1
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Holzer C, Franzke YJ. Beyond Electrons: Correlation and Self-Energy in Multicomponent Density Functional Theory. Chemphyschem 2024; 25:e202400120. [PMID: 38456204 DOI: 10.1002/cphc.202400120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2024] [Revised: 03/07/2024] [Accepted: 03/08/2024] [Indexed: 03/09/2024]
Abstract
Post-Kohn-Sham methods are used to evaluate the ground-state correlation energy and the orbital self-energy of systems consisting of multiple flavors of different fermions. Starting from multicomponent density functional theory, suitable ways to arrive at the corresponding multicomponent random-phase approximation and the multicomponent Green's functionG W ${GW}$ approximation, including relativistic effects, are outlined. Given the importance of both of this methods in the development of modern Kohn-Sham density functional approximations, this work will provide a foundation to design advanced multicomponent density functional approximations. Additionally, theG W ${GW}$ quasiparticle energies are needed to study light-matter interactions with the Bethe-Salpeter equation.
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Affiliation(s)
- Christof Holzer
- Karlsruhe Institute of Technology (KIT), Institute of Theoretical Solid State Physics, Kaiserstraße 12, 76131, Karlsruhe, Germany
| | - Yannick J Franzke
- Friedrich Schiller University Jena, Otto Schott Institute of Materials Research, Löbdergraben 32, 07743, Jena, Germany
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2
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Marie A, Loos PF. Reference Energies for Valence Ionizations and Satellite Transitions. J Chem Theory Comput 2024; 20:4751-4777. [PMID: 38776293 PMCID: PMC11171335 DOI: 10.1021/acs.jctc.4c00216] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2024] [Revised: 04/10/2024] [Accepted: 04/11/2024] [Indexed: 05/24/2024]
Abstract
Upon ionization of an atom or a molecule, another electron (or more) can be simultaneously excited. These concurrently generated states are called "satellites" (or shakeup transitions) as they appear in ionization spectra as higher-energy peaks with weaker intensity and larger width than the main peaks associated with single-particle ionizations. Satellites, which correspond to electronically excited states of the cationic species, are notoriously challenging to model using conventional single-reference methods due to their high excitation degree compared to the neutral reference state. This work reports 42 satellite transition energies and 58 valence ionization potentials (IPs) of full configuration interaction quality computed in small molecular systems. Following the protocol developed for the quest database [Véril, M.; Scemama, A.; Caffarel, M.; Lipparini, F.; Boggio-Pasqua, M.; Jacquemin, D.; and Loos, P.-F. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2021, 11, e1517], these reference energies are computed using the configuration interaction using a perturbative selection made iteratively (CIPSI) method. In addition, the accuracy of the well-known coupled-cluster (CC) hierarchy (CC2, CCSD, CC3, CCSDT, CC4, and CCSDTQ) is gauged against these new accurate references. The performances of various approximations based on many-body Green's functions (GW, GF2, and T-matrix) for IPs are also analyzed. Their limitations in correctly modeling satellite transitions are discussed.
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Affiliation(s)
- Antoine Marie
- Laboratoire de Chimie et Physique
Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse 31062, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique
Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse 31062, France
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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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Amblard D, Blase X, Duchemin I. Static versus dynamically polarizable environments within the many-body GW formalism. J Chem Phys 2024; 160:154104. [PMID: 38624115 DOI: 10.1063/5.0203637] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2024] [Accepted: 03/28/2024] [Indexed: 04/17/2024] Open
Abstract
Continuum- or discrete-polarizable models for the study of optoelectronic processes in embedded subsystems rely mostly on the restriction of the surrounding electronic dielectric response to its low frequency limit. Such a description hinges on the assumption that the electrons in the surrounding medium react instantaneously to any excitation in the central subsystem, thus treating the environment in the adiabatic limit. Exploiting a recently developed embedded GW formalism with an environment described at the fully ab initio level, we assess the merits of the adiabatic limit with respect to an environment where the full dynamics of the dielectric response are considered. Furthermore, we show how to properly take the static limit of the environment's susceptibility by introducing the so-called Coulomb-hole and screened-exchange contributions to the reaction field. As a first application, we consider a C60 molecule at the surface of a C60 crystal, namely, a case where the dynamics of the embedded and embedding subsystems are similar. The common adiabatic assumption, when properly treated, generates errors below 10% on the polarization energy associated with frontier energy levels and associated energy gaps. Finally, we consider a water molecule inside a metallic nanotube, the worst case for the environment's adiabatic limit. The error on the gap polarization energy remains below 10%, even though the error on the frontier orbital polarization energies can reach a few tenths of an electronvolt.
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Affiliation(s)
- David Amblard
- University Grenoble Alpes, CNRS, Inst NEEL, F-38042 Grenoble, France
| | - Xavier Blase
- University Grenoble Alpes, CNRS, Inst NEEL, F-38042 Grenoble, France
| | - Ivan Duchemin
- University Grenoble Alpes, CEA, IRIG-MEM-L_Sim, 38054 Grenoble, France
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7
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Knysh I, Raimbault D, Duchemin I, Blase X, Jacquemin D. Assessing the accuracy of TD-DFT excited-state geometries through optimal tuning with GW energy levels. J Chem Phys 2024; 160:144115. [PMID: 38602292 DOI: 10.1063/5.0203818] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2024] [Accepted: 03/25/2024] [Indexed: 04/12/2024] Open
Abstract
We study the accuracy of excited state (ES) geometries using optimally tuned LC-PBE functionals with tuning based on GW quasiparticle energies. We compare the results obtained with the PBE, PBE0, non-tuned, and tuned LC-PBE functionals with available high-level CC reference values as well as experimental data. First, we compare ES geometrical parameters obtained for three different types of systems: molecules composed of a few atoms, 4-(dimethylamino)benzonitrile (DMABN), and conjugated dyes. To this end, we used wave-function results as benchmarks. Next, we evaluate the accuracy of the theoretically simulated spectra as compared to the experimental ones for five large dyes. Our results show that, besides small compact molecules for which tuning LC-PBE does not allow obtaining geometries more accurate than those computed with standard functionals, tuned range-separated functionals are clearly to be favored, not only for ES geometries but also for 0-0 energies, band shapes, and intensities for absorption and emission spectra. In particular, the results indicate that GW-tuned LC-PBE functionals provide improved matching with experimental spectra as compared to conventionally tuned functionals. It is an open question whether TD-DFT with GW-tuned functionals can qualitatively mimic the actual many-body Bethe-Salpeter (BSE/GW) formalism for which analytic ionic gradients remain to be developed.
