1
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Li J, Yang W. Chemical Potentials and the One-Electron Hamiltonian of the Second-Order Perturbation Theory from the Functional Derivative Approach. J Phys Chem A 2024; 128:4876-4885. [PMID: 38842399 DOI: 10.1021/acs.jpca.4c01574] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2024]
Abstract
We develop a functional derivative approach to calculate the chemical potentials of second-order perturbation theory (MP2). In the functional derivative approach, the correlation part of the MP2 chemical potential, which is the derivative of the MP2 correlation energy with respect to the occupation number of frontier orbitals, is obtained from the chain rule via the noninteracting Green's function. First, the MP2 correlation energy is expressed in terms of the noninteracting Green's function, and its functional derivative to the noninteracting Green's function is the second-order self-energy. Then, the derivative of the noninteracting Green's function to the occupation number is obtained by including the orbital relaxation effect. We show that the MP2 chemical potentials obtained from the functional derivative approach agree with that obtained from the finite difference approach. The one-electron Hamiltonian, defined as the derivative of the MP2 energy with respect to the one particle density matrix, is also derived using the functional derivative approach, which can be used in the self-consistent calculations of MP2 and double-hybrid density functionals. The developed functional derivative approach is promising for calculating the chemical potentials and the one-electron Hamiltonian of approximate functionals and many-body perturbation approaches dependent explicitly on the noninteracting Green's function.
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Affiliation(s)
- Jiachen Li
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
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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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Dhawan D, Zgid D, Motta M. Quantum Algorithm for Imaginary-Time Green's Functions. J Chem Theory Comput 2024; 20:4629-4638. [PMID: 38761142 DOI: 10.1021/acs.jctc.4c00241] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/20/2024]
Abstract
Green's function methods lead to ab initio, systematically improvable simulations of molecules and materials while providing access to multiple experimentally observable properties such as the density of states and the spectral function. The calculation of the exact one-particle Green's function remains a significant challenge for classical computers and was attempted only on very small systems. Here, we present a hybrid quantum-classical algorithm to calculate the imaginary-time one-particle Green's function. The proposed algorithm combines the variational quantum eigensolver and the quantum subspace expansion methods to calculate Green's function in Lehmann's representation. We demonstrate the validity of this algorithm by simulating H2 and H4 on quantum simulators and on IBM's quantum devices.
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Affiliation(s)
- Diksha Dhawan
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24060, United States
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Mario Motta
- IBM Quantum, Almaden Research Center, San Jose, California 95120, United States
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4
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Wen M, Abraham V, Harsha G, Shee A, Whaley KB, Zgid D. Comparing Self-Consistent GW and Vertex-Corrected G0W0 ( G0W0Γ) Accuracy for Molecular Ionization Potentials. J Chem Theory Comput 2024; 20:3109-3120. [PMID: 38573104 DOI: 10.1021/acs.jctc.3c01279] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/05/2024]
Abstract
We test the performance of self-consistent GW and several representative implementations of vertex-corrected G0W0 (G0W0Γ). These approaches are tested on benchmark data sets covering full valence spectra (first ionization potentials and some inner valence shell excitations). For small molecules, when comparing against state-of-the-art wave function techniques, our results show that full self-consistency in the GW scheme either systematically outperforms vertex-corrected G0W0 or gives results of at least comparative quality. Moreover, G0W0Γ results in additional computational cost when compared to G0W0 or self-consistent GW. The dependency of G0W0Γ on the starting mean-field solution is frequently more dominant than the magnitude of the vertex correction itself. Consequently, for molecular systems, self-consistent GW performed on the imaginary axis (and then followed by modern analytical continuation techniques) offers a more reliable approach to make predictions of ionization potentials.
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Affiliation(s)
- Ming Wen
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - 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
| | - Avijit Shee
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - K Birgitta Whaley
- Department of Chemistry, University of California, Berkeley, California 94720-1460, United States
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
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5
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Venturella C, Hillenbrand C, Li J, Zhu T. Machine Learning Many-Body Green's Functions for Molecular Excitation Spectra. J Chem Theory Comput 2024; 20:143-154. [PMID: 38150268 DOI: 10.1021/acs.jctc.3c01146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2023]
Abstract
We present a machine learning (ML) framework for predicting Green's functions of molecular systems, from which photoemission spectra and quasiparticle energies at quantum many-body level can be obtained. Kernel ridge regression is adopted to predict self-energy matrix elements on compact imaginary frequency grids from static and dynamical mean-field electronic features, which gives direct access to real-frequency many-body Green's functions through analytic continuation and Dyson's equation. Feature and self-energy matrices are represented in a symmetry-adapted intrinsic atomic orbital plus projected atomic orbital basis to enforce rotational invariance. We demonstrate good transferability and high data efficiency of the proposed ML method across molecular sizes and chemical species by showing accurate predictions of density of states (DOS) and quasiparticle energies at the level of many-body perturbation theory (GW) or full configuration interaction. For the ML model trained on 48 out of 1995 molecules randomly sampled from the QM7 and QM9 data sets, we report the mean absolute errors of ML-predicted highest occupied and lowest unoccupied molecular orbital energies to be 0.13 and 0.10 eV, respectively, compared to GW@PBE0. We further showcase the capability of this method by applying the same ML model to predict DOS for significantly larger organic molecules with up to 44 heavy atoms.
