1
|
Šulka M, Šulková K, Jurečka P, Dubecký M. Dynamic and Nondynamic Electron Correlation Energy Decomposition Based on the Node of the Hartree-Fock Slater Determinant. J Chem Theory Comput 2023; 19:8147-8155. [PMID: 37942987 DOI: 10.1021/acs.jctc.3c00828] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2023]
Abstract
Distinguishing between dynamic and nondynamic electron correlation energy is a fundamental concept in quantum chemistry. It can be challenging to make a clear distinction between the two types of correlation energy or to determine their actual contributions in specific cases using wave function theory. This is because both single-reference and multireference methods cover both types of correlation energy to some extent. Fixed-node diffusion quantum Monte Carlo (FNDMC) accurately covers dynamic correlations, but it is limited in overall accuracy by the node of the trial wave function. We introduce a methodology for partitioning an exact electron correlation energy into its dynamic and nondynamic components. This is accomplished by restricting a ground-state solution from sharing its node with a spin-restricted Hartree-Fock Slater determinant. The FNDMC method is used as a tool to conveniently project out a lowest-energy state obeying such a boundary condition. The proposed approach provides an unambiguous and useful procedure for separating electron correlation energy, as demonstrated on multiple systems, including the He atom, bond breaking of H2, the parametric H2-H2 system, the Be-Ne atomic series with low- and high-spin states for C, N, and O atoms, and small molecules such as BH, HF, and CO at both equilibrium and elongated configurations, respectively.
Collapse
Affiliation(s)
- Martin Šulka
- Advanced Technologies Research Institute, Faculty of Materials Science and Technology in Trnava, Slovak University of Technology in Bratislava, Bottova 25, Trnava 917 24, Slovakia
| | - Katarína Šulková
- Advanced Technologies Research Institute, Faculty of Materials Science and Technology in Trnava, Slovak University of Technology in Bratislava, Bottova 25, Trnava 917 24, Slovakia
| | - Petr Jurečka
- Department of Physical Chemistry, Faculty of Science, Palacky University Olomouc, 17. listopadu 12, Olomouc 779 00, Czech Republic
| | - Matúš Dubecký
- Advanced Technologies Research Institute, Faculty of Materials Science and Technology in Trnava, Slovak University of Technology in Bratislava, Bottova 25, Trnava 917 24, Slovakia
- Department of Physics, Faculty of Science, University of Ostrava, 30. dubna 22, Ostrava 701 03, Czech Republic
| |
Collapse
|
2
|
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.
Collapse
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
| |
Collapse
|
3
|
Dubecký M, Minárik S, Karlický F. Benchmarking fundamental gap of Sc 2C(OH) 2 MXene by many-body methods. J Chem Phys 2023; 158:054703. [PMID: 36754808 DOI: 10.1063/5.0140315] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
Sc2C(OH)2 is a prototypical non-magnetic member of MXenes, a promising transition-metal-based 2D material family, with a direct bandgap. We provide here a benchmark of its fundamental gap Δ obtained from many-body GW and fixed-node diffusion Monte Carlo methods. Both approaches independently arrive at a similar value of Δ ∼ 1.3 eV, suggesting the validity of both methods. Such a bandgap makes Sc2C(OH)2 a 2D semiconductor suitable for optoelectronic applications. The absorbance spectra and the first exciton binding energy (0.63 eV), based on the Bethe-Salpeter equation, are presented as well. The reported results may serve to delineate experimental uncertainties and enable selection of reasonable approximations such as density functional theory functionals, for use in modeling of related MXenes.
