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Roller D, Rappe AM, Kronik L, Hellman O. Finite Difference Interpolation for Reduction of Grid-Related Errors in Real-Space Pseudopotential Density Functional Theory. J Chem Theory Comput 2023. [PMID: 37384777 DOI: 10.1021/acs.jctc.3c00217] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/01/2023]
Abstract
The real-space pseudopotential approach is a well-known method for large-scale density functional theory (DFT) calculations. One of its main limitations, however, is the introduction of errors associated with the positioning of the underlying real-space grid, a phenomenon usually known as the "egg-box" effect. The effect can be controlled by using a finer grid, but this raises the cost of the calculations or even undermines their feasibility altogether. Therefore, there is ongoing interest in the reduction of the effect per a given real-space grid. Here, we present a finite difference interpolation of electron orbitals as a means of exploiting the high resolution of the pseudopotential to reduce egg-box effects systematically. We implement the method in PARSEC, a finite difference real-space pseudopotential DFT code, and demonstrate error mitigation and improved convergence at a low additional computational cost.
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Affiliation(s)
- Deena Roller
- Weizmann Institute of Science, Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Rehovoth 76100, Israel
| | - Andrew M Rappe
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Leeor Kronik
- Weizmann Institute of Science, Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Rehovoth 76100, Israel
| | - Olle Hellman
- Weizmann Institute of Science, Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Rehovoth 76100, Israel
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Manzhos S, Ihara M, Carrington T. Using Collocation to Solve the Schrödinger Equation. J Chem Theory Comput 2023; 19:1641-1656. [PMID: 36974479 DOI: 10.1021/acs.jctc.2c01232] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/10/2023]
Abstract
We review the collocation approach to the solution of the Schrödinger equation and its uses in applications. Interrelations between collocation and other methods are highlighted. We also stress advantages and disadvantages of the rectangular collocation formulation. Using collocation makes it possible to use any, e.g. optimized, coordinates and basis functions, including nonintegrable basis functions, and provides a straightforward way of dealing with singularities in the potential. In addition, we stress that using collocation facilitates tuning the shape of basis functions and the placement of points, both of which can be done with machine-learning methods. Applications to electronic and vibrational problems are reviewed focusing on calculations for molecules on surfaces for which there are few variational calculations. Collocation has advantages when potential energy surfaces are unavailable, in particular, for molecule-surface systems, and for systems for which standard direct product quadrature grids, often used with variational methods, are costly.
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Affiliation(s)
- Sergei Manzhos
- School of Materials and Chemical Technology, Tokyo Institute of Technology, Ookayama 2-12-1, Meguro-ku, Tokyo 152-8552, Japan
| | - Manabu Ihara
- School of Materials and Chemical Technology, Tokyo Institute of Technology, Ookayama 2-12-1, Meguro-ku, Tokyo 152-8552, Japan
| | - Tucker Carrington
- Department of Chemistry, Queen’s University, 90 Bader Lane, Kingston, Ontario K7L 3N6, Canada
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Ratcliff LE, Dawson W, Fisicaro G, Caliste D, Mohr S, Degomme A, Videau B, Cristiglio V, Stella M, D’Alessandro M, Goedecker S, Nakajima T, Deutsch T, Genovese L. Flexibilities of wavelets as a computational basis set for large-scale electronic structure calculations. J Chem Phys 2020; 152:194110. [PMID: 33687268 DOI: 10.1063/5.0004792] [Citation(s) in RCA: 39] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Laura E. Ratcliff
- Department of Materials, Imperial College London, London SW7 2AZ, United Kingdom
| | | | - Giuseppe Fisicaro
- Consiglio Nazionale delle Ricerche, Istituto per la Microelettronica e Microsistemi (CNR-IMM), Z.I. VIII Strada 5, I-95121 Catania, Italy
| | - Damien Caliste
- Univ. Grenoble Alpes, CEA, IRIG-MEM-L_Sim, 38000 Grenoble, France
| | - Stephan Mohr
- Barcelona Supercomputing Center (BSC), Barcelona, Spain
- Nextmol (Bytelab Solutions SL), Barcelona, Spain
| | - Augustin Degomme
- Univ. Grenoble Alpes, CEA, IRIG-MEM-L_Sim, 38000 Grenoble, France
| | - Brice Videau
- Univ. Grenoble Alpes, CEA, IRIG-MEM-L_Sim, 38000 Grenoble, France
| | | | - Martina Stella
- Department of Materials, Imperial College London, London SW7 2AZ, United Kingdom
| | - Marco D’Alessandro
- Istituto di Struttura della Materia-CNR (ISM-CNR), Via del Fosso del Cavaliere 100, 00133 Roma, Italy
| | | | | | - Thierry Deutsch
- Univ. Grenoble Alpes, CEA, IRIG-MEM-L_Sim, 38000 Grenoble, France
| | - Luigi Genovese
- Univ. Grenoble Alpes, CEA, IRIG-MEM-L_Sim, 38000 Grenoble, France
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Duchemin I, Li J, Blase X. Hybrid and Constrained Resolution-of-Identity Techniques for Coulomb Integrals. J Chem Theory Comput 2017; 13:1199-1208. [DOI: 10.1021/acs.jctc.6b01215] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ivan Duchemin
- INAC, SP2M/L_Sim,
CEA/UJF Cedex 09, Université Grenoble Alpes, 38054 Grenoble, France
| | - Jing Li
- Université Grenoble Alpes, CNRS, Inst NEEL, F-38042 Grenoble, France
| | - Xavier Blase
- Université Grenoble Alpes, CNRS, Inst NEEL, F-38042 Grenoble, France
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Ryu S, Choi S, Hong K, Kim WY. Supersampling method for efficient grid-based electronic structure calculations. J Chem Phys 2016; 144:094101. [DOI: 10.1063/1.4942925] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Affiliation(s)
- Seongok Ryu
- Department of Chemistry, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, South Korea
| | - Sunghwan Choi
- Department of Chemistry, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, South Korea
- Supercomputing Service Center, Korea Institute of Science and Technology Information, 245 Daehak-ro, Yuseong-gu, Daejeon 34141, South Korea
| | - Kwangwoo Hong
- Department of Chemistry, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, South Korea
| | - Woo Youn Kim
- Department of Chemistry, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, South Korea
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