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Lang H, Sato T. Time-dependent orbital-optimized coupled-cluster methods families for fermion-mixtures dynamics. J Chem Phys 2024; 161:114114. [PMID: 39291685 DOI: 10.1063/5.0227236] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2024] [Accepted: 09/03/2024] [Indexed: 09/19/2024] Open
Abstract
Five time-dependent orbital optimized coupled-cluster methods, of which four can converge to the time-dependent complete active space self-consistent-field method, are presented for fermion-mixtures with arbitrary fermion kinds and numbers. Truncation schemes maintaining the intragroup orbital rotation invariance, as well as equations of motion of coupled-cluster (CC) amplitudes and orbitals, are derived. Present methods are compact CC-parameterization alternatives to the time-dependent multiconfiguration self-consistent-field method for systems consisting of arbitrarily different kinds and numbers of interacting fermions. Theoretical analysis of applications of present methods to various chemical systems is reported.
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Affiliation(s)
- Haifeng Lang
- Department of Nuclear Engineering and Management, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Takeshi Sato
- Department of Nuclear Engineering and Management, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
- Photon Science Center, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
- Research Institute for Photon Science and Laser Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
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2
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Sardar S. An Exhaustive Quantum-Classical Study of C 6F 6+ Using the Newly Formulated Parallel TDDVR Method. J Phys Chem A 2024; 128:5777-5795. [PMID: 38979982 DOI: 10.1021/acs.jpca.4c02108] [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
We recently implemented our parallelized quantum-classical dynamical approach, known as the Time-Dependent Discrete Variable Representation (TDDVR) method, which is applied to the spectroscopically important hexafluorobenzene (HFBz) radical cation, where several conical intersections exist in their seven lowest excited electronic states (S11B2u, S21E1g, S31B1u, S41E1u, and S51A2u) considering degeneracy among potential energy surfaces (PESs), to demonstrate their various dynamical aspects. This new parallel version shows almost linear scalability with increasing number of computing processors. To get photoelectron (PE) spectra, Mass-Analyzed Threshold Ionization (MATI) spectra, population dynamics, and many other dynamical observables, the first-principles dynamics is applied at the state-of-the-art level to the corresponding Hamiltonian, where the Jahn-Teller (JT) and pseudo-Jahn-Teller (PJT) type interactions are involved in those coupled seven electronic states. The quantum-classical method is used to thoroughly analyze the effects of these couplings on the nuclear dynamics of the involved electronic states, and the findings are compared with those observables obtained from experiments. Intrinsic dynamical properties are explained using the reduced densities of the wave packet (WP) in a coupled electronic manifold. The PE and MATI spectra of HFBz computed using TDDVR are found to be in good agreement with earlier experimental data and other theoretically simulated spectra.
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Affiliation(s)
- Subhankar Sardar
- Department of Chemistry, Bhatter College, Dantan, P.O. Dantan, Paschim Medinipur, Pin 721426, India
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3
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Høyer NM, Christiansen O. Quasi-direct Quantum Molecular Dynamics: The Time-Dependent Adaptive Density-Guided Approach for Potential Energy Surface Construction. J Chem Theory Comput 2024; 20:558-579. [PMID: 38183272 DOI: 10.1021/acs.jctc.3c00962] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2024]
Abstract
We present a new quasi-direct quantum molecular dynamics computational method which offers a compromise between quantum dynamics using a precomputed potential energy surface (PES) and fully direct quantum dynamics. This method is termed the time-dependent adaptive density-guided approach (TD-ADGA) and is a method for constructing a PES on the fly during a dynamics simulation. This is achieved by acquisition of new single-point (SP) calculations and refitting of the PES, depending on the need of the dynamics. The TD-ADGA is a further development of the adaptive density-guided approach (ADGA) for PES construction where the placement of SPs is guided by the density of the nuclear wave function. In TD-ADGA, the ADGA framework has been integrated into the time propagation of the time-dependent nuclear wave function and we use the reduced one-mode density of this wave function to guide when and where new SPs are placed. The PES is thus extended or updated if the wave function moves into new areas or if a certain area becomes more important. Here, we derive equations for the reduced one-mode density for the time-dependent Hartree (TDH) method and for multiconfiguration time-dependent Hartree (MCTDH) methods, but the TD-ADGA can be used with any time-dependent wave function method as long as a density is available. The TD-ADGA method has been investigated on molecular systems containing single- and double-minimum potentials and on single-mode and multi-mode systems. We explore different approaches to handle the fact that the TD-ADGA involves a PES that changes during the computation and show how results can be obtained that are in very good agreement with results obtained by using an accurate reference PES. Dynamics with TD-ADGA is essentially a black box procedure, where only the initialization of the system and how to compute SPs must be provided. The TD-ADGA thus makes it easier to carry out quantum molecular dynamics and the quasi-direct framework opens up the possibility to compute quantum dynamics accurately for larger molecular systems.