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Affiliation(s)
- Christian Venturella
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | | | - Jiachen Li
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Tianyu Zhu
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
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6
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Mejía L, Yin J, Reichman DR, Baer R, Yang C, Rabani E. Stochastic Real-Time Second-Order Green's Function Theory for Neutral Excitations in Molecules and Nanostructures. J Chem Theory Comput 2023; 19:5563-5571. [PMID: 37539990 DOI: 10.1021/acs.jctc.3c00296] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/05/2023]
Abstract
We present a real-time second-order Green's function (GF) method for computing excited states in molecules and nanostructures, with a computational scaling of O(Ne3), where Ne is the number of electrons. The cubic scaling is achieved by adopting the stochastic resolution of the identity to decouple the 4-index electron repulsion integrals. To improve the time propagation and the spectral resolution, we adopt the dynamic mode decomposition technique and assess the accuracy and efficiency of the combined approach for a chain of hydrogen dimer molecules of different lengths. We find that the stochastic implementation accurately reproduces the deterministic results for the electronic dynamics and excitation energies. Furthermore, we provide a detailed analysis of the statistical errors, bias, and long-time extrapolation. Overall, the approach offers an efficient route to investigate excited states in extended systems with open or closed boundary conditions.
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Affiliation(s)
- Leopoldo Mejía
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Jia Yin
- Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - David R Reichman
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Roi Baer
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Chao Yang
- Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Eran Rabani
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- The Raymond and Beverly Sackler Center of Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
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7
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Coveney CJN, Tew DP. A Regularized Second-Order Correlation Method from Green's Function Theory. J Chem Theory Comput 2023. [PMID: 37367932 DOI: 10.1021/acs.jctc.3c00246] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/28/2023]
Abstract
We present a scalable single-particle framework to treat electronic correlation in molecules and materials motivated by Green's function theory. We derive a size-extensive Brillouin-Wigner perturbation theory from the single-particle Green's function by introducing the Goldstone self-energy. This new ground state correlation energy, referred to as Quasi-Particle MP2 theory (QPMP2), avoids the characteristic divergences present in both second-order Møller-Plesset perturbation theory and Coupled Cluster Singles and Doubles within the strongly correlated regime. We show that the exact ground state energy and properties of the Hubbard dimer are reproduced by QPMP2 and demonstrate the advantages of the approach for larger Hubbard models where the metal-to-insulator transition is qualitatively reproduced, contrasting with the complete failure of traditional methods. We apply this formalism to characteristic strongly correlated molecular systems and show that QPMP2 provides an efficient, size-consistent regularization of MP2.
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Affiliation(s)
| | - David P Tew
- Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
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8
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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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9
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Izsák R, Ivanov AV, Blunt NS, Holzmann N, Neese F. Measuring Electron Correlation: The Impact of Symmetry and Orbital Transformations. J Chem Theory Comput 2023; 19:2703-2720. [PMID: 37022051 PMCID: PMC10210250 DOI: 10.1021/acs.jctc.3c00122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2023] [Indexed: 04/07/2023]
Abstract
In this perspective, the various measures of electron correlation used in wave function theory, density functional theory and quantum information theory are briefly reviewed. We then focus on a more traditional metric based on dominant weights in the full configuration solution and discuss its behavior with respect to the choice of the N-electron and the one-electron basis. The impact of symmetry is discussed, and we emphasize that the distinction among determinants, configuration state functions and configurations as reference functions is useful because the latter incorporate spin-coupling into the reference and should thus reduce the complexity of the wave function expansion. The corresponding notions of single determinant, single spin-coupling and single configuration wave functions are discussed and the effect of orbital rotations on the multireference character is reviewed by analyzing a simple model system. In molecular systems, the extent of correlation effects should be limited by finite system size and in most cases the appropriate choices of one-electron and N-electron bases should be able to incorporate these into a low-complexity reference function, often a single configurational one.
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Affiliation(s)
- Róbert Izsák
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Aleksei V. Ivanov
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Nick S. Blunt
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Nicole Holzmann
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Frank Neese
- Max-Planck
Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
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10
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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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11
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Dou W, Lee J, Zhu J, Mejía L, Reichman DR, Baer R, Rabani E. Time-Dependent Second-Order Green's Function Theory for Neutral Excitations. J Chem Theory Comput 2022; 18:5221-5232. [PMID: 36040050 DOI: 10.1021/acs.jctc.2c00057] [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]
Abstract
We develop a time-dependent second-order Green's function theory (GF2) for calculating neutral excited states in molecules. The equation of motion for the lesser Green's function (GF) is derived within the adiabatic approximation to the Kadanoff-Baym (KB) equation, using the second-order Born approximation for the self-energy. In the linear response regime, we recast the time-dependent KB equation into a Bethe-Salpeter-like equation (GF2-BSE), with a kernel approximated by the second-order Coulomb self-energy. We then apply our GF2-BSE to a set of molecules and atoms and find that GF2-BSE is superior to configuration interaction with singles (CIS) and/or time-dependent Hartree-Fock (TDHF), particularly for charge-transfer excitations, and is comparable to CIS with perturbative doubles (CIS(D)) in most cases.
