1
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Nakano K, Sorella S, Alfè D, Zen A. Beyond Single-Reference Fixed-Node Approximation in Ab Initio Diffusion Monte Carlo Using Antisymmetrized Geminal Power Applied to Systems with Hundreds of Electrons. J Chem Theory Comput 2024; 20:4591-4604. [PMID: 38788330 DOI: 10.1021/acs.jctc.4c00139] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/26/2024]
Abstract
Diffusion Monte Carlo (DMC) is an exact technique to project out the ground state (GS) of a Hamiltonian. Since the GS is always bosonic, in Fermionic systems, the projection needs to be carried out while imposing antisymmetric constraints, which is a nondeterministic polynomial hard problem. In practice, therefore, the application of DMC on electronic structure problems is made by employing the fixed-node (FN) approximation, consisting of performing DMC with the constraint of having a fixed, predefined nodal surface. How do we get the nodal surface? The typical approach, applied in systems having up to hundreds or even thousands of electrons, is to obtain the nodal surface from a preliminary mean-field approach (typically, a density functional theory calculation) used to obtain a single Slater determinant. This is known as single reference. In this paper, we propose a new approach, applicable to systems as large as the C60 fullerene, which improves the nodes by going beyond the single reference. In practice, we employ an implicitly multireference ansatz (antisymmetrized geminal power wave function constraint with molecular orbitals), initialized on the preliminary mean-field approach, which is relaxed by optimizing a few parameters of the wave function determining the nodal surface by minimizing the FN-DMC energy. We highlight the improvements of the proposed approach over the standard single-reference method on several examples and, where feasible, the computational gain over the standard multireference ansatz, which makes the methods applicable to large systems. We also show that physical properties relying on relative energies, such as binding energies, are affordable and reliable within the proposed scheme.
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Affiliation(s)
- Kousuke Nakano
- Center for Basic Research on Materials, National Institute for Materials Science (NIMS), Tsukuba, Ibaraki 305-0047, Japan
- International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, Italy
| | - Sandro Sorella
- International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, Italy
| | - Dario Alfè
- Dipartimento di Fisica Ettore Pancini, Università di Napoli Federico II, Monte S. Angelo, 80126 Napoli, Italy
- Department of Earth Sciences, University College London, Gower Street, London WC1E 6BT, U.K
- Thomas Young Centre and London Centre for Nanotechnology, 17-19 Gordon Street, London WC1H 0AH, U.K
| | - Andrea Zen
- Dipartimento di Fisica Ettore Pancini, Università di Napoli Federico II, Monte S. Angelo, 80126 Napoli, Italy
- Department of Earth Sciences, University College London, Gower Street, London WC1E 6BT, U.K
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2
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Sukurma Z, Schlipf M, Humer M, Taheridehkordi A, Kresse G. Toward Large-Scale AFQMC Calculations: Large Time Step Auxiliary-Field Quantum Monte Carlo. J Chem Theory Comput 2024; 20:4205-4217. [PMID: 38750634 PMCID: PMC11137827 DOI: 10.1021/acs.jctc.4c00304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2024] [Revised: 04/29/2024] [Accepted: 05/06/2024] [Indexed: 05/29/2024]
Abstract
We report modifications of the ph-AFQMC algorithm that allow the use of large time steps and reliable time step extrapolation. Our modified algorithm eliminates size-consistency errors present in the standard algorithm when large time steps are employed. We investigate various methods to approximate the exponential of the one-body operator within the AFQMC framework, distinctly demonstrating the superiority of Krylov methods over the conventional Taylor expansion. We assess various propagators within AFQMC and demonstrate that the Split-2 propagator is the optimal method, exhibiting the smallest time-step errors. For the HEAT set molecules, the time-step extrapolated energies deviate on average by only 0.19 kcal/mol from the accurate small time-step energies. For small water clusters, we obtain accurate complete basis-set binding energies using time-step extrapolation with a mean absolute error of 0.07 kcal/mol compared to CCSD(T). Using large time-step ph-AFQMC for the N2 dimer, we show that accurate bond lengths can be obtained while reducing CPU time by an order of magnitude.
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Affiliation(s)
- Zoran Sukurma
- University
of Vienna, Faculty of Physics and Center for Computational Materials
Science, Kolingasse 14-16, A-1090 Vienna, Austria
- University
of Vienna, Faculty of Physics
& Vienna Doctoral School in Physics, Boltzmanngasse 5, A-1090 Vienna, Austria
| | - Martin Schlipf
- VASP
Software GmbH, Berggasse
21/14, 1090 Vienna, Austria
| | - Moritz Humer
- University
of Vienna, Faculty of Physics and Center for Computational Materials
Science, Kolingasse 14-16, A-1090 Vienna, Austria
- University
of Vienna, Faculty of Physics
& Vienna Doctoral School in Physics, Boltzmanngasse 5, A-1090 Vienna, Austria
| | - Amir Taheridehkordi
- University
of Vienna, Faculty of Physics and Center for Computational Materials
Science, Kolingasse 14-16, A-1090 Vienna, Austria
| | - Georg Kresse
- University
of Vienna, Faculty of Physics and Center for Computational Materials
Science, Kolingasse 14-16, A-1090 Vienna, Austria
- VASP
Software GmbH, Sensengasse
8, 1090 Vienna, Austria
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3
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Dobrautz W, Sokolov IO, Liao K, Ríos PL, Rahm M, Alavi A, Tavernelli I. Toward Real Chemical Accuracy on Current Quantum Hardware Through the Transcorrelated Method. J Chem Theory Comput 2024; 20:4146-4160. [PMID: 38723159 PMCID: PMC11137825 DOI: 10.1021/acs.jctc.4c00070] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2024] [Revised: 04/15/2024] [Accepted: 04/16/2024] [Indexed: 05/29/2024]
Abstract
Quantum computing is emerging as a new computational paradigm with the potential to transform several research fields including quantum chemistry. However, current hardware limitations (including limited coherence times, gate infidelities, and connectivity) hamper the implementation of most quantum algorithms and call for more noise-resilient solutions. We propose an explicitly correlated Ansatz based on the transcorrelated (TC) approach to target these major roadblocks directly. This method transfers, without any approximation, correlations from the wave function directly into the Hamiltonian, thus reducing the resources needed to achieve accurate results with noisy quantum devices. We show that the TC approach allows for shallower circuits and improves the convergence toward the complete basis set limit, providing energies within chemical accuracy to experiment with smaller basis sets and, thus, fewer qubits. We demonstrate our method by computing bond lengths, dissociation energies, and vibrational frequencies close to experimental results for the hydrogen dimer and lithium hydride using two and four qubits, respectively. To demonstrate our approach's current and near-term potential, we perform hardware experiments, where our results confirm that the TC method paves the way toward accurate quantum chemistry calculations already on today's quantum hardware.
