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de Moura CEV, Sokolov AY. Efficient Spin-Adapted Implementation of Multireference Algebraic Diagrammatic Construction Theory. I. Core-Ionized States and X-ray Photoelectron Spectra. J Phys Chem A 2024; 128:5816-5831. [PMID: 38962857 DOI: 10.1021/acs.jpca.4c03161] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/05/2024]
Abstract
We present an efficient implementation of multireference algebraic diagrammatic construction theory (MR-ADC) for simulating core-ionized states and X-ray photoelectron spectra (XPS). Taking advantage of spin adaptation, automatic code generation, and density fitting, our implementation can perform calculations for molecules with more than 1500 molecular orbitals, incorporating static and dynamic correlation in the ground and excited electronic states. We demonstrate the capabilities of MR-ADC methods by simulating the XPS spectra of substituted ferrocene complexes and azobenzene isomers. For the ground electronic states of these molecules, the XPS spectra computed using the extended second-order MR-ADC method (MR-ADC(2)-X) are in a very good agreement with available experimental results. We further show that MR-ADC can be used as a tool for interpreting or predicting the results of time-resolved XPS measurements by simulating the core ionization spectra of azobenzene along its photoisomerization, including the XPS signatures of excited states and the minimum energy conical intersection. This work is the first in a series of publications reporting the efficient implementations of MR-ADC methods.
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Affiliation(s)
- Carlos E V de Moura
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
| | - Alexander Yu Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
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2
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Li C, Mao S, Huang R, Evangelista FA. Frozen Natural Orbitals for the State-Averaged Driven Similarity Renormalization Group. J Chem Theory Comput 2024; 20:4170-4181. [PMID: 38747709 DOI: 10.1021/acs.jctc.4c00152] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/29/2024]
Abstract
We present a reduced-cost implementation of the state-averaged driven similarity renormalization group (SA-DSRG) based on the frozen natural orbital (FNO) approach. The natural orbitals (NOs) are obtained by diagonalizing the one-body reduced density matrix from SA-DSRG second-order perturbation theory (SA-DSRG-PT2). We consider three criteria to truncate the virtual NOs for the subsequent electron correlation treatment beyond SA-DSRG-PT2. An additive second-order correction is applied to the SA-DSRG Hamiltonian to reintroduce correlation effects from the discarded orbitals. The FNO SA-DSRG method is benchmarked on 35 small organic molecules in the QUEST database. When keeping 98-99% of the cumulative occupation numbers, the mean absolute error in the vertical transition energies due to FNO is less than 0.01 eV. Using the same FNO threshold, we observe a speedup of 9 times compared to the conventional SA-DSRG implementation for nickel carbonyl with a quadruple-ζ basis set. The FNO approach enables nonperturbative SA-DSRG computations on chloroiron corrole [FeCl(C19H11N4)] with more than 1000 basis functions, surpassing the current limit of a conventional implementation.
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Affiliation(s)
- Chenyang Li
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Shuxian Mao
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Renke Huang
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
| | - Francesco A Evangelista
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
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3
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Kulahlioglu AH, Dreuw A. Dense-sparse quantum Monte Carlo algebraic diagrammatic construction and importance ranking. J Chem Phys 2024; 160:204111. [PMID: 38785284 DOI: 10.1063/5.0209137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2024] [Accepted: 05/07/2024] [Indexed: 05/25/2024] Open
Abstract
Quantum Monte Carlo Algebraic Diagrammatic Construction (QMCADC) has been proposed as a reformulation of the second-order ADC scheme for the polarization propagator within the projection quantum Monte Carlo formalism. Dense-sparse partitioning and importance ranking filtering strategies are now exploited to accelerate its convergence and to alleviate the sign problem inherent in such calculations. By splitting the configuration space into dense and sparse subsets, the corresponding projection operator is decomposed into four distinct blocks. Deterministic calculations handle the dense-to-dense and sparse-to-dense blocks, while the remaining blocks, dense-to-sparse and sparse-to-sparse, are stochastically evaluated. The dense set is efficiently stored in a fixed-size array, and the sparse set is represented through conventional floating random Monte Carlo walks. The stochastic projection is further refined through importance ranking criteria, enabling a reduction in the required number of walkers with a controllable bias. Our results demonstrate the integration of dense-sparse partitioning with importance ranking filtering to significantly enhance the efficiency of QMCADC, enabling large-scale molecular excited-state calculations. Furthermore, this novel approach maximizes the utilization of the sparsity of ADC(2), transforming QMCADC into a tailored framework for ADC calculations.
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Affiliation(s)
- Adem Halil Kulahlioglu
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
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4
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Rana M, Ghosh A. Full Dynamical and Ab Initio Investigation of the Electron Transfer-Mediated Decay Mechanism of He + in the Presence of Heavier Alkali Dimers. J Phys Chem A 2024; 128:1973-1983. [PMID: 38447163 DOI: 10.1021/acs.jpca.3c07115] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/08/2024]
Abstract
We have studied the electron transfer-mediated decay (ETMD) process for the 1s ionized state of the He atom in the presence of a heavier alkali homonuclear dimer (Na2, K2, and Rb2) as well as heteronuclear dimer (LiNa, NaK, and KRb). In our computation, we have considered all the alkali dimers being in the singlet electronic ground state. The electron transfer from the alkali dimer to He (1s-1) leads to the emission of another electron from the alkali dimer into the continuum. We have investigated the impact of the distance of the He atom from the center of mass of the alkali dimer on the ETMD decay width. We also performed the Born-Oppenheimer molecular dynamics simulation to understand the impact of nuclear dynamics on the ETMD process.
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Affiliation(s)
- Meenakshi Rana
- Department of Chemistry, Ashoka University, Sonipat, Haryana 131029, India
| | - Aryya Ghosh
- Department of Chemistry, Ashoka University, Sonipat, Haryana 131029, India
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5
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Di Felice R, Mayes ML, Richard RM, Williams-Young DB, Chan GKL, de Jong WA, Govind N, Head-Gordon M, Hermes MR, Kowalski K, Li X, Lischka H, Mueller KT, Mutlu E, Niklasson AMN, Pederson MR, Peng B, Shepard R, Valeev EF, van Schilfgaarde M, Vlaisavljevich B, Windus TL, Xantheas SS, Zhang X, Zimmerman PM. A Perspective on Sustainable Computational Chemistry Software Development and Integration. J Chem Theory Comput 2023; 19:7056-7076. [PMID: 37769271 PMCID: PMC10601486 DOI: 10.1021/acs.jctc.3c00419] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2023] [Indexed: 09/30/2023]
Abstract
The power of quantum chemistry to predict the ground and excited state properties of complex chemical systems has driven the development of computational quantum chemistry software, integrating advances in theory, applied mathematics, and computer science. The emergence of new computational paradigms associated with exascale technologies also poses significant challenges that require a flexible forward strategy to take full advantage of existing and forthcoming computational resources. In this context, the sustainability and interoperability of computational chemistry software development are among the most pressing issues. In this perspective, we discuss software infrastructure needs and investments with an eye to fully utilize exascale resources and provide unique computational tools for next-generation science problems and scientific discoveries.
