1
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Liu L, Xu Q, Dos Anjos Cunha L, Xin H, Head-Gordon M, Qian J. Real-Space Pseudopotential Method for the Calculation of Third-Row Elements X-ray Photoelectron Spectroscopic Signatures. J Chem Theory Comput 2024. [PMID: 38970155 DOI: 10.1021/acs.jctc.4c00535] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/08/2024]
Abstract
X-ray photoelectron spectroscopy (XPS) is a powerful characterization technique that unveils subtle chemical environment differences via core-electron binding energy (CEBE) analysis. We extend the development of real-space pseudopotential methods to calculating 1s, 2s, and 2p3/2 CEBEs of third-row elements (S, P, and Si) within the framework of Kohn-Sham density-functional theory (KS-DFT). The new approach systematically prevents variational collapse and simplifies core-excited orbital selection within dense energy level distributions. However, careful error cancellation analysis is required to achieve accuracy comparable to all-electron methods and experiments. Combined with real-space KS-DFT implementation, this development enables large-scale simulations with both Dirichlet boundary conditions and periodic boundary conditions.
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Affiliation(s)
- Liping Liu
- Department of Chemical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24060, United States
| | - Qiang Xu
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Leonardo Dos Anjos Cunha
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, United States
| | - Hongliang Xin
- Department of Chemical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24060, United States
| | - Martin Head-Gordon
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, United States
| | - Jin Qian
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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2
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Abraham V, Harsha G, Zgid D. Relativistic Fully Self-Consistent GW for Molecules: Total Energies and Ionization Potentials. J Chem Theory Comput 2024; 20:4579-4590. [PMID: 38778459 DOI: 10.1021/acs.jctc.4c00075] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/25/2024]
Abstract
The fully self-consistent GW (scGW) method with an iterative solution of the Dyson equation provides a consistent approach for describing the ground and excited states without any dependence on the mean-field reference. In this work, we present a relativistic version of scGW for molecules containing heavy elements using the exact two-component (X2C) Coulomb approximation. We benchmark SOC-81 data set containing closed shell heavy elements for the first ionization potential using the fully self-consistent GW as well as one-shot GW. The self-consistent GW provides superior results compared to G0W0 with PBE reference and comparable results to G0W0 with PBE0 while also removing the starting point dependence. The photoelectron spectra obtained at the X2C level demonstrate very good agreement with the experimental spectra. We also observe that scGW provides very good estimation of ionization potential for the inner d-shell orbitals. Additionally, using the well-conserved total energy, we investigate the equilibrium bond length and harmonic frequencies of a few halogen dimers using scGW. Overall, our findings demonstrate the applicability of the fully self-consistent GW method for accurate ionization potential, photoelectron spectra, and total energies in finite systems with heavy elements with a reasonable computational scaling.
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Affiliation(s)
- Vibin Abraham
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Gaurav Harsha
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
- Department of Physics and Astronomy, University of Michigan, Ann Arbor, Michigan 48109, United States
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3
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Gao W, Tang Z, Zhao J, Chelikowsky JR. Efficient Full-Frequency GW Calculations Using a Lanczos Method. PHYSICAL REVIEW LETTERS 2024; 132:126402. [PMID: 38579203 DOI: 10.1103/physrevlett.132.126402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2023] [Accepted: 02/21/2024] [Indexed: 04/07/2024]
Abstract
The GW approximation is widely used for reliable and accurate modeling of single-particle excitations. It also serves as a starting point for many theoretical methods, such as its use in the Bethe-Salpeter equation (BSE) and dynamical mean-field theory. However, full-frequency GW calculations for large systems with hundreds of atoms remain computationally challenging, even after years of efforts to reduce the prefactor and improve scaling. We propose a method that reformulates the correlation part of the GW self-energy as a resolvent of a Hermitian matrix, which can be efficiently and accurately computed using the standard Lanczos method. This method enables full-frequency GW calculations of material systems with a few hundred atoms on a single computing workstation. We further demonstrate the efficiency of the method by calculating the defect-state energies of silicon quantum dots with diameters up to 4 nm and nearly 2,000 silicon atoms using only 20 computational nodes.
