1
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Li J, Zhu T. Restoring translational symmetry in periodic all-orbital dynamical mean-field theory simulations. Faraday Discuss 2024. [PMID: 39076013 DOI: 10.1039/d4fd00068d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/31/2024]
Abstract
Dynamical mean-field theory (DMFT) and its cluster extensions provide an efficient Green's function formalism to simulate spectral properties of periodic systems at the quantum many-body level. However, traditional cluster DMFT breaks translational invariance in solid-state materials, and the best strategy to capture non-local correlation effects within cluster DMFT remains elusive. In this work, we investigate the use of overlapping atom-centered impurity fragments in recently-developed ab initio all-orbital DMFT, where all local orbitals within the impurity are treated with high-level quantum chemistry impurity solvers. We demonstrate how the translational symmetry of the lattice self-energy can be restored by designing symmetry-adapted embedding problems, which results in an improved description of spectral functions in two-dimensional boron nitride monolayers and graphene at the levels of many-body perturbation theory (GW) and coupled-cluster theory. Furthermore, we study the convergence of self-energy and density of states as the embedding size is systematically expanded in one-shot and self-consistent DMFT calculations.
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Affiliation(s)
- Jiachen Li
- Department of Chemistry, Yale University, New Haven, CT, 06520, USA.
| | - Tianyu Zhu
- Department of Chemistry, Yale University, New Haven, CT, 06520, USA.
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2
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Li J, Yang W. Chemical Potentials and the One-Electron Hamiltonian of the Second-Order Perturbation Theory from the Functional Derivative Approach. J Phys Chem A 2024; 128:4876-4885. [PMID: 38842399 DOI: 10.1021/acs.jpca.4c01574] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2024]
Abstract
We develop a functional derivative approach to calculate the chemical potentials of second-order perturbation theory (MP2). In the functional derivative approach, the correlation part of the MP2 chemical potential, which is the derivative of the MP2 correlation energy with respect to the occupation number of frontier orbitals, is obtained from the chain rule via the noninteracting Green's function. First, the MP2 correlation energy is expressed in terms of the noninteracting Green's function, and its functional derivative to the noninteracting Green's function is the second-order self-energy. Then, the derivative of the noninteracting Green's function to the occupation number is obtained by including the orbital relaxation effect. We show that the MP2 chemical potentials obtained from the functional derivative approach agree with that obtained from the finite difference approach. The one-electron Hamiltonian, defined as the derivative of the MP2 energy with respect to the one particle density matrix, is also derived using the functional derivative approach, which can be used in the self-consistent calculations of MP2 and double-hybrid density functionals. The developed functional derivative approach is promising for calculating the chemical potentials and the one-electron Hamiltonian of approximate functionals and many-body perturbation approaches dependent explicitly on the noninteracting Green's function.
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Affiliation(s)
- Jiachen Li
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
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3
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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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4
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Tölle J, Kin-Lic Chan G. AB-G0W0: A practical G0W0 method without frequency integration based on an auxiliary boson expansion. J Chem Phys 2024; 160:164108. [PMID: 38656438 DOI: 10.1063/5.0195934] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2024] [Accepted: 04/07/2024] [Indexed: 04/26/2024] Open
Abstract
Common G0W0 implementations rely on numerical or analytical frequency integration to determine the G0W0 self-energy, which results in a variety of practical complications. Recently, we have demonstrated an exact connection between the G0W0 approximation and equation-of-motion quantum chemistry approaches [J. Tölle and G. Kin-Lic Chan, J. Chem. Phys. 158, 124123 (2023)]. Based on this connection, we propose a new method to determine G0W0 quasiparticle energies, which completely avoids frequency integration and its associated problems. To achieve this, we make use of an auxiliary boson (AB) expansion. We name the new approach AB-G0W0 and demonstrate its practical applicability in a range of molecular problems.
