1
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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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Woźniak AP, Moszyński R. Modeling of High-Harmonic Generation in the C 60 Fullerene Using Ab Initio, DFT-Based, and Semiempirical Methods. J Phys Chem A 2024; 128:2683-2702. [PMID: 38534023 PMCID: PMC11017253 DOI: 10.1021/acs.jpca.3c07865] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2023] [Revised: 03/04/2024] [Accepted: 03/13/2024] [Indexed: 03/28/2024]
Abstract
We report calculations of the high-harmonic generation spectra of the C60 fullerene molecule carried out by employing a diverse set of real-time time-dependent quantum chemical methods. All methodologies involve expanding the propagated electronic wave function in bases consisting of the ground and singly excited time-independent eigenstates obtained through the solution of the corresponding linear-response equations. We identify the correlation and exchange effect in the spectra by comparing the results from methods relying on the Hartree-Fock reference determinant with those obtained using approaches based on the density functional theory with different exchange-correlation functionals. The effect of the full random-phase approximation treatment of the excited electronic states is also analyzed and compared with the configuration interaction singles and the Tamm-Dancoff approximation. We also showcase the fact that the real-time extension of the semiempirical method INDO/S can be effectively applied for an approximate description of laser-driven dynamics in large systems.
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Affiliation(s)
| | - Robert Moszyński
- Faculty of Chemistry, University
of Warsaw, Pasteura 1, Warsaw 02-093, Poland
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3
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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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4
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Williams-Young DB, Yuwono SH, DePrince III AE, Yang C. Approximate Exponential Integrators for Time-Dependent Equation-of-Motion Coupled Cluster Theory. J Chem Theory Comput 2023; 19:9177-9186. [PMID: 38086060 PMCID: PMC10753770 DOI: 10.1021/acs.jctc.3c00911] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2023] [Revised: 10/09/2023] [Accepted: 10/16/2023] [Indexed: 12/27/2023]
Abstract
With a growing demand for time-domain simulations of correlated many-body systems, the development of efficient and stable integration schemes for the time-dependent Schrödinger equation is of keen interest in modern electronic structure theory. In this work, we present two approaches for the formation of the quantum propagator for time-dependent equation-of-motion coupled cluster theory based on the Chebyshev and Arnoldi expansions of the complex, nonhermitian matrix exponential, respectively. The proposed algorithms are compared with the short-iterative Lanczos method of Cooper et al. [J. Phys. Chem. A 2021 125, 5438-5447], the fourth-order Runge-Kutta method, and exact dynamics for a set of small but challenging test problems. For each of the cases studied, both of the proposed integration schemes demonstrate superior accuracy and efficiency relative to the reference simulations.
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Affiliation(s)
- David B. Williams-Young
- Applied
Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Stephen H. Yuwono
- Department
of Chemistry and Biochemistry, Florida State
University, Tallahassee, Florida 32306, United States
| | - A. Eugene DePrince III
- Department
of Chemistry and Biochemistry, Florida State
University, Tallahassee, Florida 32306, United States
| | - Chao Yang
- Applied
Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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5
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Ofstad BS, Wibowo-Teale M, Kristiansen HE, Aurbakken E, Kitsaras MP, Schøyen ØS, Hauge E, Irons TJP, Kvaal S, Stopkowicz S, Wibowo-Teale AM, Pedersen TB. Magnetic optical rotation from real-time simulations in finite magnetic fields. J Chem Phys 2023; 159:204109. [PMID: 38018753 DOI: 10.1063/5.0171927] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2023] [Accepted: 11/01/2023] [Indexed: 11/30/2023] Open
Abstract
We present a numerical approach to magnetic optical rotation based on real-time time-dependent electronic-structure theory. Not relying on perturbation expansions in the magnetic field strength, the formulation allows us to test the range of validity of the linear relation between the rotation angle per unit path length and the magnetic field strength that was established empirically by Verdet 160 years ago. Results obtained from time-dependent coupled-cluster and time-dependent current density-functional theory are presented for the closed-shell molecules H2, HF, and CO in magnetic fields up to 55 kT at standard temperature and pressure conditions. We find that Verdet's linearity remains valid up to roughly 10-20 kT, above which significant deviations from linearity are observed. Among the three current density-functional approximations tested in this work, the current-dependent Tao-Perdew-Staroverov-Scuseria hybrid functional performs the best in comparison with time-dependent coupled-cluster singles and doubles results for the magnetic optical rotation.
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Affiliation(s)
- Benedicte Sverdrup Ofstad
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
| | - Meilani Wibowo-Teale
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Håkon Emil Kristiansen
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
| | - Einar Aurbakken
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
| | - Marios Petros Kitsaras
- Physical and Theoretical Chemistry, Saarland University, Campus B2.2, 66123 Saarbruecken, Germany
| | | | - Eirill Hauge
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
- Department of Numerical Analysis and Scientific Computing, Simula Research Laboratory, 0164 Oslo, Norway
| | - Tom J P Irons
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Simen Kvaal
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
| | - Stella Stopkowicz
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
- Physical and Theoretical Chemistry, Saarland University, Campus B2.2, 66123 Saarbruecken, Germany
| | - Andrew M Wibowo-Teale
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Thomas Bondo Pedersen
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
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6
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Peyton BG, Stewart ZJ, Weidman JD, Wilson AK. Tailoring light-induced charge transfer and intersystem crossing in FeCO using time-dependent spin-orbit configuration interaction. J Chem Phys 2023; 159:204108. [PMID: 38014783 DOI: 10.1063/5.0173529] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2023] [Accepted: 11/02/2023] [Indexed: 11/29/2023] Open
Abstract
Real-time (RT) electronic structure methods provide a natural framework for describing light-matter interactions in arbitrary time-dependent electromagnetic fields (EMF). Optically induced excited state transitions are of particular interest, which require tuned EMF to drive population transfer to and from the specific state(s) of interest. Intersystem crossing, or spin-flip, may be driven through shaped EMF or laser pulses. These transitions can result in long-lived "spin-trapped" excited states, which are especially useful for materials requiring charge separation or protracted excited state lifetimes. Time-dependent configuration interaction (TDCI) is unique among RT methods in that it may be implemented in a basis of eigenstates, allowing for rapid propagation of the time-dependent Schrödinger equation. The recent spin-orbit TDCI (TD-SOCI) enables a real-time description of spin-flip dynamics in an arbitrary EMF and, therefore, provides an ideal framework for rational pulse design. The present study explores the mechanism of multiple spin-flip pathways for a model transition metal complex, FeCO, using shaped pulses designed to drive controlled intersystem crossing and charge transfer. These results show that extremely tunable excited state dynamics can be achieved by considering the dipole transition matrix elements between the states of interest.
