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Yuan X, Halbert L, Pototschnig JV, Papadopoulos A, Coriani S, Visscher L, Pereira Gomes AS. Formulation and Implementation of Frequency-Dependent Linear Response Properties with Relativistic Coupled Cluster Theory for GPU-Accelerated Computer Architectures. J Chem Theory Comput 2024; 20:677-694. [PMID: 38193434 DOI: 10.1021/acs.jctc.3c00812] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2024]
Abstract
We present the development and implementation of relativistic coupled cluster linear response theory (CC-LR), which allows the determination of molecular properties arising from time-dependent or time-independent electric, magnetic, or mixed electric-magnetic perturbations (within a common gauge origin for the magnetic properties) as well as taking into account the finite lifetime of excited states in the framework of damped response theory. We showcase our implementation, which is capable to offload the computationally intensive tensor contractions characteristic of coupled cluster theory onto graphical processing units, in the calculation of (a) frequency-(in)dependent dipole-dipole polarizabilities of IIB atoms and selected diatomic molecules, with a particular emphasis on the calculation of valence absorption cross sections for the I2 molecule; (b) indirect spin-spin coupling constants for benchmark systems such as the hydrogen halides (HX, X = F-I) as well the H2Se-H2O dimer as a prototypical system containing hydrogen bonds; and (c) optical rotations at the sodium D line for hydrogen peroxide analogues (H2Y2, Y = O, S, Se, Te). Thanks to this implementation, we are able to show the similarities in performance, but often the significant discrepancies, between CC-LR and approximate methods such as density functional theory. Comparing standard CC response theory with the flavor based upon the equation of motion formalism, we find that for valence properties such as polarizabilities, the two frameworks yield very similar results across the periodic table as found elsewhere in the literature; for properties that probe the core region, such as spin-spin couplings, on the other hand, we show a progressive differentiation between the two as relativistic effects become more important. Our results also suggest that as one goes down the periodic table, it may become increasingly difficult to measure pure optical rotation at the sodium D line due to the appearance of absorbing states.
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Affiliation(s)
- Xiang Yuan
- Univ. Lille, CNRS, UMR 8523─PhLAM─Physique des Lasers Atomes et Molécules, F-59000 Lille, France
- Department of Chemistry and Pharmaceutical Sciences, Faculty of Science, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
| | - Loïc Halbert
- Univ. Lille, CNRS, UMR 8523─PhLAM─Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - Johann Valentin Pototschnig
- Department of Chemistry and Pharmaceutical Sciences, Faculty of Science, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
| | - Anastasios Papadopoulos
- Department of Chemistry and Pharmaceutical Sciences, Faculty of Science, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
| | - Sonia Coriani
- DTU Chemistry─Department of Chemistry, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
| | - Lucas Visscher
- Department of Chemistry and Pharmaceutical Sciences, Faculty of Science, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
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Zamok L, Coriani S, Sauer SPA. A tale of two vectors: A Lanczos algorithm for calculating RPA mean excitation energies. J Chem Phys 2022; 156:014102. [PMID: 34998356 DOI: 10.1063/5.0071144] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The experimental and theoretical determination of the mean excitation energy, I(0), and the stopping power, S(v), of a material is of great interest in particle and material physics and radiation therapy. For calculations of I(0), the complete set of electronic transitions in a given basis set is required, effectively limiting such calculations to systems with a small number of electrons, even at the random-phase approximation (RPA)/time-dependent Hartree-Fock (TDHF) or time-dependent density-functional theory level. To overcome such limitations, we present here the implementation of a Lanczos algorithm adapted for the paired RPA/TDHF eigenvalue problem in the Dalton program and show that it provides good approximation of the entire RPA eigenspectra in a reduced space. We observe rapid convergence of I(0) with the number of Lanczos vectors as the algorithm favors the transitions with large contributions. In most cases, the algorithm recovers RPA I(0) values of up to 0.5% accuracy at less than a quarter of the full space size. The algorithm not only exploits the RPA paired structure to save computational resources but also preserves certain sum-over-states properties, as first demonstrated by Johnson et al. [Comput. Phys. Commun. 120, 155 (1999)]. The block Lanczos RPA solver, as presented here, thus shows promise for computing mean excitation energies for systems larger than what was computationally feasible before.
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Affiliation(s)
- Luna Zamok
- Department of Chemistry, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - Sonia Coriani
- Department of Chemistry, Technical University of Denmark, Kemitorvet Bldg. 207, 2800 Kongens Lyngby, Denmark
| | - Stephan P A Sauer
- Department of Chemistry, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
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Madsen D, Christiansen O, König C. Anharmonic vibrational spectra from double incremental potential energy and dipole surfaces. Phys Chem Chem Phys 2018; 20:3445-3456. [DOI: 10.1039/c7cp07190f] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Using incremental approaches, size limitations for property surface generations are pushed significantly, enabling accurate large molecule anharmonic vibrational spectra calculations.
