1
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Reinholdt P, Kjellgren ER, Fuglsbjerg JH, Ziems KM, Coriani S, Sauer SPA, Kongsted J. Subspace Methods for the Simulation of Molecular Response Properties on a Quantum Computer. J Chem Theory Comput 2024; 20:3729-3740. [PMID: 38691524 DOI: 10.1021/acs.jctc.4c00211] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/03/2024]
Abstract
We explore Davidson methods for obtaining excitation energies and other linear response properties within the recently developed quantum self-consistent linear response (q-sc-LR) method. Davidson-type methods allow for obtaining only a few selected excitation energies without explicitly constructing the electronic Hessian since they only require the ability to perform Hessian-vector multiplications. We apply the Davidson method to calculate the excitation energies of hydrogen chains (up to H10) and analyze aspects of statistical noise for computing excitation energies on quantum simulators. Additionally, we apply Davidson methods for computing linear response properties such as static polarizabilities for H2, LiH, H2O, OH-, and NH3, and show that unitary coupled cluster outperforms classical projected coupled cluster for molecular systems with strong correlation. Finally, we formulate the Davidson method for damped (complex) linear response, with application to the nitrogen K-edge X-ray absorption of ammonia, and the C6 coefficients of H2, LiH, H2O, OH-, and NH3.
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Affiliation(s)
- Peter Reinholdt
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
| | - Erik Rosendahl Kjellgren
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
| | | | - Karl Michael Ziems
- Department of Chemistry, Technical University of Denmark, Kemitorvet Building 207, DK-2800 Kongens Lyngby, Denmark
| | - Sonia Coriani
- Department of Chemistry, Technical University of Denmark, Kemitorvet Building 207, DK-2800 Kongens Lyngby, Denmark
| | - Stephan P A Sauer
- Department of Chemistry, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark
| | - Jacob Kongsted
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
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2
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Yuan X, Halbert L, Pototschnig JV, Papadopoulos A, Coriani S, Visscher L, Pereira Gomes AS. Formulation and Implementation of Frequency-Dependent Linear Response Properties with Relativistic Coupled Cluster Theory for GPU-Accelerated Computer Architectures. J Chem Theory Comput 2024; 20:677-694. [PMID: 38193434 DOI: 10.1021/acs.jctc.3c00812] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2024]
Abstract
We present the development and implementation of relativistic coupled cluster linear response theory (CC-LR), which allows the determination of molecular properties arising from time-dependent or time-independent electric, magnetic, or mixed electric-magnetic perturbations (within a common gauge origin for the magnetic properties) as well as taking into account the finite lifetime of excited states in the framework of damped response theory. We showcase our implementation, which is capable to offload the computationally intensive tensor contractions characteristic of coupled cluster theory onto graphical processing units, in the calculation of (a) frequency-(in)dependent dipole-dipole polarizabilities of IIB atoms and selected diatomic molecules, with a particular emphasis on the calculation of valence absorption cross sections for the I2 molecule; (b) indirect spin-spin coupling constants for benchmark systems such as the hydrogen halides (HX, X = F-I) as well the H2Se-H2O dimer as a prototypical system containing hydrogen bonds; and (c) optical rotations at the sodium D line for hydrogen peroxide analogues (H2Y2, Y = O, S, Se, Te). Thanks to this implementation, we are able to show the similarities in performance, but often the significant discrepancies, between CC-LR and approximate methods such as density functional theory. Comparing standard CC response theory with the flavor based upon the equation of motion formalism, we find that for valence properties such as polarizabilities, the two frameworks yield very similar results across the periodic table as found elsewhere in the literature; for properties that probe the core region, such as spin-spin couplings, on the other hand, we show a progressive differentiation between the two as relativistic effects become more important. Our results also suggest that as one goes down the periodic table, it may become increasingly difficult to measure pure optical rotation at the sodium D line due to the appearance of absorbing states.
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Affiliation(s)
- Xiang Yuan
- Univ. Lille, CNRS, UMR 8523─PhLAM─Physique des Lasers Atomes et Molécules, F-59000 Lille, France
- Department of Chemistry and Pharmaceutical Sciences, Faculty of Science, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
| | - Loïc Halbert
- Univ. Lille, CNRS, UMR 8523─PhLAM─Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - Johann Valentin Pototschnig
- Department of Chemistry and Pharmaceutical Sciences, Faculty of Science, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
| | - Anastasios Papadopoulos
- Department of Chemistry and Pharmaceutical Sciences, Faculty of Science, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
| | - Sonia Coriani
- DTU Chemistry─Department of Chemistry, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
| | - Lucas Visscher
- Department of Chemistry and Pharmaceutical Sciences, Faculty of Science, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
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3
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Williams-Young DB, Yuwono SH, DePrince III AE, Yang C. Approximate Exponential Integrators for Time-Dependent Equation-of-Motion Coupled Cluster Theory. J Chem Theory Comput 2023; 19:9177-9186. [PMID: 38086060 PMCID: PMC10753770 DOI: 10.1021/acs.jctc.3c00911] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2023] [Revised: 10/09/2023] [Accepted: 10/16/2023] [Indexed: 12/27/2023]
Abstract
With a growing demand for time-domain simulations of correlated many-body systems, the development of efficient and stable integration schemes for the time-dependent Schrödinger equation is of keen interest in modern electronic structure theory. In this work, we present two approaches for the formation of the quantum propagator for time-dependent equation-of-motion coupled cluster theory based on the Chebyshev and Arnoldi expansions of the complex, nonhermitian matrix exponential, respectively. The proposed algorithms are compared with the short-iterative Lanczos method of Cooper et al. [J. Phys. Chem. A 2021 125, 5438-5447], the fourth-order Runge-Kutta method, and exact dynamics for a set of small but challenging test problems. For each of the cases studied, both of the proposed integration schemes demonstrate superior accuracy and efficiency relative to the reference simulations.