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Affiliation(s)
- Werner Dobrautz
- Department
of Chemistry and Chemical Engineering, Chalmers
University of Technology, 41296 Gothenburg, Sweden
| | - Igor O. Sokolov
- IBM
Quantum, IBM Research Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - Ke Liao
- Max
Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
| | - Pablo López Ríos
- Max
Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
| | - Martin Rahm
- Department
of Chemistry and Chemical Engineering, Chalmers
University of Technology, 41296 Gothenburg, Sweden
| | - Ali Alavi
- Max
Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Lensfield
Road, Cambridge CB2 1EW, U.K.
| | - Ivano Tavernelli
- IBM
Quantum, IBM Research Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
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4
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Annaberdiyev A, Ganesh P, Krogel JT. Enhanced Twist-Averaging Technique for Magnetic Metals: Applications Using Quantum Monte Carlo. J Chem Theory Comput 2024; 20:2786-2797. [PMID: 38498904 DOI: 10.1021/acs.jctc.4c00058] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/20/2024]
Abstract
We propose an improved twist-averaging (TA) scheme for quantum Monte Carlo methods that use converged Kohn-Sham or Hartree-Fock orbitals as the reference. This TA technique is tailored to sample the Brillouin zone of magnetic metals, although it naturally extends to nonmagnetic (NM) conducting systems. The proposed scheme aims to reproduce the reference magnetization and achieves charge neutrality by construction, thus avoiding the large energy fluctuations and the postprocessing needed to correct the energies. It shows the most robust convergence of total energy and magnetism to the thermodynamic limit (TDL) when compared to four other TA schemes. Diffusion Monte Carlo applications are shown on NM Al and ferromagnetic α-Fe. The cohesive energy of Al in the TDL shows an excellent agreement with the experimental result. Furthermore, the magnetic moments in α-Fe exhibit rapid convergence with an increasing number of twists.
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Affiliation(s)
- Abdulgani Annaberdiyev
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
| | - Panchapakesan Ganesh
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
| | - Jaron T Krogel
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
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5
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Li X, Huang JC, Zhang GZ, Li HE, Cao CS, Lv D, Hu HS. A Nonstochastic Optimization Algorithm for Neural-Network Quantum States. J Chem Theory Comput 2023; 19:8156-8165. [PMID: 37962975 DOI: 10.1021/acs.jctc.3c00831] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2023]
Abstract
Neural-network quantum states (NQS) employ artificial neural networks to encode many-body wave functions in a second quantization through variational Monte Carlo (VMC). They have recently been applied to accurately describe electronic wave functions of molecules and have shown the challenges in efficiency compared with traditional quantum chemistry methods. Here, we introduce a general nonstochastic optimization algorithm for NQS in chemical systems, which deterministically generates a selected set of important configurations simultaneously with energy evaluation of NQS. This method bypasses the need for Markov-chain Monte Carlo within the VMC framework, thereby accelerating the entire optimization process. Furthermore, this newly developed nonstochastic optimization algorithm for NQS offers comparable or superior accuracy compared to its stochastic counterpart and ensures more stable convergence. The application of this model to test molecules exhibiting strong electron correlations provides further insight into the performance of NQS in chemical systems and opens avenues for future enhancements.
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Affiliation(s)
- Xiang Li
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Jia-Cheng Huang
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Guang-Ze Zhang
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Hao-En Li
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Chang-Su Cao
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
- ByteDance Research, Zhonghang Plaza, No. 43, North Third Ring West Road, Haidian District, Beijing 100089, China
| | - Dingshun Lv
- ByteDance Research, Zhonghang Plaza, No. 43, North Third Ring West Road, Haidian District, Beijing 100089, China
| | - Han-Shi Hu
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
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6
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Neufeld VA, Berkelbach TC. Highly Accurate Electronic Structure of Metallic Solids from Coupled-Cluster Theory with Nonperturbative Triple Excitations. PHYSICAL REVIEW LETTERS 2023; 131:186402. [PMID: 37977636 DOI: 10.1103/physrevlett.131.186402] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2023] [Accepted: 09/28/2023] [Indexed: 11/19/2023]
Abstract
Coupled-cluster theory with single, double, and perturbative triple excitations (CCSD(T))-often considered the "gold standard" of main-group quantum chemistry-is inapplicable to three-dimensional metals due to an infrared divergence, preventing its application to many important problems in materials science. We study the full, nonperturbative inclusion of triple excitations (CCSDT) and propose a new, iterative method, which we call ring-CCSDT, that resums the essential triple excitations with the same N^{7} run-time scaling as CCSD(T). CCSDT and ring-CCSDT are used to calculate the correlation energy of the uniform electron gas at metallic densities and the structural properties of solid lithium. Inclusion of connected triple excitations is shown to be essential to achieving high accuracy. We also investigate semiempirical CC methods based on spin-component scaling and the distinguishable cluster approximation and find that they enhance the accuracy of their parent ab initio methods.
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Affiliation(s)
- Verena A Neufeld
- 1Department of Chemistry, Columbia University, New York, New York 10027, USA
- 2Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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7
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Masios N, Irmler A, Schäfer T, Grüneis A. Averting the Infrared Catastrophe in the Gold Standard of Quantum Chemistry. PHYSICAL REVIEW LETTERS 2023; 131:186401. [PMID: 37977639 DOI: 10.1103/physrevlett.131.186401] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2023] [Accepted: 09/27/2023] [Indexed: 11/19/2023]
Abstract
Coupled-cluster theories can be used to compute ab initio electronic correlation energies of real materials with systematically improvable accuracy. However, the widely used coupled cluster singles and doubles plus perturbative triples [CCSD(T)] method is only applicable to insulating materials. For zero-gap materials the truncation of the underlying many-body perturbation expansion leads to an infrared catastrophe. Here, we present a novel perturbative triples formalism denoted as (cT) that yields convergent correlation energies in metallic systems. Furthermore, the computed correlation energies for the three-dimensional uniform electron gas at metallic densities are in good agreement with quantum Monte Carlo results. At the same time the newly proposed method retains all desirable properties of CCSD(T) such as its accuracy for insulating systems as well as its low computational cost compared to a full inclusion of the triples. This paves the way for ab initio calculations of real metals with chemical accuracy.
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Affiliation(s)
- Nikolaos Masios
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, 1040 Vienna, Austria
| | - Andreas Irmler
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, 1040 Vienna, Austria
| | - Tobias Schäfer
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, 1040 Vienna, Austria
| | - Andreas Grüneis
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, 1040 Vienna, Austria
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8
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Ichibha T, Nikaido Y, Bennett MC, Krogel JT, Hongo K, Maezono R, Reboredo FA. Locality error free effective core potentials for 3d transition metal elements developed for the diffusion Monte Carlo method. J Chem Phys 2023; 159:164114. [PMID: 37888761 DOI: 10.1063/5.0175381] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2023] [Accepted: 10/05/2023] [Indexed: 10/28/2023] Open
Abstract
Pseudopotential locality errors have hampered the applications of the diffusion Monte Carlo (DMC) method in materials containing transition metals, in particular oxides. We have developed locality error free effective core potentials, pseudo-Hamiltonians, for transition metals ranging from Cr to Zn. We have modified a procedure published by some of us in Bennett et al. [J. Chem. Theory Comput. 18, 828 (2022)]. We carefully optimized our pseudo-Hamiltonians and achieved transferability errors comparable to the best semilocal pseudopotentials used with DMC but without incurring in locality errors. Our pseudo-Hamiltonian set (named OPH23) bears the potential to significantly improve the accuracy of many-body-first-principles calculations in fundamental science research of complex materials involving transition metals.
