1
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Greiner J, Gauss J, Eriksen JJ. Exploiting Non-Abelian Point-Group Symmetry to Estimate the Exact Ground-State Correlation Energy of Benzene in a Polarized Split-Valence Triple-Zeta Basis Set. J Phys Chem Lett 2024; 15:9881-9887. [PMID: 39302884 DOI: 10.1021/acs.jpclett.4c02267] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/22/2024]
Abstract
Local electronic-structure methods in quantum chemistry operate on the ability to compress electron correlations more efficiently in a basis of spatially localized molecular orbitals than in a parent set of canonical orbitals. However, many typical choices of localized orbitals tend to be related by selected, near-exact symmetry operations whenever a molecule belongs to a point group, a feature which remains largely unexploited in most local correlation methods. The present Letter demonstrates how to leverage a recent unitary protocol for enforcing symmetry properties among localized orbitals to yield a high-accuracy estimate of the exact ground-state correlation energy of benzene (D6h) in correlation-consistent polarized basis sets of both double- and triple-ζ quality. Through an initial application to many-body expanded full configuration interaction (MBE-FCI) theory, we show how molecular point-group symmetry can lead to computational savings that are inversely proportional to the order of the point group in a manner generally applicable to the acceleration of modern local correlation methods.
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Affiliation(s)
- Jonas Greiner
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, 55128 Mainz, Germany
| | - Jürgen Gauss
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, 55128 Mainz, Germany
| | - Janus J Eriksen
- DTU Chemistry, Technical University of Denmark, Kemitorvet Bldg. 206, 2800 Kgs. Lyngby, Denmark
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2
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Burton HGA, Loos PF. Rationale for the extrapolation procedure in selected configuration interaction. J Chem Phys 2024; 160:104102. [PMID: 38456526 DOI: 10.1063/5.0192458] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2023] [Accepted: 02/18/2024] [Indexed: 03/09/2024] Open
Abstract
Selected configuration interaction (SCI) methods have emerged as state-of-the-art methodologies for achieving high accuracy and generating benchmark reference data for ground and excited states in small molecular systems. However, their precision relies heavily on extrapolation procedures to produce a final estimate of the exact result. Using the structure of the exact electronic energy landscape, we provide a rationale for the common linear extrapolation of the variational energy as a function of the second-order perturbative correction. In particular, we demonstrate that the energy gap and the coupling between the so-called internal and external spaces are the key factors determining the rate at which the linear regime is reached. Starting from the first principles, we also derive a new non-linear extrapolation formula that improves the post-processing of data generated from SCI methods and can be applied to both ground- and excited-state energies.
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Affiliation(s)
- Hugh G A Burton
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
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3
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Weber JL, Vuong H, Friesner RA, Reichman DR. Expanding the Design Space of Constraints in Auxiliary-Field Quantum Monte Carlo. J Chem Theory Comput 2023; 19:7567-7576. [PMID: 37889331 DOI: 10.1021/acs.jctc.3c00654] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2023]
Abstract
We formulate and characterize a new constraint for auxiliary-field quantum Monte Carlo (AFQMC) applicable for general fermionic systems, which allows for the accumulation of phase in the random walk but disallows walkers with a magnitude of phase greater than π with respect to the trial wave function. For short imaginary times, before walkers accumulate sizable phase values, this approach is equivalent to exact free projection, allowing one to observe the accumulation of bias associated with the constraint and thus estimate its magnitude a priori. We demonstrate the stability of this constraint over arbitrary imaginary times and system sizes, highlighting the removal of noise due to the fermionic sign problem. Benchmark total energies for a variety of weakly and strongly correlated molecular systems reveal a distinct bias with respect to standard phaseless AFQMC, with a comparative increase in accuracy given sufficient quality of the trial wave function for the set of studied cases. We then take this constraint, termed linecut AFQMC (lc-AFQMC), and systematically release it (lcR-AFQMC), providing a route to obtain a smooth bridge between constrained AFQMC and the exact free projection results.