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Affiliation(s)
- David B. Williams-Young
- Applied
Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Stephen H. Yuwono
- Department
of Chemistry and Biochemistry, Florida State
University, Tallahassee, Florida 32306, United States
| | - A. Eugene DePrince III
- Department
of Chemistry and Biochemistry, Florida State
University, Tallahassee, Florida 32306, United States
| | - Chao Yang
- Applied
Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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4
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Franzke Y, Holzer C, Andersen JH, Begušić T, Bruder F, Coriani S, Della Sala F, Fabiano E, Fedotov DA, Fürst S, Gillhuber S, Grotjahn R, Kaupp M, Kehry M, Krstić M, Mack F, Majumdar S, Nguyen BD, Parker SM, Pauly F, Pausch A, Perlt E, Phun GS, Rajabi A, Rappoport D, Samal B, Schrader T, Sharma M, Tapavicza E, Treß RS, Voora V, Wodyński A, Yu JM, Zerulla B, Furche F, Hättig C, Sierka M, Tew DP, Weigend F. TURBOMOLE: Today and Tomorrow. J Chem Theory Comput 2023; 19:6859-6890. [PMID: 37382508 PMCID: PMC10601488 DOI: 10.1021/acs.jctc.3c00347] [Citation(s) in RCA: 37] [Impact Index Per Article: 37.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2023] [Indexed: 06/30/2023]
Abstract
TURBOMOLE is a highly optimized software suite for large-scale quantum-chemical and materials science simulations of molecules, clusters, extended systems, and periodic solids. TURBOMOLE uses Gaussian basis sets and has been designed with robust and fast quantum-chemical applications in mind, ranging from homogeneous and heterogeneous catalysis to inorganic and organic chemistry and various types of spectroscopy, light-matter interactions, and biochemistry. This Perspective briefly surveys TURBOMOLE's functionality and highlights recent developments that have taken place between 2020 and 2023, comprising new electronic structure methods for molecules and solids, previously unavailable molecular properties, embedding, and molecular dynamics approaches. Select features under development are reviewed to illustrate the continuous growth of the program suite, including nuclear electronic orbital methods, Hartree-Fock-based adiabatic connection models, simplified time-dependent density functional theory, relativistic effects and magnetic properties, and multiscale modeling of optical properties.
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Affiliation(s)
- Yannick
J. Franzke
- Fachbereich
Chemie, Philipps-Universität Marburg, Hans-Meerwein-Str. 4, 35032 Marburg, Germany
| | - Christof Holzer
- Institute
of Theoretical Solid State Physics, Karlsruhe
Institute of Technology (KIT), Wolfgang-Gaede-Str. 1, 76131 Karlsruhe, Germany
| | - Josefine H. Andersen
- DTU
Chemistry, Department of Chemistry, Technical
University of Denmark, Kemitorvet Building 207, DK-2800 Kongens Lyngby, Denmark
| | - Tomislav Begušić
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
| | - Florian Bruder
- Fachbereich
Chemie, Philipps-Universität Marburg, Hans-Meerwein-Str. 4, 35032 Marburg, Germany
| | - Sonia Coriani
- DTU
Chemistry, Department of Chemistry, Technical
University of Denmark, Kemitorvet Building 207, DK-2800 Kongens Lyngby, Denmark
| | - Fabio Della Sala
- Institute
for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
- Center for
Biomolecular Nanotechnologies @UNILE, Istituto
Italiano di Tecnologia, Via Barsanti, 73010 Arnesano, Italy
| | - Eduardo Fabiano
- Institute
for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
- Center for
Biomolecular Nanotechnologies @UNILE, Istituto
Italiano di Tecnologia, Via Barsanti, 73010 Arnesano, Italy
| | - Daniil A. Fedotov
- DTU
Chemistry, Department of Chemistry, Technical
University of Denmark, Kemitorvet Building 207, DK-2800 Kongens Lyngby, Denmark
- Institute
of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Susanne Fürst
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17 Juni 135, 10623, Berlin, Germany
| | - Sebastian Gillhuber
- Institute
of Inorganic Chemistry, Karlsruhe Institute
of Technology (KIT), Engesserstr. 15, 76131 Karlsruhe, Germany
| | - Robin Grotjahn
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Martin Kaupp
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17 Juni 135, 10623, Berlin, Germany
| | - Max Kehry
- Institute
of Physical Chemistry, Karlsruhe Institute
of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Marjan Krstić
- Institute
of Theoretical Solid State Physics, Karlsruhe
Institute of Technology (KIT), Wolfgang-Gaede-Str. 1, 76131 Karlsruhe, Germany
| | - Fabian Mack
- Institute
of Physical Chemistry, Karlsruhe Institute
of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Sourav Majumdar
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Brian D. Nguyen
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Shane M. Parker
- Department
of Chemistry, Case Western Reserve University, 10900 Euclid Ave, Cleveland, Ohio 44106 United States
| | - Fabian Pauly
- Institute
of Physics, University of Augsburg, Universitätsstr. 1, 86159 Augsburg, Germany
| | - Ansgar Pausch
- Institute
of Physical Chemistry, Karlsruhe Institute
of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Eva Perlt
- Otto-Schott-Institut
für Materialforschung, Friedrich-Schiller-Universität
Jena, Löbdergraben
32, 07743 Jena, Germany
| | - Gabriel S. Phun
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Ahmadreza Rajabi
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Dmitrij Rappoport
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Bibek Samal
- Department
of Chemical Sciences, Tata Institute of
Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
| | - Tim Schrader
- Otto-Schott-Institut
für Materialforschung, Friedrich-Schiller-Universität
Jena, Löbdergraben
32, 07743 Jena, Germany
| | - Manas Sharma
- Otto-Schott-Institut
für Materialforschung, Friedrich-Schiller-Universität
Jena, Löbdergraben
32, 07743 Jena, Germany
| | - Enrico Tapavicza
- Department
of Chemistry and Biochemistry, California
State University, Long Beach, 1250 Bellflower Boulevard, Long
Beach, California 90840-9507, United States
| | - Robert S. Treß
- Lehrstuhl
für Theoretische Chemie, Ruhr-Universität
Bochum, 44801 Bochum, Germany
| | - Vamsee Voora
- Department
of Chemical Sciences, Tata Institute of
Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
| | - Artur Wodyński
- Institut
für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17 Juni 135, 10623, Berlin, Germany
| | - Jason M. Yu
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Benedikt Zerulla
- Institute
of Nanotechnology, Karlsruhe Institute of
Technology (KIT), Hermann-von-Helmholtz-Platz
1, 76344 Eggenstein-Leopoldshafen Germany
| | - Filipp Furche
- Department
of Chemistry, University of California,
Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
| | - Christof Hättig
- Lehrstuhl
für Theoretische Chemie, Ruhr-Universität
Bochum, 44801 Bochum, Germany
| | - Marek Sierka
- Otto-Schott-Institut
für Materialforschung, Friedrich-Schiller-Universität
Jena, Löbdergraben
32, 07743 Jena, Germany
| | - David P. Tew
- Physical
and Theoretical Chemistry Laboratory, University
of Oxford, South Parks
Road, Oxford OX1 3QZ, United Kingdom
| | - Florian Weigend
- Fachbereich
Chemie, Philipps-Universität Marburg, Hans-Meerwein-Str. 4, 35032 Marburg, Germany
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5
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Papapostolou A, Scheurer M, Dreuw A, Rehn DR. responsefun: Fun with Response Functions in the Algebraic Diagrammatic Construction Framework. J Chem Theory Comput 2023; 19:6375-6391. [PMID: 37676497 DOI: 10.1021/acs.jctc.3c00456] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/08/2023]
Abstract
We present the open-source responsefun package, which implements a universally applicable procedure for computing molecular response properties within the algebraic diagrammatic construction (ADC) framework, exploiting the intermediate state representation (ISR) approach. With symbolic mathematics, the user can simply enter textbook sum-over-states (SOS) expressions from time-dependent perturbation theory, which are then automatically translated into the corresponding symbolic ADC/ISR formulations. Using the data structures provided by the hybrid Python/C++ module adcc for calculating excited states with ADC, the specified response property is directly evaluated, and the result is returned to the user. Employing the novel responsefun package, we present the first ADC/ISR calculations of second-order hyperpolarizability tensors and three-photon-absorption matrix elements.