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Affiliation(s)
- Rosa Di Felice
- Departments
of Physics and Astronomy and Quantitative and Computational Biology, University of Southern California, Los Angeles, California 90089, United States
- CNR-NANO
Modena, Modena 41125, Italy
| | - Maricris L. Mayes
- Department
of Chemistry and Biochemistry, University
of Massachusetts Dartmouth, North Dartmouth, Massachusetts 02747, United States
| | | | | | - Garnet Kin-Lic Chan
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
| | - Wibe A. de Jong
- Lawrence
Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Niranjan Govind
- Physical
Sciences Division, Pacific Northwest National
Laboratory, Richland, Washington 99354, United States
| | - Martin Head-Gordon
- Pitzer Center
for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Matthew R. Hermes
- Department
of Chemistry, Chicago Center for Theoretical Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Karol Kowalski
- Physical
Sciences Division, Pacific Northwest National
Laboratory, Richland, Washington 99354, United States
| | - Xiaosong Li
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Hans Lischka
- Department
of Chemistry and Biochemistry, Texas Tech
University, Lubbock, Texas 79409, United States
| | - Karl T. Mueller
- Physical
and Computational Sciences Directorate, 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
| | - Anders M. N. Niklasson
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Mark R. Pederson
- Department
of Physics, The University of Texas at El
Paso, El Paso, Texas 79968, United States
| | - Bo Peng
- Physical
Sciences Division, Pacific Northwest National
Laboratory, Richland, Washington 99354, United States
| | - Ron Shepard
- Chemical
Sciences and Engineering Division, Argonne
National Laboratory, Lemont, Illinois 60439, United States
| | - Edward F. Valeev
- Department
of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | | | - Bess Vlaisavljevich
- Department
of Chemistry, University of South Dakota, Vermillion, South Dakota 57069, United States
| | - Theresa L. Windus
- Department
of Chemistry, Iowa State University and
Ames Laboratory, Ames, Iowa 50011, United States
| | - Sotiris S. Xantheas
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
- Advanced
Computing, Mathematics and Data Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Xing Zhang
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
| | - Paul M. Zimmerman
- Department
of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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6
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Kähler S, Cebreiro-Gallardo A, Pokhilko P, Casanova D, Krylov AI. State-Interaction Approach for Evaluating g-Tensors within EOM-CC and RAS-CI Frameworks: Theory and Benchmarks. J Phys Chem A 2023; 127:8459-8472. [PMID: 37774315 DOI: 10.1021/acs.jpca.3c04134] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/01/2023]
Abstract
Among various techniques designed for studying open-shell species, electron paramagnetic resonance (EPR) spectroscopy plays an important role. The key quantity measured by EPR is the g-tensor, describing the coupling between an external magnetic field and molecular electronic spin. One theoretical framework for quantum chemistry calculations of g-tensors is based on response theory, which involves substantial developments that are specific to the underlying electronic structure models. A simplified and easier-to-implement approach is based on the state-interaction scheme, in which perturbation is included by considering a small number of states. We describe and benchmark the state-interaction approach using equation-of-motion coupled-cluster and restricted-active-space configuration interaction wave functions. The analysis confirms that this approach can deliver accurate results and highlights caveats of applying it, such as a choice of the reference state, convergence with respect to the number of states used in calculations, etc. The analysis also contributes toward a better understanding of challenges in calculations of higher-order properties using approximate wave functions.
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Affiliation(s)
- Sven Kähler
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States
| | | | - Pavel Pokhilko
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States
| | - David Casanova
- Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
- IKERBASQUE, Basque Foundation for Science, 48009 Bilbao, Euskadi, Spain
| | - Anna I Krylov
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States
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7
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Mukhopadhyay T, Jangid B, Dutta AK. State-specific frozen natural orbital for reduced-cost algebraic diagrammatic construction calculations: The application to ionization problem. J Chem Phys 2023; 159:084113. [PMID: 37638624 DOI: 10.1063/5.0160024] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2023] [Accepted: 08/03/2023] [Indexed: 08/29/2023] Open
Abstract
We have developed a reduced-cost algebraic diagrammatic construction (ADC) method based on state-specific frozen natural orbital and natural auxiliary functions. The newly developed method has been benchmarked on the GW100 test set for the ionization problem. The use of state-specific natural orbitals drastically reduces the size of the virtual space with a systematically controllable accuracy and offers a significant speedup over the standard ionization potential (IP)-ADC(3) method. The accuracy of the method can be controlled by two thresholds and nearly a black box to use. The inclusion of the perturbative correction significantly improves the accuracy of the calculated IP values, and the efficiency of the method has been demonstrated by calculating the IP of a molecule with 60 atoms and more than 2216 basis functions.
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Affiliation(s)
- Tamoghna Mukhopadhyay
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Bhavnesh Jangid
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Achintya Kumar Dutta
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
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8
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Dreuw A, Papapostolou A, Dempwolff AL. Algebraic Diagrammatic Construction Schemes Employing the Intermediate State Formalism: Theory, Capabilities, and Interpretation. J Phys Chem A 2023; 127:6635-6646. [PMID: 37498297 DOI: 10.1021/acs.jpca.3c02761] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/28/2023]
Abstract
Algebraic diagrammatic construction (ADC) schemes represent a family of ab initio methods for the calculation of excited electronic states and electron-detached and -attached states. All ADC methods have been demonstrated to possess great potential for molecular applications, e.g., for the calculation of absorption or photoelectron spectra or electron attachment processes. ADC originates from Green's function or propagator theory; however, most recent ADC developments heavily rely on the intermediate state representation or effective Liouvillian formalisms, which comprise new ADC methods and computational schemes for high-order properties. The different approaches for the calculation of excitation energies, ionization potentials, and electron affinities are intimately related, and they provide a coherent description of these quantities at equivalent levels of theory and with comparable errors. Most quantum chemical program packages contain ADC methods; however, the most complete ADC suite of methods can be found in the recent release of Q-Chem.
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Affiliation(s)
- Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, 69120 Heidelberg, Germany
| | - Antonia Papapostolou
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, 69120 Heidelberg, Germany
| | - Adrian L Dempwolff
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, 69120 Heidelberg, Germany
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9
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Banerjee S, Sokolov AY. Algebraic Diagrammatic Construction Theory for Simulating Charged Excited States and Photoelectron Spectra. J Chem Theory Comput 2023. [PMID: 37191264 DOI: 10.1021/acs.jctc.3c00251] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
Charged excitations are electronic transitions that involve a change in the total charge of a molecule or material. Understanding the properties and reactivity of charged species requires insights from theoretical calculations that can accurately describe orbital relaxation and electron correlation effects in open-shell electronic states. In this Review, we describe the current state of algebraic diagrammatic construction (ADC) theory for simulating charged excitations and its recent developments. We start with a short overview of ADC formalism for the one-particle Green's function, including its single- and multireference formulations and extension to periodic systems. Next, we focus on the capabilities of ADC methods and discuss recent findings about their accuracy for calculating a wide range of excited-state properties. We conclude our Review by outlining possible directions for future developments of this theoretical approach.
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Affiliation(s)
- Samragni Banerjee
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
| | - Alexander Yu Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
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10
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Kulahlioglu AH, Dreuw A. The Multistate Quantum Monte Carlo Algebraic Diagrammatic Construction Method. J Phys Chem A 2023; 127:2161-2175. [PMID: 36847774 DOI: 10.1021/acs.jpca.2c08391] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/01/2023]
Abstract
A multistate formulation of the recently developed quantum Monte Carlo (QMC) algebraic diagrammatic construction (ADC) method, QMCADC, is presented. QMCADC solves the Hermitian eigenvalue problem of the second-order ADC scheme for the polarization propagator stochastically by combining ADC schemes with projector quantum Monte Carlo (PQMC). It allows for massively parallel distributed computing and exploits the sparsity of the effective ADC matrix, thereby relaxing memory and processing requirements of ADC methods significantly. Here, the theory and implementation of the multistate variant of QMCADC are described, and our first proof-of-principle calculations for various molecular systems are shown. Indeed, multistate QMCADC enables sampling of an arbitrary number of low-lying excited states and can reproduce their vertical excitation energies with a marginal controllable error. The performance of multistate QMCADC is examined in terms of state-wise and overall accuracy as well as with respect to the balance in the treatments of excited states relatively to each other. The results are very promising as they show bias and imbalances among excited states to diminish as the number of sampling points increases. Furthermore, the impact of the quality of trial wave functions on the vertical excitation energies is investigated. A black-box approach for the generation of high quality trial wave functions internally is given.
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Affiliation(s)
- Adem Halil Kulahlioglu
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
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11
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Jayadev NK, Ferino-Pérez A, Matz F, Krylov AI, Jagau TC. The Auger spectrum of benzene. J Chem Phys 2023; 158:064109. [PMID: 36792526 DOI: 10.1063/5.0138674] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
We present an ab initio computational study of the Auger electron spectrum of benzene. Auger electron spectroscopy exploits the Auger-Meitner effect, and although it is established as an analytic technique, the theoretical modeling of molecular Auger spectra from first principles remains challenging. Here, we use coupled-cluster theory and equation-of-motion coupled-cluster theory combined with two approaches to describe the decaying nature of core-ionized states: (i) Feshbach-Fano resonance theory and (ii) the method of complex basis functions. The spectra computed with these two approaches are in excellent agreement with each other and also agree well with experimental Auger spectra of benzene. The Auger spectrum of benzene features two well-resolved peaks at Auger electron energies above 260 eV, which correspond to final states with two electrons removed from the 1e1g and 3e2g highest occupied molecular orbitals. At lower Auger electron energies, the spectrum is less well resolved, and the peaks comprise multiple final states of the benzene dication. In line with theoretical considerations, singlet decay channels contribute more to the total Auger intensity than the corresponding triplet decay channels.