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Affiliation(s)
- Wenjie Dou
- Department of Chemistry, School of Science, Westlake University, Hangzhou, Zhejiang 310024, China.,Department of Physics, School of Science, Westlake University, Hangzhou, Zhejiang 310024, China.,Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, China
| | - Joonho Lee
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Jian Zhu
- Department of Chemistry, School of Science, Westlake University, Hangzhou, Zhejiang 310024, China.,Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, China
| | - Leopoldo Mejía
- Department of Chemistry, University of California, Berkeley, California 94720, United States.,Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - David R Reichman
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Roi Baer
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Eran Rabani
- Department of Chemistry, University of California, Berkeley, California 94720, United States.,Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States.,The Raymond and Beverly Sackler Center of Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
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12
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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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13
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Prokopiou G, Hartstein M, Govind N, Kronik L. Optimal Tuning Perspective of Range-Separated Double Hybrid Functionals. J Chem Theory Comput 2022; 18:2331-2340. [PMID: 35369687 PMCID: PMC9009176 DOI: 10.1021/acs.jctc.2c00082] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2022] [Indexed: 11/29/2022]
Abstract
We study the optimal tuning of the free parameters in range-separated double hybrid functionals, based on enforcing the exact conditions of piecewise linearity and spin constancy. We find that introducing the range separation in both the exchange and the correlation terms allows for the minimization of both fractional charge and fractional spin errors for singlet atoms. The optimal set of parameters is system specific, underlining the importance of the tuning procedure. We test the performance of the resulting optimally tuned functionals for the dissociation curves of diatomic molecules. We find that they recover the correct dissociation curve for the one-electron system, H2+, and improve the dissociation curves of many-electron molecules such as H2 and Li2, but they also yield a nonphysical maximum and only converge to the correct dissociation limit at very large distances.
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Affiliation(s)
- Georgia Prokopiou
- Department
of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Rehovoth 76100, Israel
| | - Michal Hartstein
- Department
of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Rehovoth 76100, Israel
| | - Niranjan Govind
- Physical
and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Leeor Kronik
- Department
of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Rehovoth 76100, Israel
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14
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Pokhilko P, Yeh CN, Zgid D. Iterative subspace algorithms for finite-temperature solution of Dyson equation. J Chem Phys 2022; 156:094101. [DOI: 10.1063/5.0082586] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Abstract
One-particle Green’s functions obtained from the self-consistent solution of the Dyson equation can be employed in the evaluation of spectroscopic and thermodynamic properties for both molecules and solids. However, typical acceleration techniques used in the traditional quantum chemistry self-consistent algorithms cannot be easily deployed for the Green’s function methods because of a non-convex grand potential functional and a non-idempotent density matrix. Moreover, the optimization problem can become more challenging due to the inclusion of correlation effects, changing chemical potential, and fluctuations of the number of particles. In this paper, we study acceleration techniques to target the self-consistent solution of the Dyson equation directly. We use the direct inversion in the iterative subspace (DIIS), the least-squared commutator in the iterative subspace (LCIIS), and the Krylov space accelerated inexact Newton method (KAIN). We observe that the definition of the residual has a significant impact on the convergence of the iterative procedure. Based on the Dyson equation, we generalize the concept of the commutator residual used in DIIS and LCIIS and compare it with the difference residual used in DIIS and KAIN. The commutator residuals outperform the difference residuals for all considered molecular and solid systems within both GW and GF2. For a number of bond-breaking problems, we found that an easily obtained high-temperature solution with effectively suppressed correlations is a very effective starting point for reaching convergence of the problematic low-temperature solutions through a sequential reduction of temperature during calculations.
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Affiliation(s)
- Pavel Pokhilko
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Chia-Nan Yeh
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
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15
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Shee A, Yeh CN, Zgid D. Exploring Coupled Cluster Green's Function as a Method for Treating System and Environment in Green's Function Embedding Methods. J Chem Theory Comput 2022; 18:664-676. [PMID: 34989565 DOI: 10.1021/acs.jctc.1c00712] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
Within the self-energy embedding theory (SEET) framework, we study the coupled cluster Green's function (GFCC) method in two different contexts: as a method to treat either the system or the environment present in the embedding construction. Our study reveals that when GFCC is used to treat the environment we do not see improvement in total energies in comparison to the coupled cluster method itself. To rationalize this puzzling result, we analyze the performance of GFCC as an impurity solver with a series of transition metal oxides. These studies shed light on the strength and weaknesses of such a solver and demonstrate that such a solver gives very accurate results when the size of the impurity is small. We investigate if it is possible to achieve a systematic accuracy of the embedding solution when we increase the size of the impurity problem. We found that in such a case, the performance of the solver worsens, both in terms of finding the ground state solution of the impurity problem and the self-energies produced. We concluded that increasing the rank of GFCC solver is necessary to be able to enlarge impurity problems and achieve a reliable accuracy. We also have shown that natural orbitals from weakly correlated perturbative methods are better suited than symmetrized atomic orbitals (SAO) when the total energy of the system is the target quantity.
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Affiliation(s)
- Avijit Shee
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Chia-Nan Yeh
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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16
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Dhawan D, Metcalf M, Zgid D. Dynamical Self-energy Mapping (DSEM) for Creation of Sparse Hamiltonians Suitable for Quantum Computing. J Chem Theory Comput 2021; 17:7622-7631. [PMID: 34739754 DOI: 10.1021/acs.jctc.1c00931] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
We present a two-step procedure called the dynamical self-energy mapping (DSEM) that allows us to find a sparse Hamiltonian representation for molecular problems. In the first part of this procedure, the approximate self-energy of a molecular system is evaluated using a low-level method and subsequently a sparse Hamiltonian is found that best recovers this low-level dynamic self-energy. In the second step, such a sparse Hamiltonian is used by a high-level method that delivers a highly accurate dynamical part of the self-energy that is employed in later calculations. The tests conducted on small molecular problems show that the sparse Hamiltonian parameterizations lead to very good total energies. DSEM has the potential to be used as a classical-quantum hybrid algorithm for quantum computing where the sparse Hamiltonian containing only O(n2) terms on a Gaussian orbital basis, where n is the number of orbitals in the system, could reduce the depth of the quantum circuit by at least an order of magnitude when compared with simulations involving a full Hamiltonian.