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Affiliation(s)
- Benjamin G Peyton
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
| | - Zachary J Stewart
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
| | - Jared D Weidman
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
| | - Angela K Wilson
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
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7
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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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8
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Peyton BG, Wang Z, Crawford TD. Reduced Scaling Real-Time Coupled Cluster Theory. J Phys Chem A 2023; 127:8486-8499. [PMID: 37782945 DOI: 10.1021/acs.jpca.3c05151] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/04/2023]
Abstract
Real-time coupled cluster (CC) methods have several advantages over their frequency-domain counterparts, namely, response and equation of motion CC theories. Broadband spectra, strong fields, and pulse manipulation allow for the simulation of complex spectroscopies that are unreachable using frequency-domain approaches. Due to the high-order polynomial scaling, the required numerical time propagation of the CC residual expressions is a computationally demanding process. This scaling may be reduced by local correlation schemes, which aim to reduce the size of the (virtual) orbital space by truncation according to user-defined parameters. We present the first application of local correlation to real-time CC. As in previous studies of locally correlated frequency-domain CC, traditional local correlation schemes are of limited utility for field-dependent properties; however, a perturbation-aware scheme proves promising. A detailed analysis of the amplitude dynamics suggests that the main challenge is a strong time dependence of the wave function sparsity.
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Affiliation(s)
- Benjamin G Peyton
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Zhe Wang
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - T Daniel Crawford
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
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9
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Morassut C, Coccia E, Luppi E. Quantitative performance analysis and comparison of optimal-continuum Gaussian basis sets for high-harmonic generation spectra. J Chem Phys 2023; 159:124108. [PMID: 38127378 DOI: 10.1063/5.0153825] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2023] [Accepted: 08/24/2023] [Indexed: 12/23/2023] Open
Abstract
Quantum-chemistry methods in the time domain with Gaussian basis sets are increasingly used to compute high-harmonic generation (HHG) spectra of atomic and molecular systems. The quality of these approaches is limited by the accuracy of Gaussian basis sets to describe continuum energy states. In the literature, optimal-continuum Gaussian basis sets have been proposed: Kaufmann et al. [J. Phys. B: At., Mol. Opt. Phys. 22, 2223 (1989)], Woźniak et al. [J. Chem. Phys. 154, 094111 (2021)], Nestmann and Peyerimhoff [J. Phys. B: At., Mol. Opt. Phys. 23, L773 (1990)], Faure et al. [Comput. Phys. Commun. 144, 224 (2002)], and Krause et al. [J. Chem. Phys. 140, 174113 (2014)]. In this work, we have compared the performances of these basis sets to simulate HHG spectra of H atom at different laser intensities. We have also investigated different strategies to balance basis sets with these continuum functions, together with the role of angular momentum. To quantify the performance of the different basis sets, we introduce local and global HHG descriptors. Comparisons with the grid and exact calculations are also provided.
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Affiliation(s)
- C Morassut
- Laboratoire de Chimie Théorique, Sorbonne Université, CNRS, Paris F-75005, France
- Dipartimento di Scienze Chimiche e Farmaceutiche, Università di Trieste, Via L. Giorgieri 1, 34127 Trieste, Italy
| | - E Coccia
- Dipartimento di Scienze Chimiche e Farmaceutiche, Università di Trieste, Via L. Giorgieri 1, 34127 Trieste, Italy
| | - E Luppi
- Laboratoire de Chimie Théorique, Sorbonne Université, CNRS, Paris F-75005, France
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10
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Luppi E, Coccia E. Role of Inner Molecular Orbitals in High-Harmonic Generation Spectra of Aligned Uracil. J Phys Chem A 2023; 127:7335-7343. [PMID: 37640677 DOI: 10.1021/acs.jpca.3c03990] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/31/2023]
Abstract
In this work, we decompose the high-harmonic generation (HHG) signal of aligned gas-phase uracil into single molecular-orbital (MO) contributions. We compute HHG spectra for a pulse linearly polarized perpendicular to the molecular plane, with an intensity of 0.6 and 0.85 × 1014 W/cm2 and a wavelength of 800 nm. We use the real-time time-dependent Configuration Interaction with singles method, coupled to a Gaussian-based representation of the time-dependent wavefunction. The strong-field dynamics is affected by the energy of the ionization/recombination channels and by the coupling between the orbital symmetry and laser polarization. In the configuration studied here, we expect that π-type MOs favorably couple with the incoming pulse and play a substantial role in generating the HHG spectrum. Indeed, we show that HOMO, HOMO - 1, and HOMO - 4, which all are π-like, determine the intensity of harmonic peaks at different energies, while HOMO - 2 and HOMO - 3 provide a smaller contribution. It is worth mentioning that HOMO - 4 produces a stronger signal than that from HOMO - 1, even though the corresponding ionization energy, in an one-electron picture, is around 2.5 eV larger and more than 4 eV larger than the HOMO one.
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Affiliation(s)
- Eleonora Luppi
- Laboratoire de Chimie Théorique, Sorbonne Université, CNRS, Paris F-75005, France
| | - Emanuele Coccia
- Department of Chemical and Pharmaceutical Sciences, University of Trieste, via L. Giorgieri 1, Trieste 34127, Italy
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11
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Yuwono SH, Cooper BC, Zhang T, Li X, DePrince AE. Time-dependent equation-of-motion coupled-cluster simulations with a defective Hamiltonian. J Chem Phys 2023; 159:044113. [PMID: 37497820 DOI: 10.1063/5.0157852] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2023] [Accepted: 07/11/2023] [Indexed: 07/28/2023] Open
Abstract
Simulations of laser-induced electron dynamics in a molecular system are performed using time-dependent (TD) equation-of-motion (EOM) coupled-cluster (CC) theory. The target system has been chosen to highlight potential shortcomings of truncated TD-EOM-CC methods [represented in this work by TD-EOM-CC with single and double excitations (TD-EOM-CCSD)], where unphysical spectroscopic features can emerge. Specifically, we explore driven resonant electronic excitations in magnesium fluoride in the proximity of an avoided crossing. Near the avoided crossing, the CCSD similarity-transformed Hamiltonian is defective, meaning that it has complex eigenvalues, and oscillator strengths may take on negative values. When an external field is applied to drive transitions to states exhibiting these traits, unphysical dynamics are observed. For example, the stationary states that make up the time-dependent state acquire populations that can be negative, exceed one, or even complex-valued.
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Affiliation(s)
- Stephen H Yuwono
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
| | - Brandon C Cooper
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
| | - Tianyuan Zhang
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | - A Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
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12
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Babbush R, Huggins WJ, Berry DW, Ung SF, Zhao A, Reichman DR, Neven H, Baczewski AD, Lee J. Quantum simulation of exact electron dynamics can be more efficient than classical mean-field methods. Nat Commun 2023; 14:4058. [PMID: 37429883 DOI: 10.1038/s41467-023-39024-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2022] [Accepted: 05/26/2023] [Indexed: 07/12/2023] Open
Abstract
Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree-Fock and density functional theory but offer higher accuracy. Accordingly, quantum computers have been predominantly regarded as competitors to only the most accurate and costly classical methods for treating electron correlation. However, here we tighten bounds showing that certain first-quantized quantum algorithms enable exact time evolution of electronic systems with exponentially less space and polynomially fewer operations in basis set size than conventional real-time time-dependent Hartree-Fock and density functional theory. Although the need to sample observables in the quantum algorithm reduces the speedup, we show that one can estimate all elements of the k-particle reduced density matrix with a number of samples scaling only polylogarithmically in basis set size. We also introduce a more efficient quantum algorithm for first-quantized mean-field state preparation that is likely cheaper than the cost of time evolution. We conclude that quantum speedup is most pronounced for finite-temperature simulations and suggest several practically important electron dynamics problems with potential quantum advantage.