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Affiliation(s)
- Antonia Papapostolou
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University Heidelberg, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Maximilian Scheurer
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University Heidelberg, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University Heidelberg, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Dirk R Rehn
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University Heidelberg, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
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6
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Avramopoulos A, Reis H, Tzeli D, Zaleśny R, Papadopoulos MG. Photoswitchable Molecular Units with Tunable Nonlinear Optical Activity: A Theoretical Investigation. Molecules 2023; 28:5646. [PMID: 37570617 PMCID: PMC10419997 DOI: 10.3390/molecules28155646] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2023] [Revised: 07/20/2023] [Accepted: 07/20/2023] [Indexed: 08/13/2023] Open
Abstract
The first-, second-, and third-order molecular nonlinear optical properties, including two-photon absorption of a series of derivatives, involving two dithienylethene (DTE) groups connected by several molecular linkers (bis(ethylene-1,2-dithiolato)Ni- (NiBDT), naphthalene, quasilinear oligothiophene chains), are investigated by employing density functional theory (DFT). These properties can be efficiently controlled by DTE switches, in connection with light of appropriate frequency. NiBDT, as a linker, is associated with a greater contrast, in comparison to naphthalene, between the first and second hyperpolarizabilities of the "open-open" and the "closed-closed" isomers. This is explained by invoking the low-lying excited states of NiBDT. It is shown that the second hyperpolarizability can be used as an index, which follows the structural changes induced by photochromism. Assuming a Förster type transfer mechanism, the intramolecular excited-state energy transfer (EET) mechanism is studied. Two important parameters related to this are computed: the electronic coupling (VDA) between the donor and acceptor fragments as well as the overlap between the absorption and emission spectra of the donor and acceptor groups. NiBDT as a linker is associated with a low electronic coupling, VDA, value. We found that VDA is affected by molecular geometry. Our results predict that the linker strongly influences the communication between the open-closed DTE groups. The sensitivity of the molecular nonlinear optical properties could assist with identification of molecular isomers.
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Affiliation(s)
| | - Heribert Reis
- Institute of Chemical Biology, National Hellenic Research Foundation, 11635 Athens, Greece; (H.R.); (M.G.P.)
| | - Demeter Tzeli
- Laboratory of Physical Chemistry, Department of Chemistry, National and Kapodistrian University of Athens, 15784 Athens, Greece;
- Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, 11635 Athens, Greece
| | - Robert Zaleśny
- Faculty of Chemistry, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, PL-50370 Wrocław, Poland;
| | - Manthos G. Papadopoulos
- Institute of Chemical Biology, National Hellenic Research Foundation, 11635 Athens, Greece; (H.R.); (M.G.P.)
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7
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Scheurer M, Papapostolou A, Fransson T, Norman P, Dreuw A, Rehn DR. Solving response expressions in the ADC/ISR framework. J Chem Phys 2023; 158:084105. [PMID: 36859074 DOI: 10.1063/5.0139721] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/09/2023] Open
Abstract
We present an implementation for the calculation of molecular response properties using the algebraic-diagrammatic construction (ADC)/intermediate state representation approach. For the second-order ADC model [ADC(2)], a memory-efficient ansatz avoiding the storage of double excitation amplitudes is investigated. We compare the performance of different numerical algorithms for the solution of the underlying response equations for ADC(2) and show that our approach also strongly improves the convergence behavior for the investigated algorithms compared with the standard implementation. All routines are implemented in an open-source Python library.
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Affiliation(s)
- Maximilian Scheurer
- Interdisciplinary Center for Scientific Computing, University of Heidelberg, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Antonia Papapostolou
- Interdisciplinary Center for Scientific Computing, University of Heidelberg, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Thomas Fransson
- Division of Theoretical Chemistry and Biology, School of Biotechnology, Royal Institute of Technology, SE-10044 Stockholm, Sweden
| | - Patrick Norman
- Division of Theoretical Chemistry and Biology, Royal Institute of Technology, SE-10044 Stockholm, Sweden
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, University of Heidelberg, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Dirk R Rehn
- Interdisciplinary Center for Scientific Computing, University of Heidelberg, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
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8
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Datar A, Wright C, Matthews DA. Theoretical Investigation of the X-ray Stark Effect in Small Molecules. J Phys Chem A 2023; 127:1576-1587. [PMID: 36787229 DOI: 10.1021/acs.jpca.2c08311] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/15/2023]
Abstract
We have studied the Stark effect in the soft x-ray region for various small molecules by calculating the field-dependent x-ray absorption spectra. This effect is explained in terms of the response of molecular orbitals (core and valence), the molecular dipole moment, and the molecular geometry to the applied electric field. A number of consistent trends are observed linking the computed shifts in absorption energies and intensities with specific features of the molecular electronic structure. We find that both the virtual molecular orbitals (valence and/or Rydberg) as well as the core orbitals contribute to observed trends in a complementary fashion. This initial study highlights the potential impact of x-ray Stark spectroscopy as a tool to study electronic structure and environmental perturbations at a submolecular scale.
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Affiliation(s)
- Avdhoot Datar
- Department of Chemistry, Southern Methodist University, Dallas, Texas 75275, United States
| | - Catherine Wright
- Department of Chemistry, Southern Methodist University, Dallas, Texas 75275, United States
| | - Devin A Matthews
- Department of Chemistry, Southern Methodist University, Dallas, Texas 75275, United States
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9
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Schnack-Petersen AK, Moitra T, Folkestad SD, Coriani S. New Implementation of an Equation-of-Motion Coupled-Cluster Damped-Response Framework with Illustrative Applications to Resonant Inelastic X-ray Scattering. J Phys Chem A 2023; 127:1775-1793. [PMID: 36763003 DOI: 10.1021/acs.jpca.2c08181] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/11/2023]
Abstract
We present an implementation of a damped response framework for calculating resonant inelastic X-ray scattering (RIXS) at the equation-of-motion coupled-cluster singles and doubles (CCSD) and second-order approximate coupled-cluster singles and doubles (CC2) levels of theory in the open-source program eT. This framework lays the foundation for future extension to higher excitation methods (notably, the coupled-cluster singles and doubles with perturbative triples, CC3) and to multilevel approaches. Our implementation adopts a fully relaxed ground state and different variants of the core-valence separation projection technique to address convergence issues. Illustrative results are compared with those obtained within the frozen-core core-valence separated approach, available in Q-Chem, as well as with experiment. The performance of the CC2 method is evaluated in comparison with that of CCSD. It is found that, while the CC2 method is noticeably inferior to CCSD for X-ray absorption spectra, the quality of the CC2 RIXS spectra is often comparable to that of the CCSD level of theory, when the same valence excited states are probed. Finally, we present preliminary RIXS results for a solvated molecule in aqueous solution.
