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Kaupp M, Wodyński A, Arbuznikov AV, Fürst S, Schattenberg CJ. Toward the Next Generation of Density Functionals: Escaping the Zero-Sum Game by Using the Exact-Exchange Energy Density. Acc Chem Res 2024; 57:1815-1826. [PMID: 38905497 PMCID: PMC11223257 DOI: 10.1021/acs.accounts.4c00209] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2024] [Revised: 05/29/2024] [Accepted: 06/03/2024] [Indexed: 06/23/2024]
Abstract
ConspectusKohn-Sham density functional theory (KS DFT) is arguably the most widely applied electronic-structure method with tens of thousands of publications each year in a wide variety of fields. Its importance and usefulness can thus hardly be overstated. The central quantity that determines the accuracy of KS DFT calculations is the exchange-correlation functional. Its exact form is unknown, or better "unknowable", and therefore the derivation of ever more accurate yet efficiently applicable approximate functionals is the "holy grail" in the field. In this context, the simultaneous minimization of so-called delocalization errors and static correlation errors is the greatest challenge that needs to be overcome as we move toward more accurate yet computationally efficient methods. In many cases, an improvement on one of these two aspects (also often termed fractional-charge and fractional-spin errors, respectively) generates a deterioration in the other one. Here we report on recent notable progress in escaping this so-called "zero-sum-game" by constructing new functionals based on the exact-exchange energy density. In particular, local hybrid and range-separated local hybrid functionals are discussed that incorporate additional terms that deal with static correlation as well as with delocalization errors. Taking hints from other coordinate-space models of nondynamical and strong electron correlations (the B13 and KP16/B13 models), position-dependent functions that cover these aspects in real space have been devised and incorporated into the local-mixing functions determining the position-dependence of exact-exchange admixture of local hybrids as well as into the treatment of range separation in range-separated local hybrids. While initial functionals followed closely the B13 and KP16/B13 frameworks, meanwhile simpler real-space functions based on ratios of semilocal and exact-exchange energy densities have been found, providing a basis for relatively simple and numerically convenient functionals. Notably, the correction terms can either increase or decrease exact-exchange admixture locally in real space (and in interelectronic-distance space), leading even to regions with negative admixture in cases of particularly strong static correlations. Efficient implementations into a fast computer code (Turbomole) using seminumerical integration techniques make such local hybrid and range-separated local hybrid functionals promising new tools for complicated composite systems in many research areas, where simultaneously small delocalization errors and static correlation errors are crucial. First real-world application examples of the new functionals are provided, including stretched bonds, symmetry-breaking and hyperfine coupling in open-shell transition-metal complexes, as well as a reduction of static correlation errors in the computation of nuclear shieldings and magnetizabilities. The newest versions of range-separated local hybrids (e.g., ωLH23tdE) retain the excellent frontier-orbital energies and correct asymptotic exchange-correlation potential of the underlying ωLH22t functional while improving substantially on strong-correlation cases. The form of these functionals can be further linked to the performance of the recent impactful deep-neural-network "black-box" functional DM21, which itself may be viewed as a range-separated local hybrid.
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Affiliation(s)
- Martin Kaupp
- Institut für Chemie,
Theoretische Chemie/Quantenchemie, Technische
Universität Berlin, Sekr. C7, Strasse des 17. Juni 115, 10623 Berlin, Germany
| | - Artur Wodyński
- Institut für Chemie,
Theoretische Chemie/Quantenchemie, Technische
Universität Berlin, Sekr. C7, Strasse des 17. Juni 115, 10623 Berlin, Germany
| | - Alexei V. Arbuznikov
- Institut für Chemie,
Theoretische Chemie/Quantenchemie, Technische
Universität Berlin, Sekr. C7, Strasse des 17. Juni 115, 10623 Berlin, Germany
| | - Susanne Fürst
- Institut für Chemie,
Theoretische Chemie/Quantenchemie, Technische
Universität Berlin, Sekr. C7, Strasse des 17. Juni 115, 10623 Berlin, Germany
| | - Caspar J. Schattenberg
- Institut für Chemie,
Theoretische Chemie/Quantenchemie, Technische
Universität Berlin, Sekr. C7, Strasse des 17. Juni 115, 10623 Berlin, Germany
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Terayama K, Osaki Y, Fujita T, Tamura R, Naito M, Tsuda K, Matsui T, Sumita M. Koopmans' Theorem-Compliant Long-Range Corrected (KTLC) Density Functional Mediated by Black-Box Optimization and Data-Driven Prediction for Organic Molecules. J Chem Theory Comput 2023; 19:6770-6781. [PMID: 37729470 DOI: 10.1021/acs.jctc.3c00764] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/22/2023]
Abstract
Density functional theory (DFT) is a significant computational tool that has substantially influenced chemistry, physics, and materials science. DFT necessitates parametrized approximation for determining an expected value. Hence, to predict the properties of a given molecule using DFT, appropriate parameters of the functional should be set for each molecule. Herein, we optimize the parameters of range-separated functionals (LC-BLYP and CAM-B3LYP) via Bayesian optimization (BO) to satisfy Koopmans' theorem. Our results demonstrate the effectiveness of the BO in optimizing functional parameters. Particularly, Koopmans' theorem-compliant LC-BLYP (KTLC-BLYP) shows results comparable to the experimental UV-absorption values. Furthermore, we prepared an optimized parameter dataset of KTLC-BLYP for over 3000 molecules through BO for satisfying Koopmans' theorem. We have developed a machine learning model on this dataset to predict the parameters of the LC-BLYP functional for a given molecule. The prediction model automatically predicts the appropriate parameters for a given molecule and calculates the corresponding values. The approach in this paper would be useful to develop new functionals and to update the previously developed functionals.