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Affiliation(s)
| | | | - Dominic W Berry
- Department of Physics and Astronomy, Macquarie University, Sydney, NSW, Australia
| | - Shu Fay Ung
- Department of Chemistry, Columbia University, New York, NY, USA
| | - Andrew Zhao
- Google Quantum AI, Venice, CA, USA
- Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM, USA
| | | | | | - Andrew D Baczewski
- Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories, Albuquerque, NM, USA
| | - Joonho Lee
- Google Quantum AI, Venice, CA, USA.
- Department of Chemistry, Columbia University, New York, NY, USA.
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, USA.
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13
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Pathak H, Panyala A, Peng B, Bauman NP, Mutlu E, Rehr JJ, Vila FD, Kowalski K. Real-Time Equation-of-Motion Coupled-Cluster Cumulant Green's Function Method: Heterogeneous Parallel Implementation Based on the Tensor Algebra for Many-Body Methods Infrastructure. J Chem Theory Comput 2023; 19:2248-2257. [PMID: 37096369 DOI: 10.1021/acs.jctc.3c00045] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/26/2023]
Abstract
We report the implementation of the real-time equation-of-motion coupled-cluster (RT-EOM-CC) cumulant Green's function method [ J. Chem. Phys. 2020, 152, 174113] within the Tensor Algebra for Many-body Methods (TAMM) infrastructure. TAMM is a massively parallel heterogeneous tensor library designed for utilizing forthcoming exascale computing resources. The two-body electron repulsion matrix elements are Cholesky-decomposed, and we imposed spin-explicit forms of the various operators when evaluating the tensor contractions. Unlike our previous real algebra Tensor Contraction Engine (TCE) implementation, the TAMM implementation supports fully complex algebra. The RT-EOM-CC singles (S) and doubles (D) time-dependent amplitudes are propagated using a first-order Adams-Moulton method. This new implementation shows excellent scalability tested up to 500 GPUs using the Zn-porphyrin molecule with 655 basis functions, with parallel efficiencies above 90% up to 400 GPUs. The TAMM RT-EOM-CCSD was used to study core photoemission spectra in the formaldehyde and ethyl trifluoroacetate (ESCA) molecules. Simulations of the latter involve as many as 71 occupied and 649 virtual orbitals. The relative quasiparticle ionization energies and overall spectral functions agree well with available experimental results.
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Affiliation(s)
- Himadri Pathak
- Advanced Computing, Mathematics, and Data Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Ajay Panyala
- Advanced Computing, Mathematics, and Data Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Bo Peng
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Nicholas P Bauman
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Erdal Mutlu
- Advanced Computing, Mathematics, and Data Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - John J Rehr
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
| | - Fernando D Vila
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
| | - Karol Kowalski
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
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14
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Ofstad BS, Kristiansen HE, Aurbakken E, Schøyen ØS, Kvaal S, Pedersen TB. Adiabatic extraction of nonlinear optical properties from real-time time-dependent electronic-structure theory. J Chem Phys 2023; 158:2882246. [PMID: 37093994 DOI: 10.1063/5.0145521] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2023] [Accepted: 03/27/2023] [Indexed: 04/26/2023] Open
Abstract
Real-time simulations of laser-driven electron dynamics contain information about molecular optical properties through all orders in response theory. These properties can be extracted by assuming convergence of the power series expansion of induced electric and magnetic multipole moments. However, the accuracy relative to analytical results from response theory quickly deteriorates for higher-order responses due to the presence of high-frequency oscillations in the induced multipole moment in the time domain. This problem has been ascribed to missing higher-order corrections. We here demonstrate that the deviations are caused by nonadiabatic effects arising from the finite-time ramping from zero to full strength of the external laser field. Three different approaches, two using a ramped wave and one using a pulsed wave, for extracting electrical properties from real-time time-dependent electronic-structure simulations are investigated. The standard linear ramp is compared to a quadratic ramp, which is found to yield highly accurate results for polarizabilities, and first and second hyperpolarizabilities, at roughly half the computational cost. Results for the third hyperpolarizability are presented along with a simple, computable measure of reliability.
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Affiliation(s)
- Benedicte Sverdrup Ofstad
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
| | - Håkon Emil Kristiansen
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
| | - Einar Aurbakken
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
| | | | - Simen Kvaal
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
| | - Thomas Bondo Pedersen
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
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15
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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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16
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Pathak H, Sato T, Ishikawa KL. Time-dependent optimized coupled-cluster method with doubles and perturbative triples for first principles simulation of multielectron dynamics. Front Chem 2022; 10:982120. [PMID: 36176891 PMCID: PMC9513851 DOI: 10.3389/fchem.2022.982120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2022] [Accepted: 08/09/2022] [Indexed: 12/05/2022] Open
Abstract
We report the formulation of a new, cost-effective approximation method in the time-dependent optimized coupled-cluster (TD-OCC) framework [T. Sato et al., J. Chem. Phys. 148, 051101 (2018)] for first-principles simulations of multielectron dynamics in an intense laser field. The method, designated as TD-OCCD(T), is a time-dependent, orbital-optimized extension of the “gold-standard” CCSD(T) method in the ground-state electronic structure theory. The equations of motion for the orbital functions and the coupled-cluster amplitudes are derived based on the real-valued time-dependent variational principle using the fourth-order Lagrangian. The TD-OCCD(T) is size extensive and gauge invariant, and scales as O(N7) with respect to the number of active orbitals N. The pilot application of the TD-OCCD(T) method to the strong-field ionization and high-order harmonic generation from a Kr atom is reported in comparison with the results of the previously developed methods, such as the time-dependent complete-active-space self-consistent field (TD-CASSCF), TD-OCC with double and triple excitations (TD-OCCDT), TD-OCC with double excitations (TD-OCCD), and the time-dependent Hartree-Fock (TDHF) methods.