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Affiliation(s)
| | - Torsha Moitra
- DTU Chemistry, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark.,Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiTThe Arctic University of Norway, 9037 Tromsø, Norway
| | - Sarai Dery Folkestad
- Department of Chemistry, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
| | - Sonia Coriani
- DTU Chemistry, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark.,Department of Chemistry, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
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10
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Arias-Martinez JE, Cunha LA, Oosterbaan KJ, Lee J, Head-Gordon M. Accurate core excitation and ionization energies from a state-specific coupled-cluster singles and doubles approach. Phys Chem Chem Phys 2022; 24:20728-20741. [PMID: 36004629 DOI: 10.1039/d2cp01998a] [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
We investigate the use of orbital-optimized references in conjunction with single-reference coupled-cluster theory with single and double substitutions (CCSD) for the study of core excitations and ionizations of 18 small organic molecules, without the use of response theory or equation-of-motion (EOM) formalisms. Three schemes are employed to successfully address the convergence difficulties associated with the coupled-cluster equations, and the spin contamination resulting from the use of a spin symmetry-broken reference, in the case of excitations. In order to gauge the inherent potential of the methods studied, an effort is made to provide reasonable basis set limit estimates for the transition energies. Overall, we find that the two best-performing schemes studied here for ΔCCSD are capable of predicting excitation and ionization energies with errors comparable to experimental accuracies. The proposed ΔCCSD schemes reduces statistical errors against experimental excitation energies by more than a factor of two when compared to the frozen-core core-valence separated (FC-CVS) EOM-CCSD approach - a successful variant of EOM-CCSD tailored towards core excitations.
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Affiliation(s)
- Juan E Arias-Martinez
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA. .,Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Leonardo A Cunha
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA. .,Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Katherine J Oosterbaan
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA.
| | - Joonho Lee
- Department of Chemistry, Columbia University, New York 10027, USA
| | - Martin Head-Gordon
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA. .,Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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11
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Niemeyer N, Caricato M, Neugebauer J. Origin invariant electronic circular dichroism in the length dipole gauge without London atomic orbitals. J Chem Phys 2022; 156:154114. [PMID: 35459317 DOI: 10.1063/5.0088922] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We present a method for obtaining origin-independent electronic circular dichroism (ECD) in the length-gauge representation LG(OI) without the usage of London atomic orbitals. This approach builds upon the work by Caricato [J. Chem. Phys. 153, 151101 (2020)] and is applied to rotatory strengths and ECD spectra from damped response theory. Numerical results are presented for time-dependent Hartree-Fock and density-functional theory, the second-order algebraic diagrammatic construction method, and linear-response coupled-cluster theory with singles and approximate doubles. We can support the finding that the common choice of placing the gauge origin in the center of mass of a molecule in conventional length-gauge calculations involving chiroptical properties might not be optimal and show that LG(OI) is a valuable alternative for the origin-independent calculation of ECD spectra. We show that, for a limited test set, the convergence of the rotatory strengths calculated with the LG(OI) approach toward the basis-set limit tends to be faster than for the established velocity gauge representation. Relationships between the sum-over-states expression of the optical rotation in the LG(OI) framework and its representation in terms of response functions are analyzed.
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Affiliation(s)
- Niklas Niemeyer
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster, Corrensstraße 40, 48149 Münster, Germany
| | - Marco Caricato
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, USA
| | - Johannes Neugebauer
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster, Corrensstraße 40, 48149 Münster, Germany
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12
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Andersen JH, Nanda KD, Krylov AI, Coriani S. Probing Molecular Chirality of Ground and Electronically Excited States in the UV-vis and X-ray Regimes: An EOM-CCSD Study. J Chem Theory Comput 2022; 18:1748-1764. [PMID: 35187935 DOI: 10.1021/acs.jctc.1c00937] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present several strategies for computing electronic circular dichroism (CD) spectra across different frequency ranges at the equation-of-motion coupled-cluster singles and doubles level of theory. CD spectra of both ground and electronically excited states are discussed. For selected cases, the approach is compared with coupled-cluster linear response results as well as time-dependent density functional theory. The extension of the theory to include the effect of spin-orbit coupling is presented and illustrated by calculations of X-ray CD spectra at the L-edge.
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Affiliation(s)
- Josefine H Andersen
- DTU Chemistry, Technical University of Denmark, Kemitorvet Bldg 207, DK-2800 Kongens Lyngby, Denmark
| | - Kaushik D Nanda
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States
| | - Anna I Krylov
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States
| | - Sonia Coriani
- DTU Chemistry, Technical University of Denmark, Kemitorvet Bldg 207, DK-2800 Kongens Lyngby, Denmark
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13
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Nanda KD, Krylov AI. The orbital picture of the first dipole hyperpolarizability from many-body response theory. J Chem Phys 2021; 154:184109. [PMID: 34241029 DOI: 10.1063/5.0049184] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Abstract
We present an approach for obtaining a molecular orbital picture of the first dipole hyperpolarizability (β) from correlated many-body electronic structure methods. Ab initio calculations of β rely on quadratic response theory, which recasts the sum-over-all-states expression of β into a closed-form expression by calculating a handful of first- and second-order response states; for resonantly enhanced β, damped response theory is used. These response states are then used to construct second-order response reduced one-particle density matrices (1PDMs), which, upon visualization in terms of natural orbitals (NOs), facilitate a rigorous and black-box mapping of the underlying electronic structure with β. We explain the interpretation of different components of the response 1PDMs and the corresponding NOs within both the undamped and damped response theory framework. We illustrate the utility of this new tool by deconstructing β for cis-difluoroethene, para-nitroaniline, and hemibonded OH· + H2O complex, computed within the framework of coupled-cluster singles and doubles response theory, in terms of the underlying response 1PDMs and NOs for a range of frequencies.
