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Højlund MG, Zoccante A, Christiansen O. Time-dependent coupled cluster with orthogonal adaptive basis functions: General formalism and application to the vibrational problem. J Chem Phys 2024; 160:024105. [PMID: 38189608 DOI: 10.1063/5.0186000] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2023] [Accepted: 12/15/2023] [Indexed: 01/09/2024] Open
Abstract
We derive equations of motion for bivariational wave functions with orthogonal adaptive basis sets and specialize the formalism to the coupled cluster Ansatz. The equations are related to the biorthogonal case in a transparent way, and similarities and differences are analyzed. We show that the amplitude equations are identical in the orthogonal and biorthogonal formalisms, while the linear equations that determine the basis set time evolution differ by symmetrization. Applying the orthogonal framework to the nuclear dynamics problem, we introduce and implement the orthogonal time-dependent modal vibrational coupled cluster (oTDMVCC) method and benchmark it against exact reference results for four triatomic molecules as well as a reduced-dimensional (5D) trans-bithiophene model. We confirm numerically that the biorthogonal TDMVCC hierarchy converges to the exact solution, while oTDMVCC does not. The differences between TDMVCC and oTDMVCC are found to be small for three of the five cases, but we also identify one case where the formal deficiency of the oTDMVCC approach results in clear and visible errors relative to the exact result. For the remaining example, oTDMVCC exhibits rather modest but visible errors.
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Affiliation(s)
- Mads Greisen Højlund
- Department of Chemistry, Aarhus University, Langelandsgade 140, 8000 Aarhus C, Denmark
| | - Alberto Zoccante
- Dipartimento di Scienze e Innovazione Tecnologica, Università del Piemonte Orientale (UPO), Via T. Michel 11, 15100 Alessandria, Italy
| | - Ove Christiansen
- Department of Chemistry, Aarhus University, Langelandsgade 140, 8000 Aarhus C, Denmark
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Højlund MG, Jensen AB, Zoccante A, Christiansen O. Bivariational time-dependent wave functions with biorthogonal adaptive basis sets: General formulation and regularization of equations of motion through polar decomposition. J Chem Phys 2022; 157:234104. [PMID: 36550053 DOI: 10.1063/5.0127431] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022] Open
Abstract
We derive general bivariational equations of motion (EOMs) for time-dependent wave functions with biorthogonal time-dependent basis sets. The time-dependent basis functions are linearly parameterized and their fully variational time evolution is ensured by solving a set of so-called constraint equations, which we derive for arbitrary wave function expansions. The formalism allows division of the basis set into an active basis and a secondary basis, ensuring a flexible and compact wave function. We show how the EOMs specialize to a few common wave function forms, including coupled cluster and linearly expanded wave functions. It is demonstrated, for the first time, that the propagation of such wave functions is not unconditionally stable when a secondary basis is employed. The main signature of the instability is a strong increase in non-orthogonality, which eventually causes the calculation to fail; specifically, the biorthogonal active bra and ket bases tend toward spanning different spaces. Although formally allowed, this causes severe numerical issues. We identify the source of this problem by reparametrizing the time-dependent basis set through polar decomposition. Subsequent analysis allows us to remove the instability by setting appropriate matrix elements to zero. Although this solution is not fully variational, we find essentially no deviation in terms of autocorrelation functions relative to the variational formulation. We expect that the results presented here will be useful for the formal analysis of bivariational time-dependent wave functions for electronic and nuclear dynamics in general and for the practical implementation of time-dependent CC wave functions in particular.
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Affiliation(s)
- Mads Greisen Højlund
- Department of Chemistry, University of Aarhus, Langelandsgade 140, DK-8000 Aarhus C, Denmark
| | | | - Alberto Zoccante
- Dipartimento di Scienze e Innovazione Tecnologica, Universitá del Piemonte Orientale (UPO), Via T. Michel 11, 15100 Alessandria, Italy
| | - Ove Christiansen
- Department of Chemistry, University of Aarhus, Langelandsgade 140, DK-8000 Aarhus C, Denmark
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Ozaki Y, Beć KB, Morisawa Y, Yamamoto S, Tanabe I, Huck CW, Hofer TS. Advances, challenges and perspectives of quantum chemical approaches in molecular spectroscopy of the condensed phase. Chem Soc Rev 2021; 50:10917-10954. [PMID: 34382961 DOI: 10.1039/d0cs01602k] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The purpose of this review is to demonstrate advances, challenges and perspectives of quantum chemical approaches in molecular spectroscopy of the condensed phase. Molecular spectroscopy, particularly vibrational spectroscopy and electronic spectroscopy, has been used extensively for a wide range of areas of chemical sciences and materials science as well as nano- and biosciences because it provides valuable information about structure, functions, and reactions of molecules. In the meantime, quantum chemical approaches play crucial roles in the spectral analysis. They also yield important knowledge about molecular and electronic structures as well as electronic transitions. The combination of spectroscopic approaches and quantum chemical calculations is a powerful tool for science, in general. Thus, our article, which treats various spectroscopy and quantum chemical approaches, should have strong implications in the wider scientific community. This review covers a wide area of molecular spectroscopy from far-ultraviolet (FUV, 120-200 nm) to far-infrared (FIR, 400-10 cm-1)/terahertz and Raman spectroscopy. As quantum chemical approaches, we introduce several anharmonic approaches such as vibrational self-consistent field (VSCF) and the combination of periodic harmonic calculations with anharmonic corrections based on finite models, grid-based techniques like the Numerov approach, the Cartesian coordinate tensor transfer (CCT) method, Symmetry-Adapted Cluster Configuration-Interaction (SAC-CI), and the ZINDO (Semi-empirical calculations at Zerner's Intermediate Neglect of Differential Overlap). One can use anharmonic approaches and grid-based approaches for both infrared (IR) and near-infrared (NIR) spectroscopy, while CCT methods are employed for Raman, Raman optical activity (ROA), FIR/terahertz and low-frequency Raman spectroscopy. Therefore, this review overviews cross relations between molecular spectroscopy and quantum chemical approaches, and provides various kinds of close-reality advanced spectral simulation for condensed phases.