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Affiliation(s)
- Johannes Tölle
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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5
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Yeh CN, Morales MA. Low-Scaling Algorithms for GW and Constrained Random Phase Approximation Using Symmetry-Adapted Interpolative Separable Density Fitting. J Chem Theory Comput 2024; 20:3184-3198. [PMID: 38597496 DOI: 10.1021/acs.jctc.4c00085] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/11/2024]
Abstract
We present low-scaling algorithms for GW and constrained random phase approximation based on a symmetry-adapted interpolative separable density fitting (ISDF) procedure that incorporates the space-group symmetries of crystalline systems. The resulting formulations scale cubically, with respect to system size, and linearly with the number of k-points, regardless of the choice of single-particle basis and whether a quasiparticle approximation is employed. We validate these methods through comparisons with published literature and demonstrate their efficiency in treating large-scale systems through the construction of downfolded many-body Hamiltonians for carbon dimer defects embedded in hexagonal boron nitride supercells. Our work highlights the efficiency and general applicability of ISDF in the context of large-scale many-body calculations with k-point sampling beyond density functional theory.
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Affiliation(s)
- Chia-Nan Yeh
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States
| | - Miguel A Morales
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States
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6
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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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7
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Graml M, Zollner K, Hernangómez-Pérez D, Faria Junior PE, Wilhelm J. Low-Scaling GW Algorithm Applied to Twisted Transition-Metal Dichalcogenide Heterobilayers. J Chem Theory Comput 2024; 20:2202-2208. [PMID: 38353944 PMCID: PMC10938508 DOI: 10.1021/acs.jctc.3c01230] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2023] [Revised: 12/30/2023] [Accepted: 01/08/2024] [Indexed: 03/13/2024]
Abstract
The GW method is widely used for calculating the electronic band structure of materials. The high computational cost of GW algorithms prohibits their application to many systems of interest. We present a periodic, low-scaling, and highly efficient GW algorithm that benefits from the locality of the Gaussian basis and the polarizability. The algorithm enables G0W0 calculations on a MoSe2/WS2 bilayer with 984 atoms per unit cell, in 42 h using 1536 cores. This is 4 orders of magnitude faster than a plane-wave G0W0 algorithm, allowing for unprecedented computational studies of electronic excitations at the nanoscale.
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Affiliation(s)
- Maximilian Graml
- Institute
of Theoretical Physics, University of Regensburg, 93053 Regensburg, Germany
- Regensburg
Center for Ultrafast Nanoscopy (RUN), University
of Regensburg, 93053 Regensburg, Germany
| | - Klaus Zollner
- Institute
of Theoretical Physics, University of Regensburg, 93053 Regensburg, Germany
| | - Daniel Hernangómez-Pérez
- Department
of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Paulo E. Faria Junior
- Institute
of Theoretical Physics, University of Regensburg, 93053 Regensburg, Germany
| | - Jan Wilhelm
- Institute
of Theoretical Physics, University of Regensburg, 93053 Regensburg, Germany
- Regensburg
Center for Ultrafast Nanoscopy (RUN), University
of Regensburg, 93053 Regensburg, Germany
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8
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Scott CJC, Booth GH. Rigorous Screened Interactions for Realistic Correlated Electron Systems. PHYSICAL REVIEW LETTERS 2024; 132:076401. [PMID: 38427856 DOI: 10.1103/physrevlett.132.076401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2023] [Revised: 12/05/2023] [Accepted: 01/19/2024] [Indexed: 03/03/2024]
Abstract
We derive a widely applicable first-principles approach for determining two-body, static effective interactions for low-energy Hamiltonians with quantitative accuracy. The algebraic construction rigorously conserves all instantaneous two-point correlation functions in a chosen model space at the level of the random phase approximation, improving upon the traditional uncontrolled static approximations. Applied to screened interactions within a quantum embedding framework, we demonstrate these faithfully describe the relaxation of local subspaces via downfolding high-energy physics in molecular systems, as well as enabling a systematically improvable description of the long-range plasmonic contributions in extended graphene.
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Affiliation(s)
- Charles J C Scott
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
| | - George H Booth
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
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9
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Vo EA, Wang X, Berkelbach TC. Performance of periodic EOM-CCSD for bandgaps of inorganic semiconductors and insulators. J Chem Phys 2024; 160:044106. [PMID: 38265084 DOI: 10.1063/5.0187856] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2023] [Accepted: 12/19/2023] [Indexed: 01/25/2024] Open
Abstract
We calculate bandgaps of 12 inorganic semiconductors and insulators composed of atoms from the first three rows of the Periodic Table using periodic equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD). Our calculations are performed with atom-centered triple-zeta basis sets and up to 64 k-points in the Brillouin zone. We analyze the convergence behavior with respect to the number of orbitals and number of k-points sampled using composite corrections and extrapolations to produce our final values. When accounting for electron-phonon corrections to experimental bandgaps, we find that EOM-CCSD has a mean signed error of -0.12 eV and a mean absolute error of 0.42 eV; the largest outliers are C (error of -0.93 eV), BP (-1.00 eV), and LiH (+0.78 eV). Surprisingly, we find that the more affordable partitioned EOM-MP2 theory performs as well as EOM-CCSD.