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Affiliation(s)
- Kaushik D Nanda
- Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482, USA
| | - Anna I Krylov
- Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482, USA
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14
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Fedotov DA, Coriani S, Hättig C. Damped (linear) response theory within the resolution-of-identity coupled cluster singles and approximate doubles (RI-CC2) method. J Chem Phys 2021; 154:124110. [PMID: 33810703 DOI: 10.1063/5.0042759] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Abstract
An implementation of a complex solver for the solution of the linear equations required to compute the complex response functions of damped response theory is presented for the resolution-of-identity (RI) coupled cluster singles and approximate doubles (CC2) method. The implementation uses a partitioned formulation that avoids the storage of double excitation amplitudes to make it applicable to large molecules. The solver is the keystone element for the development of the damped coupled cluster response formalism for linear and nonlinear effects in resonant frequency regions at the RI-CC2 level of theory. Illustrative results are reported for the one-photon absorption cross section of C60, the electronic circular dichroism of n-helicenes (n = 5, 6, 7), and the C6 dispersion coefficients of a set of selected organic molecules and fullerenes.
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Affiliation(s)
- Daniil A Fedotov
- DTU Chemistry, Technical University of Denmark, Kemitorvet Bldg. 207, DK-2800 Kongens Lyngby, Denmark
| | - Sonia Coriani
- DTU Chemistry, Technical University of Denmark, Kemitorvet Bldg. 207, DK-2800 Kongens Lyngby, Denmark
| | - Christof Hättig
- Arbeitsgruppe Quantenchemie, Ruhr-Universität Bochum, D-44780 Bochum, Germany
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15
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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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16
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Bauman NP, Liu H, Bylaska EJ, Krishnamoorthy S, Low GH, Granade CE, Wiebe N, Baker NA, Peng B, Roetteler M, Troyer M, Kowalski K. Toward Quantum Computing for High-Energy Excited States in Molecular Systems: Quantum Phase Estimations of Core-Level States. J Chem Theory Comput 2021; 17:201-210. [PMID: 33332965 DOI: 10.1021/acs.jctc.0c00909] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Abstract
This paper explores the utility of the quantum phase estimation (QPE) algorithm in calculating high-energy excited states characterized by the promotion of electrons occupying core-level shells. These states have been intensively studied over the last few decades, especially in supporting the experimental effort at light sources. Results obtained with QPE are compared with various high-accuracy many-body techniques developed to describe core-level states. The feasibility of the quantum phase estimator in identifying classes of challenging shake-up states characterized by the presence of higher-order excitation effects is discussed. We also demonstrate the utility of the QPE algorithm in targeting excitations from specific centers in a molecule. Lastly, we discuss how the lowest-order Trotter formula can be applied to reducing the complexity of the ansatz without affecting the error.
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Affiliation(s)
- Nicholas P Bauman
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Hongbin Liu
- Microsoft Quantum, Redmond, Washington 98052, United States
| | - Eric J Bylaska
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Sriram Krishnamoorthy
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Guang Hao Low
- Microsoft Quantum, Redmond, Washington 98052, United States
| | | | - Nathan Wiebe
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Nathan A Baker
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Bo Peng
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | | | | | - Karol Kowalski
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
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17
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Nanda KD, Krylov AI. Cherry-picking resolvents: A general strategy for convergent coupled-cluster damped response calculations of core-level spectra. J Chem Phys 2020; 153:141104. [DOI: 10.1063/5.0020843] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Affiliation(s)
- Kaushik D. Nanda
- Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482, USA
| | - Anna I. Krylov
- Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482, USA
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18
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Faber R, Ghidinelli S, Hättig C, Coriani S. Magnetic circular dichroism spectra from resonant and damped coupled cluster response theory. J Chem Phys 2020; 153:114105. [PMID: 32962374 DOI: 10.1063/5.0013398] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
Abstract
A computational expression for the Faraday A term of magnetic circular dichroism (MCD) is derived within coupled cluster response theory and alternative computational expressions for the B term are discussed. Moreover, an approach to compute the (temperature-independent) MCD ellipticity in the context of coupled cluster damped response is presented, and its equivalence with the stick-spectrum approach in the limit of infinite lifetimes is demonstrated. The damped response approach has advantages for molecular systems or spectral ranges with a high density of states. Illustrative results are reported at the coupled cluster singles and doubles level and compared to time-dependent density functional theory results.
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Affiliation(s)
- R Faber
- DTU Chemistry, Technical University of Denmark, Kemitorvet Bldg. 207, DK-2800 Kongens Lyngby, Denmark
| | - S Ghidinelli
- Department of Molecular and Translational Medicine, Università degli Studi di Brescia, Viale Europa 11, I-25123 Brescia, Italy
| | - C Hättig
- Arbeitsgruppe Quantenchemie, Ruhr-Universität Bochum, Bochum D-44780, Germany
| | - S Coriani
- DTU Chemistry, Technical University of Denmark, Kemitorvet Bldg. 207, DK-2800 Kongens Lyngby, Denmark
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19
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Scheurer M, Fransson T, Norman P, Dreuw A, Rehn DR. Complex excited state polarizabilities in the ADC/ISR framework. J Chem Phys 2020; 153:074112. [DOI: 10.1063/5.0012120] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Affiliation(s)
- Maximilian Scheurer
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Thomas Fransson
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
- Department of Physics, AlbaNova University Center, Stockholm University, Stockholm SE-106 91, Sweden
| | - Patrick Norman
- Department of Theoretical Chemistry and Biology, School of Engineering Sciences in Chemistry, Biotechnology and Health, KTH Royal Institute of Technology, SE-106 91 Stockholm, Sweden
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
| | - Dirk R. Rehn
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
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20
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Herbst MF, Fransson T. Quantifying the error of the core-valence separation approximation. J Chem Phys 2020; 153:054114. [PMID: 32770930 DOI: 10.1063/5.0013538] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
For the calculation of core-excited states probed through X-ray absorption spectroscopy, the core-valence separation (CVS) scheme has become a vital tool. This approach allows us to target such states with high specificity, albeit introducing an error. We report the implementation of a post-processing step for CVS excitations obtained within the algebraic-diagrammatic construction scheme for the polarization propagator, which removes this error. Based on this, we provide a detailed analysis of the CVS scheme, identifying its accuracy to be dominated by an error balance between two neglected couplings, one between core and valence single excitations and the other between single and double core excitations. The selection of the basis set is shown to be vital for a proper description of both couplings, with tight polarizing functions being necessary for a good balance of errors. The CVS error is confirmed to be stable across multiple systems, with an element-specific spread for K-edge spectrum calculations of only about ±0.02 eV. A systematic lowering of the CVS error by 0.02 eV-0.03 eV is noted when considering excitations to extremely diffuse states, emulating ionization.