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Affiliation(s)
- Weiwei Gao
- Key Laboratory of Materials Modification by Laser, Ion and Electron Beams, Ministry of Education, Dalian University of Technology, Dalian 116024, China
| | - Zhao Tang
- Center for Computational Materials, Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, USA
| | - Jijun Zhao
- Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, School of Physics, South China Normal University, Guangzhou 510006, China
| | - James R Chelikowsky
- Center for Computational Materials, Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, USA
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
- McKetta Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA
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4
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Tölle J, Niemeyer N, Neugebauer J. Accelerating Analytic-Continuation GW Calculations with a Laplace Transform and Natural Auxiliary Functions. J Chem Theory Comput 2024; 20:2022-2032. [PMID: 38469629 DOI: 10.1021/acs.jctc.3c01264] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/13/2024]
Abstract
We present a simple and accurate GW implementation based on a combination of a Laplace transform (LT) and other acceleration techniques used in post-self-consistent field quantum chemistry, namely, natural auxiliary functions and the frozen-core approximation. The LT-GW approach combines three major benefits: (a) a small prefactor for computational scaling, (b) easy integration into existing molecular GW implementations, and (c) significant performance improvements for a wide range of possible applications. Illustrating these advantages for systems consisting of up to 352 atoms and 7412 basis functions, we further demonstrate the benefits of this approach combined with an efficient implementation of the Bethe-Salpeter equation.
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Affiliation(s)
- Johannes Tölle
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Niklas Niemeyer
- University of Münster, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Corrensstraße 36, Münster 48149, Germany
| | - Johannes Neugebauer
- University of Münster, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Corrensstraße 36, Münster 48149, Germany
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5
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Delesma FA, Leucke M, Golze D, Rinke P. Benchmarking the accuracy of the separable resolution of the identity approach for correlated methods in the numeric atom-centered orbitals framework. J Chem Phys 2024; 160:024118. [PMID: 38205851 DOI: 10.1063/5.0184406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2023] [Accepted: 12/19/2023] [Indexed: 01/12/2024] Open
Abstract
Four-center two-electron Coulomb integrals routinely appear in electronic structure algorithms. The resolution-of-the-identity (RI) is a popular technique to reduce the computational cost for the numerical evaluation of these integrals in localized basis-sets codes. Recently, Duchemin and Blase proposed a separable RI scheme [J. Chem. Phys. 150, 174120 (2019)], which preserves the accuracy of the standard global RI method with the Coulomb metric and permits the formulation of cubic-scaling random phase approximation (RPA) and GW approaches. Here, we present the implementation of a separable RI scheme within an all-electron numeric atom-centered orbital framework. We present comprehensive benchmark results using the Thiel and the GW100 test set. Our benchmarks include atomization energies from Hartree-Fock, second-order Møller-Plesset (MP2), coupled-cluster singles and doubles, RPA, and renormalized second-order perturbation theory, as well as quasiparticle energies from GW. We found that the separable RI approach reproduces RI-free HF calculations within 9 meV and MP2 calculations within 1 meV. We have confirmed that the separable RI error is independent of the system size by including disordered carbon clusters up to 116 atoms in our benchmarks.