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Affiliation(s)
- Nayanthara K Jayadev
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
| | | | - Florian Matz
- Department of Chemistry, KU Leuven, B-3001 Leuven, Belgium
| | - Anna I Krylov
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
| | - Thomas-C Jagau
- Department of Chemistry, KU Leuven, B-3001 Leuven, Belgium
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12
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Wang M, Fang WH, Li C. Assessment of State-Averaged Driven Similarity Renormalization Group on Vertical Excitation Energies: Optimal Flow Parameters and Applications to Nucleobases. J Chem Theory Comput 2023; 19:122-136. [PMID: 36534617 DOI: 10.1021/acs.jctc.2c00966] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
We present a comprehensive excited-state benchmark for the state-averaged (SA) driven similarity renormalization group (DSRG) [Li, C.; Evangelista, F. A. J. Chem. Phys. 2018, 148, 124106]. Following the QUEST database [Véril, M.; Scemama, A.; Caffarel, M.; Lipparini, F.; Boggio-Pasqua, M.; Jacquemin, D.; Loos, P.-F. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2021, 11, e1517], 280 vertical transition energies of 35 medium-sized molecules are computed using the SA-DSRG derived second- and third-order perturbation theories (PT2/PT3) along with a nonperturbative approach [sq-LDSRG(2)]. Comparing to the theoretical best estimates, the optimal flow parameter is found to be 0.35 and 2.0 Eh-2 for SA-DSRG-PT2 and SA-DSRG-PT3, respectively. For SA-sq-LDSRG(2), a flow parameter of 1.5 Eh-2 provides converged equations without compromising the accuracy. We then assess the accuracy of the SA-DSRG hierarchy using these parameters. The SA-DSRG-PT2 scheme outperforms the level-shifted CASPT2 by 0.10 eV in mean absolute error (MAE), yet this accuracy is slightly inferior than that of CASPT2 with the ionization-potential-electron-affinity shift. Both SA-DSRG-PT3 and SA-sq-LDSRG(2) yield a MAE of 0.10 eV, which is comparable to that of CASPT3 (0.09 eV). Finally, we compute vertical excitation energies of several low-lying singlet states of nucleobases. The SA-sq-LDSRG(2) approach provides highly accurate results for π → π* excitations, while n → π* transitions are better described by SA-DSRG-PT3.
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Affiliation(s)
- Meng Wang
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Wei-Hai Fang
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Chenyang Li
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
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13
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Banerjee S, Sokolov AY. Non-Dyson Algebraic Diagrammatic Construction Theory for Charged Excitations in Solids. J Chem Theory Comput 2022; 18:5337-5348. [PMID: 35976918 DOI: 10.1021/acs.jctc.2c00565] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present the first implementation and applications of non-Dyson algebraic diagrammatic construction theory for charged excitations in three-dimensional periodic solids (EA/IP-ADC). The EA/IP-ADC approach has a computational cost similar to the ground-state Møller-Plesset perturbation theory, enabling efficient calculations of a variety of crystalline excited-state properties (e.g., band structure, band gap, density of states) sampled in the Brillouin zone. We use EA/IP-ADC to compute the quasiparticle band structures and band gaps of several materials (from large-gap atomic and ionic solids to small-gap semiconductors) and analyze the errors of EA/IP-ADC approximations up to the third order in perturbation theory. Our work also reports the first-ever calculations of ground-state properties (equation-of-state and lattice constants) of three-dimensional crystalline systems using a periodic implementation of third-order Møller-Plesset perturbation theory (MP3).
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Affiliation(s)
- Samragni Banerjee
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
| | - Alexander Yu Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
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14
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Brumboiu IE, Fransson T. Core-hole delocalization for modeling X-ray spectroscopies: A cautionary tale. J Chem Phys 2022; 156:214109. [DOI: 10.1063/5.0088195] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The influence of core-hole delocalization for X-ray photoelectron, X-ray absorption, and X-ray emission spectrum calculations is investigated in detail, using approaches including response theory, transition-potential methods, and ground state schemes. The question of a localized/delocalized vacancy is relevant for systems with symmetrically equivalent atoms, as well as near-degeneracies which can distribute the core-orbitals over several atoms. We show that issues relating to core-hole delocalization are present for calculations considering explicit core-hole states, e.g. when using a core-excited or core-ionized reference state, or for fractional occupation numbers. Including electron correlation eventually alleviates the issues, but even using CCSD(T) there is a noticable discrepancy between core-ionization energies obtained with a localized and delocalized core-hole (0.5 eV for the carbon K-edge). Within density functional theory, the discrepancy correlates to the exchange interaction involving the core orbitals of the same spin symmetry as the delocalized core-hole. The use of a localized core-hole allows for a reasonably good inclusion of relaxation at lower level of theory, whereas the proper symmetry solution involving a delocalized core-hole requires higher levels of theory to account for the correlation effects involved in orbital relaxation. For linear response methods, we further show that if X-ray absorption spectra are modelled by considering symmetry-unique sets of atoms, care has to be taken such that there are no delocalizations of the core orbitals, which would otherwise introduce shifts in absolute energies and relative features.
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Affiliation(s)
- Iulia Emilia Brumboiu
- Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Torun Institute of Physics, Poland
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15
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Dreuw A, Fransson T. Using core-hole reference states for calculating X-ray photoelectron and emission spectra. Phys Chem Chem Phys 2022; 24:11259-11267. [PMID: 35481477 DOI: 10.1039/d2cp00584k] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
For the calculation of core-ionization energies (IEs), X-ray photoelectron spectra (XPS), and X-ray emission spectra (XES), a commonly applied approach is to use non-Aufbau reference states with a core-hole as either final (IE and XPS) or initial (XES) state. However, such reference states can introduce numerical instabilities in post-HF methods, relating to the denominator of the energy corrections involved. This may become arbitrarily close to zero if a negative virtual orbital is present, e.g. a core-hole, leading to near-singularities. The resulting instabilities lead to severe convergence issues of the calculation schemes and, in addition, can strongly affect both energies and intensities, with oscillator strengths seen to reach values up to 4 × 107. For the K-edge we propose freezing the highest-energy virtual orbitals which contribute to any denominator below a threshold of 0.1 Hartree. Stable and reliable spectra are then produced, with minimal influence due to freezing energetically high-lying virtual orbitals (typically removing <5% of the total number of MOs). The developed protocol is here tested for Møller-Plesset perturbation theory and for the algebraic diagrammatic construction scheme for the polarization propagator, and it is also relevant for coupled cluster theory and other related methods.
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Affiliation(s)
- Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, Heidelberg 69120, Germany
| | - Thomas Fransson
- Department of Theoretical Chemistry and Biology, KTH Royal Institute of Technology, Stockholm 10691, Sweden.
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16
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Hodecker M, Dempwolff AL, Schirmer J, Dreuw A. Theoretical analysis and comparison of unitary coupled-cluster and algebraic-diagrammatic construction methods for ionization. J Chem Phys 2022; 156:074104. [DOI: 10.1063/5.0070967] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Affiliation(s)
- Manuel Hodecker
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Adrian L. Dempwolff
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Jochen Schirmer
- Theoretical Chemistry, Heidelberg University, Im Neuenheimer Feld 229, 69120 Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
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17
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Mester D, Kállay M. Accurate Spectral Properties within Double-Hybrid Density Functional Theory: A Spin-Scaled Range-Separated Second-Order Algebraic-Diagrammatic Construction-Based Approach. J Chem Theory Comput 2022; 18:865-882. [PMID: 35023739 PMCID: PMC8830052 DOI: 10.1021/acs.jctc.1c01100] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2021] [Indexed: 01/08/2023]
Abstract
Our second-order algebraic-diagrammatic construction [ADC(2)]-based double-hybrid (DH) ansatz (J. Chem. Theory Comput. 2019, 15, 4440. DOI: 10.1021/acs.jctc.9b00391) is combined with range-separation techniques. In the present scheme, both the exchange and the correlation contributions are range-separated, while spin-scaling approaches are also applied. The new methods are thoroughly tested for the most popular benchmark sets including 250 singlet and 156 triplet excitations, as well as 80 oscillator strengths. It is demonstrated that the range separation for the correlation contributions is highly recommended for both the genuine and the ADC(2)-based DH approaches. Our results show that the latter scheme slightly but consistently outperforms the former one for single excitation dominated transitions. Furthermore, states with larger fractions of double excitations are assessed as well, and challenging charge-transfer excitations are also discussed, where the recently proposed spin-scaled long-range corrected DHs fail. The suggested iterative fourth-power scaling RS-PBE-P86/SOS-ADC(2) method, using only three adjustable parameters, provides the most robust and accurate excitation energies within the DH theory. In addition, the relative error of the oscillator strengths is reduced by 65% compared to the best genuine DH functionals.