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Affiliation(s)
- Tom Ichibha
- School of Information Science, JAIST, Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Yutaka Nikaido
- School of Information Science, JAIST, Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan
| | - M Chandler Bennett
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Jaron T Krogel
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Kenta Hongo
- Research Center for Advanced Computing Infrastructure, JAIST, Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan
| | - Ryo Maezono
- School of Information Science, JAIST, Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan
| | - Fernando A Reboredo
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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9
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Wines D, Tiihonen J, Saritas K, Krogel JT, Ataca C. A Quantum Monte Carlo Study of the Structural, Energetic, and Magnetic Properties of Two-Dimensional H and T Phase VSe 2. J Phys Chem Lett 2023; 14:3553-3560. [PMID: 37017431 DOI: 10.1021/acs.jpclett.3c00497] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/19/2023]
Abstract
Previous works have controversially claimed near-room-temperature ferromagnetism in two-dimensional (2D) VSe2, with conflicting results throughout the literature. These discrepancies in magnetic properties between both phases (T and H) of 2D VSe2 are most likely due to the structural parameters being coupled to the magnetic properties. Specifically, both phases have a close lattice match and similar total energies, which makes it difficult to determine which phase is being observed experimentally. In this study, we used a combination of density functional theory, highly accurate diffusion Monte Carlo (DMC), and a surrogate Hessian line-search optimization technique to resolve the previously reported discrepancy in structural parameters and relative phase stability. With DMC accuracy, we determined the free-standing geometry of both phases and constructed a phase diagram. Our findings demonstrate the successes of the DMC method coupled with the surrogate Hessian structural optimization technique when applied to a 2D magnetic system.
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Affiliation(s)
- Daniel Wines
- Materials Science and Engineering Division, National Institute of Standards and Technology (NIST), Gaithersburg, Maryland 20899, United States
| | - Juha Tiihonen
- Department of Physics, Nanoscience Center, University of Jyväskylä, P.O. Box 35, 40014 Jyväskylä, Finland
| | - Kayahan Saritas
- Material Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
| | - Jaron T Krogel
- Material Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
| | - Can Ataca
- Department of Physics, University of Maryland Baltimore County, Baltimore, Maryland 21250, United States
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10
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Ren W, Fu W, Wu X, Chen J. Towards the ground state of molecules via diffusion Monte Carlo on neural networks. Nat Commun 2023; 14:1860. [PMID: 37012248 PMCID: PMC10070323 DOI: 10.1038/s41467-023-37609-3] [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: 05/24/2022] [Accepted: 03/20/2023] [Indexed: 04/05/2023] Open
Abstract
Diffusion Monte Carlo (DMC) based on fixed-node approximation has enjoyed significant developments in the past decades and become one of the go-to methods when accurate ground state energy of molecules and materials is needed. However, the inaccurate nodal structure hinders the application of DMC for more challenging electronic correlation problems. In this work, we apply the neural-network based trial wavefunction in fixed-node DMC, which allows accurate calculations of a broad range of atomic and molecular systems of different electronic characteristics. Our method is superior in both accuracy and efficiency compared to state-of-the-art neural network methods using variational Monte Carlo (VMC). We also introduce an extrapolation scheme based on the empirical linearity between VMC and DMC energies, and significantly improve our binding energy calculation. Overall, this computational framework provides a benchmark for accurate solutions of correlated electronic wavefunction and also sheds light on the chemical understanding of molecules.
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Affiliation(s)
- Weiluo Ren
- ByteDance Research, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, People's Republic of China.
| | - Weizhong Fu
- ByteDance Research, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, People's Republic of China
- School of Physics, Peking University, 100871, Beijing, People's Republic of China
| | - Xiaojie Wu
- ByteDance Research, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, People's Republic of China
| | - Ji Chen
- School of Physics, Peking University, 100871, Beijing, People's Republic of China.
- Interdisciplinary Institute of Light-Element Quantum Materials, Frontiers Science Center for Nano-Optoelectronics, Peking University, 100871, Beijing, People's Republic of China.
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11
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Wines D, Choudhary K, Tavazza F. Systematic DFT+U and Quantum Monte Carlo Benchmark of Magnetic Two-Dimensional (2D) CrX 3 (X = I, Br, Cl, F). THE JOURNAL OF PHYSICAL CHEMISTRY. C, NANOMATERIALS AND INTERFACES 2023; 127:10.1021/acs.jpcc.2c06733. [PMID: 36727030 PMCID: PMC9888057 DOI: 10.1021/acs.jpcc.2c06733] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
The search for two-dimensional (2D) magnetic materials has attracted a great deal of attention because of the experimental synthesis of 2D CrI3, which has a measured Curie temperature of 45 K. Often times, these monolayers have a higher degree of electron correlation and require more sophisticated methods beyond density functional theory (DFT). Diffusion Monte Carlo (DMC) is a correlated electronic structure method that has been demonstrated to be successful for calculating the electronic and magnetic properties of a wide variety of 2D and bulk systems, since it has a weaker dependence on the Hubbard parameter (U) and density functional. In this study, we designed a workflow that combines DFT +U and DMC in order to treat 2D correlated magnetic systems. We chose monolayer CrX3 (X = I, Br, Cl, F), with a stronger focus on CrI3 and CrBr3, as a case study due to the fact that they have been experimentally realized and have a finite critical temperature. With this DFT+U and DMC workflow and the analytical method of Torelli and Olsen, we estimated a maximum value of 43.56 K for the Tc of CrI3 and 20.78 K for the Tc of CrBr3, in addition to analyzing the spin densities and magnetic properties with DMC and DFT+U. We expect that running this workflow for a well-known material class will aid in the future discovery and characterization of lesser known and more complex correlated 2D magnetic materials.
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Affiliation(s)
- Daniel Wines
- Materials Science and Engineering Division, National Institute of Standards and Technology (NIST), Gaithersburg, Maryland 20899, United States
| | - Kamal Choudhary
- Materials Science and Engineering Division, National Institute of Standards and Technology (NIST), Gaithersburg, Maryland 20899, United States; Theiss Research, La Jolla, California 92037, United States
| | - Francesca Tavazza
- Materials Science and Engineering Division, National Institute of Standards and Technology (NIST), Gaithersburg, Maryland 20899, United States
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12
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Li X, Li Z, Chen J. Ab initio calculation of real solids via neural network ansatz. Nat Commun 2022; 13:7895. [PMID: 36550157 PMCID: PMC9780243 DOI: 10.1038/s41467-022-35627-1] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2022] [Accepted: 12/13/2022] [Indexed: 12/24/2022] Open
Abstract
Neural networks have been applied to tackle many-body electron correlations for small molecules and physical models in recent years. Here we propose an architecture that extends molecular neural networks with the inclusion of periodic boundary conditions to enable ab initio calculation of real solids. The accuracy of our approach is demonstrated in four different types of systems, namely the one-dimensional periodic hydrogen chain, the two-dimensional graphene, the three-dimensional lithium hydride crystal, and the homogeneous electron gas, where the obtained results, e.g. total energies, dissociation curves, and cohesive energies, reach a competitive level with many traditional ab initio methods. Moreover, electron densities of typical systems are also calculated to provide physical intuition of various solids. Our method of extending a molecular neural network to periodic systems can be easily integrated into other neural network structures, highlighting a promising future of ab initio solution of more complex solid systems using neural network ansatz, and more generally endorsing the application of machine learning in materials simulation and condensed matter physics.