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Affiliation(s)
- Himadri Pathak
- Department of Nuclear Engineering and Management, School of Engineering, The University of Tokyo, Tokyo, Japan
| | - Takeshi Sato
- Department of Nuclear Engineering and Management, School of Engineering, The University of Tokyo, Tokyo, Japan
- Photon Science Center, School of Engineering, The University of Tokyo, Tokyo, Japan
- Research Institute for Photon Science and Laser Technology, The University of Tokyo, Tokyo, Japan
- *Correspondence: Takeshi Sato,
| | - Kenichi L. Ishikawa
- Department of Nuclear Engineering and Management, School of Engineering, The University of Tokyo, Tokyo, Japan
- Photon Science Center, School of Engineering, The University of Tokyo, Tokyo, Japan
- Research Institute for Photon Science and Laser Technology, The University of Tokyo, Tokyo, Japan
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17
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Vila FD, Rehr JJ, Pathak H, Peng B, Panyala A, Mutlu E, Bauman NP, Kowalski K. Real-time equation-of-motion CC cumulant and CC Green's function simulations of photoemission spectra of water and water dimer. J Chem Phys 2022; 157:044101. [DOI: 10.1063/5.0099192] [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
Newly developed coupled-cluster (CC) methods enable simulations of ionization potentials and spectral functions of molecular systems in a wide range of energy scales ranging from core-binding to valence. This paper discusses results obtained with the real-time equation-of-motion CC cumulant approach (RT-EOM-CC), and CC Green's function (CCGF) approaches in applications to the water and water dimer molecules. We compare the ionization potentials obtained with these methods for the valence region with the results obtained with the CCSD(T) formulation as a difference of energies for N and N-1 electron systems. All methods show good agreement with each other. They also agree well with experiment, with errors usually below 0.1 eV for the ionization potentials.We also analyze unique features of the spectral functions, associated with the position of satellite peaks, obtained with the RT-EOM-CC and CCGF methods employing single and double excitations, as a function of the monomer OH bond length and the proton transfer coordinate in the dimer. Finally, we analyze the impact of the basis set effects on the quality of calculated ionization potentials and find that the basis set effects are less pronounced for the augmented-type sets.
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Affiliation(s)
| | - John J. Rehr
- Department of Physics, University of Washington College of Arts and Sciences, United States of America
| | - Himadri Pathak
- Pacific Northwest National Laboratory, Pacific Northwest National Laboratory, United States of America
| | - Bo Peng
- Pacific Northwest National Laboratory, United States of America
| | - Ajay Panyala
- Pacific Northwest National Laboratory, United States of America
| | - Erdal Mutlu
- Pacific Northwest National Laboratory, United States of America
| | | | - Karol Kowalski
- Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, United States of America
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18
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Kristiansen HE, Ofstad BS, Hauge E, Aurbakken E, Schøyen ØS, Kvaal S, Pedersen TB. Linear and Nonlinear Optical Properties from TDOMP2 Theory. J Chem Theory Comput 2022; 18:3687-3702. [PMID: 35436120 PMCID: PMC9202312 DOI: 10.1021/acs.jctc.1c01309] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
![]()
We present a derivation
of real-time (RT) time-dependent orbital-optimized
Møller–Plesset (TDOMP2) theory and its biorthogonal companion,
time-dependent non-orthogonal OMP2 theory, starting from the time-dependent
bivariational principle and a parametrization based on the exponential
orbital-rotation operator formulation commonly used in the time-independent
molecular electronic structure theory. We apply the TDOMP2 method
to extract absorption spectra and frequency-dependent polarizabilities
and first hyperpolarizabilities from RT simulations, comparing the
results with those obtained from conventional time-dependent coupled-cluster
singles and doubles (TDCCSD) simulations and from its second-order
approximation, TDCC2. We also compare our results with those from
CCSD and CC2 linear and quadratic response theories. Our results indicate
that while TDOMP2 absorption spectra are of the same quality as TDCC2
spectra, including core excitations where optimized orbitals might
be particularly important, frequency-dependent polarizabilities and
hyperpolarizabilities from TDOMP2 simulations are significantly closer
to TDCCSD results than those from TDCC2 simulations.
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Affiliation(s)
- Håkon Emil Kristiansen
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo N-0315, Norway
| | - Benedicte Sverdrup Ofstad
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo N-0315, Norway
| | - Eirill Hauge
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo N-0315, Norway.,Simula Research Laboratory, Kristian Augusts Gate 23, Oslo 0164, Norway
| | - Einar Aurbakken
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo N-0315, Norway
| | | | - Simen Kvaal
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo N-0315, Norway.,Centre for Advanced Study at the Norwegian Academy of Science and Letters, Drammensveien 78, Oslo N-0271, Norway
| | - Thomas Bondo Pedersen
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo N-0315, Norway.,Centre for Advanced Study at the Norwegian Academy of Science and Letters, Drammensveien 78, Oslo N-0271, Norway
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19
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Wozniak AP, Przybytek M, Lewenstein M, Moszynski R. Effects of electronic correlation on the high harmonic generation in helium: a time-dependent configuration interaction singles vs time-dependent full configuration interaction study. J Chem Phys 2022; 156:174106. [DOI: 10.1063/5.0087384] [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
In this paper, we investigate the effects of full electronic correlation on the high harmonic generation in the helium atom subjected to laser pulses of extremely high intensity. To do this, we perform real-time propagations of the helium atom wavefunction using quantum chemistry methods coupled to Gaussian basis sets. The calculations are done within the real-time time-dependent configuration interaction framework, at two levels of theory: time-dependent configuration interation with single excitations (TD-CIS, uncorrelated method) and time-dependent full configuration interaction (TD-FCI, fully correlated method). The electronic wavefunction is expanded in Dunning basis sets supplemented with functions adapted to describing highly excited and continuum states. We also compare the TD-CI results with grid-based propagations of the helium atom within the single-active-electron approximation. Our results show that when including the dynamical electron correlation, a noticeable improvement to the description of HHG can be achieved, in terms of e.g. a more constant intensity in the lower energy part of the harmonic plateau. However, such effects can be captured only if the basis set used suffices to reproduce the most basic features, such as the HHG cutoff position, at the uncorrelated level of theory.
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20
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Vila FD, Kowalski K, Peng B, Kas JJ, Rehr JJ. Real-Time Equation-of-Motion CCSD Cumulant Green's Function. J Chem Theory Comput 2022; 18:1799-1807. [PMID: 35157796 DOI: 10.1021/acs.jctc.1c01179] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Many-body excitations in X-ray photoemission spectra have been difficult to simulate from first principles. We have recently developed a cumulant-based one-electron Green's function method using the real-time coupled-cluster-singles equation-of-motion approach (RT-EOM-CCS) that provides a general framework for treating these problems. Here we extend this approach to include double excitations in the ground-state energy and in the coupled cluster amplitudes, which have been implemented using subroutines generated by the Tensor Contraction Engine (TCE). As in the case of the singles approximation, RT-EOM-CCSD yields a nonperturbative cumulant form of the Green's function in terms of the time-dependent cluster amplitudes, adding nonlinear corrections to the traditional cumulant forms. The extended approach is applied to the core-hole spectral function for small molecular systems. We find that, when core-optimized basis sets are used, the doubles contributions reduce the mean absolute errors in the core binding energies of the 10e systems from 0.8 to 0.3 eV. They also significantly improve the quasiparticle-satellite gap by reducing its overestimation from about 3-5 to about 0-1 eV in CH4, NH3, and H2O, and also improving the overall shape of the satellite features. Finally, we demonstrate the application of the new implementation to the larger, classical XPS ESCA series of molecules and show that the singles approximation can be paired with a modest basis set to study carbon speciation.