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Affiliation(s)
| | - Moritz Leucke
- Faculty for Chemistry and Food Chemistry, Technische Universität Dresden, 01062 Dresden, Germany
| | - Dorothea Golze
- Faculty for Chemistry and Food Chemistry, Technische Universität Dresden, 01062 Dresden, Germany
| | - Patrick Rinke
- Department of Applied Physics, Aalto University, FI-02150 Espoo, Finland
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6
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Mejia-Rodriguez D, Kunitsa AA, Fulton JL, Aprà E, Govind N. G0W0 Ionization Potentials of First-Row Transition Metal Aqua Ions. J Phys Chem A 2023; 127:9684-9694. [PMID: 37938891 DOI: 10.1021/acs.jpca.3c04419] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2023]
Abstract
We report computations of the vertical ionization potentials within the GW approximation of the near-complete series of first-row transition metal (V-Cu) aqua ions in their most common oxidation states, i.e., V3+, Cr3+, Cr2+, Mn2+, Fe3+, Fe2+, Co2+, Ni2+, and Cu2+. The d-orbital occupancy of these systems spans a broad range from d2 to d9. All of the structures were first optimized at the density functional theory level using a large cluster of explicit water molecules that are embedded in a continuum solvation model. Vertical ionization potentials were computed with the one-shot G0W0 approach on a range of transition metal ion clusters (6, 18, 40, and 60 explicit water molecules), wherein the convergence with respect to the basis set size was evaluated using the systems with 40 water molecules. We assess the results using three different density functional approximations as starting points for the vertical ionization potential calculations, namely, G0W0@PBE, G0W0@PBE0, and G0W0@r2SCAN. While the predicted ground-state structures are similar to all three exchange-correlation functionals, the vertical ionization potentials were in closer agreement with experiment when using the G0W0@PBE0 and G0W0@r2SCAN approaches, with the r2SCAN-based calculations being significantly less expensive. Computed bond distances and vertical ionization potentials for all structures are in good agreement with available experimental data.
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Affiliation(s)
- Daniel Mejia-Rodriguez
- Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
- Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Alexander A Kunitsa
- Zapata Computing, Inc., 100 Federal Street, Boston, Massachusetts 02110, United States
| | - John L Fulton
- Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Edoardo Aprà
- Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Niranjan Govind
- Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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7
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Mejia-Rodriguez D, Aprà E, Autschbach J, Bauman NP, Bylaska EJ, Govind N, Hammond JR, Kowalski K, Kunitsa A, Panyala A, Peng B, Rehr JJ, Song H, Tretiak S, Valiev M, Vila FD. NWChem: Recent and Ongoing Developments. J Chem Theory Comput 2023; 19:7077-7096. [PMID: 37458314 DOI: 10.1021/acs.jctc.3c00421] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2023]
Abstract
This paper summarizes developments in the NWChem computational chemistry suite since the last major release (NWChem 7.0.0). Specifically, we focus on functionality, along with input blocks, that is accessible in the current stable release (NWChem 7.2.0) and in the "master" development branch, interfaces to quantum computing simulators, interfaces to external libraries, the NWChem github repository, and containerization of NWChem executable images. Some ongoing developments that will be available in the near future are also discussed.
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Affiliation(s)
- Daniel Mejia-Rodriguez
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Edoardo Aprà
- Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Jochen Autschbach
- Department of Chemistry, University at Buffalo, State University of New York, Buffalo, New York 14260-3000, United States
| | - Nicholas P Bauman
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Eric J Bylaska
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Niranjan Govind
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Jeff R Hammond
- Accelerated Computing, NVIDIA Helsinki Oy, Porkkalankatu 1, 00180 Helsinki, Finland
| | - Karol Kowalski
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Alexander Kunitsa
- Zapata Computing, Inc., 100 Federal Street, Boston, Massachusetts 02110, United States
| | - Ajay Panyala
- Advanced Computing, Mathematics, and Data Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Bo Peng
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - John J Rehr
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
| | - Huajing Song
- Physics and Chemistry of Materials, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Sergei Tretiak
- Physics and Chemistry of Materials, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
- Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Marat Valiev
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Fernando D Vila
- Department of Physics, University of Washington, Seattle, Washington 98195, United States