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Affiliation(s)
- Iryna Knysh
- Nantes Université, CNRS, CEISAM UMR 6230, F-44000 Nantes, France
| | - Denez Raimbault
- Nantes Université, CNRS, CEISAM UMR 6230, F-44000 Nantes, France
| | - Ivan Duchemin
- Université Grenoble Alpes, CEA, IRIG-MEM-L_Sim, 38054 Grenoble, France
| | - Xavier Blase
- Université Grenoble Alpes, CNRS, Institut, Néel F-38042, Grenoble
| | - Denis Jacquemin
- Nantes Université, CNRS, CEISAM UMR 6230, F-44000 Nantes, France
- Institut Universitaire de France, 75005 Paris, France
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8
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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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9
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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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10
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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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11
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Altman AR, Kundu S, da Jornada FH. Mixed Stochastic-Deterministic Approach for Many-Body Perturbation Theory Calculations. PHYSICAL REVIEW LETTERS 2024; 132:086401. [PMID: 38457735 DOI: 10.1103/physrevlett.132.086401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2023] [Revised: 08/24/2023] [Accepted: 12/05/2023] [Indexed: 03/10/2024]
Abstract
We present an approach for GW calculations of quasiparticle energies with quasiquadratic scaling by approximating high-energy contributions to the Green's function in its Lehmann representation with effective stochastic vectors. The method is easy to implement without altering the GW code, converges rapidly with stochastic parameters, and treats systems of various dimensionality and screening response. Our calculations on a 5.75° twisted MoS_{2} bilayer show how large-scale GW methods include geometry relaxations and electronic correlations on an equal basis in structurally nontrivial materials.
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Affiliation(s)
- Aaron R Altman
- Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, USA
| | - Sudipta Kundu
- Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, USA
| | - Felipe H da Jornada
- Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
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12
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Leppert L. Excitons in metal-halide perovskites from first-principles many-body perturbation theory. J Chem Phys 2024; 160:050902. [PMID: 38341699 DOI: 10.1063/5.0187213] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2023] [Accepted: 12/19/2023] [Indexed: 02/13/2024] Open
Abstract
Metal-halide perovskites are a structurally, chemically, and electronically diverse class of semiconductors with applications ranging from photovoltaics to radiation detectors and sensors. Understanding neutral electron-hole excitations (excitons) is key for predicting and improving the efficiency of energy-conversion processes in these materials. First-principles calculations have played an important role in this context, allowing for a detailed insight into the formation of excitons in many different types of perovskites. Such calculations have demonstrated that excitons in some perovskites significantly deviate from canonical models due to the chemical and structural heterogeneity of these materials. In this Perspective, I provide an overview of calculations of excitons in metal-halide perovskites using Green's function-based many-body perturbation theory in the GW + Bethe-Salpeter equation approach, the prevalent method for calculating excitons in extended solids. This approach readily considers anisotropic electronic structures and dielectric screening present in many perovskites and important effects, such as spin-orbit coupling. I will show that despite this progress, the complex and diverse electronic structure of these materials and its intricate coupling to pronounced and anharmonic structural dynamics pose challenges that are currently not fully addressed within the GW + Bethe-Salpeter equation approach. I hope that this Perspective serves as an inspiration for further exploring the rich landscape of excitons in metal-halide perovskites and other complex semiconductors and for method development addressing unresolved challenges in the field.
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Affiliation(s)
- Linn Leppert
- MESA+ Institute for Nanotechnology, University of Twente, 7500 AE Enschede, The Netherlands
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13
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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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14
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Knysh I, Villalobos-Castro JDJ, Duchemin I, Blase X, Jacquemin D. Excess and excited-state dipole moments of real-life dyes: a comparison between wave-function, BSE/ GW, and TD-DFT values. Phys Chem Chem Phys 2023; 25:29993-30004. [PMID: 37905396 DOI: 10.1039/d3cp04467j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2023]
Abstract
In this work, we assess the accuracy of the Bethe-Salpeter equation (BSE) many-body Green's function formalism, adopting the eigenvalue-self-consistent evGW exchange-correlation kernel, for the calculation of the excited-state (μES) and excess dipole moments (Δμ), the latter ones being the changes of dipole amplitude between the ground and excited states (ES), in organic dyes. We compare the results obtained with wave-function methods [ADC(2), CC2, and CCSD], time-dependent density functional theory (TD-DFT), and BSE/evGW levels of theory. First, we compute the evolution of the dipole moments of the two lowest singlet excited states of 4-(dimethylamino)benzonitrile (DMABN) upon twisting of the amino group. Next, we use a set of 25 dyes having ES characters ranging from locally excited to charge transfer to determine both μES and Δμ. For DMABN our results show that BSE/evGW provides Δμ values closer to the CCSD reference and more consistent trends than TD-DFT. Moreover, a statistical analysis of both Δμ and μES for the set of 25 dyes shows that the BSE/evGW accuracy is comparable or sometimes slightly better than that of TD-M06-2X and TD-CAM-B3LYP, BSE/evGW outperforming TD-DFT in challenging cases (zwitterionic and cyanine transitions). Finally, the starting point dependency of BSE/evGW seems to be larger for Δμ, ES dipoles, and oscillator strengths than for transition energies.
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Affiliation(s)
- Iryna Knysh
- Nantes Université, CNRS, CEISAM UMR 6230, F-44000 Nantes, France.
| | | | - Ivan Duchemin
- Université Grenoble Alpes, CEA, IRIG-MEM-L_Sim, 38054 Grenoble, France
| | - Xavier Blase
- Université Grenoble Alpes, CNRS, Institut Néel, F-38042 Grenoble, France.
| | - Denis Jacquemin
- Nantes Université, CNRS, CEISAM UMR 6230, F-44000 Nantes, France.
