Complex at Harwell, Didcot OX11 0FA, United
Kingdom
- Department
of Chemistry, University College London, London WC1E 6BT, United Kingdom
| | - Andrew M. Beale
- Research
Complex at Harwell, Didcot OX11 0FA, United
Kingdom
- Department
of Chemistry, University College London, London WC1E 6BT, United Kingdom
| | - Silvia Bordiga
- Department
of Chemistry, University of Turin, 10124 Turin, Italy
| | - Johan Hofkens
- Department
of Chemistry, KU Leuven, 3000 Leuven, Belgium
- Max Planck
Institute for Polymer Research, 55128 Mainz, Germany
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7
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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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8
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Erba A, Desmarais JK, Casassa S, Civalleri B, Donà L, Bush IJ, Searle B, Maschio L, Edith-Daga L, Cossard A, Ribaldone C, Ascrizzi E, Marana NL, Flament JP, Kirtman B. CRYSTAL23: A Program for Computational Solid State Physics and Chemistry. J Chem Theory Comput 2023; 19:6891-6932. [PMID: 36502394 PMCID: PMC10601489 DOI: 10.1021/acs.jctc.2c00958] [Citation(s) in RCA: 20] [Impact Index Per Article: 20.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2022] [Indexed: 12/14/2022]
Abstract
The Crystal program for quantum-mechanical simulations of materials has been bridging the realm of molecular quantum chemistry to the realm of solid state physics for many years, since its first public version released back in 1988. This peculiarity stems from the use of atom-centered basis functions within a linear combination of atomic orbitals (LCAO) approach and from the corresponding efficiency in the evaluation of the exact Fock exchange series. In particular, this has led to the implementation of a rich variety of hybrid density functional approximations since 1998. Nowadays, it is acknowledged by a broad community of solid state chemists and physicists that the inclusion of a fraction of Fock exchange in the exchange-correlation potential of the density functional theory is key to a better description of many properties of materials (electronic, magnetic, mechanical, spintronic, lattice-dynamical, etc.). Here, the main developments made to the program in the last five years (i.e., since the previous release, Crystal17) are presented and some of their most noteworthy applications reviewed.
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Affiliation(s)
- Alessandro Erba
- Dipartimento
di Chimica, Università di Torino, via Giuria 5, 10125 Torino, Italy
| | - Jacques K. Desmarais
- Dipartimento
di Chimica, Università di Torino, via Giuria 5, 10125 Torino, Italy
| | - Silvia Casassa
- Dipartimento
di Chimica, Università di Torino, via Giuria 5, 10125 Torino, Italy
| | - Bartolomeo Civalleri
- Dipartimento
di Chimica, Università di Torino, via Giuria 5, 10125 Torino, Italy
| | - Lorenzo Donà
- Dipartimento
di Chimica, Università di Torino, via Giuria 5, 10125 Torino, Italy
| | - Ian J. Bush
- STFC
Rutherford Appleton Laboratory, Chilton Didcot, Oxfordshire OX11 0QX, United Kingdom
| | - Barry Searle
- SFTC
Daresbury Laboratory, Daresbury, Cheshire WA4 4AD, United Kingdom
| | - Lorenzo Maschio
- Dipartimento
di Chimica, Università di Torino, via Giuria 5, 10125 Torino, Italy
| | - Loredana Edith-Daga
- Dipartimento
di Chimica, Università di Torino, via Giuria 5, 10125 Torino, Italy
| | - Alessandro Cossard
- Dipartimento
di Chimica, Università di Torino, via Giuria 5, 10125 Torino, Italy
| | - Chiara Ribaldone
- Dipartimento
di Chimica, Università di Torino, via Giuria 5, 10125 Torino, Italy
| | - Eleonora Ascrizzi
- Dipartimento
di Chimica, Università di Torino, via Giuria 5, 10125 Torino, Italy
| | - Naiara L. Marana
- Dipartimento
di Chimica, Università di Torino, via Giuria 5, 10125 Torino, Italy
| | - Jean-Pierre Flament
- Université
de Lille, CNRS, UMR 8523 — PhLAM — Physique des Lasers, Atomes et Molécules, 59000 Lille, France
| | - Bernard Kirtman
- Department
of Chemistry and Biochemistry, University
of California, Santa
Barbara, California 93106, United States
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9
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Sharma D, Roy TK. Accuracy of Different Electronic Basis Set Families for Anharmonic Molecular Vibrations: A Comprehensive Benchmark Study. J Phys Chem A 2023; 127:7132-7147. [PMID: 37603414 DOI: 10.1021/acs.jpca.3c02874] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/23/2023]
Abstract
In this work, the accuracy and convergence of different electronic basis set families for the computation of anharmonic molecular vibrational spectroscopic calculations are benchmarked. A series of 39 different basis sets from different families following their hierarchy are assessed on VSCF and VSCF-PT2 algorithms with commonly used MP2 and DFT based B3LYP-D potentials for a set of molecular systems. Such an effort has been validated in a previous work ( J. Phys. Chem. A 2020, 124, 9203-9221) with split-valence basis sets for fundamentals and intensities. Here, fundamental transitions, vibrationally excited states, and intensities are compared with the experimental data to estimate the accuracy for a series of Jensen, Dunning, Calendar, Karlsruhe, and Sapporo basis set families. The convergence of basis sets are also compared with the large ANO basis set. Comprehensive statistical error analysis in terms of accuracy and precision was carried out to assess the performance of each basis set. It is observed that the improvement for the calculated harmonic and anharmonic values from the smaller basis sets to the medium (i.e., triple-ξ) is considerable. Beyond this, from medium to large basis sets, the convergence is slow and mostly posits nearly converged values. Basis sets with and without diffuse functions offer characteristically different accuracies and convergence patterns. Finally, recommendations are given on the choice of basis set chosen as black-box which can balance between accuracy and computational time, estimation of the errors, and their selections especially for large molecules.