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8
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Freixas VM, Rouxel JR, Nam Y, Tretiak S, Govind N, Mukamel S. X-ray and Optical Circular Dichroism as Local and Global Ultrafast Chiral Probes of [12]Helicene Racemization. J Am Chem Soc 2023; 145:21012-21019. [PMID: 37704187 DOI: 10.1021/jacs.3c07032] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/15/2023]
Abstract
Chirality is a fundamental molecular property that plays a crucial role in biophysics and drug design. Optical circular dichroism (OCD) is a well-established chiral spectroscopic probe in the UV-visible regime. Chirality is most commonly associated with a localized chiral center. However, some compounds such as helicenes (Figure 1) are chiral due to their screwlike global structure. In these highly conjugated systems, some electric and magnetic allowed transitions are distributed across the entire molecule, and OCD thus probes the global molecular chirality. Recent advances in X-ray sources, in particular the control of their polarization and spatial profiles, have enabled X-ray circular dichroism (XCD), which, in contrast to OCD, can exploit the localized and element-specific nature of X-ray electronic transitions. XCD therefore is more sensitive to local structures, and the chirality probed with it can be referred to as local. During the racemization of helicene, between opposite helical structures, the screw handedness can flip locally, making the molecule globally achiral while retaining a local handedness. Here, we use the racemization mechanism of [12]helicene as a model to demonstrate the capabilities of OCD and XCD as time-dependent probes for global and local chiralities, respectively. Our simulations demonstrate that XCD provides an excellent spectroscopic probe for the time-dependent local chirality of molecules.
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Affiliation(s)
- Victor M Freixas
- Department of Chemistry and Physics and Astronomy, University of California, Irvine, California 92697-2025, United States
| | - Jérémy R Rouxel
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Yeonsig Nam
- Department of Chemistry and Physics and Astronomy, University of California, Irvine, California 92697-2025, United States
| | - Sergei Tretiak
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Niranjan Govind
- Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Shaul Mukamel
- Department of Chemistry and Physics and Astronomy, University of California, Irvine, California 92697-2025, United States
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9
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Förster A, van Lenthe E, Spadetto E, Visscher L. Two-Component GW Calculations: Cubic Scaling Implementation and Comparison of Vertex-Corrected and Partially Self-Consistent GW Variants. J Chem Theory Comput 2023; 19:5958-5976. [PMID: 37594901 PMCID: PMC10501001 DOI: 10.1021/acs.jctc.3c00512] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2023] [Indexed: 08/20/2023]
Abstract
We report an all-electron, atomic orbital (AO)-based, two-component (2C) implementation of the GW approximation (GWA) for closed-shell molecules. Our algorithm is based on the space-time formulation of the GWA and uses analytical continuation (AC) of the self-energy, and pair-atomic density fitting (PADF) to switch between AO and auxiliary basis. By calculating the dynamical contribution to the GW self-energy at a quasi-one-component level, our 2C-GW algorithm is only about a factor of 2-3 slower than in the scalar relativistic case. Additionally, we present a 2C implementation of the simplest vertex correction to the self-energy, the statically screened G3W2 correction. Comparison of first ionization potentials (IPs) of a set of 67 molecules with heavy elements (a subset of the SOC81 set) calculated with our implementation against results from the WEST code reveals mean absolute deviations (MAD) of around 70 meV for G0W0@PBE and G0W0@PBE0. We check the accuracy of our AC treatment by comparison to full-frequency GW calculations, which shows that in the absence of multisolution cases, the errors due to AC are only minor. This implies that the main sources of the observed deviations between both implementations are the different single-particle bases and the pseudopotential approximation in the WEST code. Finally, we assess the performance of some (partially self-consistent) variants of the GWA for the calculation of first IPs by comparison to vertical experimental reference values. G0W0@PBE0 (25% exact exchange) and G0W0@BHLYP (50% exact exchange) perform best with mean absolute deviations (MAD) of about 200 meV. Explicit treatment of spin-orbit effects at the 2C level is crucial for systematic agreement with experiment. On the other hand, eigenvalue-only self-consistent GW (evGW) and quasi-particle self-consistent GW (qsGW) significantly overestimate the IPs. Perturbative G3W2 corrections increase the IPs and therefore improve the agreement with experiment in cases where G0W0 alone underestimates the IPs. With a MAD of only 140 meV, 2C-G0W0@PBE0 + G3W2 is in best agreement with the experimental reference values.