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Affiliation(s)
- Michael F Herbst
- CERMICS, École des Ponts ParisTech, 6-8 Avenue Blaise Pascal, 77455 Marne-la-Vallée, France; Inria Paris, 75589 Paris Cedex 12, France; and Sorbonne Universitée, Institut des Sciences du Calcul et des Données, ISCD, 75005 Paris, France
| | - Thomas Fransson
- Interdisciplinary Center for Scientific Computing, Heidelberg University, 69120 Heidelberg, Germany and Fysikum, Stockholm University, Albanova, 10691 Stockholm, Sweden
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21
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Matthews DA. EOM-CC methods with approximate triple excitations applied to core excitation and ionisation energies. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1771448] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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22
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Faber R, Coriani S. Core–valence-separated coupled-cluster-singles-and-doubles complex-polarization-propagator approach to X-ray spectroscopies. Phys Chem Chem Phys 2020; 22:2642-2647. [DOI: 10.1039/c9cp03696b] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
The iterative subspace algorithm to solve the CCSD complex linear response equations has been modified to include a core–valence separation projection step to overcome convergence problems. Illustrative results are reported for XAS, XCD, XES and RIXS.
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Affiliation(s)
- Rasmus Faber
- DTU Chemistry - Department of Chemistry
- Technical University of Denmark
- DK-2800 Kongens Lyngby
- Denmark
| | - Sonia Coriani
- DTU Chemistry - Department of Chemistry
- Technical University of Denmark
- DK-2800 Kongens Lyngby
- Denmark
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23
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Nanda KD, Vidal ML, Faber R, Coriani S, Krylov AI. How to stay out of trouble in RIXS calculations within equation-of-motion coupled-cluster damped response theory? Safe hitchhiking in the excitation manifold by means of core–valence separation. Phys Chem Chem Phys 2020; 22:2629-2641. [DOI: 10.1039/c9cp03688a] [Citation(s) in RCA: 34] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
We present a novel approach with robust convergence of the response equations for computing resonant inelastic X-ray scattering (RIXS) cross sections within the equation-of-motion coupled-cluster (EOM-CC) framework.
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Affiliation(s)
- Kaushik D. Nanda
- Department of Chemistry
- University of Southern California
- Los Angeles
- USA
| | - Marta L. Vidal
- DTU Chemistry – Department of Chemistry
- Technical University of Denmark
- DK-2800
- Denmark
| | - Rasmus Faber
- DTU Chemistry – Department of Chemistry
- Technical University of Denmark
- DK-2800
- Denmark
| | - Sonia Coriani
- DTU Chemistry – Department of Chemistry
- Technical University of Denmark
- DK-2800
- Denmark
| | - Anna I. Krylov
- Department of Chemistry
- University of Southern California
- Los Angeles
- USA
- The Hamburg Centre for Ultrafast Imaging
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24
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Myhre RH, Coriani S, Koch H. X-ray and UV Spectra of Glycine within Coupled Cluster Linear Response Theory. J Phys Chem A 2019; 123:9701-9711. [PMID: 31549830 DOI: 10.1021/acs.jpca.9b06590] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The coupled cluster models CCSD and CC3 are used to investigate the (core) excited states and ionization energies of glycine in the gas phase. Excited states and ionization energies in the UV spectral range are calculated using a standard coupled cluster linear response, while core-level excited states and ionization potentials are calculated using the core-valence separation approximation. The temperature dependence from different conformers is also assessed.
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Affiliation(s)
- Rolf H Myhre
- Department of Chemistry , Norwegian University of Science and Technology, NTNU , 7491 Trondheim , Norway.,Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry , University of Oslo , 0315 Oslo , Norway
| | - Sonia Coriani
- DTU Chemistry , Technical University of Denmark , DK-2800 Kongens Lyngby , Denmark.,Aarhus Institute of Advanced Studies , Aarhus University , DK-8000 Aarhus C , Denmark
| | - Henrik Koch
- Department of Chemistry , Norwegian University of Science and Technology, NTNU , 7491 Trondheim , Norway.,Scuola Normale Superiore , Piazza dei Cavalieri 7 , 56126 Pisa , Italy
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25
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Stetina TF, Kasper JM, Li X. Modeling L2,3-edge X-ray absorption spectroscopy with linear response exact two-component relativistic time-dependent density functional theory. J Chem Phys 2019; 150:234103. [DOI: 10.1063/1.5091807] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Torin F. Stetina
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | - Joseph M. Kasper
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
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26
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Peng R, Copan AV, Sokolov AY. Simulating X-ray Absorption Spectra with Linear-Response Density Cumulant Theory. J Phys Chem A 2019; 123:1840-1850. [DOI: 10.1021/acs.jpca.8b12259] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Ruojing Peng
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
| | - Andreas V. Copan
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - Alexander Yu. Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
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27
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Maradzike E, DePrince AE. Modeling core-level excitations with variationally optimized reduced-density matrices and the extended random phase approximation. J Chem Phys 2018; 149:234101. [PMID: 30579305 DOI: 10.1063/1.5048924] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The information contained within ground-state one- and two-electron reduced-density matrices (RDMs) can be used to compute wave functions and energies for electronically excited states through the extended random phase approximation (ERPA). The ERPA is an appealing framework for describing excitations out of states obtained via the variational optimization of the two-electron RDM (2-RDM), as the variational 2-RDM (v2RDM) approach itself can only be used to describe the lowest-energy state of a given spin symmetry. The utility of the ERPA for predicting near-edge features relevant to x-ray absorption spectroscopy is assessed for the case that the 2-RDM is obtained from a ground-state v2RDM-driven complete active space self-consistent field (CASSCF) computation. A class of killer conditions for the CASSCF-specific ERPA excitation operator is derived, and it is demonstrated that a reliable description of core-level excitations requires an excitation operator that fulfills these conditions; the core-valence separation (CVS) scheme yields such an operator. Absolute excitation energies evaluated within the CASSCF/CVS-ERPA framework are slightly more accurate than those obtained from the usual random phase approximation (RPA), but the CVS-ERPA is not more accurate than RPA for predicting the relative positions of near-edge features. Nonetheless, CVS-ERPA is established as a reasonable starting point for the treatment of core-level excitations using variationally optimized 2-RDMs.
