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Fanta R, Dubecký M. Noncovalent Interactions by the Quantum Monte Carlo Method: Strong Influence of Isotropic Jastrow Cutoff Radii. J Chem Theory Comput 2021; 17:4242-4249. [PMID: 34169721 DOI: 10.1021/acs.jctc.1c00467] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present a paradigmatic example of a strong effect of Jastrow cutoff radii setup on the accuracy of noncovalent interaction energy differences within one-determinant Slater-Jastrow fixed-node diffusion Monte Carlo (1FNDMC) simulations using isotropic Jastrow terms and effective-core potentials. Analysis of total energies, absolute and relative errors, and local energy variance of energy differences vs the reference results suggests a simple procedure to marginalize the related biases. The presented data showcase improvements in dispersion-bounded systems within such a 1FNDMC method.
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Affiliation(s)
- Roman Fanta
- Department of Physics, Faculty of Science, University of Ostrava, 30. dubna 22, 701 03 Ostrava, Czech Republic
| | - Matúš Dubecký
- Department of Physics, Faculty of Science, University of Ostrava, 30. dubna 22, 701 03 Ostrava, Czech Republic.,ATRI, Faculty of Materials Science and Technology in Trnava, Slovak University of Technology in Bratislava, J. Bottu 25, 917 24 Trnava, Slovakia
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2
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Nasiri S, Zahedi M. Quantum Monte Carlo simulations using Slater-Jastrow-backflow wave function. COMPUT THEOR CHEM 2020. [DOI: 10.1016/j.comptc.2020.112978] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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3
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Wang G, Annaberdiyev A, Mitas L. Binding and excitations in SixHy molecular systems using quantum Monte Carlo. J Chem Phys 2020; 153:144303. [DOI: 10.1063/5.0022814] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Affiliation(s)
- Guangming Wang
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695-8202, USA
| | - Abdulgani Annaberdiyev
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695-8202, USA
| | - Lubos Mitas
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695-8202, USA
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4
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Influence of pseudopotentials on excitation energies from selected configuration interaction and diffusion Monte Carlo. RESULTS IN CHEMISTRY 2019. [DOI: 10.1016/j.rechem.2019.100002] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
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5
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Scemama A, Benali A, Jacquemin D, Caffarel M, Loos PF. Excitation energies from diffusion Monte Carlo using selected configuration interaction nodes. J Chem Phys 2018; 149:034108. [DOI: 10.1063/1.5041327] [Citation(s) in RCA: 44] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Anthony Scemama
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Anouar Benali
- Computational Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Denis Jacquemin
- Laboratoire CEISAM—UMR CNRS 6230, Université de Nantes, 2 Rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France
| | - Michel Caffarel
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France
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6
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Gasperich K, Deible M, Jordan KD. H4: A model system for assessing the performance of diffusion Monte Carlo calculations using a single Slater determinant trial function. J Chem Phys 2017; 147:074106. [DOI: 10.1063/1.4986216] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Kevin Gasperich
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Michael Deible
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Kenneth D. Jordan
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
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7
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A benchmark study of Li 2 + , Li 2 − , LiH + and LiH − : Quantum Monte-Carlo and coupled-cluster computations. COMPUT THEOR CHEM 2017. [DOI: 10.1016/j.comptc.2017.05.015] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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8
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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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9
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Loos P, Gill PMW. The uniform electron gas. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2016. [DOI: 10.1002/wcms.1257] [Citation(s) in RCA: 68] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Affiliation(s)
| | - Peter M. W. Gill
- Research School of Chemistry Australian National University Canberra Australia
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10
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Deible MJ, Kessler M, Gasperich KE, Jordan KD. Quantum Monte Carlo calculation of the binding energy of the beryllium dimer. J Chem Phys 2015; 143:084116. [PMID: 26328827 DOI: 10.1063/1.4929351] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The accurate calculation of the binding energy of the beryllium dimer is a challenging theoretical problem. In this study, the binding energy of Be2 is calculated using the diffusion Monte Carlo (DMC) method, using single Slater determinant and multiconfigurational trial functions. DMC calculations using single-determinant trial wave functions of orbitals obtained from density functional theory calculations overestimate the binding energy, while DMC calculations using Hartree-Fock or CAS(4,8), complete active space trial functions significantly underestimate the binding energy. In order to obtain an accurate value of the binding energy of Be2 from DMC calculations, it is necessary to employ trial functions that include excitations outside the valence space. Our best estimate DMC result for the binding energy of Be2, obtained by using configuration interaction trial functions and extrapolating in the threshold for the configurations retained in the trial function, is 908 cm(-1), only slightly below the 935 cm(-1) value derived from experiment.
