1
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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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2
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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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3
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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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4
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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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5
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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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6
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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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7
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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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8
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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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9
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Langkabel F, Albrecht PA, Bande A, Krause P. Making Optical Excitations Visible - an Exciton Wavefunction Extension to the Time-dependent Configuration Interaction Method. Chem Phys 2022. [DOI: 10.1016/j.chemphys.2022.111502] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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10
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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: 6] [Impact Index Per Article: 2.0] [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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11
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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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12
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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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13
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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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14
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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: 10] [Impact Index Per Article: 3.3] [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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15
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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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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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