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Affiliation(s)
- F D Vila
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
| | - K Kowalski
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - B Peng
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - J J Kas
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
| | - J J Rehr
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
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21
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Lesiuk M. Quintic-scaling rank-reduced coupled cluster theory with single and double excitations. J Chem Phys 2022; 156:064103. [DOI: 10.1063/5.0071916] [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
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22
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Coccia E, Luppi E. Time-dependent ab initioapproaches for high-harmonic generation spectroscopy. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 34:073001. [PMID: 34731835 DOI: 10.1088/1361-648x/ac3608] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2021] [Accepted: 11/03/2021] [Indexed: 06/13/2023]
Abstract
High-harmonic generation (HHG) is a nonlinear physical process used for the production of ultrashort pulses in XUV region, which are then used for investigating ultrafast phenomena in time-resolved spectroscopies. Moreover, HHG signal itself encodes information on electronic structure and dynamics of the target, possibly coupled to the nuclear degrees of freedom. Investigating HHG signal leads to HHG spectroscopy, which is applied to atoms, molecules, solids and recently also to liquids. Analysing the number of generated harmonics, their intensity and shape gives a detailed insight of, e.g., ionisation and recombination channels occurring in the strong-field dynamics. A number of valuable theoretical models has been developed over the years to explain and interpret HHG features, with the three-step model being the most known one. Originally, these models neglect the complexity of the propagating electronic wavefunction, by only using an approximated formulation of ground and continuum states. Many effects unravelled by HHG spectroscopy are instead due to electron correlation effects, quantum interference, and Rydberg-state contributions, which are all properly captured by anab initioelectronic-structure approach. In this review we have collected recent advances in modelling HHG by means ofab initiotime-dependent approaches relying on the propagation of the time-dependent Schrödinger equation (or derived equations) in presence of a very intense electromagnetic field. We limit ourselves to gas-phase atomic and molecular targets, and to solids. We focus on the various levels of theory employed for describing the electronic structure of the target, coupled with strong-field dynamics and ionisation approaches, and on the basis used to represent electronic states. Selected applications and perspectives for future developments are also given.
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Affiliation(s)
- Emanuele Coccia
- Dipartimento di Scienze Chimiche e Farmaceutiche, University of Trieste, via Giorgieri 1, 34127 Trieste, Italy
| | - Eleonora Luppi
- Sorbonne Universités, UPMC Univ Paris 06, UMR 7616, Laboratoire de Chimie Théorique, F-75005 Paris, France
- CNRS, UMR 7616, Laboratoire de Chimie Théorique, F-75005 Paris, France
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23
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Grobas Illobre P, Marsili M, Corni S, Stener M, Toffoli D, Coccia E. Time-Resolved Excited-State Analysis of Molecular Electron Dynamics by TDDFT and Bethe-Salpeter Equation Formalisms. J Chem Theory Comput 2021; 17:6314-6329. [PMID: 34486881 PMCID: PMC8515806 DOI: 10.1021/acs.jctc.1c00211] [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: 03/01/2021] [Indexed: 12/16/2022]
Abstract
In this work, a theoretical and computational set of tools to study and analyze time-resolved electron dynamics in molecules, under the influence of one or more external pulses, is presented. By coupling electronic-structure methods with the resolution of the time-dependent Schrödinger equation, we developed and implemented the time-resolved induced density of the electronic wavepacket, the time-resolved formulation of the differential projection density of states (ΔPDOS), and of transition contribution map (TCM) to look at the single-electron orbital occupation and localization change in time. Moreover, to further quantify the possible charge transfer, we also defined the energy-integrated ΔPDOS and the fragment-projected TCM. We have used time-dependent density-functional theory (TDDFT), as implemented in ADF software, and the Bethe-Salpeter equation, as provided by MolGW package, for the description of the electronic excited states. This suite of postprocessing tools also provides the time evolution of the electronic states of the system of interest. To illustrate the usefulness of these postprocessing tools, excited-state populations have been computed for HBDI (the chromophore of GFP) and DNQDI molecules interacting with a sequence of two pulses. Time-resolved descriptors have been applied to study the time-resolved electron dynamics of HBDI, DNQDI, LiCN (being a model system for dipole switching upon highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) electronic excitation), and Ag22. The computational analysis tools presented in this article can be employed to help the interpretation of fast and ultrafast spectroscopies on molecular, supramolecular, and composite systems.
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Affiliation(s)
- P. Grobas Illobre
- Dipartimento
di Scienze Chimiche e Farmaceutiche, Universitá
di Trieste, via L. Giorgieri 1, Trieste 34127, Italy
| | - M. Marsili
- Dipartimento
di Scienze Chimiche, Universitá di
Padova, via Marzolo 1, Padova 35131, Italy
| | - S. Corni
- Dipartimento
di Scienze Chimiche, Universitá di
Padova, via Marzolo 1, Padova 35131, Italy
- CNR
Istituto di Nanoscienze, via Campi 213/A, Modena 41125, Italy
| | - M. Stener
- Dipartimento
di Scienze Chimiche e Farmaceutiche, Universitá
di Trieste, via L. Giorgieri 1, Trieste 34127, Italy
| | - D. Toffoli
- Dipartimento
di Scienze Chimiche e Farmaceutiche, Universitá
di Trieste, via L. Giorgieri 1, Trieste 34127, Italy
| | - E. Coccia
- Dipartimento
di Scienze Chimiche e Farmaceutiche, Universitá
di Trieste, via L. Giorgieri 1, Trieste 34127, Italy
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24
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Peng R, White AF, Zhai H, Kin-Lic Chan G. Conservation laws in coupled cluster dynamics at finite temperature. J Chem Phys 2021; 155:044103. [PMID: 34340387 DOI: 10.1063/5.0059257] [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
We extend the finite-temperature Keldysh non-equilibrium coupled cluster theory (Keldysh-CC) [A. F. White and G. K.-L. Chan, J. Chem. Theory Comput. 15, 6137-6253 (2019)] to include a time-dependent orbital basis. When chosen to minimize the action, such a basis restores local and global conservation laws (Ehrenfest's theorem) for all one-particle properties while remaining energy conserving for time-independent Hamiltonians. We present the time-dependent Keldysh orbital-optimized coupled cluster doubles method in analogy with the formalism for zero-temperature dynamics, extended to finite temperatures through the time-dependent action on the Keldysh contour. To demonstrate the conservation property and understand the numerical performance of the method, we apply it to several problems of non-equilibrium finite-temperature dynamics: a 1D Hubbard model with a time-dependent Peierls phase, laser driving of molecular H2, driven dynamics in warm-dense silicon, and transport in the single impurity Anderson model.