- Institut Universitaire de France, F-75005 Paris, France
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15
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Amblard D, Blase X, Duchemin I. Many-body GW calculations with very large scale polarizable environments made affordable: A fully ab initio QM/QM approach. J Chem Phys 2023; 159:164107. [PMID: 37873961 DOI: 10.1063/5.0168755] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2023] [Accepted: 10/05/2023] [Indexed: 10/25/2023] Open
Abstract
We present a many-body GW formalism for quantum subsystems embedded in discrete polarizable environments containing up to several hundred thousand atoms described at a fully ab initio random phase approximation level. Our approach is based on a fragment approximation in the construction of the Green's function and independent-electron susceptibilities. Further, the environing fragments susceptibility matrices are reduced to a minimal but accurate representation preserving low order polarizability tensors through a constrained minimization scheme. This approach dramatically reduces the cost associated with inverting the Dyson equation for the screened Coulomb potential W, while preserving the description of short to long-range screening effects. The efficiency and accuracy of the present scheme is exemplified in the paradigmatic cases of fullerene bulk, surface, subsurface, and slabs with varying number of layers.
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Affiliation(s)
- David Amblard
- Univ. Grenoble Alpes, CNRS, Institut NEEL, F-38042 Grenoble, France
| | - Xavier Blase
- Univ. Grenoble Alpes, CNRS, Institut NEEL, F-38042 Grenoble, France
| | - Ivan Duchemin
- Univ. Grenoble Alpes, CEA, IRIG-MEM-L_Sim, 38054 Grenoble, France
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16
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Besalú-Sala P, Bruneval F, Pérez-Jiménez ÁJ, Sancho-García JC, Rodríguez-Mayorga M. RPA, an Accurate and Fast Method for the Computation of Static Nonlinear Optical Properties. J Chem Theory Comput 2023; 19:6062-6069. [PMID: 37696751 PMCID: PMC10861135 DOI: 10.1021/acs.jctc.3c00674] [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: 06/20/2023] [Indexed: 09/13/2023]
Abstract
The accurate computation of static nonlinear optical properties (SNLOPs) in large polymers requires accounting for electronic correlation effects with a reasonable computational cost. The Random Phase Approximation (RPA) used in the adiabatic connection fluctuation theorem is known to be a reliable and cost-effective method to render electronic correlation effects when combined with density-fitting techniques and integration over imaginary frequencies. We explore the ability of the RPA energy expression to predict SNLOPs by evaluating RPA electronic energies in the presence of finite electric fields to obtain (using the finite difference method) static polarizabilities and hyperpolarizabilities. We show that the RPA based on hybrid functional self-consistent field calculations yields accurate SNLOPs as the best-tuned double-hybrid functionals developed today, with the additional advantage that the RPA avoids any system-specific adjustment.
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Affiliation(s)
- Pau Besalú-Sala
- Department
of Chemistry and Pharmaceutical Sciences, Amsterdam Institute for
Molecular and Life Sciences (AIMMS), Vrije
Universiteit Amsterdam, De Boelelaan 1083, HV Amsterdam 1081, The Netherlands
- Institut
de Química Computacional i Catàlisi and Departament
de Química, Universitat de Girona, Girona 17003, Spain
| | - Fabien Bruneval
- Université
Paris-Saclay, CEA, Service de recherche en Corrosion et Comportement
des Matériaux, SRMP, Gif-sur-Yvette 91191, France
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17
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Yeh CN, Morales MA. Low-Scaling Algorithm for the Random Phase Approximation Using Tensor Hypercontraction with k-point Sampling. J Chem Theory Comput 2023; 19:6197-6207. [PMID: 37624575 DOI: 10.1021/acs.jctc.3c00615] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/26/2023]
Abstract
We present a low-scaling algorithm for the random phase approximation (RPA) with k-point sampling in the framework of tensor hypercontraction (THC) for electron repulsion integrals (ERIs). The THC factorization is obtained via a revised interpolative separable density fitting (ISDF) procedure with a momentum-dependent auxiliary basis for generic single-particle Bloch orbitals. Our formulation does not require preoptimized interpolating points or auxiliary bases, and the accuracy is systematically controlled by the number of interpolating points. The resulting RPA algorithm scales linearly with the number of k-points and cubically with the system size without any assumption on sparsity or locality of orbitals. The errors of ERIs and RPA energy show rapid convergence with respect to the size of the THC auxiliary basis, suggesting a promising and robust direction to construct efficient algorithms of higher order many-body perturbation theories for large-scale systems.
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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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18
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Li J, Yu J, Chen Z, Yang W. Linear Scaling Calculations of Excitation Energies with Active-Space Particle-Particle Random-Phase Approximation. J Phys Chem A 2023; 127:7811-7822. [PMID: 37695567 DOI: 10.1021/acs.jpca.3c02834] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/12/2023]
Abstract
We developed an efficient active-space particle-particle random-phase approximation (ppRPA) approach to calculate accurate charge-neutral excitation energies of molecular systems. The active-space ppRPA approach constrains both indexes in particle and hole pairs in the ppRPA matrix, which only selects frontier orbitals with dominant contributions to low-lying excitation energies. It employs the truncation in both orbital indexes in the particle-particle and the hole-hole spaces. The resulting matrix, whose eigenvalues are excitation energies, has a dimension that is independent of the size of the systems. The computational effort for the excitation energy calculation, therefore, scales linearly with system size and is negligible compared with the ground-state calculation of the (N - 2)-electron system, where N is the electron number of the molecule. With the active space consisting of 30 occupied and 30 virtual orbitals, the active-space ppRPA approach predicts the excitation energies of valence, charge-transfer, Rydberg, double, and diradical excitations with the mean absolute errors (MAEs) smaller than 0.03 eV compared with the full-space ppRPA results. As a side product, we also applied the active-space ppRPA approach in the renormalized singles (RS) T-matrix approach. Combining the non-interacting pair approximation that approximates the contribution to the self-energy outside the active space, the active-space GRSTRS@PBE approach predicts accurate absolute and relative core-level binding energies with the MAEs around 1.58 and 0.3 eV, respectively. The developed linear scaling calculation of excitation energies is promising for applications to large and complex systems.