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Affiliation(s)
- Ethan A Vo
- Department of Chemistry, Columbia University, New York, New York 10027, USA
| | - Xiao Wang
- Department of Chemistry and Biochemistry, University of California, Santa Cruz, California 95064, USA
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10
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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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11
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Venturella C, Hillenbrand C, Li J, Zhu T. Machine Learning Many-Body Green's Functions for Molecular Excitation Spectra. J Chem Theory Comput 2024; 20:143-154. [PMID: 38150268 DOI: 10.1021/acs.jctc.3c01146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2023]
Abstract
We present a machine learning (ML) framework for predicting Green's functions of molecular systems, from which photoemission spectra and quasiparticle energies at quantum many-body level can be obtained. Kernel ridge regression is adopted to predict self-energy matrix elements on compact imaginary frequency grids from static and dynamical mean-field electronic features, which gives direct access to real-frequency many-body Green's functions through analytic continuation and Dyson's equation. Feature and self-energy matrices are represented in a symmetry-adapted intrinsic atomic orbital plus projected atomic orbital basis to enforce rotational invariance. We demonstrate good transferability and high data efficiency of the proposed ML method across molecular sizes and chemical species by showing accurate predictions of density of states (DOS) and quasiparticle energies at the level of many-body perturbation theory (GW) or full configuration interaction. For the ML model trained on 48 out of 1995 molecules randomly sampled from the QM7 and QM9 data sets, we report the mean absolute errors of ML-predicted highest occupied and lowest unoccupied molecular orbital energies to be 0.13 and 0.10 eV, respectively, compared to GW@PBE0. We further showcase the capability of this method by applying the same ML model to predict DOS for significantly larger organic molecules with up to 44 heavy atoms.
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Affiliation(s)
- Christian Venturella
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | | | - Jiachen Li
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Tianyu Zhu
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
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12
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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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13
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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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14
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Tölle J, Kin-Lic Chan G. Exact relationships between the GW approximation and equation-of-motion coupled-cluster theories through the quasi-boson formalism. J Chem Phys 2023; 158:124123. [PMID: 37003772 DOI: 10.1063/5.0139716] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/03/2023] Open
Abstract
We describe the relationship between the GW approximation and various equation-of-motion (EOM) coupled-cluster (CC) theories. We demonstrate the exact equivalence of the G0W0 approximation and the propagator theory for an electron-boson problem in a particular excitation basis. From there, we establish equivalence within the quasi-boson picture to the IP+EA-EOM unitary CC propagator. We analyze the incomplete description of screening provided by the standard similarity-transformed IP+EA-EOM-CC and the recently introduced G0W0 Tamm-Dancoff approximation. We further consider the approximate decoupling of IP and EA sectors in EOM-CC treatments and devise the analogous particle-hole decoupling approach for the G0W0 approximation. Finally, we numerically demonstrate the exact relationships and magnitude of the approximations in the calculations of a set of molecular ionization potentials and electron affinities.
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Affiliation(s)
- Johannes Tölle
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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15
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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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16
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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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17
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Laughon K, Yu JM, Zhu T. Periodic Coupled-Cluster Green's Function for Photoemission Spectra of Realistic Solids. J Phys Chem Lett 2022; 13:9122-9128. [PMID: 36162126 DOI: 10.1021/acs.jpclett.2c02534] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
We present an efficient implementation of the coupled-cluster Green's function (CCGF) method for simulating photoemission spectra of periodic systems. We formulate the periodic CCGF approach with Brillouin zone sampling in the Gaussian basis at the coupled-cluster singles and doubles (CCSD) level. To enable CCGF calculations of realistic solids, we propose an active-space self-energy correction scheme by combining CCGF with the cheaper many-body perturbation theory (GW) and implement the model order reduction (MOR) frequency interpolation technique. We find that the active-space self-energy correction and MOR techniques significantly reduce the computational cost of CCGF while maintaining the high accuracy. We apply the developed CCGF approaches to compute spectral properties and band structure of silicon (Si) and zinc oxide (ZnO) crystals using triple-ζ Gaussian basis sets and medium-size k-point sampling and find good agreement with experimental measurements.