Collapse
Affiliation(s)
- Matúš Dubecký
- Department of Physics, University of Ostrava, 30. dubna 22, 701 03 Ostrava, Czech Republic
| | - Stanislav Minárik
- ATRI, Slovak University of Technology in Bratislava, J. Bottu 25, 917 24 Trnava, Slovakia
| | - František Karlický
- Department of Physics, University of Ostrava, 30. dubna 22, 701 03 Ostrava, Czech Republic
| |
Collapse
|
4
|
Dubecký M, Karlický F, Minárik S, Mitas L. Fundamental gap of fluorographene by many-body GW and fixed-node diffusion Monte Carlo methods. J Chem Phys 2020; 153:184706. [DOI: 10.1063/5.0030952] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- 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
| | - František Karlický
- Department of Physics, Faculty of Science, University of Ostrava, 30. dubna 22, 701 03 Ostrava, Czech Republic
| | - Stanislav Minárik
- ATRI, Faculty of Materials Science and Technology in Trnava, Slovak University of Technology in Bratislava, J. Bottu 25, 917 24 Trnava, Slovakia
| | - Lubos Mitas
- Department of Physics and CHiPS, North Carolina State University, Raleigh, North Carolina 27695, USA
| |
Collapse
|
5
|
Hong I, Ahn J, Shin H, Bae H, Lee H, Benali A, Kwon Y. Competition between Hückel’s Rule and Jahn–Teller Distortion in Small Carbon Rings: A Quantum Monte Carlo Study. J Phys Chem A 2020; 124:3636-3640. [DOI: 10.1021/acs.jpca.0c02577] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Iuegyun Hong
- Department of Physics, Konkuk University, Seoul 05029, Korea
| | - Jeonghwan Ahn
- Department of Physics, Konkuk University, Seoul 05029, Korea
| | - Hyeondeok Shin
- Computational Science Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - Hyeonhu Bae
- Department of Physics, Konkuk University, Seoul 05029, Korea
| | - Hoonkyung Lee
- Department of Physics, Konkuk University, Seoul 05029, Korea
| | - Anouar Benali
- Computational Science Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - Yongkyung Kwon
- Department of Physics, Konkuk University, Seoul 05029, Korea
| |
Collapse
|
6
|
Ditte M, Dubecký M. Fractional Charge by Fixed-Node Diffusion Monte Carlo Method. PHYSICAL REVIEW LETTERS 2019; 123:156402. [PMID: 31702309 DOI: 10.1103/physrevlett.123.156402] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2019] [Indexed: 06/10/2023]
Abstract
Fixed-node diffusion Monte Carlo (FNDMC) method is a stochastic quantum many-body approach that has a great potential in electronic structure theory. We examine how FNDMC total energy E(N) satisfies exact constraints, linearity and derivative discontinuity, versus fractional electron number N, if combined with mean-field trial wave functions that miss such features. H and Cl atoms with fractional charge reveal that FNDMC method is well able to restore the piecewise linearity of E(N). The method uses ensemble and projector ingredients to achieve the correct charge localization. A water-solvated Cl^{-} complex illustrates superior performance of FNDMC method for charged noncovalent systems.
Collapse
Affiliation(s)
- Matej Ditte
- Department of Physics, University of Ostrava, 30. dubna 22, 701 03 Ostrava, Czech Republic
| | - Matúš Dubecký
- Department of Physics, University of Ostrava, 30. dubna 22, 701 03 Ostrava, Czech Republic
- ATRI, Slovak University of Technology, J. Bottu 25, 917 24 Trnava, Slovakia
| |
Collapse
|
7
|
Pineda Flores SD, Neuscamman E. Excited State Specific Multi-Slater Jastrow Wave Functions. J Phys Chem A 2019; 123:1487-1497. [DOI: 10.1021/acs.jpca.8b10671] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- Sergio D. Pineda Flores
- Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Eric Neuscamman
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| |
Collapse
|
8
|
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.
Collapse
Affiliation(s)
- Jeongnim Kim
- Intel Corporation, Hillsboro, OR 987124, United States of America
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
Collapse
|
9
|
Dubecký M. Noncovalent Interactions by Fixed-Node Diffusion Monte Carlo: Convergence of Nodes and Energy Differences vs Gaussian Basis-Set Size. J Chem Theory Comput 2017; 13:3626-3635. [DOI: 10.1021/acs.jctc.7b00537] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- 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, Slovak University of Technology, Paulínska
16, 917 24 Trnava, Slovakia
| |
Collapse
|
10
|
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
|
11
|
Dubecký M. Bias cancellation in one-determinant fixed-node diffusion Monte Carlo: Insights from fermionic occupation numbers. Phys Rev E 2017; 95:033308. [PMID: 28415179 DOI: 10.1103/physreve.95.033308] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2016] [Indexed: 06/07/2023]
Abstract
The accuracy of the fixed-node diffusion Monte Carlo (FNDMC) depends on the node location of the supplied trial state Ψ_{T}. The practical FNDMC approaches available for large systems rely on compact yet effective Ψ_{T}, most often containing an explicitly correlated single Slater determinant (SD). However, SD nodes may be better suited to one system than to another, which may possibly lead to inaccurate FNDMC energy differences. It remains a challenge how to estimate nonequivalence or appropriateness of SDs. Here we use the differences of a measure based on the Euclidean distance between the natural orbital occupation number (NOON) vector of the SD and the exact solution in the NOON vector space, which can be viewed as a measure of SD nonequivalence and as a qualitative measure of the expected degree of nondynamic-correlation-related bias in FNDMC energy differences. This is explored on a set of small noncovalent complexes and covalent bond breaking of Si_{2} vs N_{2}. It turns out that NOON-based measures well reflect the magnitude and sign of the bias present in the data available, thus providing insights into the nature of bias cancellation in SD FNDMC energy differences.
