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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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2
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Madsen NK, Jensen RB, Christiansen O. Calculating vibrational excitation energies using tensor-decomposed vibrational coupled-cluster response theory. J Chem Phys 2021; 154:054113. [DOI: 10.1063/5.0037240] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Affiliation(s)
- Niels Kristian Madsen
- Department of Chemistry, University of Aarhus, Langelandsgade 140, DK–8000 Aarhus C, Denmark
| | - Rasmus Berg Jensen
- Department of Chemistry, University of Aarhus, Langelandsgade 140, DK–8000 Aarhus C, Denmark
| | - Ove Christiansen
- Department of Chemistry, University of Aarhus, Langelandsgade 140, DK–8000 Aarhus C, Denmark
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3
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Erfort S, Tschöpe M, Rauhut G. Toward a fully automated calculation of rovibrational infrared intensities for semi-rigid polyatomic molecules. J Chem Phys 2020; 152:244104. [DOI: 10.1063/5.0011832] [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)
- Sebastian Erfort
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Martin Tschöpe
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Guntram Rauhut
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
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4
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Madsen NK, Hansen MB, Zoccante A, Monrad K, Hansen MB, Christiansen O. Exponential parameterization of wave functions for quantum dynamics: Time-dependent Hartree in second quantization. J Chem Phys 2018; 149:134110. [DOI: 10.1063/1.5049344] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [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
| | - Alberto Zoccante
- Department of Chemistry, University of Aarhus, Langelandsgade 140, DK-8000 Aarhus C, Denmark
| | - Kasper Monrad
- Department of Chemistry, University of Aarhus, Langelandsgade 140, DK-8000 Aarhus C, Denmark
| | - Mikkel Bo 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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Madsen NK, Godtliebsen IH, Losilla SA, Christiansen O. Tensor-decomposed vibrational coupled-cluster theory: Enabling large-scale, highly accurate vibrational-structure calculations. J Chem Phys 2018; 148:024103. [DOI: 10.1063/1.5001569] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | | | | | - Ove Christiansen
- Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark
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6
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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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Petrenko T, Rauhut G. A new efficient method for the calculation of interior eigenpairs and its application to vibrational structure problems. J Chem Phys 2017; 146:124101. [DOI: 10.1063/1.4978581] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] 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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8
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Ostrowski L, Ziegler B, Rauhut G. Tensor decomposition in potential energy surface representations. J Chem Phys 2016; 145:104103. [DOI: 10.1063/1.4962368] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Affiliation(s)
- Lukas Ostrowski
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Benjamin Ziegler
- 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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9
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Meier P, Oschetzki D, Pfeiffer F, Rauhut G. Towards an automated and efficient calculation of resonating vibrational states based on state-averaged multiconfigurational approaches. J Chem Phys 2015; 143:244111. [DOI: 10.1063/1.4938280] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Patrick Meier
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Dominik Oschetzki
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Florian Pfeiffer
- 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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11
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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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12
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Godtliebsen IH, Hansen MB, Christiansen O. Tensor decomposition techniques in the solution of vibrational coupled cluster response theory eigenvalue equations. J Chem Phys 2015; 142:024105. [DOI: 10.1063/1.4905160] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | | | - Ove Christiansen
- Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark
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13
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List NH, Coriani S, Kongsted J, Christiansen O. Lanczos-driven coupled–cluster damped linear response theory for molecules in polarizable environments. J Chem Phys 2014; 141:244107. [DOI: 10.1063/1.4903981] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Affiliation(s)
- Nanna Holmgaard List
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark
| | - Sonia Coriani
- Dipartimento di Scienze Chimiche e Farmaceutiche, Università degli Studi di Trieste, via Giorgieri 1, 34127 Trieste, Italy
| | - Jacob Kongsted
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark
| | - Ove Christiansen
- Center for Oxygen Microscopy and Imaging, Department of Chemistry, Aarhus University, Langelandsgade 140, Aarhus 8000, Denmark
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Yu HG. A complex guided spectral transform Lanczos method for studying quantum resonance states. J Chem Phys 2014; 141:244114. [PMID: 25554140 DOI: 10.1063/1.4905083] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A complex guided spectral transform Lanczos (cGSTL) algorithm is proposed to compute both bound and resonance states including energies, widths, and wavefunctions. The algorithm comprises of two layers of complex-symmetric Lanczos iterations. A short inner layer iteration produces a set of complex formally orthogonal Lanczos polynomials. They are used to span the guided spectral transform function determined by a retarded Green operator. An outer layer iteration is then carried out with the transform function to compute the eigen-pairs of the system. The guided spectral transform function is designed to have the same wavefunctions as the eigenstates of the original Hamiltonian in the spectral range of interest. Therefore, the energies and/or widths of bound or resonance states can be easily computed with their wavefunctions or by using a root-searching method from the guided spectral transform surface. The new cGSTL algorithm is applied to bound and resonance states of HO2, and compared to previous calculations.
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Affiliation(s)
- Hua-Gen Yu
- Department of Chemistry, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
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Thomsen B, Yagi K, Christiansen O. Optimized coordinates in vibrational coupled cluster calculations. J Chem Phys 2014. [DOI: 10.1063/1.4870775] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
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Kauczor J, Norman P, Christiansen O, Coriani S. Communication: A reduced-space algorithm for the solution of the complex linear response equations used in coupled cluster damped response theory. J Chem Phys 2013; 139:211102. [DOI: 10.1063/1.4840275] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
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Horný Ľ, Schaefer HF, Ünlü F, Willeke M. Theoretical investigation of the cyclopropene radical cation c-C 3H +• 4: structure, energetics and spectroscopic properties †. Mol Phys 2013. [DOI: 10.1080/00268976.2013.806684] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Ľuboš Horný
- Laboratory of Physical Chemistry, , ETH Zürich, Zürich, 8093, Switzerland
| | - Henry F. Schaefer
- Center for Computational Quantum Chemistry, University of Georgia , Athens, Georgia, 30602-2525, USA
| | - Fatih Ünlü
- Laboratory of Physical Chemistry, , ETH Zürich, Zürich, 8093, Switzerland
| | - Martin Willeke
- Department of Materials, , ETH Zürich, Zürich, 8093, Switzerland
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19
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Godtliebsen IH, Christiansen O. A band Lanczos approach for calculation of vibrational coupled cluster response functions: simultaneous calculation of IR and Raman anharmonic spectra for the complex of pyridine and a silver cation. Phys Chem Chem Phys 2013; 15:10035-48. [DOI: 10.1039/c3cp50283j] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
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20
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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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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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