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Affiliation(s)
- Katelyn Laughon
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Jason M Yu
- Department of Chemistry, University of California, Irvine, Irvine, California 92697, United States
| | - Tianyu Zhu
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
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18
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Brigiano FS, Bazin D, Tielens F. Peculiar opportunities given by XPS spectroscopy for the clinician. CR CHIM 2022. [DOI: 10.5802/crchim.154] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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19
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Bintrim SJ, Berkelbach TC, Ye HZ. Integral-Direct Hartree-Fock and Møller-Plesset Perturbation Theory for Periodic Systems with Density Fitting: Application to the Benzene Crystal. J Chem Theory Comput 2022; 18:5374-5381. [PMID: 35969856 DOI: 10.1021/acs.jctc.2c00640] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present an algorithm and implementation of integral-direct, density-fitted Hartree-Fock (HF) and second-order Møller-Plesset perturbation theory (MP2) for periodic systems. The new code eliminates the formerly prohibitive storage requirements and allows us to study systems 1 order of magnitude larger than before at the periodic MP2 level. We demonstrate the significance of the development by studying the benzene crystal in both the thermodynamic limit and the complete basis set limit, for which we predict an MP2 cohesive energy of -72.8 kJ/mol, which is about 10-15 kJ/mol larger in magnitude than all previously reported MP2 calculations. Compared to the best theoretical estimate from literature, several modified MP2 models approach chemical accuracy in the predicted cohesive energy of the benzene crystal and hence may be promising cost-effective choices for future applications on molecular crystals.
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Affiliation(s)
- Sylvia J Bintrim
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Timothy C Berkelbach
- Department of Chemistry, Columbia University, New York, New York 10027, United States.,Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States
| | - Hong-Zhou Ye
- Department of Chemistry, Columbia University, New York, New York 10027, United States
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20
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Golze D, Hirvensalo M, Hernández-León P, Aarva A, Etula J, Susi T, Rinke P, Laurila T, Caro MA. Accurate Computational Prediction of Core-Electron Binding Energies in Carbon-Based Materials: A Machine-Learning Model Combining Density-Functional Theory and GW. CHEMISTRY OF MATERIALS : A PUBLICATION OF THE AMERICAN CHEMICAL SOCIETY 2022; 34:6240-6254. [PMID: 35910537 PMCID: PMC9330771 DOI: 10.1021/acs.chemmater.1c04279] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/13/2021] [Revised: 06/30/2022] [Indexed: 06/15/2023]
Abstract
We present a quantitatively accurate machine-learning (ML) model for the computational prediction of core-electron binding energies, from which X-ray photoelectron spectroscopy (XPS) spectra can be readily obtained. Our model combines density functional theory (DFT) with GW and uses kernel ridge regression for the ML predictions. We apply the new approach to disordered materials and small molecules containing carbon, hydrogen, and oxygen and obtain qualitative and quantitative agreement with experiment, resolving spectral features within 0.1 eV of reference experimental spectra. The method only requires the user to provide a structural model for the material under study to obtain an XPS prediction within seconds. Our new tool is freely available online through the XPS Prediction Server.