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Affiliation(s)
- Jiachen Li
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Jincheng Yu
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Zehua Chen
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
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19
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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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20
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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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21
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Kehry M, Klopper W, Holzer C. Robust relativistic many-body Green's function based approaches for assessing core ionized and excited states. J Chem Phys 2023; 159:044116. [PMID: 37522402 DOI: 10.1063/5.0160265] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2023] [Accepted: 07/12/2023] [Indexed: 08/01/2023] Open
Abstract
A two-component contour deformation (CD) based GW method that employs frequency sampling to drastically reduce the computational effort when assessing quasiparticle states far away from the Fermi level is outlined. Compared to the canonical CD-GW method, computational scaling is reduced by an order of magnitude without sacrificing accuracy. This allows for an efficient calculation of core ionization energies. The improved computational efficiency is used to provide benchmarks for core ionized states, comparing the performance of 15 density functional approximations as Kohn-Sham starting points for GW calculations on a set of 65 core ionization energies of 32 small molecules. Contrary to valence states, GW calculations on core states prefer functionals with only a moderate amount of Hartree-Fock exchange. Moreover, modern ab initio local hybrid functionals are also shown to provide excellent generalized Kohn-Sham references for core GW calculations. Furthermore, the core-valence separated Bethe-Salpeter equation (CVS-BSE) is outlined. CVS-BSE is a convenient tool to probe core excited states. The latter is tested on a set of 40 core excitations of eight small inorganic molecules. Results from the CVS-BSE method for excitation energies and the corresponding absorption cross sections are found to be in excellent agreement with those of reference damped response BSE calculations.
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Affiliation(s)
- Max Kehry
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Wim Klopper
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Straße 1, 76131 Karlsruhe, Germany
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22
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Marie A, Loos PF. A Similarity Renormalization Group Approach to Green's Function Methods. J Chem Theory Comput 2023. [PMID: 37311565 DOI: 10.1021/acs.jctc.3c00281] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
The family of Green's function methods based on the GW approximation has gained popularity in the electronic structure theory thanks to its accuracy in weakly correlated systems combined with its cost-effectiveness. Despite this, self-consistent versions still pose challenges in terms of convergence. A recent study [Monino and Loos J. Chem. Phys. 2022, 156, 231101.] has linked these convergence issues to the intruder-state problem. In this work, a perturbative analysis of the similarity renormalization group (SRG) approach is performed on Green's function methods. The SRG formalism enables us to derive, from first-principles, the expression of a naturally static and Hermitian form of the self-energy that can be employed in quasiparticle self-consistent GW (qsGW) calculations. The resulting SRG-based regularized self-energy significantly accelerates the convergence of qsGW calculations, slightly improves the overall accuracy, and is straightforward to implement in existing code.
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Affiliation(s)
- Antoine Marie
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31400 Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31400 Toulouse, France
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23
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Holzer C. Practical Post-Kohn-Sham Methods for Time-Reversal Symmetry Breaking References. J Chem Theory Comput 2023. [PMID: 37183702 DOI: 10.1021/acs.jctc.3c00156] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
The applicability of reduced scaling algorithms based on auxiliary subspace methods for the correlation energy from the random phase approximation (RPA) as well as the correlation part of the self-energy obtained from the GW method is outlined for time-reversal symmetry breaking Kohn-Sham (KS) references. The updated algorithms allow for an efficient evaluation of RPA energies and GW quasiparticle energies for molecular systems with KS references that break time-reversal symmetry. The latter occur, for example, in magnetic fields. Furthermore, KS references for relativistic open-shell molecules also break time-reversal symmetry due to the single determinant ansatz used. Errors of the updated reduced-scaling algorithms are shown to be negligible compared to reference implementations, while the overall computational scaling is reduced by 2 orders of magnitude. Ionization energies obtained from the GW approximation are shown to be robust even for the electronically complicated group of trivalent lanthanoid ions. Starting from GW quasiparticle energies, it is subsequently shown that light-matter interactions of these systems can be calculated using the Bethe-Salpeter equation (BSE). Using the combined GW-BSE method, the absorption and emission spectra of a molecular europium(III) complex can be obtained including spin-orbit coupling.
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Affiliation(s)
- Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Straße 1, 76131 Karlsruhe, Germany
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24
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Monzel L, Holzer C, Klopper W. Natural virtual orbitals for the GW method in the random-phase approximation and beyond. J Chem Phys 2023; 158:144102. [PMID: 37061489 DOI: 10.1063/5.0144469] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/17/2023] Open
Abstract
The increasingly popular GW method is becoming a convenient tool to determine vertical ionization energies in molecular systems. However, depending on the formalism used and the range of orbitals investigated, it may be hampered by a steep computational scaling. To alleviate this issue, correlated natural virtual orbitals (NVOs) based on second-order Møller-Plesset (MP2) and direct MP2 correlation energies are implemented, and the resulting correlated NVOs are tested on GW quasiparticle energies. Test cases include the popular GW variants G0W0 and evGW0 as well as more elaborate vertex corrections. We find that for increasingly larger molecular systems and basis sets, NVOs considerably improve efficiency. Furthermore, we test the performance of the truncated (frozen) NVO ansatz on the GW100 test set. For the latter, it is demonstrated that, using a carefully chosen truncation threshold, NVOs lead to a negligible loss in accuracy while providing speedups of one order of magnitude. Furthermore, we compare the resulting quasiparticle energies to very accurate vertical ionization energies obtained from coupled-cluster theory with singles, doubles, and noniterative triples [CCSD(T)], confirming that the loss in accuracy introduced by truncating the NVOs is negligible compared to the methodical errors in the GW approximation. It is also demonstrated that the choice of basis set impacts results far more than using a suitably truncated NVO space. Therefore, at the same computational expense, more accurate results can be obtained using NVOs. Finally, we provide improved reference CCSD(T) values for the GW100 test set, which have been obtained using the def2-QZVPP basis set.
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Affiliation(s)
- Laurenz Monzel
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Straße 1, 76131 Karlsruhe, Germany
| | - Wim Klopper
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
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25
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Knysh I, Letellier K, Duchemin I, Blase X, Jacquemin D. Excited state potential energy surfaces of N-phenylpyrrole upon twisting: reference values and comparison between BSE/ GW and TD-DFT. Phys Chem Chem Phys 2023; 25:8376-8385. [PMID: 36883347 DOI: 10.1039/d3cp00474k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/06/2023]
Abstract
The puzzling case of the mixing between the charge transfer (CT) and local excited (LE) characters upon twisting of the geometry of N-phenylpyrrole (N-PP) is investigated considering the six low-lying singlet excited states (ES). The theoretical calculations of the potential energy surfaces (PES) have been performed for these states using a Coupled Cluster method accounting for the impact of the contributions from the triples, many-body Green's function GW and Bethe-Salpeter equation (BSE) formalisms, as well as Time-Dependent Density Functional Theory (TD-DFT) using various exchange-correlation functionals. Our findings confirm that the BSE formalism is more reliable than TD-DFT for close-lying ES with mixed CT/LE nature. More specifically, BSE/GW yields a more accurate evolution of the excited state PES than TD-DFT when compared to the reference coupled cluster values. BSE/GW PES curves also show negligible exchange-correlation functional starting point dependency in sharp contrast with their TD-DFT counterparts.