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Affiliation(s)
- Diksha Dhawan
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Mekena Metcalf
- Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, United States
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States.,Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
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17
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Zhou Y, Gull E, Zgid D. Material-Specific Optimization of Gaussian Basis Sets against Plane Wave Data. J Chem Theory Comput 2021; 17:5611-5622. [PMID: 34448587 DOI: 10.1021/acs.jctc.1c00491] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Abstract
Since in periodic systems, a given element may be present in different spatial arrangements displaying vastly different physical and chemical properties, an elemental basis set that is independent of physical properties of materials may lead to significant simulation inaccuracies. To avoid such a lack of material specificity within a given basis set, we present a material-specific Gaussian basis optimization scheme for solids, which simultaneously minimizes the total energy of the system and optimizes the band energies when compared to the reference plane wave calculation while taking care of the overlap matrix condition number. To assess this basis set optimization scheme, we compare the quality of the Gaussian basis sets generated for diamond, graphite, and silicon via our method against the existing basis sets. The optimization scheme of this work has also been tested on the existing Gaussian basis sets for periodic systems such as MoS2 and NiO, yielding improved results.
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Affiliation(s)
- Yanbing Zhou
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Emanuel Gull
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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18
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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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19
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Pokhilko P, Zgid D. Interpretation of multiple solutions in fully iterative GF2 and GW schemes using local analysis of two-particle density matrices. J Chem Phys 2021; 155:024101. [DOI: 10.1063/5.0055191] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Pavel Pokhilko
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
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20
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Pokhilko P, Iskakov S, Yeh CN, Zgid D. Evaluation of two-particle properties within finite-temperature self-consistent one-particle Green's function methods: Theory and application to GW and GF2. J Chem Phys 2021; 155:024119. [PMID: 34266259 DOI: 10.1063/5.0054661] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
One-particle Green's function methods can model molecular and solid spectra at zero or non-zero temperatures. One-particle Green's functions directly provide electronic energies and one-particle properties, such as dipole moment. However, the evaluation of two-particle properties, such as ⟨S2⟩ and ⟨N2⟩, can be challenging because they require a solution of the computationally expensive Bethe-Salpeter equation to find two-particle Green's functions. We demonstrate that the solution of the Bethe-Salpeter equation can be completely avoided. Applying the thermodynamic Hellmann-Feynman theorem to self-consistent one-particle Green's function methods, we derive expressions for two-particle density matrices in a general case and provide explicit expressions for GF2 and GW methods. Such density matrices can be decomposed into an antisymmetrized product of correlated one-electron density matrices and the two-particle electronic cumulant of the density matrix. Cumulant expressions reveal a deviation from ensemble representability for GW, explaining its known deficiencies. We analyze the temperature dependence of ⟨S2⟩ and ⟨N2⟩ for a set of small closed-shell systems. Interestingly, both GF2 and GW show a non-zero spin contamination and a non-zero fluctuation of the number of particles for closed-shell systems at the zero-temperature limit.
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Affiliation(s)
- Pavel Pokhilko
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Sergei Iskakov
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Chia-Nan Yeh
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
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21
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Fei J, Yeh CN, Gull E. Nevanlinna Analytical Continuation. PHYSICAL REVIEW LETTERS 2021; 126:056402. [PMID: 33605755 DOI: 10.1103/physrevlett.126.056402] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2020] [Accepted: 01/15/2021] [Indexed: 06/12/2023]
Abstract
Simulations of finite temperature quantum systems provide imaginary frequency Green's functions that correspond one to one to experimentally measurable real-frequency spectral functions. However, due to the bad conditioning of the continuation transform from imaginary to real frequencies, established methods tend to either wash out spectral features at high frequencies or produce spectral functions with unphysical negative parts. Here, we show that explicitly respecting the analytic "Nevanlinna" structure of the Green's function leads to intrinsically positive and normalized spectral functions, and we present a continued fraction expansion that yields all possible functions consistent with the analytic structure. Application to synthetic trial data shows that sharp, smooth, and multipeak data is resolved accurately. Application to the band structure of silicon demonstrates that high energy features are resolved precisely. Continuations in a realistic correlated setup reveal additional features that were previously unresolved. By substantially increasing the resolution of real frequency calculations our work overcomes one of the main limitations of finite-temperature quantum simulations.
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Affiliation(s)
- Jiani Fei
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Chia-Nan Yeh
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Emanuel Gull
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
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22
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Quintas-Sánchez E, Dawes R. Spectroscopy and Scattering Studies Using Interpolated Ab Initio Potentials. Annu Rev Phys Chem 2021; 72:399-421. [PMID: 33503385 DOI: 10.1146/annurev-physchem-090519-051837] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
The Born-Oppenheimer potential energy surface (PES) has come a long way since its introduction in the 1920s, both conceptually and in predictive power for practical applications. Nevertheless, nearly 100 years later-despite astonishing advances in computational power-the state-of-the-art first-principles prediction of observables related to spectroscopy and scattering dynamics is surprisingly limited. For example, the water dimer, (H2O)2, with only six nuclei and 20 electrons, still presents a formidable challenge for full-dimensional variational calculations of bound states and is considered out of reach for rigorous scattering calculations. The extremely poor scaling of the most rigorous quantum methods is fundamental; however, recent progress in development of approximate methodologies has opened the door to fairly routine high-quality predictions, unthinkable 20 years ago. In this review, in relation to the workflow of spectroscopy and/or scattering studies, we summarize progress and challenges in the component areas of electronic structure calculations, PES fitting, and quantum dynamical calculations.