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Affiliation(s)
- Arno Förster
- Theoretical
Chemistry, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
| | - Erik van Lenthe
- Software
for Chemistry and Materials NV, 1081 HV Amsterdam, The Netherlands
| | - Edoardo Spadetto
- Software
for Chemistry and Materials NV, 1081 HV Amsterdam, The Netherlands
| | - Lucas Visscher
- Theoretical
Chemistry, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
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10
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Panadés-Barrueta RL, Golze D. Accelerating Core-Level GW Calculations by Combining the Contour Deformation Approach with the Analytic Continuation of W. J Chem Theory Comput 2023; 19:5450-5464. [PMID: 37566917 PMCID: PMC10448726 DOI: 10.1021/acs.jctc.3c00555] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2023] [Indexed: 08/13/2023]
Abstract
In recent years, the GW method has emerged as a reliable tool for computing core-level binding energies. The contour deformation (CD) technique has been established as an efficient, scalable, and numerically stable approach to compute the GW self-energy for deep core excitations. However, core-level GW calculations with CD face the challenge of higher scaling with respect to system size N compared to the conventional quartic scaling in valence-state algorithms. In this work, we present the CD-WAC method [CD with W analytic continuation (AC)], which reduces the scaling of CD applied to the inner shells from O(N5) to O(N4) by employing an AC of the screened Coulomb interaction W. Our proposed method retains the numerical accuracy of CD for the computationally challenging deep core case, yielding mean absolute errors <5 meV for well-established benchmark sets, such as CORE65, for single-shot GW calculations. More extensive testing for different GW flavors proves the reliability of the method. We have confirmed the theoretical scaling by performing scaling experiments on large acene chains and amorphous carbon clusters, achieving speedups of up to 10× for structures of only 116 atoms. This improvement in computational efficiency paves the way for more accurate and efficient core-level GW calculations on larger and more complex systems.
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Affiliation(s)
| | - Dorothea Golze
- Faculty of Chemistry and Food Chemistry, Technische Universität Dresden, Dresden 01062, Germany
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11
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Kahk JM, Lischner J. Combining the Δ-Self-Consistent-Field and GW Methods for Predicting Core Electron Binding Energies in Periodic Solids. J Chem Theory Comput 2023. [PMID: 37163299 DOI: 10.1021/acs.jctc.3c00121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/11/2023]
Abstract
For the computational prediction of core electron binding energies in solids, two distinct kinds of modeling strategies have been pursued: the Δ-Self-Consistent-Field method based on density functional theory (DFT), and the GW method. In this study, we examine the formal relationship between these two approaches and establish a link between them. The link arises from the equivalence, in DFT, between the total energy difference result for the first ionization energy, and the eigenvalue of the highest occupied state, in the limit of infinite supercell size. This link allows us to introduce a new formalism, which highlights how in DFT─even if the total energy difference method is used to calculate core electron binding energies─the accuracy of the results still implicitly depends on the accuracy of the eigenvalue at the valence band maximum in insulators, or at the Fermi level in metals. We examine whether incorporating a quasiparticle correction for this eigenvalue from GW theory improves the accuracy of the calculated core electron binding energies, and find that the inclusion of vertex corrections is required for achieving quantitative agreement with experiment.