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Affiliation(s)
- Xiang Li
- ByteDance Inc, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, China
| | - Zhe Li
- ByteDance Inc, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, China
| | - Ji Chen
- grid.11135.370000 0001 2256 9319School of Physics, Interdisciplinary Institute of Light-Element Quantum Materials, Frontiers Science Center for Nano-Optoelectronics, Peking University, Beijing, 100871 P. R. China
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13
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Simula KA, Muff JE, Makkonen I, Drummond ND. Quantum Monte Carlo Study of Positron Lifetimes in Solids. PHYSICAL REVIEW LETTERS 2022; 129:166403. [PMID: 36306750 DOI: 10.1103/physrevlett.129.166403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2021] [Revised: 05/27/2022] [Accepted: 09/22/2022] [Indexed: 06/16/2023]
Abstract
We present an analysis of positron lifetimes in solids with unprecedented depth. Instead of modeling correlation effects with density functionals, we study positron-electron wave functions with long-range correlations included. This gives new insight in understanding positron annihilation in metals, insulators, and semiconductors. By using a new quantum Monte Carlo approach for computation of positron lifetimes, an improved accuracy compared to previous computations is obtained for a representative set of materials when compared with experiment. Thus, we present a method without free parameters as a useful alternative to the already existing methods for modeling positrons in solids.
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Affiliation(s)
- K A Simula
- Department of Physics, University of Helsinki, P.O. Box 43, Helsinki FI-00014, Finland
| | - J E Muff
- Department of Physics, University of Helsinki, P.O. Box 43, Helsinki FI-00014, Finland
| | - I Makkonen
- Department of Physics, University of Helsinki, P.O. Box 43, Helsinki FI-00014, Finland
| | - N D Drummond
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
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14
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Nakatsuji H, Nakashima H. Direct local sampling method for solving the Schrödinger equation with the free complement - local Schrödinger equation theory. Chem Phys Lett 2022. [DOI: 10.1016/j.cplett.2022.140002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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15
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Scherbela M, Reisenhofer R, Gerard L, Marquetand P, Grohs P. Solving the electronic Schrödinger equation for multiple nuclear geometries with weight-sharing deep neural networks. NATURE COMPUTATIONAL SCIENCE 2022; 2:331-341. [PMID: 38177815 DOI: 10.1038/s43588-022-00228-x] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2021] [Accepted: 03/16/2022] [Indexed: 01/06/2024]
Abstract
The Schrödinger equation describes the quantum-mechanical behaviour of particles, making it the most fundamental equation in chemistry. A solution for a given molecule allows computation of any of its properties. Finding accurate solutions for many different molecules and geometries is thus crucial to the discovery of new materials such as drugs or catalysts. Despite its importance, the Schrödinger equation is notoriously difficult to solve even for single molecules, as established methods scale exponentially with the number of particles. Combining Monte Carlo techniques with unsupervised optimization of neural networks was recently discovered as a promising approach to overcome this curse of dimensionality, but the corresponding methods do not exploit synergies that arise when considering multiple geometries. Here we show that sharing the vast majority of weights across neural network models for different geometries substantially accelerates optimization. Furthermore, weight-sharing yields pretrained models that require only a small number of additional optimization steps to obtain high-accuracy solutions for new geometries.
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Affiliation(s)
- Michael Scherbela
- Research Network Data Science at University of Vienna, Vienna, Austria
| | - Rafael Reisenhofer
- Research Network Data Science at University of Vienna, Vienna, Austria.
- Faculty of Mathematics, University of Vienna, Vienna, Austria.
| | - Leon Gerard
- Research Network Data Science at University of Vienna, Vienna, Austria
| | - Philipp Marquetand
- Research Network Data Science at University of Vienna, Vienna, Austria
- Faculty of Chemistry, University of Vienna, Vienna, Austria
| | - Philipp Grohs
- Research Network Data Science at University of Vienna, Vienna, Austria
- Faculty of Mathematics, University of Vienna, Vienna, Austria
- Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Linz, Austria
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16
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Ichibha T, Neufeld VA, Hongo K, Maezono R, Thom AJW. Making the most of data: Quantum Monte Carlo postanalysis revisited. Phys Rev E 2022; 105:045313. [PMID: 35590595 DOI: 10.1103/physreve.105.045313] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2021] [Accepted: 03/10/2022] [Indexed: 06/15/2023]
Abstract
In quantum Monte Carlo (QMC) methods, energy estimators are calculated as (functions of) statistical averages of quantities sampled during a calculation. Associated statistical errors of these averages are often estimated. This error estimation is not straightforward and there are several choices of the error estimation methods. We evaluate the performance of three methods (the Straatsma method, an autoregressive model, and a blocking analysis based on von Neumann's ratio test for randomness) for the energy time series given by three QMC methods [diffusion Monte Carlo, full configuration interaction Quantum Monte Carlo (FCIQMC), and coupled cluster Monte Carlo (CCMC)]. From these analyses, we describe a hybrid analysis method which provides reliable error estimates for a series of various lengths of FCIQMC and CCMC's time series. Equally important is the estimation of the appropriate start point of the equilibrated phase. We establish that a simple mean squared error rule method as described by White [K. P. White, Jr., Simulation 69(6), 323 (1997)10.1177/003754979706900601] can provide reasonable estimations.
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Affiliation(s)
- Tom Ichibha
- School of Information Science, JAIST, 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan
| | - Verena A Neufeld
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom and Department of Chemistry, Columbia University, New York, New York 10027, USA
| | - Kenta Hongo
- Research Center for Advanced Computing Infrastructure, JAIST, 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan
| | - Ryo Maezono
- School of Information Science, JAIST, 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan
| | - Alex J W Thom
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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17
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Ishii K, Shimazaki T, Tachikawa M, Kita Y. Theoretical Study of the Isotope and Homologue Effects on Nuclear Magnetic Shielding in Water and Hydrogen Sulfide Molecules. CHEM LETT 2022. [DOI: 10.1246/cl.210760] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Kiriko Ishii
- Quantum Chemistry Division, Yokohama City University, 22-2 Seto, Kanazawa-ku, Yokohama, Kanagawa 236-0027, Japan
| | - Tomomi Shimazaki
- Quantum Chemistry Division, Yokohama City University, 22-2 Seto, Kanazawa-ku, Yokohama, Kanagawa 236-0027, Japan
| | - Masanori Tachikawa
- Quantum Chemistry Division, Yokohama City University, 22-2 Seto, Kanazawa-ku, Yokohama, Kanagawa 236-0027, Japan
| | - Yukiumi Kita
- Quantum Chemistry Division, Yokohama City University, 22-2 Seto, Kanazawa-ku, Yokohama, Kanagawa 236-0027, Japan
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18
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Weighted nodal domain averages of eigenstates for quantum Monte Carlo and beyond. Chem Phys 2022. [DOI: 10.1016/j.chemphys.2022.111483] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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19
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Klus S, Gelß P, Nüske F, Noé F. Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2021. [DOI: 10.1088/2632-2153/ac14ad] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022] Open
Abstract
Abstract
We derive symmetric and antisymmetric kernels by symmetrizing and antisymmetrizing conventional kernels and analyze their properties. In particular, we compute the feature space dimensions of the resulting polynomial kernels, prove that the reproducing kernel Hilbert spaces induced by symmetric and antisymmetric Gaussian kernels are dense in the space of symmetric and antisymmetric functions, and propose a Slater determinant representation of the antisymmetric Gaussian kernel, which allows for an efficient evaluation even if the state space is high-dimensional. Furthermore, we show that by exploiting symmetries or antisymmetries the size of the training data set can be significantly reduced. The results are illustrated with guiding examples and simple quantum physics and chemistry applications.