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Affiliation(s)
- Ernesto Quintas-Sánchez
- Department of Chemistry, Missouri University of Science and Technology, Rolla, Missouri 65409, USA;
| | - Richard Dawes
- Department of Chemistry, Missouri University of Science and Technology, Rolla, Missouri 65409, USA;
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23
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Voora VK. Molecular Electron Affinities Using the Generalized Kohn-Sham Semicanonical Projected Random Phase Approximation. J Phys Chem Lett 2021; 12:433-439. [PMID: 33356311 DOI: 10.1021/acs.jpclett.0c03362] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The suitability of one-particle energies from the generalized Kohn-Sham semicanonical projected random phase approximation (GKS-spRPA) method for electron affinities of molecules is investigated. It is shown that the GKS-spPRA effective potential includes exact exchange and polarizability-dependent correlation terms that are necessary for the correct description of anionic systems. An O(N4) implementation that enables fast computation of electron affinities is presented. For model systems, I show that the GKS-spRPA approach is applicable for valence and nonvalence type anions with a maximum error of 0.13 eV for valence anionic states and 0.03 eV for nonvalence anionic states compared to equation of motion coupled cluster methods. For a series of perhalobenzene molecules, C6X6 (X= F, Cl, Br, and I), GKS-spRPA predicts that the ground-state character changes from a nonvalence-σ* type in C6F6- to valence-π* in C6Cl6- and valence-σ* in C6Br6- and C6I6-. Experimental implications of these findings are discussed.
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Affiliation(s)
- Vamsee K Voora
- Department of Chemical Sciences, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
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24
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Backhouse OJ, Booth GH. Efficient Excitations and Spectra within a Perturbative Renormalization Approach. J Chem Theory Comput 2020; 16:6294-6304. [PMID: 32886508 DOI: 10.1021/acs.jctc.0c00701] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present a self-consistent approach for computing the correlated quasiparticle spectrum of charged excitations in iterative O[N5] computational time. This is based on the auxiliary second-order Green's function approach [Backhouse, O. J. Chem. Theory Comput., 2000], in which a self-consistent effective Hamiltonian is constructed by systematically renormalizing the dynamical effects of the self-energy at second-order perturbation theory. From extensive benchmarking across the W4-11 molecular test set, we show that the iterative renormalization and truncation of the effective dynamical resolution arising from the 2h1p and 1h2p spaces can substantially improve the quality of the resulting ionization potential and electron affinity predictions compared to benchmark values. The resulting method is shown to be superior in accuracy to similarly scaling quantum chemical methods for charged excitations in EOM-CC2 and ADC(2), across this test set, while the self-consistency also removes the dependence on the underlying mean-field reference. The approach also allows for single-shot computation of the entire quasiparticle spectrum, which is applied to the benzoquinone molecule and demonstrates the reduction in the single-particle gap due to the correlated physics, and gives direct access to the localization of the Dyson orbitals.
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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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25
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Dou W, Chen M, Takeshita TY, Baer R, Neuhauser D, Rabani E. Range-separated stochastic resolution of identity: Formulation and application to second-order Green’s function theory. J Chem Phys 2020; 153:074113. [DOI: 10.1063/5.0015177] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Wenjie Dou
- Department of Chemistry, University of California Berkeley, Berkeley, California 94720, USA
| | - Ming Chen
- Department of Chemistry, University of California Berkeley, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | | | - Roi Baer
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, USA
| | - Eran Rabani
- Department of Chemistry, University of California Berkeley, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- The Raymond and Beverly Sackler Center of Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
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26
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Dong X, Zgid D, Gull E, Strand HUR. Legendre-spectral Dyson equation solver with super-exponential convergence. J Chem Phys 2020; 152:134107. [DOI: 10.1063/5.0003145] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Xinyang Dong
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Dominika Zgid
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Emanuel Gull
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Hugo U. R. Strand
- Department of Physics, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden
- Center for Computational Quantum Physics, The Flatiron Institute, New York, New York 10010, USA
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27
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Bauman NP, Peng B, Kowalski K. Coupled Cluster Green's function formulations based on the effective Hamiltonians. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1725669] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Nicholas P. Bauman
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, Richland, WA, USA
| | - Bo Peng
- Advanced Computing, Mathematics, and Data Division, Battelle, Pacific Northwest National Laboratory, Richland, WA, USA
| | - Karol Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, Richland, WA, USA
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28
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Backhouse OJ, Nusspickel M, Booth GH. Wave Function Perspective and Efficient Truncation of Renormalized Second-Order Perturbation Theory. J Chem Theory Comput 2020; 16:1090-1104. [PMID: 31951406 DOI: 10.1021/acs.jctc.9b01182] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We present an approach to a renormalized second-order Green's function perturbation theory (GF2), which avoids all dependency on continuous variables, grids, or explicit Green's functions and is instead formulated entirely in terms of static quantities and wave functions. Correlation effects from MP2 diagrams are iteratively incorporated to modify the underlying spectrum of excitations by coupling the physical system to fictitious auxiliary degrees of freedom, allowing for single-particle orbitals to delocalize into this additional space. The overall approach is shown to be rigorously O[N5], after an appropriate compression of this auxiliary space. This is achieved via a novel scheme, which ensures that a desired number of moments of the underlying occupied and virtual spectra are conserved in the compression, allowing a rapid and systematically improvable convergence to the limit of the effective dynamical resolution. The approach is found to then allow for the qualitative description of stronger correlation effects, avoiding the divergences of MP2, as well as its orbital-optimized version. On application to the G1 test set, we find that modification up to only the third spectral moment of the underlying spectrum from which the double excitations are built are required for accurate energetics, even in strongly correlated regimes. This is beyond simple self-consistent changes to the density matrix of the system but far from requiring a description of the full dynamics of the frequency-dependent self-energy.