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Affiliation(s)
- J Matthias Kahk
- Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411 Tartu, Estonia
| | - Johannes Lischner
- Department of Physics, Department of Materials, and the Thomas Young Centre for Theory and Simulation of Materials, Imperial College London, London SW7 2AZ, United Kingdom
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12
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Jana S, Herbert JM. Slater transition methods for core-level electron binding energies. J Chem Phys 2023; 158:094111. [PMID: 36889976 DOI: 10.1063/5.0134459] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/18/2023] Open
Abstract
Methods for computing core-level ionization energies using self-consistent field (SCF) calculations are evaluated and benchmarked. These include a "full core hole" (or "ΔSCF") approach that fully accounts for orbital relaxation upon ionization, but also methods based on Slater's transition concept in which the binding energy is estimated from an orbital energy level that is obtained from a fractional-occupancy SCF calculation. A generalization that uses two different fractional-occupancy SCF calculations is also considered. The best of the Slater-type methods afford mean errors of 0.3-0.4 eV with respect to experiment for a dataset of K-shell ionization energies, a level of accuracy that is competitive with more expensive many-body techniques. An empirical shifting procedure with one adjustable parameter reduces the average error below 0.2 eV. This shifted Slater transition method is a simple and practical way to compute core-level binding energies using only initial-state Kohn-Sham eigenvalues. It requires no more computational effort than ΔSCF and may be especially useful for simulating transient x-ray experiments where core-level spectroscopy is used to probe an excited electronic state, for which the ΔSCF approach requires a tedious state-by-state calculation of the spectrum. As an example, we use Slater-type methods to model x-ray emission spectroscopy.
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Affiliation(s)
- Subrata Jana
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - John M Herbert
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
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13
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Mukatayev I, Moevus F, Sklénard B, Olevano V, Li J. XPS Core-Level Chemical Shift by Ab Initio Many-Body Theory. J Phys Chem A 2023; 127:1642-1648. [PMID: 36787463 DOI: 10.1021/acs.jpca.3c00173] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/16/2023]
Abstract
X-ray photoemission spectroscopy (XPS) provides direct information on atomic composition and stoichiometry by measuring core-electron binding energies. Moreover, from the shift of the binding energy, the so-called chemical shift, the precise chemical type of bonds can be inferred, which brings additional information on the local structure. In this work, we present a theoretical study of the chemical shift first by comparing different theories, from Hartree-Fock and density functional theory to many-body perturbation theory approaches like the GW approximation and its static version (COHSEX). The accuracy of each theory is assessed with respect to a carbon 1s chemical shift experimental benchmark measured on a set of gas-phase molecules. More importantly, by decomposing the chemical shift into different contributions according to terms in the total Hamiltonian, classical electrostatics is identified as the major contributor to the chemical shift, one order of magnitude larger than the correlation.
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Affiliation(s)
| | - Florient Moevus
- Université Grenoble Alpes, CEA, Leti, F-38000, Grenoble, France
| | - Benoît Sklénard
- Université Grenoble Alpes, CEA, Leti, F-38000, Grenoble, France.,European Theoretical Spectroscopy Facility (ETSF), bâtiment B5a Université de Liège Allée du 6 août, numéro 17 Sart-Tilman, F-38000 Grenoble, France
| | - Valerio Olevano
- European Theoretical Spectroscopy Facility (ETSF), bâtiment B5a Université de Liège Allée du 6 août, numéro 17 Sart-Tilman, F-38000 Grenoble, France.,Université Grenoble Alpes, F-38000 Grenoble, France.,CNRS, Institut Néel, F-38042 Grenoble, France
| | - Jing Li
- Université Grenoble Alpes, CEA, Leti, F-38000, Grenoble, France.,European Theoretical Spectroscopy Facility (ETSF), bâtiment B5a Université de Liège Allée du 6 août, numéro 17 Sart-Tilman, F-38000 Grenoble, France
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14
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Li J, Jin Y, Rinke P, Yang W, Golze D. Benchmark of GW Methods for Core-Level Binding Energies. J Chem Theory Comput 2022; 18:7570-7585. [PMID: 36322136 PMCID: PMC9753590 DOI: 10.1021/acs.jctc.2c00617] [Citation(s) in RCA: 19] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
The GW approximation has recently gained increasing attention as a viable method for the computation of deep core-level binding energies as measured by X-ray photoelectron spectroscopy. We present a comprehensive benchmark study of different GW methodologies (starting point optimized, partial and full eigenvalue-self-consistent, Hedin shift, and renormalized singles) for molecular inner-shell excitations. We demonstrate that all methods yield a unique solution and apply them to the CORE65 benchmark set and ethyl trifluoroacetate. Three GW schemes clearly outperform the other methods for absolute core-level energies with a mean absolute error of 0.3 eV with respect to experiment. These are partial eigenvalue self-consistency, in which the eigenvalues are only updated in the Green's function, single-shot GW calculations based on an optimized hybrid functional starting point, and a Hedin shift in the Green's function. While all methods reproduce the experimental relative binding energies well, the eigenvalue self-consistent schemes and the Hedin shift yield with mean absolute errors <0.2 eV the best results.