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Affiliation(s)
- Dhiksha Sharma
- Department of Chemistry and Chemical Sciences, Central University of Jammu, Rahya-Suchani (Bagla), Jammu, J&K 181143 India
| | - Tapta Kanchan Roy
- Department of Chemistry and Chemical Sciences, Central University of Jammu, Rahya-Suchani (Bagla), Jammu, J&K 181143 India
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10
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Mendolicchio M, Bloino J, Barone V. Perturb-Then-Diagonalize Vibrational Engine Exploiting Curvilinear Internal Coordinates. J Chem Theory Comput 2022; 18:7603-7619. [PMID: 36322968 DOI: 10.1021/acs.jctc.2c00773] [Citation(s) in RCA: 14] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
The present paper is devoted to the implementation and validation of a second-order perturbative approach to anharmonic vibrations, followed by variational treatment of strong couplings (GVPT2) based on curvilinear internal coordinates. The main difference with respect to the customary Cartesian-based formulation is that the kinetic energy operator is no longer diagonal, and has to be expanded as well, leading to additional terms which have to be taken into proper account. It is, however, possible to recast all the equations as well-defined generalizations of the corresponding Cartesian-based counterparts, thus achieving a remarkable simplification of the new implementation. Particular attention is paid to the treatment of Fermi resonances with significant number of test cases analyzed fully, validating the new implementation. The results obtained in this work confirm that curvilinear coordinates strongly reduce the strength of inter-mode couplings compared to their Cartesian counterparts. This increases the reliability of low-order perturbative treatments for semi-rigid molecules and paves the way toward the reliable representation of more flexible molecules where small- and large-amplitude motions can be safely decoupled and treated at different levels of theory.
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Affiliation(s)
- Marco Mendolicchio
- Scuola Superiore Meridionale, Largo S. Marcellino 10, Napoli I-80138, Italy
| | - Julien Bloino
- Scuola Normale Superiore, Piazza dei Cavalieri 7, Pisa I-56126, Italy
| | - Vincenzo Barone
- Scuola Normale Superiore, Piazza dei Cavalieri 7, Pisa I-56126, Italy
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11
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Tyuterev V, Tashkun S, Rey M, Nikitin A. High-order contact transformations of molecular Hamiltonians: general approach, fast computational algorithm and convergence of ro-vibrational polyad models. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2096140] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
Affiliation(s)
- Vladimir Tyuterev
- Groupe de Spectrométrie Moléculaire et Atmosphérique, Université de Reims, Reims, France
- Laboratory of Molecular Quantum Mechanics and Radiative Transfer, Tomsk State University, Tomsk, Russia
| | - Sergey Tashkun
- Laboratory of Theoretical Spectroscopy, V.E. Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences, Tomsk, Russia
| | - Michael Rey
- Groupe de Spectrométrie Moléculaire et Atmosphérique, Université de Reims, Reims, France
| | - Andrei Nikitin
- Laboratory of Theoretical Spectroscopy, V.E. Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences, Tomsk, Russia
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12
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Carvalho JR, Vidal LN. Calculation of absolute Raman scattering cross-sections using vibrational self-consistent field/vibrational configuration interaction wave functions. J Comput Chem 2022; 43:1484-1494. [PMID: 35731622 DOI: 10.1002/jcc.26951] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2022] [Revised: 05/21/2022] [Accepted: 06/02/2022] [Indexed: 11/12/2022]
Abstract
In the present study, the differential scattering cross-sections, depolarization ratios and Raman shifts of small molecular systems are obtained from configuration iteration wave functions of vibrational self-consistent field (VSCF) states. The transition polarizabilities were modeled using the Placzek approximation, neglecting those contributions not arising from the electric dipole mechanism. This theoretical approach is considered a good approximation for samples that absorb in the UV range if the excitation radiation falls in the visible region, as is the case of the molecules selected for the present study, namely: water, methane, and acetylene. Potential energy and electronic polarizability surfaces are calculated by the CCSD(T) and CC3 methods with aug-cc-p(C)V(T,Q,5)Z basis sets. The vibrational Hamiltonian includes the vibrational angular momentum contribution of the Watson kinetic energy operator. As expected, due to the variational nature of the VSCF and vibrational configuration interaction (VCI) methods, the Raman transition wavenumbers are substantially improved over the harmonic predictions. Surprisingly, the scattering cross-sections obtained using the harmonic approximation or the VSCF method better agrees with the experimental values than those cross-sections predicted using VCI wave functions. The more significant deviations of the VCI results from the experimental reference may be related to the significant uncertainties of the measured cross-sections. Still, it may also indicate that the VCI Raman transition moments may require a more accurate description of the electronic polarizability surface. Finally, the depolarization ratios calculated for H2 O and C2 D2 using harmonic and VCI wave functions have similar accuracy, whereas, for C2 H2 and C2 HD, the VCI results are more accurate.