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Affiliation(s)
- Oliver J Backhouse
- Department of Physics , King's College London , Strand , London WC2R 2LS , U.K
| | - Max Nusspickel
- 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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29
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Loos PF, Pradines B, Scemama A, Giner E, Toulouse J. Density-Based Basis-Set Incompleteness Correction for GW Methods. J Chem Theory Comput 2019; 16:1018-1028. [DOI: 10.1021/acs.jctc.9b01067] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Barthélémy Pradines
- Laboratoire de Chimie Théorique (UMR 7616), Sorbonne Université, CNRS, Paris, France
- Institut des Sciences du Calcul et des Données, Sorbonne Université, Paris, France
| | - Anthony Scemama
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Emmanuel Giner
- Laboratoire de Chimie Théorique (UMR 7616), Sorbonne Université, CNRS, Paris, France
| | - Julien Toulouse
- Laboratoire de Chimie Théorique (UMR 7616), Sorbonne Université, CNRS, Paris, France
- Institut Universitaire de France, Paris, France
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30
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Tuovinen R, Covito F, Sentef MA. Efficient computation of the second-Born self-energy using tensor-contraction operations. J Chem Phys 2019; 151:174110. [DOI: 10.1063/1.5121820] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Riku Tuovinen
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Fabio Covito
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Michael A. Sentef
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
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31
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Dou W, Takeshita TY, Chen M, Baer R, Neuhauser D, Rabani E. Stochastic Resolution of Identity for Real-Time Second-Order Green’s Function: Ionization Potential and Quasi-Particle Spectrum. J Chem Theory Comput 2019; 15:6703-6711. [DOI: 10.1021/acs.jctc.9b00918] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Wenjie Dou
- Department of Chemistry, University of California Berkeley, Berkeley, California 94720, United States
| | - Tyler Y. Takeshita
- Mercedes-Benz Research and Development North America, Sunnyvale, California 94085, United States
| | - Ming Chen
- Department of Chemistry, University of California Berkeley, Berkeley, California 94720, United States
- Materials Sciences Devision, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Roi Baer
- Fritz Haber Research Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, University of California Los Angeles, Los Angeles, California 90095, United States
| | - Eran Rabani
- Department of Chemistry, University of California Berkeley, Berkeley, California 94720, United States
- Materials Sciences Devision, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- The Raymond and Beverly Sackler Center of Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
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32
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Doran AE, Hirata S. Monte Carlo Second- and Third-Order Many-Body Green’s Function Methods with Frequency-Dependent, Nondiagonal Self-Energy. J Chem Theory Comput 2019; 15:6097-6110. [DOI: 10.1021/acs.jctc.9b00693] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Alexander E. Doran
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
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33
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Shee A, Zgid D. Coupled Cluster as an Impurity Solver for Green’s Function Embedding Methods. J Chem Theory Comput 2019; 15:6010-6024. [DOI: 10.1021/acs.jctc.9b00603] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Avijit Shee
- 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
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34
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Chatterjee K, Sokolov AY. Second-Order Multireference Algebraic Diagrammatic Construction Theory for Photoelectron Spectra of Strongly Correlated Systems. J Chem Theory Comput 2019; 15:5908-5924. [DOI: 10.1021/acs.jctc.9b00528] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Koushik Chatterjee
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
| | - Alexander Yu. Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
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35
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Takeshita TY, Dou W, Smith DGA, de Jong WA, Baer R, Neuhauser D, Rabani E. Stochastic resolution of identity second-order Matsubara Green's function theory. J Chem Phys 2019; 151:044114. [PMID: 31370516 DOI: 10.1063/1.5108840] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We develop a stochastic resolution of identity representation to the second-order Matsubara Green's function (sRI-GF2) theory. Using a stochastic resolution of the Coulomb integrals, the second order Born self-energy in GF2 is decoupled and reduced to matrix products/contractions, which reduces the computational cost from O(N5) to O(N3) (with N being the number of atomic orbitals). The current approach can be viewed as an extension to our previous work on stochastic resolution of identity second order Møller-Plesset perturbation theory [T. Y. Takeshita et al., J. Chem. Theory Comput. 13, 4605 (2017)] and offers an alternative to previous stochastic GF2 formulations [D. Neuhauser et al., J. Chem. Theory Comput. 13, 5396 (2017)]. We show that sRI-GF2 recovers the deterministic GF2 results for small systems, is computationally faster than deterministic GF2 for N > 80, and is a practical approach to describe weak correlations in systems with 103 electrons and more.