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Affiliation(s)
- Dorothea Golze
- Faculty
of Chemistry and Food Chemistry, Technische
Universität Dresden, 01062 Dresden, Germany
- Department
of Applied Physics, Aalto University, 02150 Espoo, Finland
| | - Markus Hirvensalo
- Department
of Applied Physics, Aalto University, 02150 Espoo, Finland
| | | | - Anja Aarva
- Department
of Electrical Engineering and Automation, Aalto University, 02150 Espoo, Finland
| | - Jarkko Etula
- Department
of Chemistry and Materials Science, Aalto
University, 02150 Espoo, Finland
| | - Toma Susi
- University
of Vienna, Faculty of Physics, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Patrick Rinke
- Department
of Applied Physics, Aalto University, 02150 Espoo, Finland
| | - Tomi Laurila
- Department
of Electrical Engineering and Automation, Aalto University, 02150 Espoo, Finland
- Department
of Chemistry and Materials Science, Aalto
University, 02150 Espoo, Finland
| | - Miguel A. Caro
- Department
of Electrical Engineering and Automation, Aalto University, 02150 Espoo, Finland
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21
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Zhang JR, Wang SY, Ge G, Wei M, Hua W, Ma Y. On the choice of shape and size for truncated cluster-based X-ray spectral simulations of 2D materials. J Chem Phys 2022; 157:094704. [DOI: 10.1063/5.0100175] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Truncated cluster models represent an effective way for simulating X-ray spectra of 2D materials. Here we systematically assessed the influence of two key parameters, the cluster shape (honeycomb, rectangle, or parallelogram) and size, in X-ray photoelectron (XPS) and absorption (XAS) spectra simulations of three 2D materials at five K-edges (graphene, C 1s; C3N, C/N 1s; h-BN, B/N 1s) to pursue the accuracy limit of binding energy (BE) and spectral profile predictions. Several recent XPS experiments reported BEs with differences spanning 0.3, 1.5, 0.7, 0.3, and 0.3 eV, respectively. Our calculations favor the honeycomb model for stable accuracy and fast size convergence, and a honeycomb with ~10 nm side length (120 atoms) is enough to predict accurate 1s BEs for all 2D sheets. Compared to all these experiments, predicted BEs show absolute deviations as follows: 0.4-0.7, 0.0-1.0, 0.4-1.1, 0.6-0.9, and 0.1-0.4 eV. A mean absolute deviation of 0.3 eV was achieved if we compare only to the closest experiment. We found that the sensitivity of computed BEs to different model shapes depends on systems: graphene, sensitive; C3N, weak; h-BN, very weak. This can be attributed to their more or less delocalized π electrons in this series. For this reason, a larger cluster size is required for graphene than the other two to reproduce fine structures in XAS. The general profile of XAS shows weak dependence to model shape. Our calculations provide optimal parameters and accuracy estimations that are useful for X-ray spectral simulations of general graphene-like 2D materials.
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Affiliation(s)
| | | | - Guoyan Ge
- Nanjing University of Science and Technology, China
| | - Minrui Wei
- Nanjing University of Science and Technology, China
| | - Weijie Hua
- MIIT Key Laboratory of Semiconductor Microstructure and Quantum Sensing, Department of Applied Physics, School of Science, Nanjing University of Science and Technology, China
| | - Yong Ma
- School of Physics and Electronics, Shandong Normal University, China
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22
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Zhang L, Shu Y, Xing C, Chen X, Sun S, Huang Y, Truhlar DG. Recommendation of Orbitals for G0W0 Calculations on Molecules and Crystals. J Chem Theory Comput 2022; 18:3523-3537. [PMID: 35580263 DOI: 10.1021/acs.jctc.2c00242] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The many-body GW approximation, especially the G0W0 method, has been widely used for condensed matter and molecules to calculate quasiparticle energies for ionization, electron attachment, and band gaps. Because G0W0 calculations are well-known to have a strong dependence on the orbitals, the goal of the present work is to provide guidance on the choice of density functional used to generate orbitals and to recommend a choice that gives the most broadly accurate results. We have systematically investigated the dependence of G0W0 calculations on the orbitals for 100 molecules and 8 crystals by considering orbitals obtained with a diverse set of Kohn-Sham (KS) and generalized KS (GKS) functionals (63 functionals plus Hartree-Fock). The percentage of Hartree-Fock exchange employed in density functionals has been found to have strong influence on the predicted molecular ionization energy and crystal fundamental band gaps (with optimum values between 40 and 56%), but to have less effect on predicting molecular electron affinities. The low cost of the Gaussian implementation, even with hybrid functionals in periodic calculations, the better performance of global hybrids as compared to range-separated hybrids of either than screened exchange or long-range-corrected type, and the relatively low cost of global-hybrid-functional periodic calculations using Gaussians means that one can employ global-hybrid functionals at a very reasonable cost and obtain more accurate band gaps of semiconductors than are obtained by the methods currently widely employed, namely local gradient approximations. We single out three global-hybrid functionals that give especially good results for both molecules (100 in the test set) and crystals (8 in the test set, for all of which our benchmark data are the proper band gap rather than an optical band gap uncorrected for exciton effects).