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Affiliation(s)
- Iryna Knysh
- Nantes Université, CNRS, CEISAM UMR 6230, F-44000, Nantes, France.
| | | | - Ivan Duchemin
- Université Grenoble Alpes, CEA, IRIG-MEM-L_Sim, 38054, Grenoble, France
| | - Xavier Blase
- Université Grenoble Alpes, CNRS, Institut Néel, F-38042, Grenoble, France.
| | - Denis Jacquemin
- Nantes Université, CNRS, CEISAM UMR 6230, F-44000, Nantes, France.
- Institut Universitaire de France, 75005, Paris, France
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26
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Qin X, Hu W, Yang J. Interpolative Separable Density Fitting for Accelerating Two-Electron Integrals: A Theoretical Perspective. J Chem Theory Comput 2023; 19:679-693. [PMID: 36693136 DOI: 10.1021/acs.jctc.2c00927] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
Low-rank approximations have long been considered an efficient way to accelerate electronic structure calculations associated with the evaluation of electron repulsion integrals (ERIs). As an accurate and efficient algorithm for compressing the ERI tensor, the interpolative separable density fitting (ISDF) decomposition has recently attracted great attention in this context. In this perspective, we introduce the ISDF decomposition from the theoretical aspects and technique details. The ISDF decomposition can construct a fully separable low-rank approximation (tensor hypercontraction factorization) of ERIs in real space with a cubic cost, offering great flexibility for accelerating high-scaling electronic structure calculations. We review the typical applications of ISDF in hybrid functionals, time-dependent density functional theory, and GW approximation. Finally, we discuss the promising directions for future development of ISDF.
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Affiliation(s)
- Xinming Qin
- Hefei National Research Center for Physical Sciences at the Microscale, Department of Chemical Physics, Synergetic Innovation Center of Quantum Information and Quantum Physics, and Anhui Center for Applied Mathematics, University of Science and Technology of China, Hefei, Anhui230026, China
| | - Wei Hu
- Hefei National Research Center for Physical Sciences at the Microscale, Department of Chemical Physics, Synergetic Innovation Center of Quantum Information and Quantum Physics, and Anhui Center for Applied Mathematics, University of Science and Technology of China, Hefei, Anhui230026, China
| | - Jinlong Yang
- Hefei National Research Center for Physical Sciences at the Microscale, Department of Chemical Physics, Synergetic Innovation Center of Quantum Information and Quantum Physics, and Anhui Center for Applied Mathematics, University of Science and Technology of China, Hefei, Anhui230026, China
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27
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Quintero-Monsebaiz R, Monino E, Marie A, Loos PF. Connections between many-body perturbation and coupled-cluster theories. J Chem Phys 2022; 157:231102. [PMID: 36550046 DOI: 10.1063/5.0130837] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022] Open
Abstract
Here, we build on the works of Scuseria et al. [J. Chem. Phys. 129, 231101 (2008)] and Berkelbach [J. Chem. Phys. 149, 041103 (2018)] to show connections between the Bethe-Salpeter equation (BSE) formalism combined with the GW approximation from many-body perturbation theory and coupled-cluster (CC) theory at the ground- and excited-state levels. In particular, we show how to recast the GW and Bethe-Salpeter equations as non-linear CC-like equations. Similitudes between BSE@GW and the similarity-transformed equation-of-motion CC method are also put forward. The present work allows us to easily transfer key developments and the general knowledge gathered in CC theory to many-body perturbation theory. In particular, it may provide a path for the computation of ground- and excited-state properties (such as nuclear gradients) within the GW and BSE frameworks.
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Affiliation(s)
- Raúl Quintero-Monsebaiz
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Enzo Monino
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Antoine Marie
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
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28
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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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29
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Li J, Golze D, Yang W. Combining Renormalized Singles GW Methods with the Bethe-Salpeter Equation for Accurate Neutral Excitation Energies. J Chem Theory Comput 2022; 18:6637-6645. [PMID: 36279250 PMCID: PMC9972216 DOI: 10.1021/acs.jctc.2c00686] [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 apply the renormalized singles (RS) Green's function in the Bethe-Salpeter equation (BSE)/GW approach to predict accurate neutral excitation energies of molecular systems. The BSE calculations are performed on top of the GRSWRS method, which uses the RS Green's function also for the computation of the screened Coulomb interaction W. We show that the BSE/GRSWRS approach significantly outperforms BSE/G0W0 for predicting excitation energies of valence, Rydberg, and charge-transfer (CT) excitations by benchmarking the Truhlar-Gagliardi set, Stein CT set, and an atomic Rydberg test set. For the Truhlar-Gagliardi test set, BSE/GRSWRS provides comparable accuracy to time-dependent density functional theory (TDDFT) and is slightly better than BSE starting from eigenvalue self-consistent GW (evGW). For the Stein CT test set, BSE/GRSWRS significantly outperforms BSE/G0W0 and TDDFT with the accuracy comparable to BSE/evGW. We also show that BSE/GRSWRS predicts Rydberg excitation energies of atomic systems well. Besides the excellent accuracy, BSE/GRSWRS largely eliminates the dependence on the choice of the density functional approximation. This work demonstrates that the BSE/GRSWRS approach is accurate and efficient for predicting excitation energies for a broad range of systems, which expands the applicability of the BSE/GW approach.
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Affiliation(s)
- Jiachen Li
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Dorothea Golze
- Faculty of Chemistry and Food Chemistry, Technische Universität Dresden, 01062 Dresden, Germany
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
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30
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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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Förster A, Visscher L. Quasiparticle Self-Consistent GW-Bethe-Salpeter Equation Calculations for Large Chromophoric Systems. J Chem Theory Comput 2022; 18:6779-6793. [PMID: 36201788 PMCID: PMC9648197 DOI: 10.1021/acs.jctc.2c00531] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
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The GW-Bethe–Salpeter equation
(BSE) method
is promising for calculating the low-lying excitonic states of molecular
systems. However, so far it has only been applied to rather small
molecules and in the commonly implemented diagonal approximations
to the electronic self-energy, it depends on a mean-field starting
point. We describe here an implementation of the self-consistent and
starting-point-independent quasiparticle self-consistent (qsGW)-BSE approach, which is suitable for calculations on
large molecules. We herein show that eigenvalue-only self-consistency
can lead to an unfaithful description of some excitonic states for
chlorophyll dimers while the qsGW-BSE vertical excitation
energies (VEEs) are in excellent agreement with spectroscopic experiments
for chlorophyll monomers and dimers measured in the gas phase. Furthermore,
VEEs from time-dependent density functional theory calculations tend
to disagree with experimental values and using different range-separated
hybrid (RSH) kernels does change the VEEs by up to 0.5 eV. We use
the new qsGW-BSE implementation to calculate the
lowest excitation energies of the six chromophores of the photosystem
II (PSII) reaction center (RC) with nearly 2000 correlated electrons.