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Affiliation(s)
- Tyler Y Takeshita
- Mercedes-Benz Research and Development North America, Sunnyvale, California 94085, USA
| | - Wenjie Dou
- Department of Chemistry, University of California Berkeley, Berkeley, California 94720, USA
| | - Daniel G A Smith
- The Molecular Sciences Software Institute, Blacksburg, Virginia 24060, USA
| | - Wibe A de Jong
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Roi Baer
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, USA
| | - Eran Rabani
- Department of Chemistry, University of California Berkeley, Berkeley, California 94720, USA
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36
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Teke NK, Pavošević F, Peng C, Valeev EF. Explicitly correlated renormalized second-order Green’s function for accurate ionization potentials of closed-shell molecules. J Chem Phys 2019; 150:214103. [DOI: 10.1063/1.5090983] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Nakul K. Teke
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Fabijan Pavošević
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Chong Peng
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Edward F. Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
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37
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Hirata S, Jha PK. Converging finite-temperature many-body perturbation theory in the grand canonical ensemble that conserves the average number of electrons. ANNUAL REPORTS IN COMPUTATIONAL CHEMISTRY 2019. [DOI: 10.1016/bs.arcc.2019.08.003] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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38
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Beuerle M, Ochsenfeld C. Low-scaling analytical gradients for the direct random phase approximation using an atomic orbital formalism. J Chem Phys 2018; 149:244111. [DOI: 10.1063/1.5052572] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Affiliation(s)
- Matthias Beuerle
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany and Center for Integrated Protein Science (CIPSM) at the Department of Chemistry, University of Munich (LMU), Butenandtstr. 5–13, D-81377 München, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany and Center for Integrated Protein Science (CIPSM) at the Department of Chemistry, University of Munich (LMU), Butenandtstr. 5–13, D-81377 München, Germany
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39
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Rusakov AA, Iskakov S, Tran LN, Zgid D. Self-Energy Embedding Theory (SEET) for Periodic Systems. J Chem Theory Comput 2018; 15:229-240. [DOI: 10.1021/acs.jctc.8b00927] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Alexander A. Rusakov
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Sergei Iskakov
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Lan Nguyen Tran
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
- Ho Chi Minh City Institute of Physics, Vietnam Academy of Science and Technology (VAST), Ho Chi Minh City 70000, Vietnam
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
- Center for Computational Quantum Physics, The Flatiron Institute, New York, New York 10010, United States
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40
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Welborn M, Manby FR, Miller TF. Even-handed subsystem selection in projection-based embedding. J Chem Phys 2018; 149:144101. [DOI: 10.1063/1.5050533] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Affiliation(s)
- Matthew Welborn
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Frederick R. Manby
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
| | - Thomas F. Miller
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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41
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Véril M, Romaniello P, Berger JA, Loos PF. Unphysical Discontinuities in GW Methods. J Chem Theory Comput 2018; 14:5220-5228. [DOI: 10.1021/acs.jctc.8b00745] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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42
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Abstract
We present a new theoretical approach, unrestricted self-energy embedding theory (USEET), that is a Green's function embedding theory used to study problems in which an open, embedded system exchanges electrons with the environment. USEET has a high potential to be used in studies of strongly correlated systems with an odd number of electrons and open shell systems such as transition metal complexes important in inorganic chemistry. In this paper, we show that USEET results agree very well with common quantum chemistry methods while avoiding typical bottlenecks present in these methods.
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Affiliation(s)
- Lan Nguyen Tran
- Department of Chemistry , University of Michigan , Ann Arbor , Michigan 48109 , United States
- Department of Physics , University of Michigan , Ann Arbor , Michigan 48109 , United States
- Ho Chi Minh City Institute of Physics, VAST , Ho Chi Minh City 70000 , Vietnam
| | - Sergei Iskakov
- Department of Physics , University of Michigan , Ann Arbor , Michigan 48109 , United States
| | - Dominika Zgid
- Department of Chemistry , University of Michigan , Ann Arbor , Michigan 48109 , United States
- Center for Computational Quantum Physics , The Flatiron Institute , New York , New York 10010 , United States
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43
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Lange MF, Berkelbach TC. On the Relation between Equation-of-Motion Coupled-Cluster Theory and the GW Approximation. J Chem Theory Comput 2018; 14:4224-4236. [DOI: 10.1021/acs.jctc.8b00455] [Citation(s) in RCA: 45] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Malte F. Lange
- Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, United States
| | - Timothy C. Berkelbach
- Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, United States
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44
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Peng B, Kowalski K. Green's Function Coupled-Cluster Approach: Simulating Photoelectron Spectra for Realistic Molecular Systems. J Chem Theory Comput 2018; 14:4335-4352. [PMID: 29957945 DOI: 10.1021/acs.jctc.8b00313] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
In this paper, we present an efficient implementation for the analytical energy-dependent Green's function coupled-cluster with singles and doubles (GFCCSD) approach with our first practice being computing spectral functions of realistic molecular systems. Because of its algebraic structure, the presented method is highly scalable and is capable of computing spectral function for a given molecular system in any energy region. Several typical examples have been given to demonstrate its capability of computing spectral functions not only in the valence band but also in the core-level energy region. Satellite peaks have been observed in the inner valence band and core-level energy region where a many-body effect becomes significant and the single particle picture of ionization often breaks down. The accuracy test has been carried out by extensively comparing the computed spectral functions by our GFCCSD method with experimental photoelectron spectra as well as the theoretical ionization potentials obtained from other methods. It turns out the GFCCSD method is able to provide a qualitative or semiquantitative level of description of ionization processes in both the core and valence regimes. To significantly improve the GFCCSD results for the main ionic states, a larger basis set can usually be employed, whereas the improvement of the GFCCSD results for the satellite states needs higher-order many-body terms to be included in the GFCC implementation.
