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Ludovicy J, Dahl R, Lüchow A. Toward Compact Selected Configuration Interaction Wave Functions with Quantum Monte Carlo─A Case Study of C 2. J Chem Theory Comput 2023; 19:2792-2803. [PMID: 37130194 DOI: 10.1021/acs.jctc.2c01229] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
The 1Σg+ ground state of C2 is investigated using truncated CIPSI-Jastrow CSF wave functions with Hartree-Fock orbitals within the framework of variational and diffusion quantum Monte Carlo. The truncation is performed based on the absolute value of the CI coefficients, and the Jastrow, molecular orbitals, and CI parameters are either partially or fully reoptimized with respect to the variational energy. Excellent absolute as well as bond dissociation energies are obtained at DMC level with very compact, fully optimized wave functions. By studying the expansions in more detail, we observe a change in the CI picture when reoptimizing the antisymmetric part of the CIPSI-Jastrow wave functions. Furthermore, we demonstrate that a decrease in the VMC energy as well as an improvement of the nodal surface quality can be achieved─with the same expansion size─if the CSFs are selected in the presence of a Jastrow correlation function, laying the foundation for a Jastrow selected CI scheme with quantum Monte Carlo.
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Affiliation(s)
- Jil Ludovicy
- Institute of Physical Chemistry, RWTH Aachen University, Landoltweg 2, 52074 Aachen, Germany
| | - Robin Dahl
- Institute of Physical Chemistry, RWTH Aachen University, Landoltweg 2, 52074 Aachen, Germany
| | - Arne Lüchow
- Institute of Physical Chemistry, RWTH Aachen University, Landoltweg 2, 52074 Aachen, Germany
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2
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Calcavecchia F, Holzmann M. Fermion sign problem in imaginary-time projection continuum quantum Monte Carlo with local interaction. Phys Rev E 2016; 93:043321. [PMID: 27176442 DOI: 10.1103/physreve.93.043321] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2016] [Indexed: 06/05/2023]
Abstract
We use the shadow wave function formalism as a convenient model to study the fermion sign problem affecting all projector quantum Monte Carlo methods in continuum space. We demonstrate that the efficiency of imaginary-time projection algorithms decays exponentially with increasing number of particles and/or imaginary-time propagation. Moreover, we derive an analytical expression that connects the localization of the system with the magnitude of the sign problem, illustrating this behavior through numerical results. Finally, we discuss the computational complexity of the fermion sign problem and methods for alleviating its severity.
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Affiliation(s)
- Francesco Calcavecchia
- LPMMC, UMR 5493 of CNRS, Université Grenoble Alpes, 38042 Grenoble, France; Institute of Physics, Johannes Gutenberg University, Staudingerweg 7, D-55128 Mainz, Germany; and Graduate School of Excellence Materials Science in Mainz, Staudingerweg 9, D-55128 Mainz, Germany
| | - Markus Holzmann
- LPMMC, UMR 5493 of CNRS, Université Grenoble Alpes, 38042 Grenoble, France and Institut Laue Langevin, BP 156, F-38042 Grenoble Cedex 9, France
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3
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Sorella S, Devaux N, Dagrada M, Mazzola G, Casula M. Geminal embedding scheme for optimal atomic basis set construction in correlated calculations. J Chem Phys 2015; 143:244112. [DOI: 10.1063/1.4938089] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- S. Sorella
- International School for Advanced Studies (SISSA), Via Beirut 2-4, 34014 Trieste, Italy and INFM Democritos National Simulation Center, Trieste, Italy
| | - N. Devaux
- Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Université Pierre et Marie Curie, Case 115, 4 Place Jussieu, 75252 Paris Cedex 05, France
| | - M. Dagrada
- Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Université Pierre et Marie Curie, Case 115, 4 Place Jussieu, 75252 Paris Cedex 05, France
| | - G. Mazzola
- Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland
| | - M. Casula
- CNRS and Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Université Pierre et Marie Curie, Case 115, 4 Place Jussieu, 75252 Paris Cedex 05, France
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Dagrada M, Casula M, Saitta AM, Sorella S, Mauri F. Quantum Monte Carlo Study of the Protonated Water Dimer. J Chem Theory Comput 2014; 10:1980-93. [DOI: 10.1021/ct401077x] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Mario Dagrada
- Institut
de Minéralogie, de Physique des Matériaux, et de Cosmochimie