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20
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Azadi S, Drummond ND, Foulkes WMC. Quasiparticle Effective Mass of the Three-Dimensional Fermi Liquid by Quantum Monte Carlo. PHYSICAL REVIEW LETTERS 2021; 127:086401. [PMID: 34477398 DOI: 10.1103/physrevlett.127.086401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2021] [Accepted: 07/26/2021] [Indexed: 06/13/2023]
Abstract
According to Landau's Fermi liquid theory, the main properties of the quasiparticle excitations of an electron gas are embodied in the effective mass m^{*}, which determines the energy of a single quasiparticle, and the Landau interaction function, which indicates how the energy of a quasiparticle is modified by the presence of other quasiparticles. This simple paradigm underlies most of our current understanding of the physical and chemical behavior of metallic systems. The quasiparticle effective mass of the three-dimensional homogeneous electron gas has been the subject of theoretical controversy, and there is a lack of experimental data. In this Letter, we deploy diffusion Monte Carlo (DMC) methods to calculate m^{*} as a function of density for paramagnetic and ferromagnetic three-dimensional homogeneous electron gases. The DMC results indicate that m^{*} decreases when the density is reduced, especially in the ferromagnetic case. The DMC quasiparticle energy bands exclude the possibility of a reduction in the occupied bandwidth relative to that of the free-electron model at density parameter r_{s}=4, which corresponds to Na metal.
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Affiliation(s)
- Sam Azadi
- Department of Physics and the Thomas Young Centre for Theory and Simulation of Materials, South Kensington Campus, Imperial College London, London SW7 2AZ, United Kingdom
| | - N D Drummond
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - W M C Foulkes
- Department of Physics and the Thomas Young Centre for Theory and Simulation of Materials, South Kensington Campus, Imperial College London, London SW7 2AZ, United Kingdom
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21
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Tiihonen J, Clay RC, Krogel JT. Toward quantum Monte Carlo forces on heavier ions: Scaling properties. J Chem Phys 2021; 154:204111. [PMID: 34241166 DOI: 10.1063/5.0052266] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Quantum Monte Carlo (QMC) forces have been studied extensively in recent decades because of their importance with spectroscopic observables and geometry optimization. Here, we benchmark the accuracy and computational cost of QMC forces. The zero-variance zero-bias (ZVZB) force estimator is used in standard variational and diffusion Monte Carlo simulations with mean-field based trial wavefunctions and atomic pseudopotentials. Statistical force uncertainties are obtained with a recently developed regression technique for heavy tailed QMC data [P. Lopez Rios and G. J. Conduit, Phys. Rev. E 99, 063312 (2019)]. By considering selected atoms and dimers with elements ranging from H to Zn (1 ≤ Zeff ≤ 20), we assess the accuracy and the computational cost of ZVZB forces as the effective pseudopotential valence charge, Zeff, increases. We find that the costs of QMC energies and forces approximately follow simple power laws in Zeff. The force uncertainty grows more rapidly, leading to a best case cost scaling relationship of approximately Zeff 6.5(3) for diffusion Monte Carlo. We find that the accessible system size at fixed computational cost scales as Zeff -2, insensitive to model assumptions or the use of the "space warp" variance-reduction technique. Our results predict the practical cost of obtaining forces for a range of materials, such as transition metal oxides where QMC forces have yet to be applied, and underscore the importance of further developing force variance-reduction techniques, particularly for atoms with high Zeff.
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Affiliation(s)
- Juha Tiihonen
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Raymond C Clay
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Jaron T Krogel
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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22
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Schätzle Z, Hermann J, Noé F. Convergence to the fixed-node limit in deep variational Monte Carlo. J Chem Phys 2021; 154:124108. [PMID: 33810658 DOI: 10.1063/5.0032836] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Variational quantum Monte Carlo (QMC) is an ab initio method for solving the electronic Schrödinger equation that is exact in principle, but limited by the flexibility of the available Ansätze in practice. The recently introduced deep QMC approach, specifically two deep-neural-network Ansätze PauliNet and FermiNet, allows variational QMC to reach the accuracy of diffusion QMC, but little is understood about the convergence behavior of such Ansätze. Here, we analyze how deep variational QMC approaches the fixed-node limit with increasing network size. First, we demonstrate that a deep neural network can overcome the limitations of a small basis set and reach the mean-field (MF) complete-basis-set limit. Moving to electron correlation, we then perform an extensive hyperparameter scan of a deep Jastrow factor for LiH and H4 and find that variational energies at the fixed-node limit can be obtained with a sufficiently large network. Finally, we benchmark MF and many-body Ansätze on H2O, increasing the fraction of recovered fixed-node correlation energy of single-determinant Slater-Jastrow-type Ansätze by half an order of magnitude compared to previous variational QMC results, and demonstrate that a single-determinant Slater-Jastrow-backflow version of the Ansatz overcomes the fixed-node limitations. This analysis helps understand the superb accuracy of deep variational Ansätze in comparison to the traditional trial wavefunctions at the respective level of theory and will guide future improvements of the neural-network architectures in deep QMC.
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Affiliation(s)
- Z Schätzle
- FU Berlin, Department of Mathematics and Computer Science, Arnimallee 6, 14195 Berlin, Germany
| | - J Hermann
- FU Berlin, Department of Mathematics and Computer Science, Arnimallee 6, 14195 Berlin, Germany
| | - F Noé
- FU Berlin, Department of Mathematics and Computer Science, Arnimallee 6, 14195 Berlin, Germany
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23
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Kessler J, Calcavecchia F, Kühne TD. Artificial Neural Networks as Trial Wave Functions for Quantum Monte Carlo. ADVANCED THEORY AND SIMULATIONS 2021. [DOI: 10.1002/adts.202000269] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Jan Kessler
- Dynamics of Condensed Matter and Center for Sustainable Systems Design Chair of Theoretical Chemistry University of Paderborn Warburger Str. 100 D‐33098 Paderborn Germany
| | - Francesco Calcavecchia
- Dynamics of Condensed Matter and Center for Sustainable Systems Design Chair of Theoretical Chemistry University of Paderborn Warburger Str. 100 D‐33098 Paderborn Germany
| | - Thomas D. Kühne
- Dynamics of Condensed Matter and Center for Sustainable Systems Design Chair of Theoretical Chemistry University of Paderborn Warburger Str. 100 D‐33098 Paderborn Germany
- Paderborn Center for Parallel Computing and Institute for Lightweight Design University of Paderborn Warburger Str. 100 D‐33098 Paderborn Germany
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24
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Pathak S, Busemeyer B, Rodrigues JNB, Wagner LK. Excited states in variational Monte Carlo using a penalty method. J Chem Phys 2021; 154:034101. [DOI: 10.1063/5.0030949] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Affiliation(s)
- Shivesh Pathak
- University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Brian Busemeyer
- Center for Computational Quantum Physics, Flatiron Institute, York, New York 10010, USA
| | | | - Lucas K. Wagner
- University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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25
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de Pina VG, Brito BGA, Hai GQ, Cândido L. Quantifying electron-correlation effects in small coinage-metal clusters via ab initio calculations. Phys Chem Chem Phys 2021; 23:9832-9842. [PMID: 33908436 DOI: 10.1039/d0cp06499h] [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
We investigate many-electron correlation effects in neutral and charged coinage-metal clusters Cun, Agn, and Aun (n = 1-4) via ab initio calculations using fixed-node diffusion Monte Carlo (FN-DMC) simulations, density functional theory (DFT), and the Hartree-Fock (HF) method. From very accurate FN-DMC total energies of the clusters and the HF results in the infinity large complete-basis-set limit, we obtain correlation energies in these strongly correlated many-electron clusters involving d orbitals. The obtained bond lengths of the clusters, atomic binding and dissociation energies, ionization potentials, and electron affinities are in satisfactory agreement with the available experiments. In the analysis, the electron correlation effects on these observable physical quantities are quantified by relative correlation contributions determined by the difference between the calculated FN-DMC and HF results. We show that the correlation contribution is not only significant for the quantities related to electronic structures of the coinage-metal clusters, such as electron affinity, but it is also essential for the stability of the atomic structures of these clusters. For example, the electron correlation contribution is responsible for more than 90% of the atomic binding energies of the small neutral copper clusters. We also demonstrate the orbital-occupation dependence of the correlation energy and electron pairing of the valence electrons in these coinage-metal clusters from the electron correlation-energy gain and spin-multiplicity change in the electron addition processes, which are reflected in their ionization potentials and electron affinities.