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Affiliation(s)
- Dávid Mester
- Department of Physical Chemistry and
Materials Science, Budapest University of
Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
| | - Mihály Kállay
- Department of Physical Chemistry and
Materials Science, Budapest University of
Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
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18
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Dempwolff AL, Hodecker M, Dreuw A. Vertical ionization potential benchmark for unitary coupled-cluster and algebraic-diagrammatic construction methods. J Chem Phys 2022; 156:054114. [DOI: 10.1063/5.0079047] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Adrian L. Dempwolff
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Manuel Hodecker
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
- Department of Theoretical Chemistry and Biology, KTH Royal Institute of Technology, Malvinas Väg 10, 114 28 Stockholm, Sweden
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
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19
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Kulahlioglu AH, Rehn D, Dreuw A. Quantum Monte Carlo formulation of the second order algebraic diagrammatic construction: Toward a massively parallel correlated excited state method. J Chem Phys 2022; 156:044105. [DOI: 10.1063/5.0071091] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Adem Halil Kulahlioglu
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Dirk Rehn
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
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20
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Liu J, Cheng L. Unitary coupled-cluster based self-consistent polarization propagator theory: A quadratic unitary coupled-cluster singles and doubles scheme. J Chem Phys 2021; 155:174102. [PMID: 34742195 DOI: 10.1063/5.0062090] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The development of a quadratic unitary coupled-cluster singles and doubles (qUCCSD) based self-consistent polarization propagator method is reported. We present a simple strategy for truncating the commutator expansion of the unitary version of coupled-cluster transformed Hamiltonian H̄. The qUCCSD method for the electronic ground state includes up to double commutators for the amplitude equations and up to cubic commutators for the energy expression. The qUCCSD excited-state eigenvalue equations include up to double commutators for the singles-singles block of H̄, single commutators for the singles-doubles and doubles-singles blocks, and the bare Hamiltonian for the doubles-doubles block. Benchmark qUCCSD calculations of the ground-state properties and excitation energies for representative molecules demonstrate significant improvement of the accuracy and robustness over the previous UCC3 scheme derived using Møller-Plesset perturbation theory.
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Affiliation(s)
- Junzi Liu
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
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21
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Mazin IM, Sokolov AY. Multireference Algebraic Diagrammatic Construction Theory for Excited States: Extended Second-Order Implementation and Benchmark. J Chem Theory Comput 2021; 17:6152-6165. [PMID: 34553937 DOI: 10.1021/acs.jctc.1c00684] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present an implementation and benchmark of new approximations in multireference algebraic diagrammatic construction theory for simulations of neutral electronic excitations and UV/vis spectra of strongly correlated molecular systems (MR-ADC). Following our work on the first-order MR-ADC approximation [J. Chem. Phys. 2018, 149, 204113], we report the strict and extended second-order MR-ADC methods (MR-ADC(2) and MR-ADC(2)-X) that combine the description of static and dynamic electron correlation in the ground and excited electronic states without relying on state-averaged reference wave functions. We present an extensive benchmark of the new MR-ADC methods for excited states in several small molecules, including the carbon dimer, ethylene, and butadiene. Our results demonstrate that, for weakly correlated electronic states, the MR-ADC(2) and MR-ADC(2)-X methods outperform the third-order single-reference ADC approximation and are competitive with the results from equation-of-motion coupled cluster theory. For states with multireference character, the performance of the MR-ADC methods is similar to that of an N-electron valence perturbation theory. In contrast to conventional multireference perturbation theories, the MR-ADC methods have many attractive features, such as a straightforward and efficient calculation of excited-state properties and a direct access to excitations outside of the frontier (active) orbitals.
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Affiliation(s)
- Ilia M Mazin
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
| | - Alexander Yu Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
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22
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Brumboiu IE, Rehn DR, Dreuw A, Rhee YM, Norman P. Analytical gradients for core-excited states in the algebraic diagrammatic construction (ADC) framework. J Chem Phys 2021; 155:044106. [PMID: 34340367 DOI: 10.1063/5.0058221] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Abstract
Expressions for analytical molecular gradients of core-excited states have been derived and implemented for the hierarchy of algebraic diagrammatic construction (ADC) methods up to extended second-order within the core-valence separation (CVS) approximation. We illustrate the use of CVS-ADC gradients by determining relaxed core-excited state potential energy surfaces and optimized geometries for water, formic acid, and benzene. For water, our results show that in the dissociative lowest core-excited state, a linear configuration is preferred. For formic acid, we find that the O K-edge lowest core-excited state is non-planar, a fact that is not captured by the equivalent core approximation where the core-excited atom with its hole is replaced by the "Z + 1" neighboring atom in the periodic table. For benzene, the core-excited state gradients are presented along the Jahn-Teller distorted geometry of the 1s → π* excited state. Our development may pave a new path to studying the dynamics of molecules in their core-excited states.
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Affiliation(s)
- Iulia Emilia Brumboiu
- Department of Chemistry, Pohang University of Science and Technology (POSTECH), 37673 Pohang, Republic of Korea
| | - Dirk R Rehn
- Interdisciplinary Center for Scientific Computing, Heidelberg University, 69120 Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Heidelberg University, 69120 Heidelberg, Germany
| | - Young Min Rhee
- Department of Chemistry, Korea Advanced Institute of Science and Technology, 34141 Daejeon, Republic of Korea
| | - Patrick Norman
- Department of Theoretical Chemistry and Biology, KTH Royal Institute of Technology, 10691 Stockholm, Sweden
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23
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Dempwolff AL, Belogolova AM, Trofimov AB, Dreuw A. Intermediate state representation approach to physical properties of molecular electron-attached states: Theory, implementation, and benchmarking. J Chem Phys 2021; 154:104117. [PMID: 33722034 DOI: 10.1063/5.0043337] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
Abstract
Computational schemes for comprehensive studies of molecular electron-attached states and the calculation of electron affinities (EAs) are formulated and implemented employing the intermediate state representation (ISR) formalism and the algebraic-diagrammatic construction approximation for the electron propagator (EA-ADC). These EA-ADC(n)/ISR(m) schemes allow for a consistent treatment of not only electron affinities and pole strengths up to third-order of perturbation theory (n = 3) but also one-electron properties of electron-attached states up to second order (m = 2). The EA-ADC/ISR equations were implemented in the Q-Chem program for Ŝz-adapted intermediate states, allowing also open-shell systems to be studied using unrestricted Hartree-Fock references. For benchmarking of the EA-(U)ADC/ISR schemes, EAs and dipole moments of various electron-attached states of small closed- and open-shell molecules were computed and compared to full configuration interaction data. As an illustrative example, EA-ADC(3)/ISR(2) has been applied to the thymine-thymine (6-4) DNA photolesion.