Using more than 11,000 (6000) basis functions, the calculation could
be completed in less than 5 (2) days on a single modern compute node.
In agreement with previous TD-DFT calculations using RSH kernels on
models that also do not include environmental effects, our qsGW-BSE calculations only yield states with local characters
in the low-energy spectrum of the hexameric complex. Earlier works
with RSH kernels have demonstrated that the protein environment facilitates
the experimentally observed interchromophoric charge transfer. Therefore,
future research will need to combine correlation effects beyond TD-DFT
with an explicit treatment of environmental electrostatics.
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Affiliation(s)
- Arno Förster
- Theoretical Chemistry, Vrije Universiteit, De Boelelaan 1083, NL-1081 HVAmsterdam, The Netherlands
| | - Lucas Visscher
- Theoretical Chemistry, Vrije Universiteit, De Boelelaan 1083, NL-1081 HVAmsterdam, The Netherlands
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Förster A. Assessment of the Second-Order Statically Screened Exchange Correction to the Random Phase Approximation for Correlation Energies. J Chem Theory Comput 2022; 18:5948-5965. [PMID: 36150190 PMCID: PMC9558381 DOI: 10.1021/acs.jctc.2c00366] [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: 11/30/2022]
Abstract
![]()
With increasing interelectronic distance, the screening
of the
electron–electron interaction by the presence of other electrons
becomes the dominant source of electron correlation. This effect is
described by the random phase approximation (RPA) which is therefore
a promising method for the calculation of weak interactions. The success
of the RPA relies on the cancellation of errors, which can be traced
back to the violation of the crossing symmetry of the 4-point vertex,
leading to strongly overestimated total correlation energies. By the
addition of second-order screened exchange (SOSEX) to the correlation
energy, this issue is substantially reduced. In the adiabatic connection
(AC) SOSEX formalism, one of the two electron–electron interaction
lines in the second-order exchange term is dynamically screened (SOSEX(W, vc)). A
related SOSEX expression in which both electron–electron interaction
lines are statically screened (SOSEX(W(0), W(0))) is obtained from the G3W2 contribution to the electronic self-energy. In contrast to SOSEX(W, vc), the
evaluation of this correlation energy expression does not require
an expensive numerical frequency integration and is therefore advantageous
from a computational perspective. We compare the accuracy of the statically
screened variant to RPA and RPA+SOSEX(W, vc) for a wide range of chemical
reactions. While both methods fail for barrier heights, SOSEX(W(0), W(0)) agrees very well with SOSEX(W, vc) for
charged excitations and noncovalent interactions where they lead to
major improvements over RPA.
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Affiliation(s)
- Arno Förster
- Theoretical Chemistry, Vrije Universiteit, De Boelelaan 1083, NL-1081 HV, Amsterdam, The Netherlands
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Yu VWZ, Govoni M. GPU Acceleration of Large-Scale Full-Frequency GW Calculations. J Chem Theory Comput 2022; 18:4690-4707. [PMID: 35913080 DOI: 10.1021/acs.jctc.2c00241] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Many-body perturbation theory is a powerful method to simulate electronic excitations in molecules and materials starting from the output of density functional theory calculations. By implementing the theory efficiently so as to run at scale on the latest leadership high-performance computing systems it is possible to extend the scope of GW calculations. We present a GPU acceleration study of the full-frequency GW method as implemented in the WEST code. Excellent performance is achieved through the use of (i) optimized GPU libraries, e.g., cuFFT and cuBLAS, (ii) a hierarchical parallelization strategy that minimizes CPU-CPU, CPU-GPU, and GPU-GPU data transfer operations, (iii) nonblocking MPI communications that overlap with GPU computations, and (iv) mixed precision in selected portions of the code. A series of performance benchmarks has been carried out on leadership high-performance computing systems, showing a substantial speedup of the GPU-accelerated version of WEST with respect to its CPU version. Good strong and weak scaling is demonstrated using up to 25 920 GPUs. Finally, we showcase the capability of the GPU version of WEST for large-scale, full-frequency GW calculations of realistic systems, e.g., a nanostructure, an interface, and a defect, comprising up to 10 368 valence electrons.
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Affiliation(s)
- Victor Wen-Zhe Yu
- Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Marco Govoni
- Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, United States.,Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, United States
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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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35
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Monino E, Loos PF. Unphysical discontinuities, intruder states and regularization in GW methods. J Chem Phys 2022; 156:231101. [PMID: 35732525 DOI: 10.1063/5.0089317] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
By recasting the non-linear frequency-dependent GW quasiparticle equation into a linear eigenvalue problem, we explain the appearance of multiple solutions and unphysical discontinuities in various physical quantities computed within the GW approximation. Considering the GW self-energy as an effective Hamiltonian, it is shown that these issues are key signatures of strong correlation in the (N ± 1)-electron states and can be directly related to the intruder state problem. A simple and efficient regularization procedure inspired by the similarity renormalization group is proposed to avoid such issues and speed up the convergence of partially self-consistent GW calculations.
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Affiliation(s)
- Enzo Monino
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
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36
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Dawson W, Degomme A, Stella M, Nakajima T, Ratcliff LE, Genovese L. Density functional theory calculations of large systems: Interplay between fragments, observables, and computational complexity. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2022. [DOI: 10.1002/wcms.1574] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
| | | | - Martina Stella
- Department of Materials Imperial College London London UK
| | | | | | - Luigi Genovese
- Université Grenoble Alpes, INAC‐MEM, L_Sim Grenoble France
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37
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Loos PF, Romaniello P. Static and dynamic Bethe-Salpeter equations in the T-matrix approximation. J Chem Phys 2022; 156:164101. [PMID: 35490009 DOI: 10.1063/5.0088364] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
While the well-established GW approximation corresponds to a resummation of the direct ring diagrams and is particularly well suited for weakly correlated systems, the T-matrix approximation does sum ladder diagrams up to infinity and is supposedly more appropriate in the presence of strong correlation. Here, we derive and implement, for the first time, the static and dynamic Bethe-Salpeter equations when one considers T-matrix quasiparticle energies and a T-matrix-based kernel. The performance of the static scheme and its perturbative dynamical correction are assessed by computing the neutral excited states of molecular systems. A comparison with more conventional schemes as well as other wave function methods is also reported. Our results suggest that the T-matrix-based formalism performs best in few-electron systems where the electron density remains low.