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Affiliation(s)
- Jhonatas R Carvalho
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas, USA
| | - Luciano N Vidal
- Departamento Acadêmico de Química e Biologia, Universidade Tecnológica Federal do Paraná, Curitiba, Paraná, Brazil
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13
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Schröder B, Rauhut G. Comparison of body definitions for incremental vibrational configuration interaction theory (iVCI). J Chem Phys 2022; 156:174103. [DOI: 10.1063/5.0085082] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Within incremental vibrational configuration interaction theory (iVCI), the vibrational state energy is determined by means of a many-body expansion, i.e., it is a sum of terms of increasing order, which allow for an embarrassingly parallel evaluation. The convergence of this expansion depends strongly on the definition of the underlying bodies, which essentially decompose the correlation space into fragments. The different definitions considered here comprise mode-based bodies, excitation level-based bodies, and energy-based bodies. An analysis of the convergence behavior revealed that accounting for resonances within these definitions is mandatory and leads to a substantial improvement of the convergence, that is, the expansions can be truncated at lower orders. Benchmark calculations and systematic comparisons of the different body definitions for a small set of molecules, i.e., ketene, ethene, and diborane, have been conducted to study the overall performance of these iVCI implementations with respect to accuracy and central processing unit time.
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Affiliation(s)
- Benjamin Schröder
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Guntram Rauhut
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
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14
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Chang X, Dobrolyubov EO, Krasnoshchekov SV. Fundamental studies of vibrational resonance phenomena by multivalued resummation of the divergent Rayleigh-Schrödinger perturbation theory series: deciphering polyad structures of three H 216O isotopologues. Phys Chem Chem Phys 2022; 24:6655-6675. [PMID: 35234755 DOI: 10.1039/d1cp04279c] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
Abstract
A fundamental quantitative study of the vibrational resonances of three H216O H,D-isotopologues with a quartic Watson Hamiltonian was carried out using the resummation of the high-order (∼λn, n ≤ 203) divergent Rayleigh-Schrödinger perturbation theory (RSPT) series by quartic Padé-Hermite multivalued diagonal approximants PH[m,m,m,m,m], m ≤ 40. The resonance condition between a pair of states is formulated as the existence of a common complex energy solution branch point inside the unit circle: |E(λj)|, Re(λj)2 + Im(λj)2 ≤ 1. For the matrix formulation of the vibrational problem (VCI), the existence of common branch points is governed by the Katz theorem and they can be found as roots of discriminant polynomials. The main branches of the Padé-Hermite approximants typically reproduce VCI energies with high accuracy while alternative branches often fit nearby resonant states. The resummation of the RSPT series for H2O and D2O (up to the tenth polyad) revealed not only Fermi and Darling-Dennison resonances, but also unusual (0,2,-5) and (5,-2,0) resonance effects matching the (5,2,5) polyad structure, while the (3,2,1) structure was rigorously confirmed for HDO. It is demonstrated that the (5,2,5) polyad structure ensures good organization of high-energy resonating states and breaks down the classic (2,1,2) structure. The advocated methodology of quantitative description of resonance phenomena and revealing polyad structures is suitable for larger molecules and can be adapted to linear molecules and symmetric tops. Its application ensures rigorous classification of vibrational states and can be used in quantitative vibration-rotation spectroscopy.
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Affiliation(s)
- Xuanhao Chang
- Chemistry Department, Lomonosov Moscow State University, Leninskiye Gory 1-3, Moscow, 119899, Russian Federation.
| | - Egor O Dobrolyubov
- Chemistry Department, Lomonosov Moscow State University, Leninskiye Gory 1-3, Moscow, 119899, Russian Federation.
| | - Sergey V Krasnoshchekov
- Chemistry Department, Lomonosov Moscow State University, Leninskiye Gory 1-3, Moscow, 119899, Russian Federation.
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15
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Roy TK. Performance of Vibrational Self-Consistent Field Theory for Accurate Potential Energy Surfaces: Fundamentals, Excited States, and Intensities. J Phys Chem A 2022; 126:608-622. [PMID: 35050620 DOI: 10.1021/acs.jpca.1c09989] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The performance of vibrational structure calculations beyond harmonic approximation in the framework of the vibrational self-consistent field method with second-order perturbation corrections (VSCF-PT2) is investigated in conjunction with very accurate potential energy surfaces (PESs) given by various coupled-cluster electronic structure theories. The quality of anharmonic calculations depends on the accuracy of the underlying multidimensional PES obtained from its functional form, which is given by the level of electronic structure theory. Two such highest levels of typical coupled-cluster electronic structure methods, CCSD and the ″gold standard″ CCSD(T), along with their variants such as CCD, CR-CCL (completely renormalized CR-CC(2,3) approach), and CCSD(TQ) are tested for the construction of accurate anharmonic potentials without any fitting or ad hoc scaling and using cc-pVTZ basis sets. The accuracy of VSCF-PT2 theory in comparison to experimental values is tested for a series of 16 molecules with 135 fundamental bands, 64 overtones, and combination bands and also for 39 intensities. It is found that CCD and CCSD bind the potential tighter than CCSD(T) and the computed VSCF-PT2 transitions are more blue-shifted showing higher deviation from the experiment. In general, VSCF-PT2 results computed at the CCSD(T) potential offer a good cost/accuracy ratio, with the mean absolute deviation and the mean absolute percentage error with the experiment being ∼16 cm-1 and 1.38, respectively, for fundamentals. Additionally, while the CR-CCL and CCSD(TQ) methods offer similar levels of accuracies as compared to CCSD(T), the former offers a better accuracy/cost ratio than the latter and is a suitable alternative to CCSD(T).
