1
|
Li X, Huang JC, Zhang GZ, Li HE, Shen ZP, Zhao C, Li J, Hu HS. Improved optimization for the neural-network quantum states and tests on the chromium dimer. J Chem Phys 2024; 160:234102. [PMID: 38884396 DOI: 10.1063/5.0214150] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2024] [Accepted: 05/30/2024] [Indexed: 06/18/2024] Open
Abstract
The advent of Neural-network Quantum States (NQS) has significantly advanced wave function ansatz research, sparking a resurgence in orbital space variational Monte Carlo (VMC) exploration. This work introduces three algorithmic enhancements to reduce computational demands of VMC optimization using NQS: an adaptive learning rate algorithm, constrained optimization, and block optimization. We evaluate the refined algorithm on complex multireference bond stretches of H2O and N2 within the cc-pVDZ basis set and calculate the ground-state energy of the strongly correlated chromium dimer (Cr2) in the Ahlrichs SV basis set. Our results achieve superior accuracy compared to coupled cluster theory at a relatively modest CPU cost. This work demonstrates how to enhance optimization efficiency and robustness using these strategies, opening a new path to optimize large-scale restricted Boltzmann machine-based NQS more effectively and marking a substantial advancement in NQS's practical quantum chemistry applications.
Collapse
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
| | - Zhu-Ping Shen
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Chen Zhao
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Jun Li
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
- Department of Chemistry and Guangdong Provincial Key Laboratory of Catalytic Chemistry, Southern University of Science and Technology, Shenzhen 518055, China
- Fundamental Science Center of Rare Earths, Ganjiang Innovation Academy, Chinese Academy of Sciences, Ganzhou 341000, 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
| |
Collapse
|
2
|
Rask AE, Li L, Zimmerman PM. Kohn-Sham Density in a Slater Orbital Basis Set. J Phys Chem A 2024; 128:3194-3204. [PMID: 38602291 DOI: 10.1021/acs.jpca.3c08303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/12/2024]
Abstract
Finite, atom-centered Slater basis sets are used to determine approximate Kohn-Sham molecular orbitals. This is achieved by minimizing the kinetic energy plus the sum-squared difference between the Kohn-Sham density and the full configuration interaction density. As a result of the finite basis, a weight factor is introduced to balance the two minimization components. Results herein show that this can be done systematically, without sensitive dependence on the choice of scaling factor. In addition, the algorithm is applied to the LiH diatomic for fractional electron counts, where stretching the bond introduces significant reorganization of the electron density. The analysis will show the correct KS orbital structure and reveal the effects of correlation and electron locality on the KS solutions.
Collapse
Affiliation(s)
- Alan E Rask
- SandboxAQ, 780 High Street, Palo Alto, California 94301, United States
- Department of Chemistry, University of Michigan, 930 N. University Avenue, Ann Arbor, Michigan 48109, United States
| | - Liying Li
- Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, Michigan 48109, United States
- Department of Mathematics, Southern University of Science and Technology, No. 1088 Xueyuan Road, Nanshan District, Shenzhen, 518055, Guangdong, China
| | - Paul M Zimmerman
- Department of Chemistry, University of Michigan, 930 N. University Avenue, Ann Arbor, Michigan 48109, United States
| |
Collapse
|
3
|
Prentice AW, Coe JP, Paterson MJ. Modular Approach to Selected Configuration Interaction in an Arbitrary Spin Basis: Implementation and Comparison of Approaches. J Chem Theory Comput 2023; 19:9161-9176. [PMID: 38061390 PMCID: PMC10753805 DOI: 10.1021/acs.jctc.3c00897] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2023] [Revised: 11/24/2023] [Accepted: 11/27/2023] [Indexed: 12/27/2023]
Abstract
A modular selected configuration interaction (SCI) code has been developed that is based on the existing Monte-Carlo configuration interaction code (MCCI). The modularity allows various selection protocols to be implemented with ease and allows for fair comparison between wave functions built via different criteria. We have initially implemented adaptations of existing SCI theories, which are based on either energy- or coefficient-driven selection schemes. These codes have been implemented not only in the basis of Slater determinants (SDs) but also in the basis of configuration state functions (CSFs) and extended to state-averaged regimes. This allows one to take advantage of the reduced dimensionality of the wave function in the CSF basis and also the guarantee of pure spin states. All SCI methods were found to be able to predict potential energy surfaces to high accuracy, producing compact wave functions, when compared to full configuration interaction (FCI) for a variety of bond-breaking potential energy surfaces. The compactness of the error-controlled adaptive configuration interaction approach, particularly in the CSF basis, was apparent with nonparallelity errors within chemical accuracy while containing as little as 0.02% of the FCI CSF space. The size-to-accuracy was also extended to FCI spaces approaching one billion configurations.
Collapse
Affiliation(s)
- Andrew W. Prentice
- Institute of Chemical Sciences, School
of Engineering and Physical Sciences, Heriot-Watt
University, Edinburgh EH14 4AS, U.K.
| | - Jeremy P. Coe
- Institute of Chemical Sciences, School
of Engineering and Physical Sciences, Heriot-Watt
University, Edinburgh EH14 4AS, U.K.
| | - Martin J. Paterson
- Institute of Chemical Sciences, School
of Engineering and Physical Sciences, Heriot-Watt
University, Edinburgh EH14 4AS, U.K.
| |
Collapse
|
4
|
Kanungo B, Hatch J, Zimmerman PM, Gavini V. Exact and Model Exchange-Correlation Potentials for Open-Shell Systems. J Phys Chem Lett 2023; 14:10039-10045. [PMID: 37910134 DOI: 10.1021/acs.jpclett.3c01713] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2023]
Abstract
The conventional approaches to the inverse density functional theory problem typically assume nondegeneracy of the Kohn-Sham (KS) eigenvalues, greatly hindering their use in open-shell systems. We present a generalization of the inverse density functional theory problem that can seamlessly admit degenerate KS eigenvalues. Additionally, we allow for fractional occupancy of the Kohn-Sham orbitals to also handle noninteracting ensemble-v-representable densities, as opposed to just noninteracting pure-v-representable densities. We present the exact exchange-correlation (XC) potentials for six open-shell systems─four atoms (Li, C, N, and O) and two molecules (CN and CH2)─using accurate ground-state densities from configuration interaction calculations. We compare these exact XC potentials with model XC potentials obtained using nonlocal (B3LYP, SCAN0) and local/semilocal (SCAN, PBE, PW92) XC functionals. Although the relative errors in the densities obtained from these DFT functionals are of O (10-3 to 10-2), the relative errors in the model XC potentials remain substantially large─O (10-1 to 100).
Collapse
Affiliation(s)
- Bikash Kanungo
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Jeffrey Hatch
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Paul M Zimmerman
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Vikram Gavini
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States
- Department of Materials Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States
| |
Collapse
|
5
|
Crawford TD, Krylov AI, Schaefer HF, Van Voorhis T. MQM 2022: The 10th Triennial Conference on Molecular Quantum Mechanics. J Phys Chem A 2023; 127:4897-4900. [PMID: 37317531 DOI: 10.1021/acs.jpca.3c03059] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Affiliation(s)
- T Daniel Crawford
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Anna I Krylov
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
| | - Henry F Schaefer
- Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, USA
| | - Troy Van Voorhis
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| |
Collapse
|