(IMPMC), Sorbonne Universités - UPMC Paris 06, UMR CNRS 7590, Muséum
National d’Histoire Naturelle, IRD UMR 206, 4 Place Jussieu, 75005 Paris, France
| | - Michele Casula
- Institut
de Minéralogie, de Physique des Matériaux, et de Cosmochimie
(IMPMC), Sorbonne Universités - UPMC Paris 06, UMR CNRS 7590, Muséum
National d’Histoire Naturelle, IRD UMR 206, 4 Place Jussieu, 75005 Paris, France
| | - Antonino M. Saitta
- Institut
de Minéralogie, de Physique des Matériaux, et de Cosmochimie
(IMPMC), Sorbonne Universités - UPMC Paris 06, UMR CNRS 7590, Muséum
National d’Histoire Naturelle, IRD UMR 206, 4 Place Jussieu, 75005 Paris, France
| | - Sandro Sorella
- International School for Advanced Studies (SISSA) Via Beirut 2,4 34014 Trieste, Italy and INFM Democritos National Simulation Center, Trieste, Italy
| | - Francesco Mauri
- Institut
de Minéralogie, de Physique des Matériaux, et de Cosmochimie
(IMPMC), Sorbonne Universités - UPMC Paris 06, UMR CNRS 7590, Muséum
National d’Histoire Naturelle, IRD UMR 206, 4 Place Jussieu, 75005 Paris, France
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Clark BK, Morales MA, McMinis J, Kim J, Scuseria GE. Computing the energy of a water molecule using multideterminants: A simple, efficient algorithm. J Chem Phys 2011; 135:244105. [DOI: 10.1063/1.3665391] [Citation(s) in RCA: 59] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
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6
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Tubman NM, DuBois JL, Hood RQ, Alder BJ. Prospects for release-node quantum Monte Carlo. J Chem Phys 2011; 135:184109. [DOI: 10.1063/1.3659143] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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7
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Lüchow A. Quantum Monte Carlo methods. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2011. [DOI: 10.1002/wcms.40] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
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Berner R, Lüchow A. Isomerization of Bicyclo[1.1.0]butane by Means of the Diffusion Quantum Monte Carlo Method. J Phys Chem A 2010; 114:13222-7. [DOI: 10.1021/jp108605g] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Raphael Berner
- Institute of Physical Chemistry, RWTH Aachen University, 52056 Aachen, Germany
| | - Arne Lüchow
- Institute of Physical Chemistry, RWTH Aachen University, 52056 Aachen, Germany
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9
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Corongiu G. Multiple Bonds and Excited States from the Hartree−Fock−Heitler−London Method. J Phys Chem A 2007; 111:13611-22. [DOI: 10.1021/jp0748056] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
Affiliation(s)
- Giorgina Corongiu
- Dipartimento di Scienze Chimiche ed Ambientali, Università dell'Insubria, Via Lucini 3, I-22100 Como, Italy
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Gurtubay IG, Needs RJ. Dissociation energy of the water dimer from quantum Monte Carlo calculations. J Chem Phys 2007; 127:124306. [PMID: 17902902 DOI: 10.1063/1.2770711] [Citation(s) in RCA: 52] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We report a study of the electronic dissociation energy of the water dimer using quantum Monte Carlo techniques. We have performed variational quantum Monte Carlo and diffusion quantum Monte Carlo (DMC) calculations of the electronic ground state of the water monomer and dimer using all-electron and pseudopotential approaches. We have used Slater-Jastrow trial wave functions with B3LYP type single-particle orbitals, into which we have incorporated backflow correlations. When backflow correlations are introduced, the total energy of the water monomer decreases by about 4-5 mhartree, yielding a DMC energy of -76.428 30(5) hartree, which is only 10 mhartree above the experimental value. In our pseudopotential DMC calculations, we have compared the total energies of the water monomer and dimer obtained using the locality approximation with those from the variational scheme recently proposed by Casula [Phys. Rev. B 74, 161102(R) (2006)]. The time step errors in the Casula scheme are larger, and the extrapolation of the energy to zero time step always lies above the result obtained with the locality approximation. However, the errors cancel when energy differences are taken, yielding electronic dissociation energies within error bars of each other. The dissociation energies obtained in our various all-electron and pseudopotential calculations range between 5.03(7) and 5.47(9) kcalmol and are in good agreement with experiment. Our calculations give monomer dipole moments which range between 1.897(2) and 1.909(4) D and dimer dipole moments which range between 2.628(6) and 2.672(5) D.