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Affiliation(s)
- John L Weber
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - Hung Vuong
- 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
| | - David R Reichman
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
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4
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Sukurma Z, Schlipf M, Humer M, Taheridehkordi A, Kresse G. Benchmark Phaseless Auxiliary-Field Quantum Monte Carlo Method for Small Molecules. J Chem Theory Comput 2023; 19:4921-4934. [PMID: 37470356 PMCID: PMC10413869 DOI: 10.1021/acs.jctc.3c00322] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2023] [Indexed: 07/21/2023]
Abstract
We report a scalable Fortran implementation of the phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) and demonstrate its excellent performance and beneficial scaling with respect to system size. Furthermore, we investigate modifications of the phaseless approximation that can help to reduce the overcorrelation problems common to the ph-AFQMC. We apply the method to the 26 molecules in the HEAT set, the benzene molecule, and water clusters. We observe a mean absolute deviation of the total energy of 1.15 kcal/mol for the molecules in the HEAT set, close to chemical accuracy. For the benzene molecule, the modified algorithm despite using a single-Slater-determinant trial wavefunction yields the same accuracy as the original phaseless scheme with 400 Slater determinants. Despite these improvements, we find systematic errors for the CN, CO2, and O2 molecules that need to be addressed with more accurate trial wavefunctions. For water clusters, we find that the ph-AFQMC yields excellent binding energies that differ from CCSD(T) by typically less than 0.5 kcal/mol.
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Affiliation(s)
- Zoran Sukurma
- Faculty
of Physics and Center for Computational Materials Science, University of Vienna, Kolingasse 14-16, A-1090 Vienna, Austria
- Faculty
of Physics & Vienna Doctoral School in Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
| | | | - Moritz Humer
- Faculty
of Physics and Center for Computational Materials Science, University of Vienna, Kolingasse 14-16, A-1090 Vienna, Austria
- Faculty
of Physics & Vienna Doctoral School in Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
| | - Amir Taheridehkordi
- Faculty
of Physics and Center for Computational Materials Science, University of Vienna, Kolingasse 14-16, A-1090 Vienna, Austria
| | - Georg Kresse
- Faculty
of Physics and Center for Computational Materials Science, University of Vienna, Kolingasse 14-16, A-1090 Vienna, Austria
- VASP
Software GmbH, Sensengasse 8, 1090 Vienna, Austria
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5
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Chen Y, Zhang L, E W, Car R. Hybrid Auxiliary Field Quantum Monte Carlo for Molecular Systems. J Chem Theory Comput 2023. [PMID: 37071815 PMCID: PMC10373495 DOI: 10.1021/acs.jctc.3c00038] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/20/2023]
Abstract
We propose a quantum Monte Carlo approach to solve the many-body Schrödinger equation for the electronic ground state. The method combines optimization from variational Monte Carlo and propagation from auxiliary field quantum Monte Carlo in a way that significantly alleviates the sign problem. In application to molecular systems, we obtain highly accurate results for configurations dominated by either dynamic or static electronic correlation.
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Affiliation(s)
- Yixiao Chen
- Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, United States
| | - Linfeng Zhang
- AI for Science Institute, Beijing 100080, People's Republic of China
- DP Technology, Beijing 100080, People's Republic of China
| | - Weinan E
- AI for Science Institute, Beijing 100080, People's Republic of China
- Center for Machine Learning Research, School of Mathematical Sciences, Peking University, Beijing 100084, People's Republic of China
| | - Roberto Car
- Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, United States
- Department of Chemistry, Department of Physics, Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, United States
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6
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Lee J, Pham HQ, Reichman DR. Twenty Years of Auxiliary-Field Quantum Monte Carlo in Quantum Chemistry: An Overview and Assessment on Main Group Chemistry and Bond-Breaking. J Chem Theory Comput 2022; 18:7024-7042. [PMID: 36255074 DOI: 10.1021/acs.jctc.2c00802] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
In this work, we present an overview of the phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) approach from a computational quantum chemistry perspective and present a numerical assessment of its performance on main group chemistry and bond-breaking problems with a total of 1004 relative energies. While our benchmark study is somewhat limited, we make recommendations for the use of ph-AFQMC for general main-group chemistry applications. For systems where single determinant wave functions are qualitatively accurate, we expect the accuracy of ph-AFQMC in conjunction with a single-determinant trial wave function to be between that of coupled-cluster with singles and doubles (CCSD) and CCSD with perturbative triples (CCSD(T)). For these applications, ph-AFQMC should be a method of choice when canonical CCSD(T) is too expensive to run. For systems where multireference (MR) wave functions are needed for qualitative accuracy, ph-AFQMC is far more accurate than MR perturbation theory methods and competitive with MR configuration interaction (MRCI) methods. Due to the computational efficiency of ph-AFQMC compared to MRCI, we recommended ph-AFQMC as a method of choice for handling dynamic correlation in MR problems. We conclude with a discussion of important directions for future development of the ph-AFQMC approach.