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Affiliation(s)
- Adrian L Dempwolff
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Alexandra M Belogolova
- Laboratory of Quantum Chemistry, Irkutsk State University, Karl Marx Street 1, 664003 Irkutsk, Russia
| | - Alexander B Trofimov
- Laboratory of Quantum Chemistry, Irkutsk State University, Karl Marx Street 1, 664003 Irkutsk, Russia
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
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24
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Ambroise MA, Dreuw A, Jensen F. Probing Basis Set Requirements for Calculating Core Ionization and Core Excitation Spectra Using Correlated Wave Function Methods. J Chem Theory Comput 2021; 17:2832-2842. [PMID: 33900755 DOI: 10.1021/acs.jctc.1c00042] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Abstract
We investigate the basis set requirements for the accurate calculation of core excitations and core ionizations using correlated wave functions of coupled cluster type and linear response methods for describing the excitation. When a core excitation is described as an energy difference calculated using density functional theory, the basis set can be tailored to provide a balanced description of the reference- and excited-hole states. When the core excitation process is described by coupled cluster linear response methods, however, the basis set requirements are somewhat different. A systematic study of the sensitivity of the result to the basis set parameters suggests that a relatively large set of s- and p-type basis functions in combination with a careful selection of valence and core polarization functions is required. Based on these results, we propose a hierarchical sequence of basis sets, denoted ccX-nZ (n = D, T, Q, 5) for the atoms B-Ne, which are suitable for the calculation of core excitations by the correlated wave function linear response and equation-of-motion methods. The ccX-nZ series provides lower basis set errors for a given cardinal number or number of basis functions than other existing basis sets. For large systems, the ccX-nZ basis sets can be combined with the standard basis sets by placing the ccX-nZ only on the atoms where core excitations are of interest, but the accuracy of such mixed basis sets appears to be system-dependent.
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Affiliation(s)
- Maximilien A Ambroise
- Interdisciplinary Center for Scientific Computing, University of Heidelberg, 69117 Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, University of Heidelberg, 69117 Heidelberg, Germany
| | - Frank Jensen
- Department of Chemistry, Aarhus University, DK-8000 Aarhus, Denmark
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25
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Hoffmann M, Dreuw A. Deciphering excited state properties utilizing algebraic diagrammatic construction schemes of decreasing order. J Comput Chem 2021; 42:793-800. [PMID: 33595128 DOI: 10.1002/jcc.26499] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2020] [Revised: 01/27/2021] [Accepted: 02/02/2021] [Indexed: 11/07/2022]
Abstract
Excited state properties are difficult to trace back to the common molecular orbital picture when the excited state wavefunction is a linear combination of two or more Slater determinants. Here, a theoretical methodology is introduced based on the algebraic diagrammatic construction scheme for the polarization propagator (ADC(n)) that allows to make this connection and to eventually derive structure-function relationships. The usefulness of this approach is demonstrated by an analysis of the transition dipole moments of the low-lying 1B3u and 2B3u states of anthracene and (1,4,5,8)-tetraazaanthracene.
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Affiliation(s)
- Marvin Hoffmann
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Heidelberg, Germany
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26
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Thielen SM, Hodecker M, Piazolo J, Rehn DR, Dreuw A. Unitary coupled-cluster approach for the calculation of core-excited states and x-ray absorption spectra. J Chem Phys 2021; 154:154108. [PMID: 33887935 DOI: 10.1063/5.0047134] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this work, we present the core-valence separation (CVS) approximation applied to unitary coupled-cluster (UCC) theory for the calculation of core-excited states and the simulation of x-ray absorption spectroscopy (XAS). Excitation energies and oscillator strengths of small- to medium-sized organic molecules have been computed using the second-order and extended second-order UCC schemes (CVS-UCC2 and CVS-UCC2-x) as well as the third-order scheme (CVS-UCC3). All results are compared to the corresponding algebraic-diagrammatic construction methods and experimental data. The agreement between CVS-UCC and experimental data demonstrates its potential as a new approach for the calculation of XAS.
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Affiliation(s)
- Sebastian M Thielen
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Manuel Hodecker
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Julia Piazolo
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Dirk R Rehn
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
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27
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Fransson T, Brumboiu IE, Vidal ML, Norman P, Coriani S, Dreuw A. XABOOM: An X-ray Absorption Benchmark of Organic Molecules Based on Carbon, Nitrogen, and Oxygen 1s → π* Transitions. J Chem Theory Comput 2021; 17:1618-1637. [PMID: 33544612 PMCID: PMC8023667 DOI: 10.1021/acs.jctc.0c01082] [Citation(s) in RCA: 31] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2020] [Indexed: 01/05/2023]
Abstract
The performance of several standard and popular approaches for calculating X-ray absorption spectra at the carbon, nitrogen, and oxygen K-edges of 40 primarily organic molecules up to the size of guanine has been evaluated, focusing on the low-energy and intense 1s → π* transitions. Using results obtained with CVS-ADC(2)-x and fc-CVS-EOM-CCSD as benchmark references, we investigate the performance of CC2, ADC(2), ADC(3/2), and commonly adopted density functional theory (DFT)-based approaches. Here, focus is on precision rather than on accuracy of transition energies and intensities-in other words, we target relative energies and intensities and the spread thereof, rather than absolute values. The use of exchange-correlation functionals tailored for time-dependent DFT calculations of core excitations leads to error spreads similar to those seen for more standard functionals, despite yielding superior absolute energies. Long-range corrected functionals are shown to perform particularly well compared to our reference data, showing error spreads in energy and intensity of 0.2-0.3 eV and ∼10%, respectively, as compared to 0.3-0.6 eV and ∼20% for a typical pure hybrid. In comparing intensities, state mixing can complicate matters, and techniques to avoid this issue are discussed. Furthermore, the influence of basis sets in high-level ab initio calculations is investigated, showing that reasonably accurate results are obtained with the use of 6-311++G**. We name this benchmark suite as XABOOM (X-ray absorption benchmark of organic molecules) and provide molecular structures and ground-state self-consistent field energies and spectroscopic data. We believe that it provides a good assessment of electronic structure theory methods for calculating X-ray absorption spectra and will become useful for future developments in this field.
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Affiliation(s)
- Thomas Fransson
- Interdisciplinary
Center for Scientific Computing, Ruprecht-Karls
University, Im Neuenheimer
Feld 205, 69120 Heidelberg, Germany
- Fysikum, Stockholm University, Albanova, 10691 Stockholm, Sweden
| | - Iulia E. Brumboiu
- Department
of Theoretical Chemistry and Biology, KTH
Royal Institute of Technology, 10691 Stockholm, Sweden
- Department
of Chemistry, Korea Advanced Institute of
Science and Technology, 34141 Daejeon, Korea
| | - Marta L. Vidal
- DTU
Chemistry, Technical University of Denmark, Kemitorvet Bldg 207, DK-2800 Kongens Lyngby, Denmark
| | - Patrick Norman
- Department
of Theoretical Chemistry and Biology, KTH
Royal Institute of Technology, 10691 Stockholm, Sweden
| | - Sonia Coriani
- DTU
Chemistry, Technical University of Denmark, Kemitorvet Bldg 207, DK-2800 Kongens Lyngby, Denmark
- Department
of Chemistry, NTNU-Norwegian University
of Science and Technology, N-7991 Trondheim, Norway
| | - Andreas Dreuw
- Interdisciplinary
Center for Scientific Computing, Ruprecht-Karls
University, Im Neuenheimer
Feld 205, 69120 Heidelberg, Germany
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28
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Banerjee S, Sokolov AY. Efficient implementation of the single-reference algebraic diagrammatic construction theory for charged excitations: Applications to the TEMPO radical and DNA base pairs. J Chem Phys 2021; 154:074105. [PMID: 33607870 DOI: 10.1063/5.0040317] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
We present an efficient implementation of the second- and third-order single-reference algebraic diagrammatic construction (ADC) theory for electron attachment and ionization energies and spectra [EA/IP-ADC(n), n = 2, 3]. Our new EA/IP-ADC program features spin adaptation for closed-shell systems, density fitting for efficient handling of the two-electron integral tensors, and vectorized and parallel implementation of tensor contractions. We demonstrate capabilities of our efficient implementation by applying the EA/IP-ADC(n) (n = 2, 3) methods to compute the photoelectron spectrum of the (2,2,6,6-tetramethylpiperidin-1-yl)oxyl (TEMPO) radical, as well as the vertical and adiabatic electron affinities of TEMPO and two DNA base pairs (guanine-cytosine and adenine-thymine). The spectra and electron affinities computed using large diffuse basis sets with up to 1028 molecular orbitals are found to be in good agreement with the best available results from the experiment and theoretical simulations.