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Affiliation(s)
- Ruojing Peng
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Alec F White
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Huanchen Zhai
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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25
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Cooper BC, Koulias LN, Nascimento DR, Li X, DePrince AE. Short Iterative Lanczos Integration in Time-Dependent Equation-of-Motion Coupled-Cluster Theory. J Phys Chem A 2021; 125:5438-5447. [PMID: 34121405 DOI: 10.1021/acs.jpca.1c01102] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A time-dependent (TD) formulation of equation-of-motion coupled-cluster (EOM-CC) theory can provide excited-state information over an arbitrarily wide energy window with a reduced memory footprint relative to conventional, frequency-domain EOM-CC theory. However, the floating-point costs of the time-integration required by TD-EOM-CC are generally far larger than those of the frequency-domain form of the approach. This work considers the potential of the short iterative Lanczos (SIL) integration scheme [J. Chem. Phys. 1986, 85, 5870-5876] to reduce the floating-point costs of TD-EOM-CC simulations. Low-energy and K-edge absorption features for small molecules are evaluated using TD-EOM-CC with single and double excitations, with the time-integrations carried out via SIL and fourth-order Runge-Kutta (RK4) schemes. Spectra derived from SIL- and RK4-driven simulations are nearly indistinguishable, and with an appropriately chosen subspace dimension, the SIL requires far fewer floating-point operations than are required by RK4. For K-edge spectra, SIL is the more efficient scheme by an average factor of 7.2.
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Affiliation(s)
- Brandon C Cooper
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
| | - Lauren N Koulias
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Daniel R Nascimento
- Department of Chemistry, The University of Memphis, Memphis, Tennessee 38152, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - A Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
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26
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Pathak H, Sato T, Ishikawa KL. Time-dependent optimized coupled-cluster method for multielectron dynamics. IV. Approximate consideration of the triple excitation amplitudes. J Chem Phys 2021; 154:234104. [PMID: 34241273 DOI: 10.1063/5.0054743] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Abstract
We present a cost-effective treatment of the triple excitation amplitudes in the time-dependent optimized coupled-cluster (TD-OCC) framework called TD-OCCDT(4) for studying intense laser-driven multielectron dynamics. It considers triple excitation amplitudes correct up to the fourth-order in many-body perturbation theory and achieves a computational scaling of O(N7), with N being the number of active orbital functions. This method is applied to the electron dynamics in Ne and Ar atoms exposed to an intense near-infrared laser pulse with various intensities. We benchmark our results against the TD complete-active-space self-consistent field (TD-CASSCF), TD-OCC with double and triple excitations (TD-OCCDT), TD-OCC with double excitations (TD-OCCD), and TD Hartree-Fock (TDHF) methods to understand how this approximate scheme performs in describing nonperturbatively nonlinear phenomena, such as field-induced ionization and high-harmonic generation. We find that the TD-OCCDT(4) method performs equally well as the TD-OCCDT method, almost perfectly reproducing the results of the fully correlated TD-CASSCF with a more favorable computational scaling.
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Affiliation(s)
- Himadri Pathak
- Department of Nuclear Engineering and Management, 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, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Kenichi L Ishikawa
- Department of Nuclear Engineering and Management, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
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27
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Woźniak AP, Lesiuk M, Przybytek M, Efimov DK, Prauzner-Bechcicki JS, Mandrysz M, Ciappina M, Pisanty E, Zakrzewski J, Lewenstein M, Moszyński R. A systematic construction of Gaussian basis sets for the description of laser field ionization and high-harmonic generation. J Chem Phys 2021; 154:094111. [PMID: 33685145 DOI: 10.1063/5.0040879] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A precise understanding of mechanisms governing the dynamics of electrons in atoms and molecules subjected to intense laser fields has a key importance for the description of attosecond processes such as the high-harmonic generation and ionization. From the theoretical point of view, this is still a challenging task, as new approaches to solve the time-dependent Schrödinger equation with both good accuracy and efficiency are still emerging. Until recently, the purely numerical methods of real-time propagation of the wavefunction using finite grids have been frequently and successfully used to capture the electron dynamics in small one- or two-electron systems. However, as the main focus of attoscience shifts toward many-electron systems, such techniques are no longer effective and need to be replaced by more approximate but computationally efficient ones. In this paper, we explore the increasingly popular method of expanding the wavefunction of the examined system into a linear combination of atomic orbitals and present a novel systematic scheme for constructing an optimal Gaussian basis set suitable for the description of excited and continuum atomic or molecular states. We analyze the performance of the proposed basis sets by carrying out a series of time-dependent configuration interaction calculations for the hydrogen atom in fields of intensity varying from 5 × 1013 W/cm2 to 5 × 1014 W/cm2. We also compare the results with the data obtained using Gaussian basis sets proposed previously by other authors.
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Affiliation(s)
| | - Michał Lesiuk
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Michał Przybytek
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Dmitry K Efimov
- Institute of Theoretical Physics, Jagiellonian University in Krakow, Łojasiewicza 11, 30-348 Kraków, Poland
| | - Jakub S Prauzner-Bechcicki
- Marian Smoluchowski Institute of Physics, Jagiellonian University in Krakow, Łojasiewicza 11, 30-348 Kraków, Poland
| | - Michał Mandrysz
- Institute of Theoretical Physics, Jagiellonian University in Krakow, Łojasiewicza 11, 30-348 Kraków, Poland
| | - Marcelo Ciappina
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860, Castelldefels, Barcelona, Spain
| | - Emilio Pisanty
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860, Castelldefels, Barcelona, Spain
| | - Jakub Zakrzewski
- Institute of Theoretical Physics, Jagiellonian University in Krakow, Łojasiewicza 11, 30-348 Kraków, Poland
| | - Maciej Lewenstein
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860, Castelldefels, Barcelona, Spain
| | - Robert Moszyński
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
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28
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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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29
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Pauletti CF, Coccia E, Luppi E. Role of exchange and correlation in high-harmonic generation spectra of H 2, N 2, and CO 2: Real-time time-dependent electronic-structure approaches. J Chem Phys 2021; 154:014101. [PMID: 33412879 DOI: 10.1063/5.0033072] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Abstract
This study arises from the attempt to answer the following question: how different descriptions of electronic exchange and correlation affect the high-harmonic generation (HHG) spectroscopy of H2, N2, and CO2 molecules? We compare HHG spectra for H2, N2, and CO2 with different ab initio electronic structure methods: real-time time-dependent configuration interaction and real-time time-dependent density functional theory (RT-TDDFT) using truncated basis sets composed of correlated wave functions expanded on Gaussian basis sets. In the framework of RT-TDDFT, we employ Perdew-Burke-Ernzerhof (PBE) and long-range corrected Perdew-Burke-Ernzerhof (LC-ωPBE) functionals. We study HHG spectroscopy by disentangling the effect of electronic exchange and correlation. We first analyze the electronic exchange alone, and in the case of RT-TDDFT with LC-ωPBE, we use ω = 0.3 and ω = 0.4 to tune the percentage of long-range Hartree-Fock exchange and short-range exchange PBE. Then, we added the correlation as described by the PBE functional. All the methods give very similar HHG spectra, and they seem not to be particularly sensitive to the different description of exchange and correlation or to the correct asymptotic behavior of the Coulomb potential. Despite this general trend, some differences are found in the region connecting the cutoff and the background. Here, the harmonics can be resolved with different accuracy depending on the theoretical schemes used. We believe that the investigation of the molecular continuum and its coupling with strong fields merits further theoretical investigations in the near future.