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Affiliation(s)
- Michael J Deible
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Melody Kessler
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Kevin E Gasperich
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Kenneth D Jordan
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
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11
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12
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Loos PF, Bressanini D. Nodal surfaces and interdimensional degeneracies. J Chem Phys 2015; 142:214112. [DOI: 10.1063/1.4922159] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Pierre-François Loos
- Research School of Chemistry, Australian National University, Canberra ACT 2601, Australia
| | - Dario Bressanini
- Dipartimento di Scienza e Alta Tecnologia, Università dell’Insubria, Via Lucini 3, I-22100 Como, Italy
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13
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Takeda N, Hatano Y, Yamamoto S, Tatewaki H. Counting nodal surfaces in molecular orbitals: Elimination of artificial nodes. COMPUT THEOR CHEM 2014. [DOI: 10.1016/j.comptc.2014.06.021] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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14
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Affiliation(s)
- Brian M. Austin
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California 94720, United States
| | - Dmitry Yu. Zubarev
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California 94720, United States
| | - William A. Lester
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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15
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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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16
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Fracchia F, Bressanini D, Morosi G. Quantum Monte Carlo calculations of the dimerization energy of borane. J Chem Phys 2011; 135:094503. [DOI: 10.1063/1.3629778] [Citation(s) in RCA: 7] [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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17
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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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18
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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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19
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Abstract
Abstract
The diffusion quantum Monte Carlo method (DMC) is capable of calculating accurately the electronic energy for molecules and molecular aggregates. An overview is given on recent developments for the optimization of the guide function that determines the accuracy of the method. Furthermore, the versatility of DMC is shown with applications to Rydberg states, transition metal compounds, and weakly interacting systems.
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20
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Bajdich M, Kolorenč J, Mitas L, Reynolds P. Pairing in Cold Atoms and other Applications for Quantum Monte Carlo methods. ACTA ACUST UNITED AC 2010. [DOI: 10.1016/j.phpro.2010.01.199] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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21
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Nemec N, Towler MD, Needs RJ. Benchmark all-electron ab initio quantum Monte Carlo calculations for small molecules. J Chem Phys 2010; 132:034111. [DOI: 10.1063/1.3288054] [Citation(s) in RCA: 57] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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22
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Bressanini D, Morosi G. On the nodal structure of single-particle approximation based atomic wave functions. J Chem Phys 2008; 129:054103. [DOI: 10.1063/1.2963501] [Citation(s) in RCA: 18] [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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23
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Domin D, Braïda B, Lester Jr. WA. Breathing Orbital Valence Bond Method in Diffusion Monte Carlo: C−H Bond Dissociation of Acetylene. J Phys Chem A 2008; 112:8964-9. [DOI: 10.1021/jp8020062] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Dominik Domin
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California 94720-1460, UPMC Université Paris 06, UMR 7616, Laboratoire de Chimie Théorique, Case courrier 137 4 place Jussieu, 75005, Paris, France, CNRS Centre National de la Recherche Scientifique, UMR 7616, 75252 Paris, France, and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720
| | - Benoît Braïda
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California 94720-1460, UPMC Université Paris 06, UMR 7616, Laboratoire de Chimie Théorique, Case courrier 137 4 place Jussieu, 75005, Paris, France, CNRS Centre National de la Recherche Scientifique, UMR 7616, 75252 Paris, France, and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720
| | - William A. Lester Jr.
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California 94720-1460, UPMC Université Paris 06, UMR 7616, Laboratoire de Chimie Théorique, Case courrier 137 4 place Jussieu, 75005, Paris, France, CNRS Centre National de la Recherche Scientifique, UMR 7616, 75252 Paris, France, and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720
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24
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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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25
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López Ríos P, Ma A, Drummond ND, Towler MD, Needs RJ. Inhomogeneous backflow transformations in quantum Monte Carlo calculations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:066701. [PMID: 17280171 DOI: 10.1103/physreve.74.066701] [Citation(s) in RCA: 105] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2006] [Indexed: 05/13/2023]
Abstract
An inhomogeneous backflow transformation for many-particle wave functions is presented and applied to electrons in atoms, molecules, and solids. We report variational and diffusion quantum Monte Carlo (VMC and DMC) energies for various systems and study the computational cost of using backflow wave functions. We find that inhomogeneous backflow transformations can provide a substantial increase in the amount of correlation energy retrieved within VMC and DMC calculations. The backflow transformations significantly improve the wave functions and their nodal surfaces.
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Affiliation(s)
- P López Ríos
- Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE, UK
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26
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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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Bajdich M, Mitas L, Drobný G, Wagner LK, Schmidt KE. Pfaffian pairing wave functions in electronic-structure quantum Monte Carlo simulations. PHYSICAL REVIEW LETTERS 2006; 96:130201. [PMID: 16711968 DOI: 10.1103/physrevlett.96.130201] [Citation(s) in RCA: 55] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2005] [Indexed: 05/09/2023]
Abstract
We investigate the accuracy of trial wave functions for quantum Monte Carlo based on Pfaffian functional form with singlet and triplet pairing. Using a set of first row atoms and molecules we find that these wave functions provide very consistent and systematic behavior in recovering the correlation energies on the level of 95%. In order to get beyond this limit we explore the possibilities of multi-Pfaffian pairing wave functions. We show that a small number of Pfaffians recovers another large fraction of the missing correlation energy comparable to the larger-scale configuration interaction wave functions. We also find that Pfaffians lead to substantial improvements in fermion nodes when compared to Hartree-Fock wave functions.
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Affiliation(s)
- M Bajdich
- Center for High Performance Simulation and Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
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