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Affiliation(s)
- Samragni Banerjee
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - Alexander Yu Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
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29
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Jahnke T, Hergenhahn U, Winter B, Dörner R, Frühling U, Demekhin PV, Gokhberg K, Cederbaum LS, Ehresmann A, Knie A, Dreuw A. Interatomic and Intermolecular Coulombic Decay. Chem Rev 2020; 120:11295-11369. [PMID: 33035051 PMCID: PMC7596762 DOI: 10.1021/acs.chemrev.0c00106] [Citation(s) in RCA: 65] [Impact Index Per Article: 16.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2020] [Indexed: 12/11/2022]
Abstract
Interatomic or intermolecular Coulombic decay (ICD) is a nonlocal electronic decay mechanism occurring in weakly bound matter. In an ICD process, energy released by electronic relaxation of an excited atom or molecule leads to ionization of a neighboring one via Coulombic electron interactions. ICD has been predicted theoretically in the mid nineties of the last century, and its existence has been confirmed experimentally approximately ten years later. Since then, a number of fundamental and applied aspects have been studied in this quickly growing field of research. This review provides an introduction to ICD and draws the connection to related energy transfer and ionization processes. The theoretical approaches for the description of ICD as well as the experimental techniques developed and employed for its investigation are described. The existing body of literature on experimental and theoretical studies of ICD processes in different atomic and molecular systems is reviewed.
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Affiliation(s)
- Till Jahnke
- Institut
für Kernphysik, Goethe Universität, Max-von-Laue-Str. 1, 60438 Frankfurt, Germany
| | - Uwe Hergenhahn
- Fritz-Haber-Institut
der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany
- Max
Planck Institute for Plasma Physics, Wendelsteinstr. 1, 17491 Greifswald, Germany
- Leibniz
Institute of Surface Engineering (IOM), 04318 Leipzig, Germany
| | - Bernd Winter
- Fritz-Haber-Institut
der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany
| | - Reinhard Dörner
- Institut
für Kernphysik, Goethe Universität, Max-von-Laue-Str. 1, 60438 Frankfurt, Germany
| | - Ulrike Frühling
- Institut
für Experimentalphysik and Center for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Philipp V. Demekhin
- Institut
für Physik und CINSaT, Universität
Kassel, Heinrich-Plett-Str. 40, 34132 Kassel, Germany
| | - Kirill Gokhberg
- Physical-Chemistry
Institute, Ruprecht-Karls University, Im Neuenheimer Feld 229, 69120 Heidelberg, Germany
| | - Lorenz S. Cederbaum
- Physical-Chemistry
Institute, Ruprecht-Karls University, Im Neuenheimer Feld 229, 69120 Heidelberg, Germany
| | - Arno Ehresmann
- Institut
für Physik und CINSaT, Universität
Kassel, Heinrich-Plett-Str. 40, 34132 Kassel, Germany
| | - André Knie
- Institut
für Physik und CINSaT, Universität
Kassel, Heinrich-Plett-Str. 40, 34132 Kassel, Germany
| | - Andreas Dreuw
- Interdisciplinary
Center for Scientific Computing, Ruprecht-Karls
University, Im Neuenheimer
Feld 205, 69120 Heidelberg, Germany
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30
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Chatterjee K, Sokolov AY. Extended Second-Order Multireference Algebraic Diagrammatic Construction Theory for Charged Excitations. J Chem Theory Comput 2020; 16:6343-6357. [DOI: 10.1021/acs.jctc.0c00778] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Koushik Chatterjee
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
| | - Alexander Yu. Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
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31
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Hodecker M, Dreuw A. Unitary coupled cluster ground- and excited-state molecular properties. J Chem Phys 2020; 153:084112. [PMID: 32872855 DOI: 10.1063/5.0019055] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A scheme for the calculation of molecular properties within the framework of unitary coupled-cluster (UCC) theory in both the electronic ground and excited states is presented. The scheme is based on an expectation-value ansatz, similar to the equation-of-motion coupled-cluster method or the intermediate state representation (ISR) approach of the algebraic-diagrammatic construction (ADC) scheme. Due to the UCC ansatz, the resulting equations cannot be given by closed-form expressions but need to be approximated. Explicit expressions for the expectation value of a general one-particle operator correct through second order in perturbation theory have been derived and coded for the electronic ground state as well as for excited states of predominant single-excitation character. The resulting equations are shown to be equivalent to those of the second-order ADC/ISR procedure. As first computational tests, the second-order UCC method (UCC2) and the one employing third-order amplitudes (also eigenvectors) together with the second-order density matrix, denoted as UCC3(2), are applied to the calculation of dipole moments for a series of small closed- and open-shell systems as well as 4-cyanoindole and 2,3-benzofuran and compared to full configuration interaction or experimental results. For the aromatic organic molecules, the UCC2 method is shown to be sufficient for the ground-state dipole moment, whereas the UCC3(2) scheme is superior for excited-state dipole moments.
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Affiliation(s)
- Manuel Hodecker
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
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32
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Fasshauer E. Effect of spin-orbit coupling on decay widths of electronic decay processes. J Chem Phys 2020; 152:224307. [PMID: 32534556 DOI: 10.1063/5.0002243] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Auger-Meitner processes are electronic decay processes of energetically low-lying vacancies. In these processes, the vacancy is filled by an electron of an energetically higher lying orbital, while another electron is simultaneously emitted to the continuum. In low-lying orbitals, relativistic effects can not, even for light elements, be neglected. At the same time, lifetime calculations are computationally expensive. In this context, we investigate which effect spin-orbit coupling has on Auger-Meitner decay widths and aim for a rule of thumb for the relative decay widths of initial states split by spin-orbit coupling. We base this rule of thumb on Auger-Meitner decay widths of Sr4p-1 and Ra6p-1 obtained by relativistic FanoADC-Stieltjes calculations and validate it against Auger-Meitner decay widths from the literature.
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Affiliation(s)
- Elke Fasshauer
- Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, 8000 Aarhus, Denmark
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33
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Hodecker M, Thielen SM, Liu J, Rehn DR, Dreuw A. Third-Order Unitary Coupled Cluster (UCC3) for Excited Electronic States: Efficient Implementation and Benchmarking. J Chem Theory Comput 2020; 16:3654-3663. [PMID: 32396348 DOI: 10.1021/acs.jctc.0c00335] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The efficient implementation of the third-order unitary coupled-cluster scheme (UCC3) for the calculation of excited electronic states is reported. The UCC3 scheme and its second-order UCC2 variant have been benchmarked and compared to Jacquemin's recently introduced, as well as Thiel's well-established, benchmark sets for excitation energies and oscillator strengths. For the latter, the calculation of 134 excited singlet and 71 excited triplet states of 28 small- to medium-sized organic molecules has revealed that UCC2 exhibits a mean error and standard deviation of 0.36 ± 0.41 eV for singlet states and 0.22 ± 0.21 eV for triplet states, whereas UCC3 revealed an accuracy of 0.06 ± 0.27 eV for singlet and -0.22 ± 0.15 eV for triplet states. In addition, the oscillator strengths obtained with effective transition moments correct through second order in perturbation theory are in very good agreement with literature data.
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Affiliation(s)
- Manuel Hodecker
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Sebastian M Thielen
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Junzi Liu
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Dirk R Rehn
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
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Abstract
Fano-ADC is a family of ab initio methods for the prediction of electronic decay widths in excited, singly and doubly ionized systems. It has been particularly successful in elucidating the geometry dependence of the inter-atomic decay widths in clusters and facilitated the prediction of new electronic decay phenomena. However, the available Fano-ADC schemes are limited to the second-order treatment of the initial state and the first-order treatment of the final states of the decay. This confines the applicability of the Fano-ADC approach to first-order decay processes, e.g., normal but not double Auger decay (DAD), and compromises the numerical accuracy of the schemes through the unbalanced treatment of electronic correlation. Here, we introduce the ADC(2,2) approximation for singly ionized states, which describes both initial and final states of the decay up to second order. We use the new scheme to construct the Fano-ADC(2,2) approximation for the decay widths and show that it provides superior accuracy for the decay widths of a series of processes. Moreover, the Fano-ADC(2,2) method provides access to second-order decay processes, such as DAD, which are qualitatively beyond the reach of the previously available Fano-ADC implementations.