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Affiliation(s)
| | - Emanuele Coccia
- Dipartimento di Scienze Chimiche e Farmaceutiche, Via Giorgieri 1, Trieste Italy
| | - Eleonora Luppi
- Laboratoire de Chimie Théorique, Sorbonne Université and CNRS, F-75005 Paris, France
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30
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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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31
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Vila FD, Rehr JJ, Kas JJ, Kowalski K, Peng B. Real-Time Coupled-Cluster Approach for the Cumulant Green's Function. J Chem Theory Comput 2020; 16:6983-6992. [PMID: 33108872 DOI: 10.1021/acs.jctc.0c00639] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Abstract
Green's function methods within many-body perturbation theory provide a general framework for treating electronic correlations in excited states and spectra. Here, we develop the cumulant form of the one-electron Green's function using a real-time coupled-cluster equation-of-motion approach, in an extension of our previous study (Rehr J.; et al. J. Chem. Phys. 2020, 152, 174113). The approach yields a nonperturbative expression for the cumulant in terms of the solution to a set of coupled first-order, nonlinear differential equations. The method thereby adds nonlinear corrections to traditional cumulant methods, which are linear in the self-energy. The approach is applied to the core-hole Green's function and is illustrated for a number of small molecular systems. For these systems, we find that the nonlinear contributions yield significant improvements, both for quasiparticle properties such as core-level binding energies and for inelastic losses that correspond to satellites observed in photoemission spectra.
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Affiliation(s)
- F D Vila
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
| | - J J Rehr
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
| | - J J Kas
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
| | - K Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, United States
| | - B Peng
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
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32
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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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33
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Pathak H, Sato T, Ishikawa KL. Study of laser-driven multielectron dynamics of Ne atom using time-dependent optimised second-order many-body perturbation theory. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1813910] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Affiliation(s)
- Himadri Pathak
- Department of Nuclear Engineering and Management, Graduate School of Engineering, The University of Tokyo, Tokyo, Japan
| | - Takeshi Sato
- Department of Nuclear Engineering and Management, Graduate School of Engineering, The University of Tokyo, Tokyo, Japan
- Photon Science Center, Graduate School of Engineering, The University of Tokyo, Tokyo, Japan
- Research Institute for Photon Science and Laser Technology, The University of Tokyo, Tokyo, Japan
| | - Kenichi L. Ishikawa
- Department of Nuclear Engineering and Management, Graduate School of Engineering, The University of Tokyo, Tokyo, Japan
- Photon Science Center, Graduate School of Engineering, The University of Tokyo, Tokyo, Japan
- Research Institute for Photon Science and Laser Technology, The University of Tokyo, Tokyo, Japan
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34
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Li X, Govind N, Isborn C, DePrince AE, Lopata K. Real-Time Time-Dependent Electronic Structure Theory. Chem Rev 2020; 120:9951-9993. [DOI: 10.1021/acs.chemrev.0c00223] [Citation(s) in RCA: 64] [Impact Index Per Article: 16.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195-1700, United States
| | - Niranjan Govind
- Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Christine Isborn
- Department of Chemistry and Chemical Biology, University of California, Merced, California 95343, United States
| | - A. Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
| | - Kenneth Lopata
- Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803, United States
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35
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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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36
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Pathak H, Sato T, Ishikawa KL. Time-dependent optimized coupled-cluster method for multielectron dynamics. III. A second-order many-body perturbation approximation. J Chem Phys 2020; 153:034110. [DOI: 10.1063/5.0008789] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Affiliation(s)
- Himadri Pathak
- Department of Nuclear Engineering and Management, 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, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
- Photon Science Center, 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
| | - Kenichi L. Ishikawa
- Department of Nuclear Engineering and Management, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
- Photon Science Center, 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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37
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Bodenstein T, Kvaal S. A state-specific multireference coupled-cluster method based on the bivariational principle. J Chem Phys 2020; 153:024106. [PMID: 32668937 DOI: 10.1063/5.0009429] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
A state-specific multireference coupled-cluster (MRCC) method based on Arponen's bivariational principle is presented, the bivar-MRCC method. The method is based on single-reference theory and therefore has a relatively straightforward formulation and modest computational complexity. The main difference from established methods is the bivariational formulation, in which independent parameterizations of the wave function (ket) and its complex conjugate (bra) are made. Importantly, this allows manifest multiplicative separability of the state (exact in the extended bivar-MRECC version of the method and approximate otherwise), and additive separability of the energy, while preserving polynomial scaling of the working equations. A feature of the bivariational principle is that the formal bra and ket references can be included as bivariational parameters, which eliminates much of the bias toward the formal reference. A pilot implementation is described, and extensive benchmark calculations on several standard problems are performed. The results from the bivar-MRCC method are comparable to established state-specific multireference methods. Considering the relative affordability of the bivar-MRCC method, it may become a practical tool for non-experts.
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Affiliation(s)
- Tilmann Bodenstein
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Simen Kvaal
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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38
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Chen M, Lopata K. First-Principles Simulations of X-ray Transient Absorption for Probing Attosecond Electron Dynamics. J Chem Theory Comput 2020; 16:4470-4478. [PMID: 32470295 PMCID: PMC7467644 DOI: 10.1021/acs.jctc.0c00122] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
X-ray transient absorption spectroscopy (XTAS) is a promising technique for measuring electron dynamics in molecules and solids with attosecond time resolutions. In XTAS, the elemental specificity and spatial locality of core-to-valence X-ray absorption is exploited to relate modulations in the time-resolved absorption spectra to local electron density variations around particular atoms. However, interpreting these absorption modulations and frequency shifts as a function of the time delay in terms of dynamics can be challenging. In this paper, we present a first-principles study of attosecond XTAS in a selection of simple molecules based on real-time time-dependent density functional theory (RT-TDDFT) with constrained DFT to emulate the state of the system following the interaction with a ultraviolet pump laser. In general, there is a decrease in the optical density and a blue shift in the frequency with increasing electron density around the absorbing atom. In carbon monoxide (CO), modulations in the O K-edge occur at the frequency of the valence electron dynamics, while for dioxygen (O2) they occur at twice the frequency, due to the indistinguishability of the oxygen atoms. In 4-aminophenol (H2NC6H4OH), likewise, there is a decrease in the optical density and a blue shift in the frequency for the oxygen and nitrogen K-edges with increasing charge density on the O and N, respectively. Similar effects are observed in the nitrogen K-edge for a long-range charge-transfer excitation in a benzene (C6H6)-tetracyanoethylene (C6N4; TCNE) dimer but with weaker modulations due to the delocalization of the charge across the entire TCNE molecule. Additionally, in all cases, there are pre-edge features corresponding to core transitions to depopulated orbitals. These potentially offer a background-free signal that only appears in pumped molecules.
