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Lee J, Malone FD, Morales MA, Reichman DR. Spectral Functions from Auxiliary-Field Quantum Monte Carlo without Analytic Continuation: The Extended Koopmans' Theorem Approach. J Chem Theory Comput 2021; 17:3372-3387. [PMID: 33983735 DOI: 10.1021/acs.jctc.1c00100] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Abstract
We explore the extended Koopmans' theorem (EKT) within the phaseless auxiliary-field quantum Monte Carlo (AFQMC) method. The EKT allows for the direct calculation of electron addition and removal spectral functions using reduced density matrices of the N-particle system and avoids the need for analytic continuation. The lowest level of EKT with AFQMC, called EKT1-AFQMC, is benchmarked using atoms, small molecules, 14-electron and 54-electron uniform electron gas supercells, and a minimal unit cell model of diamond at the Γ-point. Via comparison with numerically exact results (when possible) and coupled-cluster methods, we find that EKT1-AFQMC can reproduce the qualitative features of spectral functions for Koopmans-like charge excitations with errors in peak locations of less than 0.25 eV in a finite basis. We also note the numerical difficulties that arise in the EKT1-AFQMC eigenvalue problem, especially when back-propagated quantities are very noisy. We show how a systematic higher-order EKT approach can correct errors in EKT1-based theories with respect to the satellite region of the spectral function. Our work will be of use for the study of low-energy charge excitations and spectral functions in correlated molecules and solids where AFQMC can be reliably performed for both energy and back propagation.
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Affiliation(s)
- Joonho Lee
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Fionn D Malone
- Quantum Simulations Group, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, United States
| | - Miguel A Morales
- Quantum Simulations Group, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, United States
| | - David R Reichman
- Department of Chemistry, Columbia University, New York, New York 10027, United States
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Lee J, Morales MA, Malone FD. A phaseless auxiliary-field quantum Monte Carlo perspective on the uniform electron gas at finite temperatures: Issues, observations, and benchmark study. J Chem Phys 2021; 154:064109. [DOI: 10.1063/5.0041378] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Affiliation(s)
- Joonho Lee
- Department of Chemistry, Columbia University, New York, New York 10027, USA
| | - Miguel A. Morales
- Quantum Simulations Group, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, USA
| | - Fionn D. Malone
- Quantum Simulations Group, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, USA
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Malone FD, Zhang S, Morales MA. Accelerating Auxiliary-Field Quantum Monte Carlo Simulations of Solids with Graphical Processing Units. J Chem Theory Comput 2020; 16:4286-4297. [DOI: 10.1021/acs.jctc.0c00262] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Fionn D. Malone
- Quantum Simulations Group, Lawrence Livermore National Laboratory, Livermore, California 94550, United States
| | - Shuai Zhang
- Quantum Simulations Group, Lawrence Livermore National Laboratory, Livermore, California 94550, United States
| | - Miguel A. Morales
- Quantum Simulations Group, Lawrence Livermore National Laboratory, Livermore, California 94550, United States
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Lee J, Malone FD, Morales MA. An auxiliary-Field quantum Monte Carlo perspective on the ground state of the dense uniform electron gas: An investigation with Hartree-Fock trial wavefunctions. J Chem Phys 2019. [DOI: 10.1063/1.5109572] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Joonho Lee
- College of Chemistry, University of California, Berkeley, California 94720, USA
| | - Fionn D. Malone
- Quantum Simulations Group, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, USA
| | - Miguel A. Morales
- Quantum Simulations Group, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, USA
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5
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Malone FD, Zhang S, Morales MA. Overcoming the Memory Bottleneck in Auxiliary Field Quantum Monte Carlo Simulations with Interpolative Separable Density Fitting. J Chem Theory Comput 2018; 15:256-264. [DOI: 10.1021/acs.jctc.8b00944] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Fionn D. Malone
- Quantum Simulations Group, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, United States
| | - Shuai Zhang
- Quantum Simulations Group, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, United States
| | - Miguel A. Morales
- Quantum Simulations Group, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, United States
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Zhang S, Malone FD, Morales MA. Auxiliary-field quantum Monte Carlo calculations of the structural properties of nickel oxide. J Chem Phys 2018; 149:164102. [DOI: 10.1063/1.5040900] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Shuai Zhang
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Fionn D. Malone
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Miguel A. Morales
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
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7
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Ab initio computations of molecular systems by the auxiliary‐field quantum Monte Carlo method. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2018. [DOI: 10.1002/wcms.1364] [Citation(s) in RCA: 60] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Motta M, Zhang S. Computation of Ground-State Properties in Molecular Systems: Back-Propagation with Auxiliary-Field Quantum Monte Carlo. J Chem Theory Comput 2017; 13:5367-5378. [DOI: 10.1021/acs.jctc.7b00730] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Mario Motta
- Department of Physics, College of William and Mary, Williamsburg, Virginia 23187-8795, United States
| | - Shiwei Zhang
- Department of Physics, College of William and Mary, Williamsburg, Virginia 23187-8795, United States
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Shee J, Zhang S, Reichman DR, Friesner RA. Chemical Transformations Approaching Chemical Accuracy via Correlated Sampling in Auxiliary-Field Quantum Monte Carlo. J Chem Theory Comput 2017; 13:2667-2680. [DOI: 10.1021/acs.jctc.7b00224] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- James Shee
- Department
of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - Shiwei Zhang
- Department
of Physics, College of William and Mary, Williamsburg, Virginia 23187-8795, United States
| | - David R. Reichman
- Department
of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - Richard A. Friesner
- Department
of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
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Motta M, Galli DE, Moroni S, Vitali E. Imaginary time density-density correlations for two-dimensional electron gases at high density. J Chem Phys 2015; 143:164108. [DOI: 10.1063/1.4934666] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Blunt NS, Alavi A, Booth GH. Krylov-Projected Quantum Monte Carlo Method. PHYSICAL REVIEW LETTERS 2015; 115:050603. [PMID: 26274406 DOI: 10.1103/physrevlett.115.050603] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2014] [Indexed: 06/04/2023]
Abstract
We present an approach to the calculation of arbitrary spectral, thermal, and excited state properties within the full configuration interaction quzantum Monte Carlo framework. This is achieved via an unbiased projection of the Hamiltonian eigenvalue problem into a space of stochastically sampled Krylov vectors, thus, enabling the calculation of real-frequency spectral and thermal properties and avoiding explicit analytic continuation. We use this approach to calculate temperature-dependent properties and one- and two-body spectral functions for various Hubbard models, as well as isolated excited states in ab initio systems.
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Affiliation(s)
- N S Blunt
- University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom; Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany; and Department of Physics, King's College London, The Strand, London WC2R 2LS, United Kingdom
| | - Ali Alavi
- University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom; Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany; and Department of Physics, King's College London, The Strand, London WC2R 2LS, United Kingdom
| | - George H Booth
- University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom; Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany; and Department of Physics, King's College London, The Strand, London WC2R 2LS, United Kingdom
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