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Affiliation(s)
- P Kolorenč
- Charles University, Faculty of Mathematics and Physics, Institute of Theoretical Physics, V Holešovičkách 2, 180 00 Prague, Czech Republic
| | - V Averbukh
- Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
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35
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Hodecker M, Rehn DR, Dreuw A. Hermitian second-order methods for excited electronic states: Unitary coupled cluster in comparison with algebraic-diagrammatic construction schemes. J Chem Phys 2020; 152:094106. [PMID: 33480727 DOI: 10.1063/1.5142354] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Employing an intermediate state representation (ISR) approach, Hermitian second-order methods for the calculation of electronic excitation energies are presented and compared in detail. These comprise the algebraic-diagrammatic construction scheme for the polarization propagator, a hybrid second-order ISR scheme based on traditional coupled-cluster theory as well as two similar approaches based on a unitary coupled-cluster (UCC) ansatz. Although in a strict perturbation-theoretical framework all prove to be identical, differences emerge when the corresponding converged cluster amplitudes are used and depending on how the similarity-transformed UCC Hamiltonian is evaluated. The resulting excitation energies, however, do not significantly differ for systems well described by means of perturbation theory.
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Affiliation(s)
- Manuel Hodecker
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Dirk R Rehn
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
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36
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Dempwolff AL, Paul AC, Belogolova AM, Trofimov AB, Dreuw A. Intermediate state representation approach to physical properties of molecular electron-detached states. I. Theory and implementation. J Chem Phys 2020; 152:024113. [DOI: 10.1063/1.5137792] [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)
- Adrian L. Dempwolff
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Alexander C. Paul
- Department of Chemistry, Norwegian University of Science and Technology, 7491 Trondheim, Norway
| | - Alexandra M. Belogolova
- Laboratory of Quantum Chemistry, Irkutsk State University, Karl Marx Street 1, 664003 Irkutsk, Russia
- A. E. Favorsky Irkutsk Institute of Chemistry, Siberian Branch of the Russian Academy of Sciences, 1 Favorsky Street, 664033 Irkutsk, Russia
| | - Alexander B. Trofimov
- Laboratory of Quantum Chemistry, Irkutsk State University, Karl Marx Street 1, 664003 Irkutsk, Russia
- A. E. Favorsky Irkutsk Institute of Chemistry, Siberian Branch of the Russian Academy of Sciences, 1 Favorsky Street, 664033 Irkutsk, Russia
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
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37
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Banerjee S, Sokolov AY. Third-order algebraic diagrammatic construction theory for electron attachment and ionization energies: Conventional and Green’s function implementation. J Chem Phys 2019; 151:224112. [DOI: 10.1063/1.5131771] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Samragni Banerjee
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - Alexander Yu. Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
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38
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Mester D, Nagy PR, Kállay M. Reduced-Scaling Correlation Methods for the Excited States of Large Molecules: Implementation and Benchmarks for the Second-Order Algebraic-Diagrammatic Construction Approach. J Chem Theory Comput 2019; 15:6111-6126. [DOI: 10.1021/acs.jctc.9b00735] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Dávid Mester
- Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, H-1521 Budapest, P.O. Box 91, Hungary
| | - Péter R. Nagy
- Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, H-1521 Budapest, P.O. Box 91, Hungary
| | - Mihály Kállay
- Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, H-1521 Budapest, P.O. Box 91, Hungary
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39
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Chatterjee K, Sokolov AY. Second-Order Multireference Algebraic Diagrammatic Construction Theory for Photoelectron Spectra of Strongly Correlated Systems. J Chem Theory Comput 2019; 15:5908-5924. [DOI: 10.1021/acs.jctc.9b00528] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Koushik Chatterjee
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
| | - Alexander Yu. Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
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40
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Zhang T, Li C, Evangelista FA. Improving the Efficiency of the Multireference Driven Similarity Renormalization Group via Sequential Transformation, Density Fitting, and the Noninteracting Virtual Orbital Approximation. J Chem Theory Comput 2019; 15:4399-4414. [PMID: 31268704 DOI: 10.1021/acs.jctc.9b00353] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
This study examines several techniques to improve the efficiency of the linearized multireference driven similarity renormalization group truncated to one- and two-body operators [MR-LDSRG(2)]. We propose a sequential MR-LDSRG(2) [sq-MR-LDSRG(2)] scheme, in which one-body substitutions are folded exactly into the Hamiltonian. This new approach is combined with density fitting (DF) to reduce the storage cost of two-electron integrals. To further avoid storage of large four-index intermediates, we propose a noninteracting virtual orbital (NIVO) approximation of the Baker-Campbell-Hausdorff series that neglects commutators terms with three and four virtual indices. The NIVO approximation reduces the computational prefactor of the MR-LDSRG(2), bringing it closer to that of coupled cluster with singles and doubles (CCSD). We test the effect of the DF and NIVO approximations on the MR-LDSRG(2) and sq-MR-LDSRG(2) methods by computing properties of eight diatomic molecules. The diatomic constants obtained by DF-sq-MR-LDSRG(2)+NIVO are found to be as accurate as those from the original MR-LDSRG(2) and coupled cluster theory with singles, doubles, and perturbative triples. Finally, we demonstrate that the DF-sq-MR-LDSRG(2)+NIVO scheme can be applied to chemical systems with more than 550 basis functions by computing the automerization energy of cyclobutadiene with a quintuple-ζ basis set. The predicted automerization energy is found to be similar to the value computed with Mukherjee's state-specific multireference coupled cluster theory with singles and doubles.
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Affiliation(s)
- Tianyuan Zhang
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation , Emory University , Atlanta , Georgia 30322 , United States
| | - Chenyang Li
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation , Emory University , Atlanta , Georgia 30322 , United States
| | - Francesco A Evangelista
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation , Emory University , Atlanta , Georgia 30322 , United States
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41
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Mester D, Kállay M. Combined Density Functional and Algebraic-Diagrammatic Construction Approach for Accurate Excitation Energies and Transition Moments. J Chem Theory Comput 2019; 15:4440-4453. [PMID: 31265275 DOI: 10.1021/acs.jctc.9b00391] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
A composite of time-dependent density functional theory (TDDFT) and the second-order algebraic-diagrammatic construction [ADC(2)] approach is presented for efficient calculation of spectral properties of molecules. Our method can be regarded as a new excited-state double-hybrid (DH) approach or a dressed TDDFT scheme, but it can also be interpreted as an empirically tuned ADC(2) model. Several combinations of exchange-correlation functionals and spin-scaling schemes are explored. Our best-performing method includes the Perdew, Burke, and Ernzerhof exchange and Perdew's 1986 correlation functional and employs the scaled-opposite-spin approximation for the higher-order terms. The computation time of the new method scales as the fourth power of the system size, and an efficient cost-reduction approach is also presented, which further speeds up the calculations. Our benchmark calculations show that the proposed model outperforms not only the existing DH approaches and ADC(2) variants but also the considerably more expensive coupled-cluster methods.
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Affiliation(s)
- Dávid Mester
- Department of Physical Chemistry and Materials Science , Budapest University of Technology and Economics , P.O. Box 91, H-1521 Budapest , Hungary
| | - Mihály Kállay
- Department of Physical Chemistry and Materials Science , Budapest University of Technology and Economics , P.O. Box 91, H-1521 Budapest , Hungary
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42
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Ruberti M. Restricted Correlation Space B-Spline ADC Approach to Molecular Ionization: Theory and Applications to Total Photoionization Cross-Sections. J Chem Theory Comput 2019; 15:3635-3653. [PMID: 31136172 DOI: 10.1021/acs.jctc.9b00288] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Herein is presented a new approach to the ab initio algebraic diagrammatic construction (ADC) schemes for the polarization propagator, which is explicitly designed to accurately and efficiently describe molecular ionization. The restricted correlation space (RCS) version of the ADC methods up to second order of perturbation theory is derived via the intermediate state representation (ISR) and implemented in the multicenter B-spline basis set for the electronic continuum. Remarkably a general close-coupling structure of the RCS-ADC many-electron wave function, connecting the N-particle to the ( N - 1)-particle ADC intermediate states, emerges naturally as a nontrivial result of the RCS ansatz. Moreover, the introduced RCS-ADC schemes prove to be particularly manageable from a computational point of view, overcoming the practical limitations of the conventional ADC approaches. The quality of the new RCS-ADC( n) approaches is verified by performing a series of total photoionization cross-section calculations on a test set of molecules. The excellent agreement of the results with existing accurate benchmarks demonstrates that the RCS versions of the ADC schemes are optimal and quantitatively accurate methods for studying multichannel molecular photoionization.