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Affiliation(s)
- I G Gurtubay
- Theory of Condensed Matter Group, Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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Brown MD, Trail JR, Ríos PL, Needs RJ. Energies of the first row atoms from quantum Monte Carlo. J Chem Phys 2007; 126:224110. [PMID: 17581047 DOI: 10.1063/1.2743972] [Citation(s) in RCA: 72] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
All-electron variational and diffusion quantum Monte Carlo calculations of the ground state energies of the first row atoms (from Li to Ne) are reported. The authors use trial wave functions of four types: single-determinant Slater-Jastrow wave functions, multideterminant Slater-Jastrow wave functions, single-determinant Slater-Jastrow wave functions with backflow transformations, and multideterminant Slater-Jastrow wave functions with backflow transformations. At the diffusion quantum Monte Carlo level and using their multideterminant Slater-Jastrow wave functions with backflow transformations, they recover 99% or more of the correlation energies for Li, Be, B, C, N, and Ne, 97% for O, and 98% for F.
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Affiliation(s)
- M D Brown
- Theory of Condensed Matter Group, Cavendish Laboratory, J.J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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Lüchow A, Petz R, Scott TC. Direct optimization of nodal hypersurfaces in approximate wave functions. J Chem Phys 2007; 126:144110. [PMID: 17444704 DOI: 10.1063/1.2716640] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The fixed-node variant of the diffusion quantum Monte Carlo method (FN-DMC) is capable of obtaining the exact eigenvalues (albeit numerically with statistical error) of a many-electron Hamilton operator, provided that the nodal hypersurface of the exact wave function is given. The use of nodes of a trial wave function leads to the node location error. The authors have developed local criteria to assess the accuracy of the nodes based on the distances of the nodal hypersurfaces of PsiT, TPsiT, and HPsiT which coincide for the exact wave function. These criteria are used to develop direct optimization methods for the nodal hypersurface. The optimization of the nodes is demonstrated for simple wave functions of the Be atom and the C2 molecule and verified with FN-DMC calculations.
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Affiliation(s)
- Arne Lüchow
- Institut für Physikalische Chemie, RWTH Aachen University, 52056 Aachen, Germany.
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Benedek NA, Snook IK, Towler MD, Needs RJ. Quantum Monte Carlo calculations of the dissociation energy of the water dimer. J Chem Phys 2006; 125:104302. [PMID: 16999521 DOI: 10.1063/1.2338032] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We report diffusion quantum Monte Carlo (DMC) calculations of the equilibrium dissociation energy D(e) of the water dimer. The dissociation energy measured experimentally, D(0), can be estimated from D(e) by adding a correction for vibrational effects. Using the measured dissociation energy and the modern value of the vibrational energy Mas et al., [J. Chem. Phys. 113, 6687 (2000)] leads to D(e)=5.00+/-0.7 kcal mol(-1), although the result Curtiss et al., [J. Chem. Phys. 71, 2703 (1979)] D(e)=5.44+/-0.7 kcal mol(-1), which uses an earlier estimate of the vibrational energy, has been widely quoted. High-level coupled cluster calculations Klopper et al., [Phys. Chem. Chem. Phys. 2, 2227 (2000)] have yielded D(e)=5.02+/-0.05 kcal mol(-1). In an attempt to shed new light on this old problem, we have performed all-electron DMC calculations on the water monomer and dimer using Slater-Jastrow wave functions with both Hartree-Fock approximation (HF) and B3LYP density functional theory single-particle orbitals. We obtain equilibrium dissociation energies for the dimer of 5.02+/-0.18 kcal mol(-1) (HF orbitals) and 5.21+/-0.18 kcal mol(-1) (B3LYP orbitals), in good agreement with the coupled cluster results.