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Affiliation(s)
- Tapta Kanchan Roy
- Department of Chemistry and Chemical Sciences, Central University of Jammu, Rahya-Suchani (Bagla), Samba, Jammu and Kashmir 181143, India
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16
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Boyer MA, McCoy AB. A Flexible Approach to Vibrational Perturbation Theory using Sparse Matrix Methods. J Chem Phys 2022; 156:054107. [DOI: 10.1063/5.0080892] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - Anne B. McCoy
- Department of Chemistry, University of Washington, United States of America
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17
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Rath G, Kopp WA, Leonhard K. Coupled Anharmonic Thermochemistry from Stratified Monte Carlo Integration. J Chem Inf Model 2021; 61:5853-5870. [PMID: 34874733 DOI: 10.1021/acs.jcim.1c00668] [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
This study presents configuration integral Monte Carlo integration (CIMCI), a new semiclassical method for handling fully coupled anharmonicity in gas-phase thermodynamics that promises to be black boxable, to be applicable to all kinds of anharmonicity, and to scale better at higher dimensionality than other methods for handling gas-phase molecular anharmonicity. The method does so using automatically and recursively stratified, simultaneous Monte Carlo (MC) integration of multiple functions, following a modified version of the standard MISER scheme that converges at a rate of about the square of naïve MC integration. For the small systems analyzed by this study where proper reference data is available (H2O and H2O2), the method's anharmonic entropy corrections match reference data better than those of other black box anharmonic methods, e.g., vibrational perturbation theory (VPT2) and the McClurg hindered rotor model used with automatic detection of rotors; for H2O2 and NH2OH, the method is also in general agreement with one-dimensional hindered rotor treatments at low temperatures. This holds even when sampling with CIMCI is done with primitive force fields, e.g., UFF, while the competing methods are used with proper, comprehensive potentials, e.g., the M06-2X metahybrid density-functional theory (DFT) functional.
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Affiliation(s)
- Gabriel Rath
- Institute of Technical Thermodynamics, RWTH Aachen University, 52062 Aachen, Germany.,Software for Chemistry & Materials, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
| | - Wassja A Kopp
- Institute of Technical Thermodynamics, RWTH Aachen University, 52062 Aachen, Germany
| | - Kai Leonhard
- Institute of Technical Thermodynamics, RWTH Aachen University, 52062 Aachen, Germany
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18
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Alaal N, Brorsen KR. Multicomponent heat-bath configuration interaction with the perturbative correction for the calculation of protonic excited states. J Chem Phys 2021; 155:234107. [PMID: 34937361 DOI: 10.1063/5.0076006] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this study, we extend the multicomponent heat-bath configuration interaction (HCI) method to excited states. Previous multicomponent HCI studies have been performed using only the variational stage of the HCI algorithm as they have largely focused on the calculation of protonic densities. Because this study focuses on energetic quantities, a second-order perturbative correction after the variational stage is essential. Therefore, this study implements the second-order Epstein-Nesbet correction to the variational stage of multicomponent HCI for the first time. Additionally, this study introduces a new procedure for calculating reference excitation energies for multicomponent methods using the Fourier-grid Hamiltonian (FGH) method, which should allow the one-particle electronic basis set errors to be better isolated from errors arising from an incomplete description of electron-proton correlation. The excited-state multicomponent HCI method is benchmarked by computing protonic excitations of the HCN and FHF- molecules and is shown to be of similar accuracy to previous excited-state multicomponent methods such as the multicomponent time-dependent density-functional theory and equation-of-motion coupled-cluster theory relative to the new FGH reference values.
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Affiliation(s)
- Naresh Alaal
- Department of Chemistry, University of Missouri, Columbia, Missouri 65203, USA
| | - Kurt R Brorsen
- Department of Chemistry, University of Missouri, Columbia, Missouri 65203, USA
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19
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Changala PB. Vibronic mean-field and perturbation theory for Jahn-Teller and pseudo-Jahn-Teller molecules. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1962556] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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20
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Qin X, Hirata S. Finite-temperature vibrational full configuration interaction. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1949503] [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)
- Xiuyi Qin
- 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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21
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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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22
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Bhatty AU, Brorsen KR. An alternative formulation of vibrational heat-bath configuration interaction. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1936250] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Abuzar U. Bhatty
- Department of Chemistry, University of Missouri, Columbia, MO, USA
| | - Kurt R. Brorsen
- Department of Chemistry, University of Missouri, Columbia, MO, USA
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23
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Ruiz J, Misa K, Seshappan A, Keçeli M, Sode O. Exploring the anharmonic vibrational structure of carbon dioxide trimers. J Chem Phys 2021; 154:144302. [PMID: 33858169 DOI: 10.1063/5.0039793] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Our previously developed mbCO2 potential [O. Sode and J. N. Cherry, J. Comput. Chem. 38, 2763 (2017)] is used to describe the vibrational structure of the intermolecular motions of the CO2 trimers: barrel-shaped and cyclic trimers. Anharmonic corrections are accounted for using the vibrational self-consistent field theory, vibrational second-order Møller-Plesset perturbation (VMP2) theory, and vibrational configuration interaction (VCI) methods and compared with experimental observations. For the cyclic structure, we revise the assignments of two previously observed experimental peaks based on our VCI and VMP2 results. We note that the experimental band observed near 13 cm-1 is the out-of-phase out-of-plane degenerate motion with E″ symmetry, while the peak observed at 18 cm-1 likely corresponds to the symmetric out-of-plane torsion A″ vibration. Since the VCI treatment of the vibrational motions accounts for vibrational mixing and delocalization, overtones and combination bands were also observed and quantified in the intermolecular regions of the two trimer isomers.