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Affiliation(s)
- Linyao Zhang
- School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China.,School of Chemistry and Chemical Engineering, Harbin Institute of Technology, Harbin 150001, PR China
| | - Yinan Shu
- Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
| | - Chang Xing
- School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China.,School of Astronautics, Harbin Institute of Technology, Harbin 150001, PR China
| | - Xiye Chen
- School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China.,School of Chemistry and Chemical Engineering, Harbin Institute of Technology, Harbin 150001, PR China
| | - Shaozeng Sun
- School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China
| | - Yudong Huang
- School of Chemistry and Chemical Engineering, Harbin Institute of Technology, Harbin 150001, PR China
| | - Donald G Truhlar
- Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
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23
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Cho Y, Bintrim SJ, Berkelbach TC. Simplified GW/BSE Approach for Charged and Neutral Excitation Energies of Large Molecules and Nanomaterials. J Chem Theory Comput 2022; 18:3438-3446. [PMID: 35544591 DOI: 10.1021/acs.jctc.2c00087] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Inspired by Grimme's simplified Tamm-Dancoff density functional theory approach [Grimme, S. J. Chem. Phys. 2013, 138, 244104], we describe a simplified approach to excited-state calculations within the GW approximation to the self-energy and the Bethe-Salpeter equation (BSE), which we call sGW/sBSE. The primary simplification to the electron repulsion integrals yields the same structure as with tensor hypercontraction, such that our method has a storage requirement that grows quadratically with system size and computational timing that grows cubically with system size. The performance of sGW is tested on the ionization potential of the molecules in the GW100 test set, for which it differs from ab initio GW calculations by only 0.2 eV. The performance of sBSE (based on the sGW input) is tested on the excitation energies of molecules in Thiel's set, for which it differs from ab initio GW/BSE calculations by about 0.5 eV. As examples of the systems that can be routinely studied with sGW/sBSE, we calculate the band gap and excitation energy of hydrogen-passivated silicon nanocrystals with up to 2650 electrons in 4678 spatial orbitals and the absorption spectra of two large organic dye molecules with hundreds of atoms.
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Affiliation(s)
- Yeongsu Cho
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Sylvia J Bintrim
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Timothy C Berkelbach
- Department of Chemistry, Columbia University, New York, New York 10027, United States.,Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States
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24
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Yao Y, Golze D, Rinke P, Blum V, Kanai Y. All-Electron BSE@ GW Method for K-Edge Core Electron Excitation Energies. J Chem Theory Comput 2022; 18:1569-1583. [PMID: 35138865 DOI: 10.1021/acs.jctc.1c01180] [Citation(s) in RCA: 18] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
We present an accurate computational approach to calculate absolute K-edge core electron excitation energies as measured by X-ray absorption spectroscopy. Our approach employs an all-electron Bethe-Salpeter equation (BSE) formalism based on GW quasiparticle energies (BSE@GW) using numeric atom-centered orbitals (NAOs). The BSE@GW method has become an increasingly popular method for the computation of neutral valence excitation energies of molecules. However, it was so far not applied to molecular K-edge excitation energies. We discuss the influence of different numerical approximations on the BSE@GW calculation and employ in our final setup (i) exact numeric algorithms for the frequency integration of the GW self-energy, (ii) G0W0 and BSE starting points with ∼50% of exact exchange, (iii) the Tamm-Dancoff approximation and (iv) relativistic corrections. We study the basis set dependence and convergence with common Gaussian-type orbital and NAO basis sets. We identify the importance of additional spatially confined basis functions as well as of diffuse augmenting basis functions. The accuracy of our BSE@GW method is assessed for a benchmark set of small organic molecules, previously used for benchmarking the equation-of-motion coupled cluster method [Peng et al., J. Chem. Theory Comput., 2015, 11, 4146], as well as the medium-sized dibenzothiophene (DBT) molecule. Our BSE@GW results for absolute excitation energies are in excellent agreement with the experiment, with a mean average error of only 0.63 eV for the benchmark set and with errors <1 eV for the DBT molecule.