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Affiliation(s)
| | - Ove Christiansen
- Department of Chemistry, Aarhus University, DK-8000 Aarhus C, Denmark
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Jensen AB, Højlund MG, Zoccante A, Madsen NK, Christiansen O. Efficient time-dependent vibrational coupled cluster computations with time-dependent basis sets at the two-mode coupling level: Full and hybrid TDMVCC[2]. J Chem Phys 2023; 159:204106. [PMID: 38010335 DOI: 10.1063/5.0175506] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2023] [Accepted: 11/05/2023] [Indexed: 11/29/2023] Open
Abstract
The computation of the nuclear quantum dynamics of molecules is challenging, requiring both accuracy and efficiency to be applicable to systems of interest. Recently, theories have been developed for employing time-dependent basis functions (denoted modals) with vibrational coupled cluster theory (TDMVCC). The TDMVCC method was introduced along with a pilot implementation, which illustrated good accuracy in benchmark computations. In this paper, we report an efficient implementation of TDMVCC, covering the case where the wave function and Hamiltonian contain up to two-mode couplings. After a careful regrouping of terms, the wave function can be propagated with a cubic computational scaling with respect to the number of degrees of freedom. We discuss the use of a restricted set of active one-mode basis functions for each mode, as well as two interesting limits: (i) the use of a full active basis where the variational modal determination amounts essentially to the variational determination of a time-dependent reference state for the cluster expansion; and (ii) the use of a single function as an active basis for some degrees of freedom. The latter case defines a hybrid TDMVCC/TDH (time-dependent Hartree) approach that can obtain even lower computational scaling. The resulting computational scaling for hybrid and full TDMVCC[2] is illustrated for polyaromatic hydrocarbons with up to 264 modes. Finally, computations on the internal vibrational redistribution of benzoic acid (39 modes) are used to show the faster convergence of TDMVCC/TDH hybrid computations towards TDMVCC compared to simple neglect of some degrees of freedom.
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Affiliation(s)
| | - Mads Greisen Højlund
- Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark
| | - Alberto Zoccante
- Dipartimento di Scienze e Innovazione Tecnologica, Università del Piemonte Orientale (UPO), Via T. Michel 11, 15100 Alessandria, Italy
| | - Niels Kristian Madsen
- Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark
| | - Ove Christiansen
- Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark
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5
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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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Wang C, Ulusoy IS, Aebersold LE, Wilson AK. Multi-configuration electron-nuclear dynamics: An open-shell approach. J Chem Phys 2021; 155:154103. [PMID: 34686063 DOI: 10.1063/5.0063478] [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
The multi-configuration electron-nuclear dynamics for open shell systems with a spin-unrestricted formalism is described. The mean fields are evaluated using second-order reduced density matrices for electronic and nuclear degrees of freedom. Applications to light-element diatomics including equilibrium geometries, electronic energies, dipole moments, and absorption spectra are presented. The von Neumann entropies for different spin states of a LiH molecule are compared.
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Affiliation(s)
- Cong Wang
- Department of Chemistry, Michigan State University, 578 S Shaw Lane, East Lansing, Michigan 48824-1322, USA
| | - Inga S Ulusoy
- Department of Chemistry, Michigan State University, 578 S Shaw Lane, East Lansing, Michigan 48824-1322, USA
| | - Lucas E Aebersold
- Department of Chemistry, Michigan State University, 578 S Shaw Lane, East Lansing, Michigan 48824-1322, USA
| | - Angela K Wilson
- Department of Chemistry, Michigan State University, 578 S Shaw Lane, East Lansing, Michigan 48824-1322, USA
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Simmons J, Carrington Jr. T. Using collocation and solutions for a sum-of-product potential to compute vibrational energy levels for general potentials. Chem Phys Lett 2021. [DOI: 10.1016/j.cplett.2021.138967] [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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8
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Madsen NK, Jensen RB, Christiansen O. Calculating vibrational excitation energies using tensor-decomposed vibrational coupled-cluster response theory. J Chem Phys 2021; 154:054113. [DOI: 10.1063/5.0037240] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Affiliation(s)
- Niels Kristian Madsen
- Department of Chemistry, University of Aarhus, Langelandsgade 140, DK–8000 Aarhus C, Denmark
| | - Rasmus Berg Jensen
- Department of Chemistry, University of Aarhus, Langelandsgade 140, DK–8000 Aarhus C, Denmark
| | - Ove Christiansen
- Department of Chemistry, University of Aarhus, Langelandsgade 140, DK–8000 Aarhus C, Denmark
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9
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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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10
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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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11
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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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12
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Hansen MB, Madsen NK, Christiansen O. Extended vibrational coupled cluster: Stationary states and dynamics. J Chem Phys 2020; 153:044133. [DOI: 10.1063/5.0015413] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Mads Bøttger Hansen
- Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark
| | - Niels Kristian Madsen
- Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark
| | - Ove Christiansen
- Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark
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13
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Madsen NK, Hansen MB, Worth GA, Christiansen O. MR-MCTDH[n]: Flexible Configuration Spaces and Nonadiabatic Dynamics within the MCTDH[n] Framework. J Chem Theory Comput 2020; 16:4087-4097. [DOI: 10.1021/acs.jctc.0c00379] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Affiliation(s)
- Niels Kristian Madsen
- Department of Chemistry, University of Aarhus, Langelandsgade 140, DK−8000 Aarhus C, Denmark
| | - Mads Bøttger Hansen
- Department of Chemistry, University of Aarhus, Langelandsgade 140, DK−8000 Aarhus C, Denmark
| | - Graham A. Worth
- Department of Chemistry, University College London, 20, Gordon St., WC1H 0AJ London, United Kingdom
| | - Ove Christiansen
- Department of Chemistry, University of Aarhus, Langelandsgade 140, DK−8000 Aarhus C, Denmark
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