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Affiliation(s)
- Jesus Ruiz
- Department of Chemistry and Biochemistry, California State University, Los Angeles, 5151 State University Drive, Los Angeles, California 90032, USA
| | - Kyle Misa
- Department of Chemistry and Biochemistry, California State University, Los Angeles, 5151 State University Drive, Los Angeles, California 90032, USA
| | - Arabi Seshappan
- Department of Chemistry and Biochemistry, California State University, Los Angeles, 5151 State University Drive, Los Angeles, California 90032, USA
| | - Murat Keçeli
- Computational Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
| | - Olaseni Sode
- Department of Chemistry and Biochemistry, California State University, Los Angeles, 5151 State University Drive, Los Angeles, California 90032, USA
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24
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Schröder B, Rauhut G. Incremental vibrational configuration interaction theory, iVCI: Implementation and benchmark calculations. J Chem Phys 2021; 154:124114. [DOI: 10.1063/5.0045305] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023] Open
Affiliation(s)
- Benjamin Schröder
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Guntram Rauhut
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
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25
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Fetherolf JH, Berkelbach TC. Vibrational heat-bath configuration interaction. J Chem Phys 2021; 154:074104. [PMID: 33607897 PMCID: PMC7889291 DOI: 10.1063/5.0035454] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2020] [Accepted: 01/10/2021] [Indexed: 11/14/2022] Open
Abstract
We introduce vibrational heat-bath configuration interaction (VHCI) as an accurate and efficient method for calculating vibrational eigenstates of anharmonic systems. Inspired by its origin in electronic structure theory, VHCI is a selected CI approach that uses a simple criterion to identify important basis states with a pre-sorted list of anharmonic force constants. Screened second-order perturbation theory and simple extrapolation techniques provide significant improvements to variational energy estimates. We benchmark VHCI on four molecules with 12-48 degrees of freedom and use anharmonic potential energy surfaces truncated at fourth and sixth orders. When compared to other methods using the same truncated potentials, VHCI produces vibrational spectra of tens or hundreds of states with sub-wavenumber accuracy at low computational cost.
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26
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Macalik L, Wandas M, Sąsiadek W, Lorenc J, Lisiecki R, Hanuza J. Molecular structure and spectroscopic properties of new neodymium complex with 3-bromo-2-chloro-6-picolinic N-oxide showing the ligand-to-metal energy transfer. J Mol Struct 2021. [DOI: 10.1016/j.molstruc.2020.128967] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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27
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Qin X, Hirata S. Anharmonic Phonon Dispersion in Polyethylene. J Phys Chem B 2020; 124:10477-10485. [PMID: 33169996 DOI: 10.1021/acs.jpcb.0c08493] [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 second-order Green's function method for anharmonic crystals has been applied to an infinite, periodic chain of polyethylene taking into account up to quartic force constants. The frequency-independent approximation to the Dyson self-energy gives rise to numerous divergent resonances, which are fortuitous. Instead, solving the Dyson equation self-consistently with a frequency-dependent self-energy resists divergences from resonances or zero-frequency acoustic vibrations. The calculated anharmonic phonon dispersion, which nonetheless displays many true resonances, and anharmonic phonon density of states furnish hitherto unknown details that explain smaller features of observed vibrational spectra.
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Affiliation(s)
- Xiuyi Qin
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
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28
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Roy TK, Gerber RB. Dual Basis Approach for Ab Initio Anharmonic Calculations of Vibrational Spectroscopy: Application to Microsolvated Biomolecules. J Chem Theory Comput 2020; 16:7005-7016. [PMID: 32991804 DOI: 10.1021/acs.jctc.0c00725] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A dual electronic basis set approach is introduced for more efficient but accurate calculations of the anharmonic vibrational spectra in the framework of the vibrational self-consistent field (VSCF) theory. In this approach, an accurate basis set is used to compute the vibrational spectra at the harmonic level. The results are used to scale the potential surface from a more modest but much more efficient basis set. The scaling is such that at the harmonic level the new, scaled potential agrees with one of the accurate basis sets. The approach is tested in the application of the microsolvated, protected amino acid Ac-Phe-OMe, using the scaled anharmonic hybrid potential in the VSCF and VSCF-PT2 algorithms. The hybrid potential method yields results that are in good accord with the experiment and very close to those obtained in calculations with the high-level, very costly potential from the large basis set. At the same time, the hybrid potential calculations are considerably less expensive. The results of the hybrid calculations are much more accurate than those computed from the potential surface corresponding to the modest basis set. The results are very encouraging for using the hybrid potential method for inexpensive yet sufficiently accurate anharmonic calculations for the spectra of large biomolecules.