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Affiliation(s)
- Joonho Lee
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - Hung Q Pham
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - David R Reichman
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
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7
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Weber JL, Vuong H, Devlaminck PA, Shee J, Lee J, Reichman DR, Friesner RA. A Localized-Orbital Energy Evaluation for Auxiliary-Field Quantum Monte Carlo. J Chem Theory Comput 2022; 18:3447-3459. [PMID: 35507769 DOI: 10.1021/acs.jctc.2c00111] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) has recently emerged as a promising method for the production of benchmark-level simulations of medium- to large-sized molecules because of its accuracy and favorable polynomial scaling with system size. Unfortunately, the memory footprints of standard energy evaluation algorithms are nontrivial, which can significantly impact timings on graphical processing units (GPUs) where memory is limited. Previous attempts to reduce scaling by taking advantage of the low-rank structure of the Coulombic integrals have been successful but exhibit high prefactors, making their utility limited to very large systems. Here we present a complementary cubic-scaling route to reduce memory and computational scaling based on the low rank of the Coulombic interactions between localized orbitals, focusing on the application to ph-AFQMC. We show that the error due to this approximation, which we term localized-orbital AFQMC (LO-AFQMC), is systematic and controllable via a single variable and that the method is computationally favorable even for small systems. We present results demonstrating robust retention of accuracy versus both experiment and full ph-AFQMC for a variety of test cases chosen for their potential difficulty for localized-orbital-based methods, including the singlet-triplet gaps of the polyacenes benzene through pentacene, the heats of formation for a set of Platonic hydrocarbon cages, and the total energy of ferrocene, Fe(Cp)2. Finally, we reproduce our previous result for the gas-phase ionization energy of Ni(Cp)2, agreeing with full ph-AFQMC to within statistical error while using less than 1/15th of the computer time.
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Affiliation(s)
- John L Weber
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - Hung Vuong
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - Pierre A Devlaminck
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - James Shee
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Joonho Lee
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, 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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8
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Larsson HR, Zhai H, Gunst K, Chan GKL. Matrix Product States with Large Sites. J Chem Theory Comput 2022; 18:749-762. [DOI: 10.1021/acs.jctc.1c00957] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Henrik R. Larsson
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Huanchen Zhai
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Klaas Gunst
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
- Center for Molecular Modeling, Ghent University, Technologiepark 46, B-9052 Zwijnaarde, Belgium
- Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, B-9000 Ghent, Belgium
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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9
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Blunt NS. Fixed- and Partial-Node Approximations in Slater Determinant Space for Molecules. J Chem Theory Comput 2021; 17:6092-6104. [PMID: 34549947 DOI: 10.1021/acs.jctc.1c00500] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present a study of fixed- and partial-node approximations in Slater determinant basis sets, using full configuration interaction quantum Monte Carlo (FCIQMC) to perform sampling. Walker annihilation in the FCIQMC method allows partial-node simulations to be performed, relaxing the nodal constraint to converge to the FCI solution. This is applied to ab initio molecular systems, using symmetry-projected Jastrow mean-field wave functions for complete active space (CAS) problems. Convergence and the sign problem within the partial-node approximation are studied, which is shown to eventually be limited in its use due to the large walker populations required. However, the fixed-node approximation results in an accurate and practical method. We apply these approaches to various molecular systems and active spaces, including ferrocene and acenes. This also provides a test of symmetry-projected Jastrow mean-field wave functions in variational Monte Carlo for a new set of problems. For trans-polyacetylene molecules and acenes, we find that the time to perform a constant number of fixed-node FCIQMC iterations scales as O(N1.44) and O(N1.75), respectively, resulting in an efficient method for CAS-based problems that can be applied accurately to large active spaces.