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Affiliation(s)
- N A Benedek
- Department of Applied Physics, RMIT University, G.P.O. Box 2476V, Melbourne 3001, Australia
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Bande A, Lüchow A, Della Sala F, Görling A. Rydberg states with quantum Monte Carlo. J Chem Phys 2006; 124:114114. [PMID: 16555881 DOI: 10.1063/1.2180773] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Calculations on Rydberg states are performed using quantum Monte Carlo methods. Excitation energies and singlet-triplet splittings are calculated for two model systems, the carbon atom (3P and 1P) and carbon monoxide ((1Sigma and 3Sigma). Kohn-Sham wave functions constructed from open-shell localized Hartree-Fock orbitals are used as trial and guide functions. The fixed-node diffusion quantum Monte Carlo (FN-DMC) method depends strongly on the wave function's nodal hypersurface. Nodal artefacts are investigated for the ground state of the carbon atom. Their effect on the FN-DMC results can be analyzed quantitatively. FN-DMC leads to accurate excitation energies but to less accurate singlet-triplet splittings. Variational Monte Carlo calculations are able to reproduce the experimental results for both the excitation energies and the singlet-triplet splittings.
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Affiliation(s)
- Annika Bande
- Institut für Physikalische Chemie, RWTH Aachen University, Landoltweg 2, 52056 Aachen, Germany
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15
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Bressanini D, Morosi G, Tarasco S. An investigation of nodal structures and the construction of trial wave functions. J Chem Phys 2005; 123:204109. [PMID: 16351242 DOI: 10.1063/1.2128672] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The factors influencing the quality of the nodal surfaces, namely, the atomic basis set, the single-particle orbitals, and the configurations included in the wave-function expansion, are examined for a few atomic and molecular systems. The following empirical rules are found: the atomic basis set must be fairly large, complete active space and natural orbitals are usually better than Hartree-Fock orbitals, multiconfiguration expansions perform better than single-determinant wave functions, but only few configurations are effective and their choice is suggested by symmetry considerations, while too long determinantal expansions spoil the nodal surfaces. These rules allow us to reduce the nodal error and to compute the best fixed node-diffusion Monte Carlo energies for a series of dimers of first-row atoms.
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Affiliation(s)
- Dario Bressanini
- Dipartimento di Scienze Chimiche ed Ambientali, Universita' dell'Insubria, Sede di Como, via Lucini 3, 22100 Como, Italy.
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Bytautas L, Ruedenberg K. Correlation energy extrapolation by intrinsic scaling. IV. Accurate binding energies of the homonuclear diatomic molecules carbon, nitrogen, oxygen, and fluorine. J Chem Phys 2005; 122:154110. [PMID: 15945628 DOI: 10.1063/1.1869493] [Citation(s) in RCA: 93] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The method of extrapolation by intrinsic scaling, recently introduced to obtain correlation energies, is generalized to multiconfigurational reference functions and used to calculate the binding energies of the diatomic molecules C2, N2, O2, and F2. First, accurate approximations to the full configuration interaction energies of the individual molecules and their constituent atoms are determined, employing Dunning's correlation consistent double-, triple- and quadruple zeta basis sets. Then, these energies are extrapolated to their full basis set limits. Chemical accuracy is attained for the binding energies of all molecules.
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Affiliation(s)
- Laimutis Bytautas
- Department of Chemistry and Ames Laboratory USDOE, Iowa State University, Ames, Iowa 50011, USA
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Datta S, Alexander SA, Coldwell RL. Properties of selected diatomics using variational Monte Carlo methods. J Chem Phys 2004; 120:3642-7. [PMID: 15268526 DOI: 10.1063/1.1643351] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Using variational Monte Carlo and highly accurate trial wave functions optimized by Filippi and Umrigar, we calculate a number of molecular properties for the ground state of Li2, Be2, B2, C2, N2, O2, and F2. This is the first time that many of these properties have been computed.
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Affiliation(s)
- S Datta
- SN Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Calcutta 700 098, India
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Lu SI. Performance of Ornstein–Uhlenbeck diffusion quantum Monte Carlo for first-row diatomic dissociation energies and dipole moments. J Chem Phys 2003. [DOI: 10.1063/1.1558472] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Mella M, Casalegno M, Morosi G. Positron and positronium chemistry by quantum Monte Carlo. VI. The ground state of LiPs, NaPs, e+Be, and e+Mg. J Chem Phys 2002. [DOI: 10.1063/1.1486447] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Schautz F, Fahy S. Optimization of configuration interaction coefficients in multideterminant Jastrow–Slater wave functions. J Chem Phys 2002. [DOI: 10.1063/1.1447883] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Manten S, Lüchow A. On the accuracy of the fixed-node diffusion quantum Monte Carlo method. J Chem Phys 2001. [DOI: 10.1063/1.1394757] [Citation(s) in RCA: 67] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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