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Affiliation(s)
- Diana Madsen
- Department of Chemistry
- Aarhus University
- DK-8000 Aarhus C
- Denmark
| | | | - Carolin König
- Division of Theoretical Chemistry & Biology
- Royal Institute of Technology
- SE-106 91 Stockholm
- Sweden
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On the choice electronic structure method to calculate the quartic potential energy surface for the vibrational calculation of polyatomic molecules. Theor Chem Acc 2016. [DOI: 10.1007/s00214-016-1962-1] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Petrenko T, Rauhut G. Time-independent eigenstate-free calculation of vibronic spectra beyond the harmonic approximation. J Chem Phys 2015; 143:234106. [DOI: 10.1063/1.4937380] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Affiliation(s)
- Taras Petrenko
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Guntram Rauhut
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
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Godtliebsen IH, Christiansen O. Calculating vibrational spectra without determining excited eigenstates: Solving the complex linear equations of damped response theory for vibrational configuration interaction and vibrational coupled cluster states. J Chem Phys 2015; 143:134108. [DOI: 10.1063/1.4932010] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Affiliation(s)
| | - Ove Christiansen
- Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark
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König C, Christiansen O. Automatic determination of important mode–mode correlations in many-mode vibrational wave functions. J Chem Phys 2015; 142:144115. [DOI: 10.1063/1.4916518] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Carolin König
- Department of Chemistry, Aarhus University, DK-8000 Aarhus C, Denmark
| | - Ove Christiansen
- Department of Chemistry, Aarhus University, DK-8000 Aarhus C, Denmark
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Solvation effects on the static and dynamic first-order electronic and vibrational hyperpolarizabilities of uracil: a polarized continuum model investigation. ScientificWorldJournal 2014; 2013:652124. [PMID: 24453886 PMCID: PMC3885316 DOI: 10.1155/2013/652124] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2013] [Accepted: 09/18/2013] [Indexed: 11/18/2022] Open
Abstract
Electronic (β(e)) and vibrational (β(v)) first-order hyperpolarizabilities of uracil were determined in gas and water solution using the Coulomb-attenuating Density Functional Theory level with the Dunning's correlation-consistent aug-cc-pVDZ basis set. Frequency-dependent β(e) values were computed for the Second Harmonic Generation (SHG) and Electric Optical Pockels Effect (EOPE) nonlinear optical phenomena. The Polarized Continuum Model was employed to study the solvent effects on the electronic and vibrational properties. The introduction of solvation contributions increases the β(e) (static) value by ca. 110%. In comparison, smaller enhancements are found for the β(e) (EOPE) and β(e) (SHG) data evaluated at the typical wavelength of 694 nm (by 40-50%). The gas-water hyperpolarizability difference was rationalised through a density analysis study. The magnitudes of the vibrational first-order hyperpolarizabilities are comparable to their electronic counterparts and noticeably increase in solution: β(v) (EOPE) ~ β(e) (EOPE) in aqueous phase at λ = 694 nm. Analysis of the IR and Raman spectra is useful to elucidate the most important contributing modes to the vibrational first-order hyperpolarizabilities.
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Coriani S, Fransson T, Christiansen O, Norman P. Asymmetric-Lanczos-Chain-Driven Implementation of Electronic Resonance Convergent Coupled-Cluster Linear Response Theory. J Chem Theory Comput 2012; 8:1616-28. [DOI: 10.1021/ct200919e] [Citation(s) in RCA: 87] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Sonia Coriani
- Dipartimento
di Scienze Chimiche
e Farmaceutiche, Università degli Studi di Trieste, I-34127 Trieste, Italy
- Department of Chemistry, Aarhus University, DK-8000, Århus C, Denmark
| | - Thomas Fransson
- Department of Physics, Chemistry
and Biology, Linköping University, SE-581 83 Linköping, Sweden
| | - Ove Christiansen
- Department of Chemistry, Aarhus University, DK-8000, Århus C, Denmark
| | - Patrick Norman
- Department of Physics, Chemistry
and Biology, Linköping University, SE-581 83 Linköping, Sweden
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Thomsen B, Hansen MB, Seidler P, Christiansen O. Vibrational absorption spectra from vibrational coupled cluster damped linear response functions calculated using an asymmetric Lanczos algorithm. J Chem Phys 2012; 136:124101. [DOI: 10.1063/1.3690065] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
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Helgaker T, Coriani S, Jørgensen P, Kristensen K, Olsen J, Ruud K. Recent Advances in Wave Function-Based Methods of Molecular-Property Calculations. Chem Rev 2012; 112:543-631. [DOI: 10.1021/cr2002239] [Citation(s) in RCA: 463] [Impact Index Per Article: 38.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Trygve Helgaker
- Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Sonia Coriani
- Dipartimento di Scienze Chimiche e Farmaceutiche, Università degli Studi di Trieste, Via Giorgieri 1, I-34127 Trieste, Italy
| | - Poul Jørgensen
- Lundbeck Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark
| | - Kasper Kristensen
- Lundbeck Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark
| | - Jeppe Olsen
- Lundbeck Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark
| | - Kenneth Ruud
- Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Tromsø, N-9037 Tromsø, Norway
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Christiansen O. Selected new developments in vibrational structure theory: potential construction and vibrational wave function calculations. Phys Chem Chem Phys 2012; 14:6672-87. [DOI: 10.1039/c2cp40090a] [Citation(s) in RCA: 107] [Impact Index Per Article: 8.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
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Hansen MB, Christiansen O. Vibrational contributions to cubic response functions from vibrational configuration interaction response theory. J Chem Phys 2011; 135:154107. [DOI: 10.1063/1.3652895] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
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Kristensen K, Kauczor J, Thorvaldsen AJ, Jørgensen P, Kjærgaard T, Rizzo A. Damped response theory description of two-photon absorption. J Chem Phys 2011; 134:214104. [DOI: 10.1063/1.3595280] [Citation(s) in RCA: 40] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
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