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Affiliation(s)
- V G de Pina
- Instituto de Física, Universidade Federal de Goiás, 74.001-970, Goiânia, GO, Brazil.
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26
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Dornheim T, Invernizzi M, Vorberger J, Hirshberg B. Attenuating the fermion sign problem in path integral Monte Carlo simulations using the Bogoliubov inequality and thermodynamic integration. J Chem Phys 2020; 153:234104. [DOI: 10.1063/5.0030760] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Tobias Dornheim
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
| | - Michele Invernizzi
- Institute of Computational Sciences, Università Della Svizzera Italiana, 6900 Lugano, Switzerland
- National Centre for Computational Design and Discovery of Novel Materials MARVEL, Università Della Svizzera Italiana, 6900 Lugano, Switzerland
- Department of Physics, ETH Zurich, 8092 Zurich, Switzerland
| | - Jan Vorberger
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Barak Hirshberg
- Institute of Computational Sciences, Università Della Svizzera Italiana, 6900 Lugano, Switzerland
- Department of Chemistry and Applied Biosciences, ETH Zurich, 8092 Zurich, Switzerland
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27
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Upadhyay S, Dumi A, Shee J, Jordan KD. The role of high-order electron correlation effects in a model system for non-valence correlation-bound anions. J Chem Phys 2020; 153:224118. [DOI: 10.1063/5.0030942] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Affiliation(s)
- Shiv Upadhyay
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Amanda Dumi
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - James Shee
- Department of Chemistry, University of California Berkeley, Berkeley, California 94720, USA
| | - Kenneth D. Jordan
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
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28
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Powell AD, Kroes GJ, Doblhoff-Dier K. Quantum Monte Carlo calculations on dissociative chemisorption of H2 + Al(110): Minimum barrier heights and their comparison to DFT values. J Chem Phys 2020; 153:224701. [DOI: 10.1063/5.0022919] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Andrew D. Powell
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, Netherlands
| | - Geert-Jan Kroes
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, Netherlands
| | - Katharina Doblhoff-Dier
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, Netherlands
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29
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Azadi S, Booth GH, Kühne TD. Equation of state of atomic solid hydrogen by stochastic many-body wave function methods. J Chem Phys 2020; 153:204107. [DOI: 10.1063/5.0026499] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Sam Azadi
- Department of Physics, King’s College London, Strand, WC2R 2LS London, United Kingdom
| | - George H. Booth
- Department of Physics, King’s College London, Strand, WC2R 2LS London, United Kingdom
| | - Thomas D. Kühne
- Department of Chemistry, Paderborn Center for Parallel Computing, Paderborn University, 33098 Paderborn, Germany
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30
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Benali A, Gasperich K, Jordan KD, Applencourt T, Luo Y, Bennett MC, Krogel JT, Shulenburger L, Kent PRC, Loos PF, Scemama A, Caffarel M. Toward a systematic improvement of the fixed-node approximation in diffusion Monte Carlo for solids—A case study in diamond. J Chem Phys 2020; 153:184111. [DOI: 10.1063/5.0021036] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Affiliation(s)
- Anouar Benali
- Computational Sciences Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Kevin Gasperich
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Kenneth D. Jordan
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Thomas Applencourt
- Argonne Leadership Computing Facility, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Ye Luo
- Computational Sciences Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - M. Chandler Bennett
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Jaron T. Krogel
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Luke Shulenburger
- HEDP Theory Department, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Paul R. C. Kent
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
- Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Anthony Scemama
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Michel Caffarel
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France
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31
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Hermann J, Schätzle Z, Noé F. Deep-neural-network solution of the electronic Schrödinger equation. Nat Chem 2020; 12:891-897. [DOI: 10.1038/s41557-020-0544-y] [Citation(s) in RCA: 145] [Impact Index Per Article: 36.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2019] [Accepted: 08/05/2020] [Indexed: 11/09/2022]
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32
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Nakano K, Attaccalite C, Barborini M, Capriotti L, Casula M, Coccia E, Dagrada M, Genovese C, Luo Y, Mazzola G, Zen A, Sorella S. TurboRVB: A many-body toolkit for ab initio electronic simulations by quantum Monte Carlo. J Chem Phys 2020; 152:204121. [DOI: 10.1063/5.0005037] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Affiliation(s)
- Kousuke Nakano
- International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, Italy
- Japan Advanced Institute of Science and Technology (JAIST), Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan
| | - Claudio Attaccalite
- Aix-Marseille Université, CNRS, CINaM UMR 7325, Campus de Luminy, 13288 Marseille, France
| | | | - Luca Capriotti
- New York University, Tandon School of Engineering, 6 MetroTech Center, Brooklyn, New York 11201, USA
- Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Michele Casula
- Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie (IMPMC), Sorbonne Université, CNRS UMR 7590, IRD UMR 206, MNHN, 4 Place Jussieu, 75252 Paris, France
| | - Emanuele Coccia
- Department of Chemical and Pharmaceutical Sciences, University of Trieste, Via L. Giorgieri 1, 34127 Trieste, Italy
| | - Mario Dagrada
- Forescout Technologies, John F. Kennedylaan 2, 5612AB Eindhoven, The Netherlands
| | - Claudio Genovese
- International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, Italy
| | - Ye Luo
- Computational Science Division, Argonne National Laboratory, 9700 S. Cass Avenue, Lemont, Illinois 60439, USA
- Argonne Leadership Computing Facility, Argonne National Laboratory, 9700 S. Cass Avenue, Lemont, Illinois 60439, USA
| | | | - Andrea Zen
- Department of Earth Sciences, University College London, Gower Street, London WC1E 6BT, United Kingdom
- Thomas Young Centre and London Centre for Nanotechnology, 17-19 Gordon Street, London WC1H 0AH, United Kingdom
| | - Sandro Sorella
- International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, Italy
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33
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Needs RJ, Towler MD, Drummond ND, López Ríos P, Trail JR. Variational and diffusion quantum Monte Carlo calculations with the CASINO code. J Chem Phys 2020; 152:154106. [DOI: 10.1063/1.5144288] [Citation(s) in RCA: 35] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- R. J. Needs
- TCM Group, Cavendish Laboratory, University of Cambridge, 19 J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - M. D. Towler
- University College London, London WC1E 6BT, United Kingdom
| | - N. D. Drummond
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - P. López Ríos
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - J. R. Trail
- TCM Group, Cavendish Laboratory, University of Cambridge, 19 J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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34
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Ray U, Kin-Lic Chan G. Constructing auxiliary dynamics for nonequilibrium stationary states by variance minimization. J Chem Phys 2020; 152:104107. [DOI: 10.1063/1.5143144] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ushnish Ray
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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35
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Zen A, Brandenburg JG, Michaelides A, Alfè D. A new scheme for fixed node diffusion quantum Monte Carlo with pseudopotentials: Improving reproducibility and reducing the trial-wave-function bias. J Chem Phys 2019; 151:134105. [DOI: 10.1063/1.5119729] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Andrea Zen
