1
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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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2
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Hauge E, Kristiansen HE, Konecny L, Kadek M, Repisky M, Pedersen TB. Cost-Efficient High-Resolution Linear Absorption Spectra through Extrapolating the Dipole Moment from Real-Time Time-Dependent Electronic-Structure Theory. J Chem Theory Comput 2023; 19:7764-7775. [PMID: 37874968 PMCID: PMC10653104 DOI: 10.1021/acs.jctc.3c00727] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2023] [Revised: 10/02/2023] [Accepted: 10/03/2023] [Indexed: 10/26/2023]
Abstract
We present a novel function fitting method for approximating the propagation of the time-dependent electric dipole moment from real-time electronic structure calculations. Real-time calculations of the electronic absorption spectrum require discrete Fourier transforms of the electric dipole moment. The spectral resolution is determined by the total propagation time, i.e., the trajectory length of the dipole moment, causing a high computational cost. Our developed method uses function fitting on shorter trajectories of the dipole moment, achieving arbitrary spectral resolution through extrapolation. Numerical testing shows that the fitting method can reproduce high-resolution spectra by using short dipole trajectories. The method converges with as little as 100 a.u. dipole trajectories for some systems, though the difficulty converging increases with the spectral density. We also introduce an error estimate of the fit, reliably assessing its convergence and hence the quality of the approximated spectrum.
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Affiliation(s)
- Eirill Hauge
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern, 0315 Oslo, Norway
- Department
of Numerical Analysis and Scientific Computing, Simula Research Laboratory, Kristian Augusts Gate 23, 0164 Oslo, Norway
| | - Håkon Emil Kristiansen
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern, 0315 Oslo, Norway
| | - Lukas Konecny
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Tromsø—The Arctic University
of Norway, N-9037 Tromsø, Norway
- Center
for Free Electron Laser, Max Planck Institute
for the Structure and Dynamics of Matter Science, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Marius Kadek
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Tromsø—The Arctic University
of Norway, N-9037 Tromsø, Norway
- Department
of Physics, Northeastern University, Boston, Massachusetts 02115, United States
| | - Michal Repisky
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Tromsø—The Arctic University
of Norway, N-9037 Tromsø, Norway
- Department
of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University, Ilkovicova 6, SK-84215 Bratislava, Slovakia
| | - Thomas Bondo Pedersen
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern, 0315 Oslo, Norway
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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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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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5
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Wang Z, Peyton BG, Crawford TD. Accelerating Real-Time Coupled Cluster Methods with Single-Precision Arithmetic and Adaptive Numerical Integration. J Chem Theory Comput 2022; 18:5479-5491. [PMID: 35939815 DOI: 10.1021/acs.jctc.2c00490] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We explore the framework of a real-time coupled cluster method with a focus on improving its computational efficiency. Propagation of the wave function via the time-dependent Schrödinger equation places high demands on computing resources, particularly for high level theories such as coupled cluster with polynomial scaling. Similar to earlier investigations of coupled cluster properties, we demonstrate that the use of single-precision arithmetic reduces both the storage and multiplicative costs of the real-time simulation by approximately a factor of 2 with no significant impact on the resulting UV/vis absorption spectrum computed via the Fourier transform of the time-dependent dipole moment. Additional speedups─of up to a factor of 14 in test simulations of water clusters─are obtained via a straightforward GPU-based implementation as compared to conventional CPU calculations. We also find that further performance optimization is accessible through sagacious selection of numerical integration algorithms, and the adaptive methods, such as the Cash-Karp integrator, provide an effective balance between computing costs and numerical stability. Finally, we demonstrate that a simple mixed-step integrator based on the conventional fourth-order Runge-Kutta approach is capable of stable propagations even for strong external fields, provided the time step is appropriately adapted to the duration of the laser pulse with only minimal computational overhead.
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Affiliation(s)
- Zhe Wang
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Benjamin G Peyton
- 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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6
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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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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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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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9
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Durden AS, Levine BG. Floquet Time-Dependent Configuration Interaction for Modeling Ultrafast Electron Dynamics. J Chem Theory Comput 2022; 18:795-806. [DOI: 10.1021/acs.jctc.1c01009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Affiliation(s)
- Andrew S. Durden
- Department of Chemistry and Institute for Advanced Computational Science, Stony Brook University, Stony Brook, New York 11794, United States
| | - Benjamin G. Levine
- Department of Chemistry and Institute for Advanced Computational Science, Stony Brook University, Stony Brook, New York 11794, United States
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10
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Orr-Ewing AJ, Crawford TD, Zanni MT, Hartland G, Shea JE. A Venue for Advances in Experimental and Theoretical Methods in Physical Chemistry. J Phys Chem A 2022; 126:177-179. [PMID: 35045707 DOI: 10.1021/acs.jpca.1c10457] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Andrew J Orr-Ewing
- School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS, U.K
| | - T Daniel Crawford
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States.,Molecular Sciences Software Institute, 1880 Pratt Drive, Suite 1100, Blacksburg, Virginia 24060, United States
| | - Martin T Zanni
- Department of Chemistry, University of Wisconsin─Madison, 1101 University Avenue, Madison, Wisconsin 53706, United States
| | - Gregory Hartland
- University of Notre Dame, Notre Dame, Indiana 46556, United States
| | - Joan-Emma Shea
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, Santa Barbara, California 93106, United States.,Department of Physics, University of California, Santa Barbara, Santa Barbara, California 93106, United States
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