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Affiliation(s)
- Yukihiro Ozaki
- School of Biological and Environmental Sciences, Kwansei Gakuin University, Sanda, Hyogo 669-1337, Japan. and Toyota Physical and Chemical Research Institute, Yokomichi, Nagakute, Aichi 480-1192, Japan
| | - Krzysztof B Beć
- Institute of Analytical Chemistry and Radiochemistry, University of Innsbruck, Innrain 80/82, 6020 Innsbruck, Austria
| | - Yusuke Morisawa
- Department of Chemistry, School of Science and Engineering, Kindai University, Kowakae, Higashi-Osaka, Osaka 577-8502, Japan
| | - Shigeki Yamamoto
- Department of Chemistry, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Ichiro Tanabe
- Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Christian W Huck
- Institute of Analytical Chemistry and Radiochemistry, University of Innsbruck, Innrain 80/82, 6020 Innsbruck, Austria
| | - Thomas S Hofer
- Institute of General, Inorganic and Theoretical Chemistry, University of Innsbruck, Innrain 80-82, A6020 Innsbruck, Austria
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Beć KB, Grabska J, Huck CW. Current and future research directions in computer-aided near-infrared spectroscopy: A perspective. SPECTROCHIMICA ACTA. PART A, MOLECULAR AND BIOMOLECULAR SPECTROSCOPY 2021; 254:119625. [PMID: 33706116 DOI: 10.1016/j.saa.2021.119625] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2020] [Revised: 02/09/2021] [Accepted: 02/09/2021] [Indexed: 06/12/2023]
Abstract
The present review aims to draw a perspective on the vibrational spectroscopy combined with the tools of computational chemistry. This includes an overview of the accomplishments made so far, the assessment of the present development trends and the prospects for continuing these advances. State-of-the-art methods, current challenges and the expected future advances are evaluated from the point-of-view of the practical application in vibrational spectroscopy. A special attention is given to near-infrared (NIR) spectroscopy, which occupies a distinct position among the techniques of vibrational spectroscopy. As the result of intrinsically complex spectra, reliance on the anharmonicity as well as keen interest given to complex materials, NIR spectroscopy may particularly benefit from computational chemistry. The present key limitations hindering development of NIR spectroscopy are identified; these constitute primarily the limit in the treatable system size and the inability to effectively include chemical matrix effects. Given the expanding role of NIR spectroscopy in science and industry, lifting these limitations would directly enhance the general potential of this technique.
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Affiliation(s)
- Krzysztof B Beć
- Institute of Analytical Chemistry and Radiochemistry, Leopold-Franzens University, CCB-Center for Chemistry and Biomedicine, Innrain 80/82, 6020 Innsbruck, Austria
| | - Justyna Grabska
- Institute of Analytical Chemistry and Radiochemistry, Leopold-Franzens University, CCB-Center for Chemistry and Biomedicine, Innrain 80/82, 6020 Innsbruck, Austria.
| | - Christian W Huck
- Institute of Analytical Chemistry and Radiochemistry, Leopold-Franzens University, CCB-Center for Chemistry and Biomedicine, Innrain 80/82, 6020 Innsbruck, Austria
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Pedersen TB, Kristiansen HE, Bodenstein T, Kvaal S, Schøyen ØS. Interpretation of Coupled-Cluster Many-Electron Dynamics in Terms of Stationary States. J Chem Theory Comput 2021; 17:388-404. [PMID: 33337895 PMCID: PMC7808707 DOI: 10.1021/acs.jctc.0c00977] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2020] [Indexed: 01/06/2023]
Abstract
We demonstrate theoretically and numerically that laser-driven many-electron dynamics, as described by bivariational time-dependent coupled-cluster (CC) theory, may be analyzed in terms of stationary-state populations. Projectors heuristically defined from linear response theory and equation-of-motion CC theory are proposed for the calculation of stationary-state populations during interaction with laser pulses or other external forces, and conservation laws of the populations are discussed. Numerical tests of the proposed projectors, involving both linear and nonlinear optical processes for He and Be atoms and for LiH, CH+, and LiF molecules show that the laser-driven evolution of the stationary-state populations at the coupled-cluster singles-and-doubles (CCSD) level is very close to that obtained by full configuration interaction (FCI) theory, provided that all stationary states actively participating in the dynamics are sufficiently well approximated. When double-excited states are important for the dynamics, the quality of the CCSD results deteriorates. Observing that populations computed from the linear response projector may show spurious small-amplitude, high-frequency oscillations, the equation-of-motion projector emerges as the most promising approach to stationary-state populations.
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Affiliation(s)
- Thomas Bondo Pedersen
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, N-0315 Oslo, Norway
| | - Håkon Emil Kristiansen
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, N-0315 Oslo, Norway
| | - Tilmann Bodenstein
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, N-0315 Oslo, Norway
| | - Simen Kvaal
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, N-0315 Oslo, Norway
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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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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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