- Thomas Young Centre, University College London, London WC1H 0AH, United Kingdom
- London Centre for Nanotechnology, Gordon St., London WC1H 0AH, United Kingdom
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
- Department of Earth Sciences, University College London, London WC1E 6BT, United Kingdom
| | - Jan Gerit Brandenburg
- Thomas Young Centre, University College London, London WC1H 0AH, United Kingdom
- Interdisciplinary Center for Scientific Computing, University of Heidelberg, Im Neuenheimer Feld 205A, 69120 Heidelberg, Germany
| | - Angelos Michaelides
- Thomas Young Centre, University College London, London WC1H 0AH, United Kingdom
- London Centre for Nanotechnology, Gordon St., London WC1H 0AH, United Kingdom
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Dario Alfè
- Thomas Young Centre, University College London, London WC1H 0AH, United Kingdom
- London Centre for Nanotechnology, Gordon St., London WC1H 0AH, United Kingdom
- Department of Earth Sciences, University College London, London WC1E 6BT, United Kingdom
- Dipartimento di Fisica Ettore Pancini, Università di Napoli Federico II, Monte S. Angelo, I-80126 Napoli, Italy
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36
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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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37
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Ríos PL, Conduit GJ. Tail-regression estimator for heavy-tailed distributions of known tail indices and its application to continuum quantum Monte Carlo data. Phys Rev E 2019; 99:063312. [PMID: 31330629 DOI: 10.1103/physreve.99.063312] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2019] [Indexed: 11/07/2022]
Abstract
Standard statistical analysis is unable to provide reliable confidence intervals on expectation values of probability distributions that do not satisfy the conditions of the central limit theorem. We present a regression-based estimator of an arbitrary moment of a probability distribution with power-law heavy tails that exploits knowledge of the exponents of its asymptotic decay to bypass this issue entirely. Our method is applied to synthetic data and to energy and atomic force data from variational and diffusion quantum Monte Carlo calculations, whose distributions have known asymptotic forms [J. R. Trail, Phys. Rev. E 77, 016703 (2008)PLEEE81539-375510.1103/PhysRevE.77.016703; A. Badinski et al., J. Phys.: Condens. Matter 22, 074202 (2010)JCOMEL0953-898410.1088/0953-8984/22/7/074202]. We obtain convergent, accurate confidence intervals on the variance of the local energy of an electron gas and on the Hellmann-Feynman force on an atom in the all-electron carbon dimer. In each of these cases the uncertainty on our estimator is 45% and 60 times smaller, respectively, than the nominal (ill-defined) standard error.
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Affiliation(s)
- Pablo López Ríos
- Max-Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany.,Theory of Condensed Matter Group, Cavendish Laboratory, 19 J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Gareth J Conduit
- Theory of Condensed Matter Group, Cavendish Laboratory, 19 J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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38
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Luo D, Clark BK. Backflow Transformations via Neural Networks for Quantum Many-Body Wave Functions. PHYSICAL REVIEW LETTERS 2019; 122:226401. [PMID: 31283262 DOI: 10.1103/physrevlett.122.226401] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/25/2018] [Revised: 01/12/2019] [Indexed: 06/09/2023]
Abstract
Obtaining an accurate ground state wave function is one of the great challenges in the quantum many-body problem. In this Letter, we propose a new class of wave functions, neural network backflow (NNB). The backflow approach, pioneered originally by Feynman and Cohen [Phys. Rev. 102, 1189 (1956)10.1103/PhysRev.102.1189], adds correlation to a mean-field ground state by transforming the single-particle orbitals in a configuration-dependent way. NNB uses a feed-forward neural network to learn the optimal transformation via variational Monte Carlo calculations. NNB directly dresses a mean-field state, can be systematically improved, and directly alters the sign structure of the wave function. It generalizes the standard backflow [L. F. Tocchio et al., Phys. Rev. B 78, 041101(R) (2008)10.1103/PhysRevB.78.041101], which we show how to explicitly represent as a NNB. We benchmark the NNB on Hubbard models at intermediate doping, finding that it significantly decreases the relative error, restores the symmetry of both observables and single-particle orbitals, and decreases the double-occupancy density. Finally, we illustrate interesting patterns in the weights and bias of the optimized neural network.
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Affiliation(s)
- Di Luo
- Institute for Condensed Matter Theory and Department of Physics, University of Illinois at Urbana-Champaign, Illinois 61801, USA
| | - Bryan K Clark
- Institute for Condensed Matter Theory and Department of Physics, University of Illinois at Urbana-Champaign, Illinois 61801, USA
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39
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Nakano K, Maezono R, Sorella S. All-Electron Quantum Monte Carlo with Jastrow Single Determinant Ansatz: Application to the Sodium Dimer. J Chem Theory Comput 2019; 15:4044-4055. [DOI: 10.1021/acs.jctc.9b00295] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Kousuke Nakano
- International School for Advanced Studies (SISSA), Via Bonomea 265, 34136, Trieste, Italy
- School of Information Science, Japan Advanced Institute of Science and Technology (JAIST), Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan
| | - Ryo Maezono
- School of Information Science, Japan Advanced Institute of Science and Technology (JAIST), Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan
- Computational Engineering Applications Unit, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - Sandro Sorella
- International School for Advanced Studies (SISSA), Via Bonomea 265, 34136, Trieste, Italy
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40
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Wang T, Zhou X, Wang F. Performance of the Diffusion Quantum Monte Carlo Method with a Single-Slater-Jastrow Trial Wavefunction Using Natural Orbitals and Density Functional Theory Orbitals on Atomization Energies of the Gaussian-2 Set. J Phys Chem A 2019; 123:3809-3817. [DOI: 10.1021/acs.jpca.9b01933] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Ting Wang
- Institute of Atomic and Molecular Physics, Key Laboratory of High Energy Density Physics and Technology, Ministry of Education, Sichuan University, Chengdu 610065, P. R. China
| | - Xiaojun Zhou
- Institute of Atomic and Molecular Physics, Key Laboratory of High Energy Density Physics and Technology, Ministry of Education, Sichuan University, Chengdu 610065, P. R. China
| | - Fan Wang
- Institute of Atomic and Molecular Physics, Key Laboratory of High Energy Density Physics and Technology, Ministry of Education, Sichuan University, Chengdu 610065, P. R. China
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41
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Ruggeri M, Moroni S, Holzmann M. Nonlinear Network Description for Many-Body Quantum Systems in Continuous Space. PHYSICAL REVIEW LETTERS 2018; 120:205302. [PMID: 29864292 DOI: 10.1103/physrevlett.120.205302] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2017] [Indexed: 06/08/2023]
Abstract
We show that the recently introduced iterative backflow wave function can be interpreted as a general neural network in continuum space with nonlinear functions in the hidden units. Using this wave function in variational Monte Carlo simulations of liquid ^{4}He in two and three dimensions, we typically find a tenfold increase in accuracy over currently used wave functions. Furthermore, subsequent stages of the iteration procedure define a set of increasingly good wave functions, each with its own variational energy and variance of the local energy: extrapolation to zero variance gives energies in close agreement with the exact values. For two dimensional ^{4}He, we also show that the iterative backflow wave function can describe both the liquid and the solid phase with the same functional form-a feature shared with the shadow wave function, but now joined by much higher accuracy. We also achieve significant progress for liquid ^{3}He in three dimensions, improving previous variational and fixed-node energies.