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Affiliation(s)
- Elvis Maradzike
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
| | - A Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
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28
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Faber R, Coriani S. Resonant Inelastic X-ray Scattering and Nonesonant X-ray Emission Spectra from Coupled-Cluster (Damped) Response Theory. J Chem Theory Comput 2018; 15:520-528. [DOI: 10.1021/acs.jctc.8b01020] [Citation(s) in RCA: 32] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Rasmus Faber
- Department of Chemistry, Technical University of Denmark, Kemitorvet Building 207, 2800 Kongens Lyngby, Denmark
| | - Sonia Coriani
- Department of Chemistry, Technical University of Denmark, Kemitorvet Building 207, 2800 Kongens Lyngby, Denmark
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29
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Abstract
This report presents selected highlights from 2017 final birth data on key demographic, health care utilization, and infant health indicators. General fertility rates (the number of births per 1,000 females aged 15-44 years) and teen birth rates are presented by race and Hispanic origin. The use of Medicaid as the source of payment for the delivery and preterm birth rates are presented by the age of the mother. Data for 2017 are compared with 2016 for each indicator.
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30
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Norman P, Dreuw A. Simulating X-ray Spectroscopies and Calculating Core-Excited States of Molecules. Chem Rev 2018; 118:7208-7248. [DOI: 10.1021/acs.chemrev.8b00156] [Citation(s) in RCA: 164] [Impact Index Per Article: 27.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Affiliation(s)
- Patrick Norman
- Department of Theoretical Chemistry and Biology, School of Engineering Sciences in Chemistry, Biotechnology and Health, KTH Royal Institute of Technology, SE-106 91 Stockholm, Sweden
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
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31
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Kasper JM, Williams-Young DB, Vecharynski E, Yang C, Li X. A Well-Tempered Hybrid Method for Solving Challenging Time-Dependent Density Functional Theory (TDDFT) Systems. J Chem Theory Comput 2018; 14:2034-2041. [DOI: 10.1021/acs.jctc.8b00141] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Joseph M. Kasper
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | | | - Eugene Vecharynski
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Chao Yang
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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32
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Rehn DR, Dreuw A, Norman P. Resonant Inelastic X-ray Scattering Amplitudes and Cross Sections in the Algebraic Diagrammatic Construction/Intermediate State Representation (ADC/ISR) Approach. J Chem Theory Comput 2017; 13:5552-5559. [DOI: 10.1021/acs.jctc.7b00636] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Dirk R. Rehn
- Division
of Theoretical Chemistry and Biology, School of Biotechnology, Royal Institute of Technology, SE-106 91 Stockholm, Sweden
| | - Andreas Dreuw
- Interdisciplinary
Center for Scientific Computing, University of Heidelberg, Im Neuenheimer
Feld 205, 69120 Heidelberg, Germany
| | - Patrick Norman
- Division
of Theoretical Chemistry and Biology, School of Biotechnology, Royal Institute of Technology, SE-106 91 Stockholm, Sweden
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33
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Van Beeumen R, Williams-Young DB, Kasper JM, Yang C, Ng EG, Li X. Model Order Reduction Algorithm for Estimating the Absorption Spectrum. J Chem Theory Comput 2017; 13:4950-4961. [PMID: 28862869 DOI: 10.1021/acs.jctc.7b00402] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The ab initio description of the spectral interior of the absorption spectrum poses both a theoretical and computational challenge for modern electronic structure theory. Due to the often spectrally dense character of this domain in the quantum propagator's eigenspectrum for medium-to-large sized systems, traditional approaches based on the partial diagonalization of the propagator often encounter oscillatory and stagnating convergence. Electronic structure methods which solve the molecular response problem through the solution of spectrally shifted linear systems, such as the complex polarization propagator, offer an alternative approach which is agnostic to the underlying spectral density or domain location. This generality comes at a seemingly high computational cost associated with solving a large linear system for each spectral shift in some discretization of the spectral domain of interest. In this work, we present a novel, adaptive solution to this high computational overhead based on model order reduction techniques via interpolation. Model order reduction reduces the computational complexity of mathematical models and is ubiquitous in the simulation of dynamical systems and control theory. The efficiency and effectiveness of the proposed algorithm in the ab initio prediction of X-ray absorption spectra is demonstrated using a test set of challenging water clusters which are spectrally dense in the neighborhood of the oxygen K-edge. On the basis of a single, user defined tolerance we automatically determine the order of the reduced models and approximate the absorption spectrum up to the given tolerance. We also illustrate that, for the systems studied, the automatically determined model order increases logarithmically with the problem dimension, compared to a linear increase of the number of eigenvalues within the energy window. Furthermore, we observed that the computational cost of the proposed algorithm only scales quadratically with respect to the problem dimension.
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Affiliation(s)
- Roel Van Beeumen
- Computational Research Division, Lawrence Berkeley National Laboratory , Berkeley, California 94720, United States
| | - David B Williams-Young
- Department of Chemistry, University of Washington , Seattle, Washington 98195, United States
| | - Joseph M Kasper
- Department of Chemistry, University of Washington , Seattle, Washington 98195, United States
| | - Chao Yang
- Computational Research Division, Lawrence Berkeley National Laboratory , Berkeley, California 94720, United States
| | - Esmond G Ng
- Computational Research Division, Lawrence Berkeley National Laboratory , Berkeley, California 94720, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington , Seattle, Washington 98195, United States
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34
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Sadybekov A, Krylov AI. Coupled-cluster based approach for core-level states in condensed phase: Theory and application to different protonated forms of aqueous glycine. J Chem Phys 2017; 147:014107. [DOI: 10.1063/1.4990564] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Affiliation(s)
- Arman Sadybekov
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
| | - Anna I. Krylov
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
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35
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Fransson T, Rehn DR, Dreuw A, Norman P. Static polarizabilities and C6 dispersion coefficients using the algebraic-diagrammatic construction scheme for the complex polarization propagator. J Chem Phys 2017. [DOI: 10.1063/1.4977039] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Thomas Fransson
- Stanford PULSE Institute, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | - Dirk R. Rehn
- Department of Theoretical Chemistry and Biology, School of Biotechnology, Royal Institute of Technology, SE-10691 Stockholm, Sweden
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, University of Heidelberg, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Patrick Norman
- Department of Theoretical Chemistry and Biology, School of Biotechnology, Royal Institute of Technology, SE-10691 Stockholm, Sweden
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36
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Nascimento DR, DePrince AE. Linear Absorption Spectra from Explicitly Time-Dependent Equation-of-Motion Coupled-Cluster Theory. J Chem Theory Comput 2016; 12:5834-5840. [DOI: 10.1021/acs.jctc.6b00796] [Citation(s) in RCA: 52] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Daniel R. Nascimento
- Department of Chemistry and
Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
| | - A. Eugene DePrince
- Department of Chemistry and
Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
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37