Collapse
Affiliation(s)
- Matúš Dubecký
- Department of Physics, Faculty of Science, University of Ostrava, 30. dubna 22, 701 03 Ostrava, Czech Republic and ATRI, Faculty of Materials Science and Technology, Slovak University of Technology, Paulínska 16, 917 24 Trnava, Slovakia
| |
Collapse
|
12
|
Powell AD, Dawes R. Calculating potential energy curves with fixed-node diffusion Monte Carlo: CO and N2. J Chem Phys 2016; 145:224308. [DOI: 10.1063/1.4971378] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Andrew D. Powell
- Department of Chemistry, Missouri University of Science and Technology, Rolla, Missouri 65409, USA
| | - Richard Dawes
- Department of Chemistry, Missouri University of Science and Technology, Rolla, Missouri 65409, USA
| |
Collapse
|
13
|
Williams KT, Wagner LK. Using local operator fluctuations to identify wave function improvements. Phys Rev E 2016; 94:013303. [PMID: 27575232 DOI: 10.1103/physreve.94.013303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2016] [Indexed: 06/06/2023]
Abstract
A method is developed that allows analysis of quantum Monte Carlo simulations to identify errors in trial wave functions. The purpose of this method is to allow for the systematic improvement of variational wave functions by identifying degrees of freedom that are not well described by an initial trial state. We provide proof of concept implementations of this method by identifying the need for a Jastrow correlation factor and implementing a selected multideterminant wave function algorithm for small dimers that systematically decreases the variational energy. Selection of the two-particle excitations is done using the quantum Monte Carlo method within the presence of a Jastrow correlation factor and without the need to explicitly construct the determinants. We also show how this technique can be used to design compact wave functions for transition metal systems. This method may provide a route to analyze and systematically improve descriptions of complex quantum systems in a scalable way.
Collapse
Affiliation(s)
- Kiel T Williams
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Lucas K Wagner
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| |
Collapse
|
14
|
Scemama A, Applencourt T, Giner E, Caffarel M. Quantum Monte Carlo with very large multideterminant wavefunctions. J Comput Chem 2016; 37:1866-75. [DOI: 10.1002/jcc.24382] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2016] [Revised: 03/16/2016] [Accepted: 03/16/2016] [Indexed: 11/11/2022]
Affiliation(s)
- Anthony Scemama
- Lab. Chimie Et Physique Quantiques; CNRS-Université De Toulouse; France
| | | | - Emmanuel Giner
- Dipartimento Di Scienze Chimiche E Farmaceutiche; Université Degli Studi Di Ferrara; Ferrara Italy
| | - Michel Caffarel
- Lab. Chimie Et Physique Quantiques; CNRS-Université De Toulouse; France
| |
Collapse
|
15
|
Affiliation(s)
- Matúš Dubecký
- Regional
Centre of Advanced Technologies and Materials, Department of Physical
Chemistry, Faculty of Science, Palacký University Olomouc, tř.
17 listopadu 12, 771 46 Olomouc, Czech Republic
| | - Lubos Mitas
- Department
of Physics and CHiPS, North Carolina State University, Raleigh, North Carolina 27695, United States
| | - Petr Jurečka
- Regional
Centre of Advanced Technologies and Materials, Department of Physical
Chemistry, Faculty of Science, Palacký University Olomouc, tř.
17 listopadu 12, 771 46 Olomouc, Czech Republic
| |
Collapse
|
16
|
McMinis J, Morales MA, Ceperley DM, Kim J. The transition to the metallic state in low density hydrogen. J Chem Phys 2015; 143:194703. [DOI: 10.1063/1.4935808] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|