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Affiliation(s)
- Min Chen
- Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803, United States
| | - Kenneth Lopata
- Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803, United States.,Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803, United States
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39
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Kowalski K, Bauman NP. Sub-system quantum dynamics using coupled cluster downfolding techniques. J Chem Phys 2020; 152:244127. [DOI: 10.1063/5.0008436] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Karol Kowalski
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, USA
| | - Nicholas P. Bauman
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, USA
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40
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Rehr JJ, Vila FD, Kas JJ, Hirshberg NY, Kowalski K, Peng B. Equation of motion coupled-cluster cumulant approach for intrinsic losses in x-ray spectra. J Chem Phys 2020; 152:174113. [PMID: 32384843 DOI: 10.1063/5.0004865] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a combined equation of motion coupled-cluster cumulant Green's function approach for calculating and understanding intrinsic inelastic losses in core level x-ray absorption spectra (XAS) and x-ray photoemission spectra. The method is based on a factorization of the transition amplitude in the time domain, which leads to a convolution of an effective one-body absorption spectrum and the core-hole spectral function. The spectral function characterizes intrinsic losses in terms of shake-up excitations and satellites using a cumulant representation of the core-hole Green's function that simplifies the interpretation. The one-body spectrum also includes orthogonality corrections that enhance the XAS at the edge.
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Affiliation(s)
- J J Rehr
- Department of Physics, University of Washington Seattle, Seattle, Washington 98195, USA
| | - F D Vila
- Department of Physics, University of Washington Seattle, Seattle, Washington 98195, USA
| | - J J Kas
- Department of Physics, University of Washington Seattle, Seattle, Washington 98195, USA
| | - N Y Hirshberg
- Department of Physics, University of Washington Seattle, Seattle, Washington 98195, USA
| | - K Kowalski
- Physical Sciences Division, Battelle, Pacific Northwest National Laboratory, K8-91, PO Box 999, Richland, Washington 99352, USA
| | - B Peng
- Physical Sciences Division, Battelle, Pacific Northwest National Laboratory, K8-91, PO Box 999, Richland, Washington 99352, USA
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41
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Pathak H, Sato T, Ishikawa KL. Time-dependent optimized coupled-cluster method for multielectron dynamics. II. A coupled electron-pair approximation. J Chem Phys 2020; 152:124115. [DOI: 10.1063/1.5143747] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Himadri Pathak
- Department of Nuclear Engineering and Management, 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, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
- Photon Science Center, 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
| | - Kenichi L. Ishikawa
- Department of Nuclear Engineering and Management, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
- Photon Science Center, 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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42
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Kristiansen HE, Schøyen ØS, Kvaal S, Pedersen TB. Numerical stability of time-dependent coupled-cluster methods for many-electron dynamics in intense laser pulses. J Chem Phys 2020; 152:071102. [DOI: 10.1063/1.5142276] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Håkon Emil Kristiansen
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | | | - Simen Kvaal
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Thomas Bondo Pedersen
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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43
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Nascimento DR, DePrince AE. A general time-domain formulation of equation-of-motion coupled-cluster theory for linear spectroscopy. J Chem Phys 2019; 151:204107. [DOI: 10.1063/1.5125494] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Affiliation(s)
- Daniel R. Nascimento
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
| | - A. Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
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44
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Hansen MB, Madsen NK, Zoccante A, Christiansen O. Time-dependent vibrational coupled cluster theory: Theory and implementation at the two-mode coupling level. J Chem Phys 2019; 151:154116. [DOI: 10.1063/1.5117207] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] 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
| | - Alberto Zoccante
- 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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45
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Koulias LN, Williams-Young DB, Nascimento DR, DePrince AE, Li X. Relativistic Real-Time Time-Dependent Equation-of-Motion Coupled-Cluster. J Chem Theory Comput 2019; 15:6617-6624. [DOI: 10.1021/acs.jctc.9b00729] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Lauren N. Koulias
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - David B. Williams-Young
- Computational Research Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road MS 50A-3111, Berkeley, California 94720, United States
| | - Daniel R. Nascimento
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306, United States
| | - A. Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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46
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Shushkov P, Miller TF. Real-time density-matrix coupled-cluster approach for closed and open systems at finite temperature. J Chem Phys 2019; 151:134107. [DOI: 10.1063/1.5121749] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Philip Shushkov
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Thomas F. Miller
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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47
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Williams‐Young DB, Petrone A, Sun S, Stetina TF, Lestrange P, Hoyer CE, Nascimento DR, Koulias L, Wildman A, Kasper J, Goings JJ, Ding F, DePrince AE, Valeev EF, Li X. The Chronus Quantum software package. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2019. [DOI: 10.1002/wcms.1436] [Citation(s) in RCA: 34] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- David B. Williams‐Young
- Computational Research Division Lawrence Berkeley National Laboratory Berkeley California
- Department of Chemistry University of Washington Seattle Washington
| | - Alessio Petrone
- Dipartimento di Scienze Chimiche Università di Napoli “Federico II”, Complesso Universitario di M.S. Angelo Naples Italy
| | - Shichao Sun
- Department of Chemistry University of Washington Seattle Washington
| | - Torin F. Stetina
- Department of Chemistry University of Washington Seattle Washington
| | | | - Chad E. Hoyer
- Department of Chemistry University of Washington Seattle Washington
| | - Daniel R. Nascimento
- Department of Chemistry and Biochemistry Florida State University Tallahassee Florida
| | - Lauren Koulias
- Department of Chemistry University of Washington Seattle Washington
| | - Andrew Wildman
- Department of Chemistry University of Washington Seattle Washington
| | - Joseph Kasper
- Department of Chemistry University of Washington Seattle Washington
| | | | - Feizhi Ding
- Division of Chemistry and Chemical Engineering California Institute of Technology Pasadena California
| | - A. Eugene DePrince
- Department of Chemistry and Biochemistry Florida State University Tallahassee Florida
| | | | - Xiaosong Li
- Department of Chemistry University of Washington Seattle Washington
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Pedersen TB, Kvaal S. Symplectic integration and physical interpretation of time-dependent coupled-cluster theory. J Chem Phys 2019; 150:144106. [DOI: 10.1063/1.5085390] [Citation(s) in RCA: 32] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Affiliation(s)
- Thomas Bondo Pedersen
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Simen Kvaal
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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Time-Dependent Complete-Active-Space Self-Consistent-Field Method for Ultrafast Intense Laser Science. SPRINGER SERIES IN CHEMICAL PHYSICS 2018. [DOI: 10.1007/978-3-030-03786-4_8] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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