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Affiliation(s)
- M Ruberti
- Department of Physics , Imperial College London , Prince Consort Road , London SW7 2AZ , United Kingdom
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43
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Peng B, Van Beeumen R, Williams-Young DB, Kowalski K, Yang C. Approximate Green's Function Coupled Cluster Method Employing Effective Dimension Reduction. J Chem Theory Comput 2019; 15:3185-3196. [PMID: 30951302 DOI: 10.1021/acs.jctc.9b00172] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The Green's function coupled cluster (GFCC) method, originally proposed in the early 1990s, is a powerful many-body tool for computing and analyzing the electronic structure of molecular and periodic systems, especially when electrons of the system are strongly correlated. However, in order for the GFCC to become a method that may be routinely used in the electronic structure calculations, robust numerical techniques and approximations must be employed to reduce its extremely high computational overhead. In our recent studies, it has been demonstrated that the GFCC equations can be solved directly in the frequency domain using iterative linear solvers, which can be easily distributed in a massively parallel environment. In the present work, we demonstrate a successful application of model-order-reduction (MOR) techniques in the GFCC framework. Briefly speaking, for a frequency regime of interest that requires high-resolution descriptions of spectral function, instead of solving the GFCC linear equation of full dimension for every single frequency point of interest, an efficiently solvable linear system model of a reduced dimension may be built upon projecting the original GFCC linear system onto a subspace. From this reduced order model is obtained a reasonable approximation to the full dimensional GFCC linear equations in both interpolative and extrapolative spectral regions. Here, we show that the subspace can be properly constructed in an iterative manner from the auxiliary vectors of the GFCC linear equations at some selected frequencies within the spectral region of interest. During the iterations, the quality of the subspace, as well as the linear system model, can be systematically improved. The method is tested in this work in terms of the efficiency and accuracy of computing spectral functions for some typical molecular systems such as carbon monoxide, 1,3-butadiene, benzene, and adenine. To reach the same level of accuracy as that of the original GFCC method, the application of MOR in the GFCC method is able to significantly lower the original computational cost for the aforementioned molecules in designated frequency regimes. As a byproduct, the reduced order model obtained by this method is found to provide a high-quality initial guess, which improves the convergence rate for the existing iterative linear solver.
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Affiliation(s)
- Bo Peng
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle , Pacific Northwest National Laboratory , K8-91, P.O. Box 999, Richland , Washington 99352 , United States
| | - Roel Van Beeumen
- Computational Research Division , Lawrence Berkeley National Laboratory , Berkeley , California 94720 , United States
| | - David B Williams-Young
- Computational Research Division , Lawrence Berkeley National Laboratory , Berkeley , California 94720 , United States
| | - Karol Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle , Pacific Northwest National Laboratory , K8-91, P.O. Box 999, Richland , Washington 99352 , United States
| | - Chao Yang
- Computational Research Division , Lawrence Berkeley National Laboratory , Berkeley , California 94720 , United States
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44
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Hodecker M, Dempwolff AL, Rehn DR, Dreuw A. Algebraic-diagrammatic construction scheme for the polarization propagator including ground-state coupled-cluster amplitudes. I. Excitation energies. J Chem Phys 2019; 150:174104. [DOI: 10.1063/1.5081663] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Manuel Hodecker
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D–69120 Heidelberg, Germany
| | - Adrian L. Dempwolff
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D–69120 Heidelberg, Germany
| | - Dirk R. Rehn
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D–69120 Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D–69120 Heidelberg, Germany
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45
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Ghosh A, Cederbaum LS, Gokhberg K. Electron transfer mediated decay in HeLi 2 cluster: Potential energy surfaces and decay widths. J Chem Phys 2019; 150:164309. [PMID: 31042888 DOI: 10.1063/1.5082952] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Electron transfer mediated decay (ETMD) is a process responsible for double ionization of dopants in He droplets. It is initiated by producing He+ in the droplet, which is neutralized by ETMD, and has been shown to strongly enhance the dopant's double ionization cross section. The efficiency of ETMD, the spectra of emitted secondary electrons, and the character of the ionic products depend on the nuclear dynamics during the decay. To date, there has been no theoretical investigation of multimode dynamics which accompanies ETMD, which could help to understand such dynamics in a He droplet. In this article, we consider the He-Li2 cluster where an ab initio examination of multimode dynamics during the electronic decay is feasible. Moreover, this cluster can serve as a minimal model for Li2 adsorbed on the droplet's surface-a system where ETMD can be observed experimentally. In He droplets, Li2 can be formed in both the ground X1Σg + and the first excited a3Σu + states. In this article, we present ab initio potential energy surfaces of the electronic states of the He-Li2 cluster involved in ETMD, as well as the respective decay widths. We show that the structure of these surfaces and expected nuclear dynamics strongly depend on the electronic state of Li2. Thus, the overall decay rate and the appearance of the observable electron spectra will be dictated by the electronic structure of the dopant.
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Affiliation(s)
- Aryya Ghosh
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany
| | - Lorenz S Cederbaum
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany
| | - Kirill Gokhberg
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany
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46
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Dempwolff AL, Schneider M, Hodecker M, Dreuw A. Efficient implementation of the non-Dyson third-order algebraic diagrammatic construction approximation for the electron propagator for closed- and open-shell molecules. J Chem Phys 2019; 150:064108. [PMID: 30769986 DOI: 10.1063/1.5081674] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Adrian L. Dempwolff
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D–69120 Heidelberg, Germany
| | - Matthias Schneider
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D–69120 Heidelberg, Germany
| | - Manuel Hodecker
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D–69120 Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 205, D–69120 Heidelberg, Germany
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47
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Peng B, Kowalski K. Green's function coupled cluster formulations utilizing extended inner excitations. J Chem Phys 2018; 149:214102. [PMID: 30525725 DOI: 10.1063/1.5046529] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this paper, we analyze new approximations of the Green's function coupled cluster (GFCC) method where locations of poles are improved by extending the excitation level of inner auxiliary operators. These new GFCC approximations can be categorized as the GFCC-i(n, m) method, where the excitation level of the inner auxiliary operators (m) used to describe the ionization potential and electron affinity effects in the N - 1 and N + 1 particle spaces is higher than the excitation level (n) used to correlate the ground-state coupled cluster wave function for the N-electron system. Furthermore, we reveal the so-called "n + 1" rule in this category [or the GFCC-i(n, n + 1) method], which states that in order to maintain size-extensivity of the Green's function matrix elements, the excitation level of inner auxiliary operators X p (ω) and Y q (ω) cannot exceed n + 1. We also discuss the role of the moments of coupled cluster equations that in a natural way assures these properties. Our implementation in the present study is focused on the first approximation in this GFCC category, i.e., the GFCC-i(2,3) method. As our first practice, we use the GFCC-i(2,3) method to compute the spectral functions for the N2 and CO molecules in the inner and outer valence regimes. In comparison with the Green's function coupled cluster singles, doubles results, the computed spectral functions from the GFCC-i(2,3) method exhibit better agreement with the experimental results and other theoretical results, particularly in terms of providing higher resolution of satellite peaks and more accurate relative positions of these satellite peaks with respect to the main peak positions.
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Affiliation(s)
- Bo Peng
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
| | - Karol Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
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48
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Sokolov AY. Multi-reference algebraic diagrammatic construction theory for excited states: General formulation and first-order implementation. J Chem Phys 2018; 149:204113. [DOI: 10.1063/1.5055380] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Alexander Yu. Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
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49
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Ruberti M, Decleva P, Averbukh V. Full Ab Initio Many-Electron Simulation of Attosecond Molecular Pump–Probe Spectroscopy. J Chem Theory Comput 2018; 14:4991-5000. [DOI: 10.1021/acs.jctc.8b00479] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- M. Ruberti
- Department of Physics, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom
| | - P. Decleva
- Dipartimento di Scienze Chimiche, Università di Trieste, Via Giorgieri 1, I-34127 Trieste, Italy
| | - V. Averbukh
- Department of Physics, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom
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50
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Liu J, Asthana A, Cheng L, Mukherjee D. Unitary coupled-cluster based self-consistent polarization propagator theory: A third-order formulation and pilot applications. J Chem Phys 2018; 148:244110. [DOI: 10.1063/1.5030344] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Junzi Liu
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Ayush Asthana
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Debashis Mukherjee
- Raman Center for Atomic, Molecular and Optical Sciences, Indian Association for the Cultivation of Science, Kolkata 700-032, India
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