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Affiliation(s)
- Tapta Kanchan Roy
- Department of Chemistry and Chemical Sciences, Central University of Jammu, Rahya-Suchani (Bagla), Dist: Samba Jammu-181143, India
| | - R Benny Gerber
- Institute of Chemistry, The Hebrew University, Jerusalem 91904, Israel.,Department of Chemistry, University of California, Irvine, California 92697, United States
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29
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Mitra H, Roy TK. Comprehensive Benchmark Results for the Accuracy of Basis Sets for Anharmonic Molecular Vibrations. J Phys Chem A 2020; 124:9203-9221. [DOI: 10.1021/acs.jpca.0c06634] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Hrishit Mitra
- Department of Chemistry and Chemical Sciences, Central University of Jammu, Rahya-Suchani (Bagla), Jammu, Jammu and Kashmir 181143, India
| | - Tapta Kanchan Roy
- Department of Chemistry and Chemical Sciences, Central University of Jammu, Rahya-Suchani (Bagla), Jammu, Jammu and Kashmir 181143, India
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30
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Schmitz G, Klinting EL, Christiansen O. A Gaussian process regression adaptive density guided approach for potential energy surface construction. J Chem Phys 2020; 153:064105. [DOI: 10.1063/5.0015344] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Gunnar Schmitz
- Department of Chemistry, Aarhus Universitet, DK-8000 Aarhus, Denmark
| | | | - Ove Christiansen
- Department of Chemistry, Aarhus Universitet, DK-8000 Aarhus, Denmark
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31
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Ollitrault PJ, Baiardi A, Reiher M, Tavernelli I. Hardware efficient quantum algorithms for vibrational structure calculations. Chem Sci 2020; 11:6842-6855. [PMID: 32874524 PMCID: PMC7448527 DOI: 10.1039/d0sc01908a] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2020] [Accepted: 06/02/2020] [Indexed: 11/21/2022] Open
Abstract
We introduce a framework for the calculation of ground and excited state energies of bosonic systems suitable for near-term quantum devices and apply it to molecular vibrational anharmonic Hamiltonians. Our method supports generic reference modal bases and Hamiltonian representations, including the ones that are routinely used in classical vibrational structure calculations. We test different parametrizations of the vibrational wavefunction, which can be encoded in quantum hardware, based either on heuristic circuits or on the bosonic Unitary Coupled Cluster Ansatz. In particular, we define a novel compact heuristic circuit and demonstrate that it provides a good compromise in terms of circuit depth, optimization costs, and accuracy. We evaluate the requirements, number of qubits and circuit depth, for the calculation of vibrational energies on quantum hardware and compare them with state-of-the-art classical vibrational structure algorithms for molecules with up to seven atoms.
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Affiliation(s)
- Pauline J Ollitrault
- IBM Quantum , IBM Research - Zurich , Säumerstrasse 4 , 8803 Rüschlikon , Switzerland .
- Laboratory of Physical Chemistry , ETH Zürich , Vladimir-Prelog-Weg 2 , 8093 Zürich , Switzerland .
| | - Alberto Baiardi
- Laboratory of Physical Chemistry , ETH Zürich , Vladimir-Prelog-Weg 2 , 8093 Zürich , Switzerland .
| | - Markus Reiher
- Laboratory of Physical Chemistry , ETH Zürich , Vladimir-Prelog-Weg 2 , 8093 Zürich , Switzerland .
| | - Ivano Tavernelli
- IBM Quantum , IBM Research - Zurich , Säumerstrasse 4 , 8803 Rüschlikon , Switzerland .
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33
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Baiardi A, Reiher M. The density matrix renormalization group in chemistry and molecular physics: Recent developments and new challenges. J Chem Phys 2020; 152:040903. [DOI: 10.1063/1.5129672] [Citation(s) in RCA: 85] [Impact Index Per Article: 21.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
Affiliation(s)
- Alberto Baiardi
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Markus Reiher
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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34
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Lesko E, Ardiansyah M, Brorsen KR. Vibrational adaptive sampling configuration interaction. J Chem Phys 2019; 151:164103. [DOI: 10.1063/1.5126510] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ethan Lesko
- Department of Chemistry, University of Missouri, Columbia, Missouri 65203, USA
| | - Muhammad Ardiansyah
- Department of Chemistry, University of Missouri, Columbia, Missouri 65203, USA
| | - Kurt R. Brorsen
- Department of Chemistry, University of Missouri, Columbia, Missouri 65203, USA
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35
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Puzzarini C, Bloino J, Tasinato N, Barone V. Accuracy and Interpretability: The Devil and the Holy Grail. New Routes across Old Boundaries in Computational Spectroscopy. Chem Rev 2019; 119:8131-8191. [DOI: 10.1021/acs.chemrev.9b00007] [Citation(s) in RCA: 114] [Impact Index Per Article: 22.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Affiliation(s)
- Cristina Puzzarini
- Dipartimento di Chimica “Giacomo Ciamician”, Università di Bologna, Via F. Selmi 2, I-40126 Bologna, Italy
| | - Julien Bloino
- Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy
| | - Nicola Tasinato
- 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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36
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Wang S. Efficiently Calculating Anharmonic Frequencies of Molecular Vibration by Molecular Dynamics Trajectory Analysis. ACS OMEGA 2019; 4:9271-9283. [PMID: 31460016 PMCID: PMC6648323 DOI: 10.1021/acsomega.8b03364] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2018] [Accepted: 05/13/2019] [Indexed: 05/28/2023]
Abstract
Two efficient methods, the Eckart frame algorithm and the multiorder derivative algorithm, for vibrational frequency calculation directly based on the raw data of atomic trajectory from the state-of-the-art first-principles molecular dynamics simulation are presented. The Eckart frame approach is robust to retrieve the full set of anharmonic fundamental frequencies of any molecule from the atomic trajectory for a sufficiently long molecular dynamics simulation at a temperature close to 0 K. In addition to the fundamental vibrational frequencies, the multiorder derivative approach is universal for the calculations of vibrational frequencies based on the molecular dynamics result in a wide range of temperatures. The accuracy, efficiency, and applicability of these two methods are demonstrated through several successful examples in calculating the anharmonic fundamental vibrational frequencies of methane, ethylene, water, and cyclobutadiene.