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Affiliation(s)
- Michele Ruggeri
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
| | - Saverio Moroni
- DEMOCRITOS National Simulation Center, Istituto Officina dei Materiali del CNR and SISSA, Via Bonomea 265, I-34136 Trieste, Italy
| | - Markus Holzmann
- Univ. Grenoble Alpes, CNRS, LPMMC, 3800 Grenoble, France
- Institut Laue Langevin, BP 156, F-38042 Grenoble Cedex 9, France
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42
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Kim J, Baczewski AT, Beaudet TD, Benali A, Bennett MC, Berrill MA, Blunt NS, Borda EJL, Casula M, Ceperley DM, Chiesa S, Clark BK, Clay RC, Delaney KT, Dewing M, Esler KP, Hao H, Heinonen O, Kent PRC, Krogel JT, Kylänpää I, Li YW, Lopez MG, Luo Y, Malone FD, Martin RM, Mathuriya A, McMinis J, Melton CA, Mitas L, Morales MA, Neuscamman E, Parker WD, Pineda Flores SD, Romero NA, Rubenstein BM, Shea JAR, Shin H, Shulenburger L, Tillack AF, Townsend JP, Tubman NM, Van Der Goetz B, Vincent JE, Yang DC, Yang Y, Zhang S, Zhao L. QMCPACK: an open source ab initio quantum Monte Carlo package for the electronic structure of atoms, molecules and solids. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:195901. [PMID: 29582782 DOI: 10.1088/1361-648x/aab9c3] [Citation(s) in RCA: 74] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
QMCPACK is an open source quantum Monte Carlo package for ab initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum Monte Carlo algorithms include variational, diffusion, and reptation Monte Carlo. QMCPACK uses Slater-Jastrow type trial wavefunctions in conjunction with a sophisticated optimizer capable of optimizing tens of thousands of parameters. The orbital space auxiliary-field quantum Monte Carlo method is also implemented, enabling cross validation between different highly accurate methods. The code is specifically optimized for calculations with large numbers of electrons on the latest high performance computing architectures, including multicore central processing unit and graphical processing unit systems. We detail the program's capabilities, outline its structure, and give examples of its use in current research calculations. The package is available at http://qmcpack.org.
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Affiliation(s)
- Jeongnim Kim
- Intel Corporation, Hillsboro, OR 987124, United States of America
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43
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Luo H, Alavi A. Combining the Transcorrelated Method with Full Configuration Interaction Quantum Monte Carlo: Application to the Homogeneous Electron Gas. J Chem Theory Comput 2018; 14:1403-1411. [DOI: 10.1021/acs.jctc.7b01257] [Citation(s) in RCA: 36] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Hongjun Luo
- Max-Planck-Institut for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - Ali Alavi
- Max-Planck-Institut for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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44
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Blunt NS, Neuscamman E. Charge-transfer excited states: Seeking a balanced and efficient wave function ansatz in variational Monte Carlo. J Chem Phys 2017; 147:194101. [DOI: 10.1063/1.4998197] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- N. S. Blunt
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Eric Neuscamman
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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45
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Neufeld VA, Thom AJW. A study of the dense uniform electron gas with high orders of coupled cluster. J Chem Phys 2017; 147:194105. [DOI: 10.1063/1.5003794] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Verena A. Neufeld
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Alex J. W. Thom
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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46
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Scott CJC, Thom AJW. Stochastic coupled cluster theory: Efficient sampling of the coupled cluster expansion. J Chem Phys 2017; 147:124105. [DOI: 10.1063/1.4991795] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
| | - Alex J. W. Thom
- Department of Chemistry, University of Cambridge, Cambridge, United Kingdom
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47
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Brito BGA, Hai GQ, Cândido L. A quantum Monte Carlo study of the structural and electronic properties of small cationic and neutral lithium clusters. J Chem Phys 2017; 146:174306. [DOI: 10.1063/1.4982726] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- B. G. A. Brito
- Departamento de Física, Instituto de Ciências Exatas e Naturais e Educação (ICENE), Universidade Federal do Triângulo Mineiro - UFTM, 38064-200 Uberaba, Minas Gerais, Brazil
| | - G.-Q. Hai
- Instituto de Física de São Carlos, Universidade de São Paulo, 13560-970 São Carlos, São Paulo, Brazil
| | - Ladir Cândido
- Instituto de Física, Universidade Federal de Goiás - UFG, 74001-970 Goiânia, Goiás, Brazil
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48
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Per MC, Cleland DM. Energy-based truncation of multi-determinant wavefunctions in quantum Monte Carlo. J Chem Phys 2017; 146:164101. [DOI: 10.1063/1.4981527] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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49
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Azadi S, Kühne TD. High-pressure hydrogen sulfide by diffusion quantum Monte Carlo. J Chem Phys 2017; 146:084503. [DOI: 10.1063/1.4976836] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Sam Azadi
- Department of Materials Science, Royal School of Mines, Thomas Young Center, London Centre for Nanotechnology, Imperial College London, London SW7 2AZ, United Kingdom
| | - Thomas D. Kühne
- Dynamics of Condensed Matter, Department of Chemistry, University of Paderborn, Warburger Strasse 100, D-33098 Paderborn, Germany and Paderborn Center for Parallel Computing and Institute for Lightweight Design with Hybrid Systems, University of Paderborn, Warburger Strasse 100, D-33098 Paderborn, Germany
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50
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Higino Damasceno J, Teixeira Rabelo JN, Cândido L. Electron Correlation Effects in All-Metal Aromatic Clusters: A Quantum Monte Carlo Study. Inorg Chem 2016; 55:7442-7. [DOI: 10.1021/acs.inorgchem.6b00683] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- J. Higino Damasceno
- Instituto de Ciências Exatas e Tecnológicas, Universidade Federal de Goiás/Regional Jataı́, Regional Jataí BR 364, Km
195, 75801-615 Jataí, Goiás Brazil
| | | | - Ladir Cândido
- Instituto
de Física, Universidade Federal de Goiás, 74690-900 Goiânia, Goiás Brazil
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