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Affiliation(s)
- Jiachen Li
- Department
of Chemistry, Duke University, Durham, North Carolina27708, United States
| | - Ye Jin
- Department
of Chemistry, Duke University, Durham, North Carolina27708, United States
| | - Patrick Rinke
- Department
of Applied Physics, Aalto University, Otakaari 1, FI-02150Espoo, Finland
| | - Weitao Yang
- Department
of Chemistry, Duke University, Durham, North Carolina27708, United States
| | - Dorothea Golze
- Department
of Applied Physics, Aalto University, Otakaari 1, FI-02150Espoo, Finland,Faculty
of Chemistry and Food Chemistry, Technische
Universität Dresden, 01062Dresden, Germany,
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15
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Li J, Yang W. Renormalized Singles with Correlation in GW Green's Function Theory for Accurate Quasiparticle Energies. J Phys Chem Lett 2022; 13:9372-9380. [PMID: 36190273 DOI: 10.1021/acs.jpclett.2c02051] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
We apply the renormalized singles with the correlation (RSc) Green function in the GW approximation for accurate quasiparticle (QP) energies and orbitals. The RSc Green function includes singles contributions from the associated density functional approximation (DFA) and considers correlation contributions perturbatively. GRScWRSc uses the RSc Green function as the new starting point and in the formulation of the screened interaction. GRScW0 fixes the screened interaction at the DFA level. For the calculations of ionization potentials, GRScWRSc and GRScW0 significantly reduce the starting point dependence and provide accurate results with errors around 0.2 eV. For the calculations of core-level binding energies, GRScWRSc slightly overestimates the results because of underscreening, but GRScW0 with GGA functionals provides the optimal accuracy with errors of 0.40 eV. We also show that GRScWRSc predicts accurate dipole moments. GRScWRSc and GRScW0, are computationally favorable compared with any self-consistent GW methods. The RSc approach is promising for making GW and other Green function methods efficient and robust.
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Affiliation(s)
- Jiachen Li
- Department of Chemistry, Duke University, Durham, North Carolina27708, United States
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, North Carolina27708, United States
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16
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Xu Q, Prendergast D, Qian J. Real-Space Pseudopotential Method for the Calculation of 1 s Core-Level Binding Energies. J Chem Theory Comput 2022; 18:5471-5478. [PMID: 36037254 PMCID: PMC9476661 DOI: 10.1021/acs.jctc.2c00474] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
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We systematically studied a real-space pesudopotential
method for
the calculation of 1s core–electron binding
energies of second-row elements B, C, N, and O within the framework
of Kohn–Sham density functional theory (KS-DFT). With Dirichlet
boundary conditions, pseudopotential calculations can provide accurate
core–electron binding energies for molecular systems, when
compared with the results from all-electron calculations and experiments.
Furthermore, we report that with one simple additional nonself-consistent
calculation as a refinement step using a hybrid exchange-correlation
functional, we can generally improve the accuracy of binding energy
shifts, promising a strategy for improving accuracy at a much lower
computational cost. The specializations in the present approach, combined
with our efficient real-space KS-DFT implementation, provide key advantages
for calculating accurate core–electron binding energies of
large-scale systems.