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Affiliation(s)
- Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Pina Romaniello
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, Toulouse, France
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Li J, Jin Y, Su NQ, Yang W. Combining localized orbital scaling correction and Bethe-Salpeter equation for accurate excitation energies. J Chem Phys 2022; 156:154101. [PMID: 35459294 PMCID: PMC9033305 DOI: 10.1063/5.0087498] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2022] [Accepted: 03/29/2022] [Indexed: 11/14/2022] Open
Abstract
We applied localized orbital scaling correction (LOSC) in Bethe-Salpeter equation (BSE) to predict accurate excitation energies for molecules. LOSC systematically eliminates the delocalization error in the density functional approximation and is capable of approximating quasiparticle (QP) energies with accuracy similar to or better than GW Green's function approach and with much less computational cost. The QP energies from LOSC, instead of commonly used G0W0 and evGW, are directly used in BSE. We show that the BSE/LOSC approach greatly outperforms the commonly used BSE/G0W0 approach for predicting excitations with different characters. For the calculations of Truhlar-Gagliardi test set containing valence, charge transfer, and Rydberg excitations, BSE/LOSC with the Tamm-Dancoff approximation provides a comparable accuracy to time-dependent density functional theory (TDDFT) and BSE/evGW. For the calculations of Stein CT test set and Rydberg excitations of atoms, BSE/LOSC considerably outperforms both BSE/G0W0 and TDDFT approaches with a reduced starting point dependence. BSE/LOSC is, thus, a promising and efficient approach to calculate excitation energies for molecular systems.
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Affiliation(s)
- Jiachen Li
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Ye Jin
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Neil Qiang Su
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
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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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40
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Wu K, Qin X, Hu W, Yang J. Low-Rank Approximations Accelerated Plane-Wave Hybrid Functional Calculations with k-Point Sampling. J Chem Theory Comput 2021; 18:206-218. [PMID: 34918919 DOI: 10.1021/acs.jctc.1c00874] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The low-rank approximations of the adaptively compressed exchange (ACE) operator and interpolative separable density fitting (ISDF) algorithms significantly reduce the computational cost and memory usage of hybrid functional calculations in real space, but the lack of k-point sampling hinders their implementation in reciprocal space for periodic systems with the plane-wave basis set. Here, we combine the ACE operator and ISDF decomposition into a new ACE-ISDF algorithm for periodic systems in reciprocal space with k-point sampling. On the basis of the ACE-ISDF algorithm with the improved reciprocal space ACE operator and k-point Fourier convolution, the time complexity of the hybrid functional calculation is reduced from O(Ne4Nk2) to O(Ne3Nklog(Nk)) (Ne and Nk are the number of electrons and k-points, respectively) with a much smaller prefactor and much lower memory consumption compared to the standard method for periodic systems with a plane-wave basis set.
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Affiliation(s)
- Kai Wu
- Hefei National Laboratory for Physical Sciences at the Microscale, Department of Chemical Physics, Synergetic Innovation Center of Quantum Information and Quantum Physics, and Anhui Center for Applied Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xinming Qin
- Hefei National Laboratory for Physical Sciences at the Microscale, Department of Chemical Physics, Synergetic Innovation Center of Quantum Information and Quantum Physics, and Anhui Center for Applied Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Wei Hu
- Hefei National Laboratory for Physical Sciences at the Microscale, Department of Chemical Physics, Synergetic Innovation Center of Quantum Information and Quantum Physics, and Anhui Center for Applied Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jinlong Yang
- Hefei National Laboratory for Physical Sciences at the Microscale, Department of Chemical Physics, Synergetic Innovation Center of Quantum Information and Quantum Physics, and Anhui Center for Applied Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
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41
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Di Sabatino S, Loos PF, Romaniello P. Scrutinizing GW-Based Methods Using the Hubbard Dimer. Front Chem 2021; 9:751054. [PMID: 34778206 PMCID: PMC8586429 DOI: 10.3389/fchem.2021.751054] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2021] [Accepted: 09/28/2021] [Indexed: 12/03/2022] Open
Abstract
Using the simple (symmetric) Hubbard dimer, we analyze some important features of the GW approximation. We show that the problem of the existence of multiple quasiparticle solutions in the (perturbative) one-shot GW method and its partially self-consistent version is solved by full self-consistency. We also analyze the neutral excitation spectrum using the Bethe-Salpeter equation (BSE) formalism within the standard GW approximation and find, in particular, that 1) some neutral excitation energies become complex when the electron-electron interaction U increases, which can be traced back to the approximate nature of the GW quasiparticle energies; 2) the BSE formalism yields accurate correlation energies over a wide range of U when the trace (or plasmon) formula is employed; 3) the trace formula is sensitive to the occurrence of complex excitation energies (especially singlet), while the expression obtained from the adiabatic-connection fluctuation-dissipation theorem (ACFDT) is more stable (yet less accurate); 4) the trace formula has the correct behavior for weak (i.e., small U) interaction, unlike the ACFDT expression.