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37
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Erba A, Maul J, Ferrabone M, Carbonnière P, Rérat M, Dovesi R. Anharmonic Vibrational States of Solids from DFT Calculations. Part I: Description of the Potential Energy Surface. J Chem Theory Comput 2019; 15:3755-3765. [DOI: 10.1021/acs.jctc.9b00293] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Alessandro Erba
- Dipartimento di Chimica, Universitá di Torino, via Giuria 5, 10125 Torino, Italy
| | - Jefferson Maul
- Dipartimento di Chimica, Universitá di Torino, via Giuria 5, 10125 Torino, Italy
| | - Matteo Ferrabone
- Dipartimento di Chimica, Universitá di Torino, via Giuria 5, 10125 Torino, Italy
| | - Philippe Carbonnière
- IPREM, Université de Pau et des Pays de l’Adour, IPREM-CAPT UMR CNRS 5254, Hélioparc Pau Pyrénées, 2 avenue du Président Angot, 64053 PAU CEDEX 9, Pau, France
| | - Michel Rérat
- IPREM, Université de Pau et des Pays de l’Adour, IPREM-CAPT UMR CNRS 5254, Hélioparc Pau Pyrénées, 2 avenue du Président Angot, 64053 PAU CEDEX 9, Pau, France
| | - Roberto Dovesi
- Dipartimento di Chimica, Universitá di Torino, via Giuria 5, 10125 Torino, Italy
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38
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Erba A, Maul J, Ferrabone M, Dovesi R, Rérat M, Carbonnière P. Anharmonic Vibrational States of Solids from DFT Calculations. Part II: Implementation of the VSCF and VCI Methods. J Chem Theory Comput 2019; 15:3766-3777. [DOI: 10.1021/acs.jctc.9b00294] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Alessandro Erba
- Dipartimento di Chimica, Universitá di Torino, via Giuria 5, 10125 Torino, Italy
| | - Jefferson Maul
- Dipartimento di Chimica, Universitá di Torino, via Giuria 5, 10125 Torino, Italy
| | - Matteo Ferrabone
- Dipartimento di Chimica, Universitá di Torino, via Giuria 5, 10125 Torino, Italy
| | - Roberto Dovesi
- Dipartimento di Chimica, Universitá di Torino, via Giuria 5, 10125 Torino, Italy
| | - Michel Rérat
- IPREM, Université de Pau et des Pays de l’Adour, IPREM-CAPT UMR CNRS 5254, Hélioparc Pau Pyrénées, 2 avenue du Président Angot, 64053 PAU CEDEX 9, Pau, France
| | - Philippe Carbonnière
- IPREM, Université de Pau et des Pays de l’Adour, IPREM-CAPT UMR CNRS 5254, Hélioparc Pau Pyrénées, 2 avenue du Président Angot, 64053 PAU CEDEX 9, Pau, France
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39
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Maystrovsky S, Keçeli M, Sode O. Understanding the anharmonic vibrational structure of the carbon dioxide dimer. J Chem Phys 2019; 150:144302. [PMID: 30981225 DOI: 10.1063/1.5089460] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
Understanding the vibrational structure of the CO2 system is important to confirm the potential energy surface and interactions in such van der Waals complexes. In this work, we use our previously developed mbCO2 potential function to explore the vibrational structure of the CO2 monomer and dimer. The potential function has been trained to reproduce the potential energies at the CCSD(T)-F12b/aug-cc-pVTZ level of electronic structure theory. The harmonic approximation, as well as anharmonic corrections using vibrational structure theories such as vibrational self-consistent field, vibrational second-order Møller-Plesset perturbation, and vibrational configuration interaction (VCI), is applied to address the vibrational motions. We compare the vibrational results using the mbCO2 potential function with traditional electronic structure theory results and to experimental frequencies. The anharmonic results for the monomer most closely match the experimental data to within 3 cm-1, including the Fermi dyad frequencies. The intermolecular and intramolecular dimer frequencies were treated separately and show good agreement with the most recent theoretical and experimental results from the literature. The VCI treatment of the dimer vibrational motions accounts for vibrational mixing and delocalization, such that we observe the dimer Fermi resonance phenomena, both in the intramolecular and intermolecular regions.