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Affiliation(s)
- Qiang Xu
- Chemical Science Division, Lawrence Berkeley National Laboratory, Berkeley, California94720, United States
| | - David Prendergast
- Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California94720, United States
| | - Jin Qian
- Chemical Science Division, Lawrence Berkeley National Laboratory, Berkeley, California94720, United States
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17
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Mejia-Rodriguez D, Kunitsa A, Aprà E, Govind N. Basis Set Selection for Molecular Core-Level GW Calculations. J Chem Theory Comput 2022; 18:4919-4926. [PMID: 35816679 DOI: 10.1021/acs.jctc.2c00247] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The GW approximation has been recently gaining popularity among the methods for simulating molecular core-level X-ray photoemission spectra. Traditionally, Gaussian-type orbital GW core-level binding energies have been computed using either the cc-pVnZ or def2-nZVP basis set families, extrapolating the obtained results to the complete basis set limit, followed by an element-specific relativistic correction. Despite achieving rather good accuracy, it has been previously stated that these binding energies are chronically underestimated. In the present work, we show that those previous studies obtained results that were not well-converged with respect to the basis set size and that, once basis set convergence is achieved, there seems to be no such underestimation. Standard techniques known to offer a good cost-accuracy ratio in other theories demonstrate that the cc-pVnZ and def2-nZVP families exhibit contraction errors and might lead to unreliable complete basis set extrapolations for absolute binding energies, often deviating about 200-500 meV from the putative basis set limit found in this work. On the other hand, uncontracted versions of these basis sets offer vastly improved convergence. Even faster convergence can be obtained using core-rich property-optimized basis set families like pcSseg-n, pcJ-n, and ccX-nZ. Finally, we also show that the improvement observed for core properties using these specialized basis sets does not degrade their description of valence excitations: vertical ionization potentials and electron affinities computed with these basis sets converge as fast as the ones obtained with the aug-cc-pVnZ family, thus offering a balanced description of both core and valence regions.
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Affiliation(s)
- Daniel Mejia-Rodriguez
- Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Alexander Kunitsa
- Zapata Computing, Inc., 100 Federal Street, Boston, Massachusetts 02110, United States
| | - Edoardo Aprà
- Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Niranjan Govind
- Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
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18
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Bruneval F, Dattani N, van Setten MJ. The GW Miracle in Many-Body Perturbation Theory for the Ionization Potential of Molecules. Front Chem 2022; 9:749779. [PMID: 35004607 PMCID: PMC8733722 DOI: 10.3389/fchem.2021.749779] [Citation(s) in RCA: 27] [Impact Index Per Article: 13.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2021] [Accepted: 09/14/2021] [Indexed: 11/30/2022] Open
Abstract
We use the GW100 benchmark set to systematically judge the quality of several perturbation theories against high-level quantum chemistry methods. First of all, we revisit the reference CCSD(T) ionization potentials for this popular benchmark set and establish a revised set of CCSD(T) results. Then, for all of these 100 molecules, we calculate the HOMO energy within second and third-order perturbation theory (PT2 and PT3), and, GW as post-Hartree-Fock methods. We found GW to be the most accurate of these three approximations for the ionization potential, by far. Going beyond GW by adding more diagrams is a tedious and dangerous activity: We tried to complement GW with second-order exchange (SOX), with second-order screened exchange (SOSEX), with interacting electron-hole pairs (WTDHF), and with a GW density-matrix (γGW). Only the γGW result has a positive impact. Finally using an improved hybrid functional for the non-interacting Green’s function, considering it as a cheap way to approximate self-consistency, the accuracy of the simplest GW approximation improves even more. We conclude that GW is a miracle: Its subtle balance makes GW both accurate and fast.
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Affiliation(s)
- Fabien Bruneval
- CEA, Service de Recherches de Métallurgie Physique, Direction des Energies, Université Paris-Saclay, Paris, France
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