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Affiliation(s)
- Bo Peng
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory , K8-91, P.O. Box 999, Richland , Washington 99352 , United States
| | - Karol Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory , K8-91, P.O. Box 999, Richland , Washington 99352 , United States
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45
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Kosugi T, Nishi H, Furukawa Y, Matsushita YI. Comparison of Green’s functions for transition metal atoms using self-energy functional theory and coupled-cluster singles and doubles (CCSD). J Chem Phys 2018; 148:224103. [DOI: 10.1063/1.5029535] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Taichi Kosugi
- Department of Applied Physics, The University of Tokyo, Tokyo 113-8656, Japan
| | - Hirofumi Nishi
- Department of Applied Physics, The University of Tokyo, Tokyo 113-8656, Japan
| | - Yoritaka Furukawa
- Department of Applied Physics, The University of Tokyo, Tokyo 113-8656, Japan
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46
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Maitra R, Nakajima T. Correlation effects beyond coupled cluster singles and doubles approximation through Fock matrix dressing. J Chem Phys 2017; 147:204108. [PMID: 29195294 DOI: 10.1063/1.5000571] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present an accurate single reference coupled cluster theory in which the conventional Fock operator matrix is suitably dressed to simulate the effect of triple and higher excitations within a singles and doubles framework. The dressing thus invoked originates from a second-order perturbative approximation of a similarity transformed Hamiltonian and induces higher rank excitations through local renormalization of individual occupied and unoccupied orbital lines. Such a dressing is able to recover a significant amount of correlation effects beyond singles and doubles approximation, but only with an economic n5 additional cost. Due to the inclusion of higher rank excitations via the Fock matrix dressing, this method is a natural improvement over conventional coupled cluster theory with singles and doubles approximation, and this method would be demonstrated via applications on some challenging systems. This highly promising scheme has a conceptually simple structure which is also easily generalizable to a multi-reference coupled cluster scheme for treating strong degeneracy. We shall demonstrate that this method is a natural lowest order perturbative approximation to the recently developed iterative n-body excitation inclusive coupled cluster singles and doubles scheme [R. Maitra et al., J. Chem. Phys. 147, 074103 (2017)].
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Affiliation(s)
- Rahul Maitra
- Computational Molecular Science Research Team, RIKEN Advanced Institute for Computational Science, Kobe 650-0047, Japan
| | - Takahito Nakajima
- Computational Molecular Science Research Team, RIKEN Advanced Institute for Computational Science, Kobe 650-0047, Japan
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47
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Neuhauser D, Baer R, Zgid D. Stochastic Self-Consistent Second-Order Green’s Function Method for Correlation Energies of Large Electronic Systems. J Chem Theory Comput 2017; 13:5396-5403. [DOI: 10.1021/acs.jctc.7b00792] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Daniel Neuhauser
- Department
of Chemistry and Biochemistry, University of California at Los Angeles, Los Angeles, California 90095, United States
| | - Roi Baer
- Fritz
Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Dominika Zgid
- Department
of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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48
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Kananenka AA, Zgid D. Combining Density Functional Theory and Green’s Function Theory: Range-Separated, Nonlocal, Dynamic, and Orbital-Dependent Hybrid Functional. J Chem Theory Comput 2017; 13:5317-5331. [DOI: 10.1021/acs.jctc.7b00701] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Alexei A. Kananenka
- 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
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49
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Pavošević F, Peng C, Ortiz JV, Valeev EF. Communication: Explicitly correlated formalism for second-order single-particle Green’s function. J Chem Phys 2017; 147:121101. [DOI: 10.1063/1.5000916] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Affiliation(s)
- Fabijan Pavošević
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Chong Peng
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - J. V. Ortiz
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849-5312, USA
| | - Edward F. Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
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50
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Maitra R, Akinaga Y, Nakajima T. A coupled cluster theory with iterative inclusion of triple excitations and associated equation of motion formulation for excitation energy and ionization potential. J Chem Phys 2017; 147:074103. [PMID: 28830188 DOI: 10.1063/1.4985916] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A single reference coupled cluster theory that is capable of including the effect of connected triple excitations has been developed and implemented. This is achieved by regrouping the terms appearing in perturbation theory and parametrizing through two different sets of exponential operators: while one of the exponentials, involving general substitution operators, annihilates the ground state but has a non-vanishing effect when it acts on the excited determinant, the other is the regular single and double excitation operator in the sense of conventional coupled cluster theory, which acts on the Hartree-Fock ground state. The two sets of operators are solved as coupled non-linear equations in an iterative manner without significant increase in computational cost than the conventional coupled cluster theory with singles and doubles excitations. A number of physically motivated and computationally advantageous sufficiency conditions are invoked to arrive at the working equations and have been applied to determine the ground state energies of a number of small prototypical systems having weak multi-reference character. With the knowledge of the correlated ground state, we have reconstructed the triple excitation operator and have performed equation of motion with coupled cluster singles, doubles, and triples to obtain the ionization potential and excitation energies of these molecules as well. Our results suggest that this is quite a reasonable scheme to capture the effect of connected triple excitations as long as the ground state remains weakly multi-reference.
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Affiliation(s)
- Rahul Maitra
- Computational Molecular Science Research Team, RIKEN Advanced Institute for Computational Science, Kobe 650-0047, Japan
| | | | - Takahito Nakajima
- Computational Molecular Science Research Team, RIKEN Advanced Institute for Computational Science, Kobe 650-0047, Japan
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