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Affiliation(s)
- Samuel Maystrovsky
- Department of Chemistry, Biochemistry and Physics, The University of Tampa, 401 West Kennedy Boulevard, Tampa, Florida 33606, USA
| | - Murat Keçeli
- Computational Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
| | - Olaseni Sode
- Department of Chemistry, Biochemistry and Physics, The University of Tampa, 401 West Kennedy Boulevard, Tampa, Florida 33606, USA
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40
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Krasnoshchekov SV, Chang X. Ladder operators for Morse oscillator and a perturbed vibrational problem. INT REV PHYS CHEM 2019. [DOI: 10.1080/0144235x.2019.1593583] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
| | - Xuanhao Chang
- School of Nuclear Science and Engineering, Tomsk Polytechnic University, Tomsk, Russia
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41
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Kuenzer U, Hofer TS. A four-dimensional Numerov approach and its application to the vibrational eigenstates of linear triatomic molecules – The interplay between anharmonicity and inter-mode coupling. Chem Phys 2019. [DOI: 10.1016/j.chemphys.2019.01.007] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
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42
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Baiardi A, Stein CJ, Barone V, Reiher M. Optimization of highly excited matrix product states with an application to vibrational spectroscopy. J Chem Phys 2019; 150:094113. [DOI: 10.1063/1.5068747] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Alberto Baiardi
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Christopher J. Stein
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Vincenzo Barone
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - Markus Reiher
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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43
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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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44
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Kuenzer U, Klotz M, Hofer TS. Probing vibrational coupling via a grid-based quantum approach-an efficient strategy for accurate calculations of localized normal modes in solid-state systems. J Comput Chem 2018; 39:2196-2209. [PMID: 30341952 PMCID: PMC6767160 DOI: 10.1002/jcc.25533] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2018] [Revised: 06/08/2018] [Accepted: 06/29/2018] [Indexed: 11/19/2022]
Abstract
In this work an approach to investigate the properties of strongly localized vibrational modes of functional groups in bulk material and on solid-state surfaces is presented. The associated normal mode vectors are approximated solely on the basis of structural information and obtained via diagonalization of a reduced Hessian. The grid-based Numerov procedure in one and two dimensions is then applied to an adequate scan of the respective potential surface yielding the associated vibrational wave functions and energy eigenvalues. This not only provides a detailed description of anharmonic effects but also an accurate inclusion of the coupling between the investigated vibrational states on a quantum mechanical level. All results obtained for the constructed normal modes are benchmarked against their analytical counterparts obtained from the diagonalization of the total Hessian of the entire system. Three increasingly complex systems treated at quantum chemical level of theory have been considered, namely the symmetric and asymmetric stretch vibrations of an isolated water molecule, hydroxyl groups bound to the surface of GeO2 (001), α-quartz(001) and Rutil (001) as well as crystalline Li2 NH serving as an example for a bulk material. While the data obtained for the individual systems verify the applicability of the proposed methodology, comparison to experimental data demonstrates the accuracy of this methodology despite the restriction to limit this methodology to a few selected vibrational modes. The possibility to investigate vibrational phenomena of localized normal modes without the requirement of executing costly harmonic frequency calculations of the entire system enables the application of this method to cases in which the determination of normal modes is prohibitively expensive or not available for a particular level of theory. © 2018 Wiley Periodicals, Inc.
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Affiliation(s)
- Ulrich Kuenzer
- University of Innsbruck, Institute of General, Inorganic and Theoretical Chemistry, Innrain 80‐826020 InnsbruckAustria
| | - Martin Klotz
- University of Innsbruck, Institute of General, Inorganic and Theoretical Chemistry, Innrain 80‐826020 InnsbruckAustria
| | - Thomas S. Hofer
- University of Innsbruck, Institute of General, Inorganic and Theoretical Chemistry, Innrain 80‐826020 InnsbruckAustria
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45
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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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46
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Bulik IW, Frisch MJ, Vaccaro PH. Vibrational self-consistent field theory using optimized curvilinear coordinates. J Chem Phys 2017; 147:044110. [DOI: 10.1063/1.4995440] [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)
- Ireneusz W. Bulik
- Department of Chemistry, Yale University, New Haven, Connecticut 06511, USA
| | - Michael J. Frisch
- Gaussian, Inc., 340 Quinnipiac St. Bldg. 40, Wallingford, Connecticut 06492, USA
| | - Patrick H. Vaccaro
- Department of Chemistry, Yale University, New Haven, Connecticut 06511, USA
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47
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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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48
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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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49
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Yagi K, Thomsen B. Infrared Spectra of Protonated Water Clusters, H+(H2O)4, in Eigen and Zundel Forms Studied by Vibrational Quasi-Degenerate Perturbation Theory. J Phys Chem A 2017; 121:2386-2398. [DOI: 10.1021/acs.jpca.6b11189] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Affiliation(s)
- Kiyoshi Yagi
- Theoretical
Molecular Science Laboratory and ‡iTHES, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - Bo Thomsen
- Theoretical
Molecular Science Laboratory and ‡iTHES, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
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50
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Changala PB, Baraban JH. Ab initio effective rotational and rovibrational Hamiltonians for non-rigid systems via curvilinear second order vibrational Møller–Plesset perturbation theory. J Chem Phys 2016; 145:174106. [DOI: 10.1063/1.4966234] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- P. Bryan Changala
- JILA, National Institute of Standards and Technology and University of Colorado, Boulder, Colorado 80309, USA and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Joshua H. Baraban
- Department of Chemistry, University of Colorado, Boulder, Colorado 80309, USA
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