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Affiliation(s)
- Nick S Blunt
- Yusuf Hamied Department of Chemistry, Lensfield Road, Cambridge CB2 1EW, U.K.,St John's College, St John's Street, Cambridge CB2 1TP, U.K
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10
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Damour Y, Véril M, Kossoski F, Caffarel M, Jacquemin D, Scemama A, Loos PF. Accurate full configuration interaction correlation energy estimates for five- and six-membered rings. J Chem Phys 2021; 155:134104. [PMID: 34624964 DOI: 10.1063/5.0065314] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Following our recent work on the benzene molecule [P.-F. Loos, Y. Damour, and A. Scemama, J. Chem. Phys. 153, 176101 (2020)], motivated by the blind challenge of Eriksen et al. [J. Phys. Chem. Lett. 11, 8922 (2020)] on the same system, we report accurate full configuration interaction (FCI) frozen-core correlation energy estimates for 12 five- and six-membered ring molecules (cyclopentadiene, furan, imidazole, pyrrole, thiophene, benzene, pyrazine, pyridazine, pyridine, pyrimidine, s-tetrazine, and s-triazine) in the standard correlation-consistent double-ζ Dunning basis set (cc-pVDZ). Our FCI correlation energy estimates, with an estimated error smaller than 1 millihartree, are based on energetically optimized-orbital selected configuration interaction calculations performed with the configuration interaction using a perturbative selection made iteratively algorithm. Having at our disposal these accurate reference energies, the respective performance and convergence properties of several popular and widely used families of single-reference quantum chemistry methods are investigated. In particular, we study the convergence properties of (i) the Møller-Plesset perturbation series up to fifth-order (MP2, MP3, MP4, and MP5), (ii) the iterative approximate coupled-cluster series CC2, CC3, and CC4, and (iii) the coupled-cluster series CCSD, CCSDT, and CCSDTQ. The performance of the ground-state gold standard CCSD(T) as well as the completely renormalized CC model, CR-CC(2,3), is also investigated. We show that MP4 provides an interesting accuracy/cost ratio, while MP5 systematically worsens the correlation energy estimates. In addition, CC3 outperforms CCSD(T) and CR-CC(2,3), as well as its more expensive parent CCSDT. A similar trend is observed for the methods including quadruple excitations, where the CC4 model is shown to be slightly more accurate than CCSDTQ, both methods providing correlation energies within 2 millihartree of the FCI limit.
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Affiliation(s)
- Yann Damour
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Mickaël Véril
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Fábris Kossoski
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Michel Caffarel
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Denis Jacquemin
- Université de Nantes, CNRS, CEISAM UMR 6230, F-44000 Nantes, France
| | - Anthony Scemama
- 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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Mahajan A, Sharma S. Taming the Sign Problem in Auxiliary-Field Quantum Monte Carlo Using Accurate Wave Functions. J Chem Theory Comput 2021; 17:4786-4798. [PMID: 34232637 DOI: 10.1021/acs.jctc.1c00371] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We explore different ways of incorporating accurate trial wave functions into free projection auxiliary-field quantum Monte Carlo (fp-AFQMC). States employed include coupled-cluster singles and doubles, multi-Slater, and symmetry-projected mean-field wave functions. We adapt a recently proposed fast multi-Slater local energy evaluation algorithm for fp-AFQMC, making the use of long expansions from selected configuration interaction methods feasible. We demonstrate how these wave functions serve to mitigate the sign problem and accelerate convergence in quantum chemical problems, allowing the application of fp-AFQMC to systems of substantial sizes. Our calculations on the widely studied model Cu2O22+ system show that many previously reported isomerization energies differ substantially from the near-exact fp-AFQMC value.