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Besley NA. Fast Time-Dependent Density Functional Theory Calculations of the X-ray Absorption Spectroscopy of Large Systems. J Chem Theory Comput 2016; 12:5018-5025. [DOI: 10.1021/acs.jctc.6b00656] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Affiliation(s)
- Nicholas A. Besley
- School of Chemistry, University of Nottingham, University
Park, Nottingham, NG7 2RD, U.K
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38
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Myhre RH, Coriani S, Koch H. Near-Edge X-ray Absorption Fine Structure within Multilevel Coupled Cluster Theory. J Chem Theory Comput 2016; 12:2633-43. [DOI: 10.1021/acs.jctc.6b00216] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Rolf H. Myhre
- Department
of Chemistry, Norwegian University of Science and Technology (NTNU), 7491 Trondheim, Norway
- Department
of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, United States
| | - Sonia Coriani
- Dipartimento
di Scienze Chimiche e Farmaceutiche, Universitá degli Studi di Trieste, I-34127 Trieste, Italy
- Aarhus
Institute of Avanced Studies, University of Aarhus, DK-8000 Århus C, Denmark
| | - Henrik Koch
- Department
of Chemistry, Norwegian University of Science and Technology (NTNU), 7491 Trondheim, Norway
- Department
of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, United States
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39
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Fransson T, Burdakova D, Norman P. K- and L-edge X-ray absorption spectrum calculations of closed-shell carbon, silicon, germanium, and sulfur compounds using damped four-component density functional response theory. Phys Chem Chem Phys 2016; 18:13591-603. [PMID: 27136720 DOI: 10.1039/c6cp00561f] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
X-ray absorption spectra of carbon, silicon, germanium, and sulfur compounds have been investigated by means of damped four-component density functional response theory. It is demonstrated that a reliable description of relativistic effects is obtained at both K- and L-edges. Notably, an excellent agreement with experimental results is obtained for L2,3-spectra-with spin-orbit effects well accounted for-also in cases when the experimental intensity ratio deviates from the statistical one of 2 : 1. The theoretical results are consistent with calculations using standard response theory as well as recently reported real-time propagation methods in time-dependent density functional theory, and the virtues of different approaches are discussed. As compared to silane and silicon tetrachloride, an anomalous error in the absolute energy is reported for the L2,3-spectrum of silicon tetrafluoride, amounting to an additional spectral shift of ∼1 eV. This anomaly is also observed for other exchange-correlation functionals, but it is seen neither at other silicon edges nor at the carbon K-edge of fluorine derivatives of ethene. Considering the series of molecules SiH4-XFX with X = 1, 2, 3, 4, a gradual divergence from interpolated experimental ionization potentials is observed at the level of Kohn-Sham density functional theory (DFT), and to a smaller extent with the use of Hartree-Fock. This anomalous error is thus attributed partly to difficulties in correctly emulating the electronic structure effects imposed by the very electronegative fluorines, and partly due to inconsistencies in the spurious electron self-repulsion in DFT. Substitution with one, or possibly two, fluorine atoms is estimated to yield small enough errors to allow for reliable interpretations and predictions of L2,3-spectra of more complex and extended silicon-based systems.
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Affiliation(s)
- Thomas Fransson
- Department of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping, Sweden.
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40
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Petrenko T, Rauhut G. Time-independent eigenstate-free calculation of vibronic spectra beyond the harmonic approximation. J Chem Phys 2015; 143:234106. [DOI: 10.1063/1.4937380] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Affiliation(s)
- Taras Petrenko
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Guntram Rauhut
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
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41
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Fransson T, Zhovtobriukh I, Coriani S, Wikfeldt KT, Norman P, Pettersson LGM. Requirements of first-principles calculations of X-ray absorption spectra of liquid water. Phys Chem Chem Phys 2015; 18:566-83. [PMID: 26619162 DOI: 10.1039/c5cp03919c] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
A computational benchmark study on X-ray absorption spectra of water has been performed by means of transition-potential density functional theory (TP-DFT), damped time-dependent density functional theory (TDDFT), and damped coupled cluster (CC) linear response theory. For liquid water, using TDDFT with a tailored CAM-B3LYP functional and a polarizable embedding, we find that an embedding with over 2000 water molecules is required to fully converge spectral features for individual molecules, but a substantially smaller embedding can be used within averaging schemes. TP-DFT and TDDFT calculations on 100 MD structures demonstrate that TDDFT produces a spectrum with spectral features in good agreement with experiment, while it is more difficult to fully resolve the spectral features in the TP-DFT spectrum. Similar trends were also observed for calculations of bulk ice. In order to further establish the performance of these methods, small water clusters have been considered also at the CC2 and CCSD levels of theory. Issues regarding the basis set requirements for spectrum simulations of liquid water and the determination of gas-phase ionization potentials are also discussed.
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Affiliation(s)
- Thomas Fransson
- Department of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping, Sweden
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42
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Coriani S, Koch H. Communication: X-ray absorption spectra and core-ionization potentials within a core-valence separated coupled cluster framework. J Chem Phys 2015; 143:181103. [DOI: 10.1063/1.4935712] [Citation(s) in RCA: 131] [Impact Index Per Article: 14.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Sonia Coriani
- Dipartimento di Scienze Chimiche e Farmaceutiche, Università degli Studi di Trieste, I-34127 Trieste, Italy
- Aarhus Institute of Advanced Studies, Aarhus University, DK-8000 Århus C, Denmark
| | - Henrik Koch
- Department of Chemistry, Norwegian University of Science and Technology, 7491 Trondheim, Norway
- Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, USA
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43
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Godtliebsen IH, Christiansen O. Calculating vibrational spectra without determining excited eigenstates: Solving the complex linear equations of damped response theory for vibrational configuration interaction and vibrational coupled cluster states. J Chem Phys 2015; 143:134108. [DOI: 10.1063/1.4932010] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Affiliation(s)
| | - Ove Christiansen
- Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark
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44
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Peng B, Lestrange PJ, Goings JJ, Caricato M, Li X. Energy-Specific Equation-of-Motion Coupled-Cluster Methods for High-Energy Excited States: Application to K-edge X-ray Absorption Spectroscopy. J Chem Theory Comput 2015; 11:4146-53. [DOI: 10.1021/acs.jctc.5b00459] [Citation(s) in RCA: 80] [Impact Index Per Article: 8.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Bo Peng
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Patrick J. Lestrange
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Joshua J. Goings
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Marco Caricato
- Department
of Chemistry, University of Kansas, Lawrence, Kansas 66045, United States
| | - Xiaosong Li
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
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45
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Kauczor J, Norman P. Efficient Calculations of Molecular Linear Response Properties for Spectral Regions. J Chem Theory Comput 2014; 10:2449-55. [DOI: 10.1021/ct500114m] [Citation(s) in RCA: 45] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Affiliation(s)
- Joanna Kauczor
- Department of Physics, Chemistry
and Biology, Linköping University, SE-581 83 Linköping, Sweden
| | - Patrick Norman
- Department of Physics, Chemistry
and Biology, Linköping University, SE-581 83 Linköping, Sweden
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