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Affiliation(s)
- Yi Yao
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, United States
| | - Dorothea Golze
- Faculty of Chemistry and Food Chemistry, Technische Universität Dresden, 01062 Dresden, Germany.,Department of Applied Physics, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland
| | - Patrick Rinke
- Department of Applied Physics, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland
| | | | - Yosuke Kanai
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, United States
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25
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Xing X, Lin L. Staggered Mesh Method for Correlation Energy Calculations of Solids: Random Phase Approximation in Direct Ring Coupled Cluster Doubles and Adiabatic Connection Formalisms. J Chem Theory Comput 2022; 18:763-775. [PMID: 34989566 DOI: 10.1021/acs.jctc.1c00985] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We propose a staggered mesh method for correlation energy calculations of periodic systems under the random phase approximation (RPA), which generalizes the recently developed staggered mesh method for periodic second order Møller-Plesset perturbation theory (MP2) calculations [Xing; Li; Lin J. Chem. Theory Comput. 2021]. Compared to standard RPA calculations, the staggered mesh method introduces negligible additional computational cost. It avoids a significant portion of the finite-size error and can be asymptotically advantageous for quasi-1D systems and certain quasi-2D and 3D systems with high symmetries. We demonstrate the applicability of the method using two different formalisms: the direct ring coupled cluster doubles (drCCD) theory, and the adiabatic-connection (AC) fluctuation-dissipation theory. In the drCCD formalism, the second order screened exchange (SOSEX) correction can also be readily obtained using the staggered mesh method. In the AC formalism, the staggered mesh method naturally avoids the need of performing "head/wing" corrections to the dielectric operator. The effectiveness of the staggered mesh method for insulating systems is theoretically justified by investigating the finite-size error of each individual perturbative term in the RPA correlation energy, expanded as an infinite series of terms associated with ring diagrams. As a side contribution, our analysis provides proof that the finite-size error of each perturbative term of standard RPA and SOSEX calculations scales as O(Nk-1), where Nk is the number of grid points in a Monkhorst-Pack mesh.
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Affiliation(s)
- Xin Xing
- Department of Mathematics, University of California, Berkeley, California 94720, United States
| | - Lin Lin
- Department of Mathematics, University of California, Berkeley, California 94720, United States.,Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, Berkeley, California 94720, United States.,Challenge Institute for Quantum Computation, University of California, Berkeley, California 94720, United States
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26
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Kahk JM, Lischner J. Predicting Core Electron Binding Energies in Elements of the First Transition Series Using the Δ-Self-Consistent-Field Method. Faraday Discuss 2022; 236:364-373. [DOI: 10.1039/d1fd00103e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The Δ-Self-Consistent-Field (ΔSCF) method has been established as an accurate and computationally efficient approach for calculating absolute core electron binding energies for light elements up to chlorine, but relatively little...
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27
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Kahk JM, Michelitsch GS, Maurer RJ, Reuter K, Lischner J. Core Electron Binding Energies in Solids from Periodic All-Electron Δ-Self-Consistent-Field Calculations. J Phys Chem Lett 2021; 12:9353-9359. [PMID: 34549969 DOI: 10.1021/acs.jpclett.1c02380] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
Theoretical calculations of core electron binding energies are required for the interpretation of experimental X-ray photoelectron spectra, but achieving accurate results for solids has proven difficult. In this work, we demonstrate that accurate absolute core electron binding energies in both metallic and insulating solids can be obtained from periodic all-electron Δ-self-consistent-field (ΔSCF) calculations. In particular, we show that core electron binding energies referenced to the valence band maximum can be obtained as total energy differences between two (N - 1)-electron systems: one with a core hole and one with an electron removed from the highest occupied valence state. To achieve convergence with respect to the supercell size, the analogy between localized core holes and charged defects is exploited. Excellent agreement between calculated and experimental core electron binding energies is found for both metals and insulators, with a mean absolute error of 0.24 eV for the systems considered.
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Affiliation(s)
- J Matthias Kahk
- Department of Materials, Imperial College London, South Kensington, London SW7 2AZ, United Kingdom
- Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411 Tartu, Estonia
| | - Georg S Michelitsch
- Chair for Theoretical Chemistry, Technische Universität München, Lichtenbergstr. 4, D-85747 Garching, Germany
| | - Reinhard J Maurer
- Chair for Theoretical Chemistry, Technische Universität München, Lichtenbergstr. 4, D-85747 Garching, Germany
- Department of Chemistry, University of Warwick, Gibbet Hill Rd., Coventry CV4 7AL, United Kingdom
| | - Karsten Reuter
- Chair for Theoretical Chemistry, Technische Universität München, Lichtenbergstr. 4, D-85747 Garching, Germany
| | - Johannes Lischner
- Department of Physics and 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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28
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Lange MF, Berkelbach TC. Improving MP2 bandgaps with low-scaling approximations to EOM-CCSD. J Chem Phys 2021; 155:081101. [PMID: 34470354 DOI: 10.1063/5.0061242] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Despite its reasonable accuracy for ground-state properties of semiconductors and insulators, second-order Møller-Plesset perturbation theory (MP2) significantly underestimates bandgaps. In this work, we evaluate the bandgap predictions of partitioned equation-of-motion MP2 (P-EOM-MP2), which is a second-order approximation to EOM coupled-cluster theory with single and double excitations. On a test set of elemental and binary semiconductors and insulators, we find that P-EOM-MP2 overestimates bandgaps by 0.3 eV on average, which can be compared to the underestimation by 0.6 eV on average exhibited by the G0W0 approximation with a Perdew-Burke-Ernzerhof reference. We show that P-EOM-MP2, when interpreted as a Green's function-based theory, has a self-energy that includes all first- and second-order diagrams and a few third-order diagrams. We find that the GW approximation performs better for materials with small gaps and P-EOM-MP2 performs better for materials with large gaps, which we attribute to their superior treatment of screening and exchange, respectively.