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Affiliation(s)
- S. Di Sabatino
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS and ETSF, Toulouse, France
| | - P.-F. Loos
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France
| | - P. Romaniello
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS and ETSF, Toulouse, France
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42
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Förster A, Visscher L. Low-Order Scaling Quasiparticle Self-Consistent GW for Molecules. Front Chem 2021; 9:736591. [PMID: 34540804 PMCID: PMC8446457 DOI: 10.3389/fchem.2021.736591] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2021] [Accepted: 08/13/2021] [Indexed: 11/13/2022] Open
Abstract
Low-order scaling GW implementations for molecules are usually restricted to approximations with diagonal self-energy. Here, we present an all-electron implementation of quasiparticle self-consistent GW for molecular systems. We use an efficient algorithm for the evaluation of the self-energy in imaginary time, from which a static non-local exchange-correlation potential is calculated via analytical continuation. By using a direct inversion of iterative subspace method, fast and stable convergence is achieved for almost all molecules in the GW100 database. Exceptions are systems which are associated with a breakdown of the single quasiparticle picture in the valence region. The implementation is proven to be starting point independent and good agreement of QP energies with other codes is observed. We demonstrate the computational efficiency of the new implementation by calculating the quasiparticle spectrum of a DNA oligomer with 1,220 electrons using a basis of 6,300 atomic orbitals in less than 4 days on a single compute node with 16 cores. We use then our implementation to study the dependence of quasiparticle energies of DNA oligomers consisting of adenine-thymine pairs on the oligomer size. The first ionization potential in vacuum decreases by nearly 1 electron volt and the electron affinity increases by 0.4 eV going from the smallest to the largest considered oligomer. This shows that the DNA environment stabilizes the hole/electron resulting from photoexcitation/photoattachment. Upon inclusion of the aqueous environment via a polarizable continuum model, the differences between the ionization potentials reduce to 130 meV, demonstrating that the solvent effectively compensates for the stabilizing effect of the DNA environment. The electron affinities of the different oligomers are almost identical in the aqueous environment.
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Affiliation(s)
- Arno Förster
- Theoretical Chemistry, Vrije Universiteit, Amsterdam, Netherlands
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43
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Ma H, Wang L, Wan L, Li J, Qin X, Liu J, Hu W, Lin L, Yang C, Yang J. Realizing Effective Cubic-Scaling Coulomb Hole Plus Screened Exchange Approximation in Periodic Systems via Interpolative Separable Density Fitting with a Plane-Wave Basis Set. J Phys Chem A 2021; 125:7545-7557. [PMID: 34428038 DOI: 10.1021/acs.jpca.1c03762] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The GW approximation is an effective way to accurately describe the single-electron excitations of molecules and the quasiparticle energies of solids. However, a perceived drawback of the GW calculations is their high computational cost and large memory usage, which limit their applications to large systems. Herein, we demonstrate an accurate and effective low-rank approximation to accelerate non-self-consistent GW (G0W0) calculations under the static Coulomb hole plus screened exchange (COHSEX) approximation for periodic systems. Our approach is to adopt the interpolative separable density fitting (ISDF) decomposition and Cauchy's integral to construct low-rank representations of the dielectric matrix ϵ and self-energy matrix Σ. This approach reduces the number of floating point operations from O(Ne4) to O(Ne3) and requires a much smaller memory footprint. Two methods are used to select the interpolation points in ISDF, including the standard QR factorization with column pivoting (QRCP) procedure and the machine learning K-means clustering (K-means) algorithm. We demonstrate that these two methods can yield similar accuracy for both molecules and solids at much lower computational cost. In particular, K-means clustering can significantly reduce the computational cost of selecting the interpolation points by an order of magnitude compared to QRCP, resulting in an overall speedup factor of about ten times ISDF accelerated the static COHSEX calculations compared with conventional COHSEX approximation.
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Affiliation(s)
- Huanhuan Ma
- Hefei National Laboratory for Physical Sciences at the Microscale, Department of Chemical Physics, Synergetic Innovation Center of Quantum Information and Quantum Physics, and Anhui Center for Applied Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Lei Wang
- Hefei National Laboratory for Physical Sciences at the Microscale, Department of Chemical Physics, Synergetic Innovation Center of Quantum Information and Quantum Physics, and Anhui Center for Applied Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Lingyun Wan
- Hefei National Laboratory for Physical Sciences at the Microscale, Department of Chemical Physics, Synergetic Innovation Center of Quantum Information and Quantum Physics, and Anhui Center for Applied Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jielan Li
- Hefei National Laboratory for Physical Sciences at the Microscale, Department of Chemical Physics, Synergetic Innovation Center of Quantum Information and Quantum Physics, and Anhui Center for Applied Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xinming Qin
- Hefei National Laboratory for Physical Sciences at the Microscale, Department of Chemical Physics, Synergetic Innovation Center of Quantum Information and Quantum Physics, and Anhui Center for Applied Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jie Liu
- Hefei National Laboratory for Physical Sciences at the Microscale, Department of Chemical Physics, Synergetic Innovation Center of Quantum Information and Quantum Physics, and Anhui Center for Applied Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Wei Hu
- Hefei National Laboratory for Physical Sciences at the Microscale, Department of Chemical Physics, Synergetic Innovation Center of Quantum Information and Quantum Physics, and Anhui Center for Applied Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China.,Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Lin Lin
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States.,Department of Mathematics, University of California, Berkeley, California 94720, United States
| | - Chao Yang
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Jinlong Yang
- Hefei National Laboratory for Physical Sciences at the Microscale, Department of Chemical Physics, Synergetic Innovation Center of Quantum Information and Quantum Physics, and Anhui Center for Applied Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
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44
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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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Abstract
We calculate complete basis set (CBS) limit-extrapolated ionization potentials (IPs) and electron affinities (EA) with Slater-type basis sets for the molecules in the GW100 database. To this end, we present two new Slater-type orbital (STO) basis sets of triple-(TZ) and quadruple-ζ (QZ) quality, whose polarization is adequate for correlated-electron methods and which contain extra diffuse functions to be able to correctly calculate EAs of molecules with a positive lowest unoccupied molecular orbital (LUMO). We demonstrate that going from TZ to QZ quality consistently reduces the basis set error of our computed IPs and EAs, and we conclude that a good estimate of these quantities at the CBS limit can be obtained by extrapolation. With mean absolute deviations (MAD) from 70 to 85 meV, our CBS limit-extrapolated IP are in good agreement with results from FHI-AIMS, TURBOMOLE, VASP, and WEST, while they differ by more than 130 meV on average from nanoGW. With a MAD of 160 meV, our EA are also in good agreement with the WEST code. Especially for systems with positive LUMOs, the agreement is excellent. With respect to other codes, the STO-type basis sets generally underestimate EAs of small molecules with strongly bound LUMOs. With 62 meV for IPs and 93 meV for EAs, we find much better agreement with CBS limit-extrapolated results from FHI-AIMS for a set of 250 medium to large organic molecules.
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Affiliation(s)
- Arno Förster
- Theoretical Chemistry, Vrije
Universiteit, De Boelelaan
1083, NL-1081 HV Amsterdam, The Netherlands
| | - Lucas Visscher
- Theoretical Chemistry, Vrije
Universiteit, De Boelelaan
1083, NL-1081 HV Amsterdam, The Netherlands
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