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Affiliation(s)
- Ankit Mahajan
- Department of Chemistry, University of Colorado, Boulder, Colorado 80302, United States
| | - Sandeep Sharma
- Department of Chemistry, University of Colorado, Boulder, Colorado 80302, United States
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12
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Zahariev F, Gordon MS. Combined quantum Monte Carlo - effective fragment molecular orbital method: fragmentation across covalent bonds. Phys Chem Chem Phys 2021; 23:14308-14314. [PMID: 34164632 DOI: 10.1039/d0cp06528e] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The previously developed combined Quantum Monte Carlo-Effective Fragment Molecular Orbital (QMC-EFMO) method is extended to systems in which the fragmentation process cuts across covalent molecular bonds. The extended QMC-EFMO capability is demonstrated on a few model systems: the glycine tetramer, the diglycine reaction to form a dipeptide, silica-based rings, and polyalanine chains of increasing length. The agreement between full QMC and QMC-EFMO for the correlation energy is within 2 kcal mol-1 and for the correlation energy differences is within 1 kcal mol-1.
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Affiliation(s)
- F Zahariev
- Department of Chemistry and Ames Laboratory Iowa State University, Ames, IA 50011, USA.
| | - M S Gordon
- Department of Chemistry and Ames Laboratory Iowa State University, Ames, IA 50011, USA.
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13
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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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14
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Morales-Silva MA, Jordan KD, Shulenburger L, Wagner LK. Frontiers of stochastic electronic structure calculations. J Chem Phys 2021; 154:170401. [PMID: 34241059 DOI: 10.1063/5.0053674] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In recent years there has been a rapid growth in the development and application of new stochastic methods in electronic structure. These methods are quite diverse, from many-body wave function techniques in real space or determinant space to being used to sum perturbative expansions. This growth has been spurred by the more favorable scaling with the number of electrons and often better parallelization over large numbers of central processing unit (CPU) cores or graphical processing units (GPUs) than for high-end non-stochastic wave function based methods. This special issue of the Journal of Chemical Physics includes 33 papers that describe recent developments and applications in this area. As seen from the articles in the issue, stochastic electronic structure methods are applicable to both molecules and solids and can accurately describe systems with strong electron correlation. This issue was motivated, in part, by the 2019 Telluride Science Research Center workshop on Stochastic Electronic Structure Methods that we organized. Below we briefly describe each of the papers in the special issue, dividing the papers into six subtopics.
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Affiliation(s)
- Miguel A Morales-Silva
- Quantum Simulations Group, Lawrence Livermore National Laboratory, Livermore, California 94551, USA
| | - Kenneth D Jordan
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Luke Shulenburger
- HEDP Theory Department, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Lucas K Wagner
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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15
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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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16
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Abstract
We present a Perspective on what the future holds for full configuration interaction (FCI) theory, with an emphasis on conceptual rather than technical details. Upon revisiting the early history of FCI, a number of its key contemporary approximations are compared on as equal a footing as possible, using a recent blind challenge on the benzene molecule as a testbed [Eriksen et al., J. Phys. Chem. Lett., 2020 11, 8922]. In the process, we review the scope of applications for which FCI continues to prove indispensable, and the required traits in terms of robustness, efficacy, and reliability its modern approximations must satisfy are discussed. We close by conveying a number of general observations on the merits offered by the state-of-the-art alongside some of the challenges still faced to this day. While the field has altogether seen immense progress over the years-the past decade, in particular-it remains clear that our community as a whole has a substantial way to go in enhancing the overall applicability of near-exact electronic structure theory for systems of general composition and increasing size.
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Affiliation(s)
- Janus J Eriksen
- School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS, United Kingdom
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17
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Loos PF, Damour Y, Scemama A. The performance of CIPSI on the ground state electronic energy of benzene. J Chem Phys 2020; 153:176101. [DOI: 10.1063/5.0027617] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Affiliation(s)
- Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Yann Damour
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Anthony Scemama
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
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