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Affiliation(s)
- Malte F Lange
- Department of Chemistry, Columbia University, New York, New York 10027, USA
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29
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Backhouse OJ, Santana-Bonilla A, Booth GH. Scalable and Predictive Spectra of Correlated Molecules with Moment Truncated Iterated Perturbation Theory. J Phys Chem Lett 2021; 12:7650-7658. [PMID: 34351782 DOI: 10.1021/acs.jpclett.1c02383] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
A reliable and efficient computation of the entire single-particle spectrum of correlated molecules is an outstanding challenge in the field of quantum chemistry, with standard density functional theory approaches often giving an inadequate description of excitation energies and gaps. In this work, we expand upon a recently introduced approach that relies on a fully self-consistent many-body perturbation theory coupled to a nonperturbative truncation of the effective dynamics at each step. We show that this yields a low-scaling and accurate method across a diverse benchmark test set that is capable of treating moderate levels of strong correlation effects, and we detail an efficient implementation for applications involving up to ∼1000 orbitals on parallel resources. We then use this method to characterize the spectral properties of the antimalarial drug molecule artemisinin, resolving discrepancies in previous works concerning the active sites of the lowest-energy fundamental excitations of the system.
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Affiliation(s)
- Oliver J Backhouse
- Department of Physics, King's College London, Strand, London WC2R 2LS, U.K
| | | | - George H Booth
- Department of Physics, King's College London, Strand, London WC2R 2LS, U.K
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30
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Wilhelm J, Seewald P, Golze D. Low-Scaling GW with Benchmark Accuracy and Application to Phosphorene Nanosheets. J Chem Theory Comput 2021; 17:1662-1677. [DOI: 10.1021/acs.jctc.0c01282] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Affiliation(s)
- Jan Wilhelm
- Institute of Theoretical Physics, University of Regensburg, D-93053 Regensburg, Germany
| | - Patrick Seewald
- Department of Chemistry, University of Zurich, CH-8057 Zurich, Switzerland
| | - Dorothea Golze
- Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland
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31
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Bintrim SJ, Berkelbach TC. Full-frequency GW without frequency. J Chem Phys 2021; 154:041101. [PMID: 33514108 PMCID: PMC7843153 DOI: 10.1063/5.0035141] [Citation(s) in RCA: 30] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2020] [Accepted: 12/13/2020] [Indexed: 01/30/2023] Open
Abstract
Efficient computer implementations of the GW approximation must approximate a numerically challenging frequency integral; the integral can be performed analytically, but doing so leads to an expensive implementation whose computational cost scales as O(N6), where N is the size of the system. Here, we introduce a new formulation of the full-frequency GW approximation by exactly recasting it as an eigenvalue problem in an expanded space. This new formulation (1) avoids the use of time or frequency grids, (2) naturally obviates the need for the common "diagonal" approximation, (3) enables common iterative eigensolvers that reduce the canonical scaling to O(N5), and (4) enables a density-fitted implementation that reduces the scaling to O(N4). We numerically verify these scaling behaviors and test a variety of approximations that are motivated by this new formulation. The new formulation is found to be competitive with conventional O(N4) methods based on analytic continuation or contour deformation. In this new formulation, the relation of the GW approximation to configuration interaction, coupled-cluster theory, and the algebraic diagrammatic construction is made especially apparent, providing a new direction for improvements to the GW approximation.
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Affiliation(s)
- Sylvia J. Bintrim
- Department of Chemistry, Columbia University, New York, New York 10027, USA
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