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Affiliation(s)
- Kei Terayama
- Graduate School of Medical Life Science, Yokohama City University, 1-7-29 Suehiro-cho, Tsurumi-ku Kanagawa 230-0045, Japan
- Center for Advanced Intelligence Project, RIKEN, 1-4-1 Nihonbashi, Chuo-ku, Tokyo 103-0027, Japan
- MDX Research Center for Element Strategy, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama, Kanagawa 226-8501, Japan
| | - Yamato Osaki
- Department of Chemistry, Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan
| | - Takehiro Fujita
- Research Center for Macromolecules and Biomaterials, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan
| | - Ryo Tamura
- Center for Advanced Intelligence Project, RIKEN, 1-4-1 Nihonbashi, Chuo-ku, Tokyo 103-0027, Japan
- Center for Basic Research on Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
| | - Masanobu Naito
- Research Center for Macromolecules and Biomaterials, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan
| | - Koji Tsuda
- Center for Advanced Intelligence Project, RIKEN, 1-4-1 Nihonbashi, Chuo-ku, Tokyo 103-0027, Japan
- Center for Basic Research on Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
- Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5 Kashiwa-no-ha, Kashiwa, Chiba 277-8561, Japan
| | - Toru Matsui
- Department of Chemistry, Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan
| | - Masato Sumita
- Center for Advanced Intelligence Project, RIKEN, 1-4-1 Nihonbashi, Chuo-ku, Tokyo 103-0027, Japan
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Kayang KW, Volkov AN, Zhilyaev PA, Sharipov F. The ab initio potential energy curves of atom pairs and transport properties of high-temperature vapors of Cu and Si and their mixtures with He, Ar, and Xe gases. Phys Chem Chem Phys 2023; 25:4872-4898. [PMID: 36692492 DOI: 10.1039/d2cp04981c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Abstract
The potential energy curves (PECs) for the homonuclear He-He, Ar-Ar, Cu-Cu, and Si-Si dimers, as well as heteronuclear Cu-He, Cu-Ar, Cu-Xe, Si-He, Si-Ar, and Si-Xe dimers, are obtained in quantum Monte Carlo (QMC) calculations. It is shown that the QMC method provides the PECs with an accuracy comparable with that of the state-of-the-art coupled cluster singles and doubles with perturbative triples corrections [CCSD(T)] calculations. The QMC data are approximated by the Morse long range (MLR) and (12-6) Lennard-Jones (LJ) potentials. The MLR and LJ potentials are used to calculate the deflection angles in binary collisions of corresponding atom pairs and transport coefficients of Cu and Si vapors and their mixtures with He, Ar, and Xe gases in the range of temperature from 100 K to 10 000 K. It is shown that the use of the LJ potentials introduces significant errors in the transport coefficients of high-temperature vapors and gas mixtures. The mixtures with heavy noble gases demonstrate anomalous behavior when the viscosity and thermal conductivity can be larger than that of the corresponding pure substances. In the mixtures with helium, the thermal diffusion factor is found to be unusually large. The calculated viscosity and diffusivity are used to determine parameters of the variable hard sphere and variable soft sphere molecular models as well as parameters of the power-law approximations for the transport coefficients. The results obtained in the present work include all information required for kinetic or continuum simulations of dilute Cu and Si vapors and their mixtures with He, Ar, and Xe gases.
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Affiliation(s)
- Kevin W Kayang
- Department of Mechanical Engineering, University of Alabama, 7th Avenue, Tuscaloosa, AL 35487, USA.
| | - Alexey N Volkov
- Department of Mechanical Engineering, University of Alabama, 7th Avenue, Tuscaloosa, AL 35487, USA.
| | - Petr A Zhilyaev
- Skolkovo Institute of Science and Technology, 121205, Bolshoy Boulevard 30, bld. 1, Moscow, Russia
| | - Felix Sharipov
- Departamento de Física, Universidade Federal do Paraná, Caixa Postal 19044, Curitiba 81531-980, Brazil
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Gao Y, Lu Y, Zhu X. Mateverse, the Future Materials Science Computation Platform Based on Metaverse. J Phys Chem Lett 2023; 14:148-157. [PMID: 36579474 DOI: 10.1021/acs.jpclett.2c03459] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
Currently, computational materials science involves human-computer interaction through coding in software or neural networks. There is still no direct way for human intelligence endorsement. The digitalization of human intelligence should be the ultimate goal for many disciplines. In materials science, human intelligence is still irreplaceable from machine learning techniques, where humans can deal with complex correlations in the real world. We design the framework of Mateverse, a materials science computation platform based on Metaverse, which unifies human intelligence, experiment data, and theoretical simulations. In Mateverse, we intensively study the properties of H2O, including the liquid and solid phases. We show that we can optimize a new water force field (which we name TIP4P-Meta) directly from the interactions between human and visible properties of H2O. This force field is validated to be better than the conventional water model, and new ice polymorphs can be generated. We believe our platform can provide valuable hints in the paradigm upgrade in future computational materials science development.
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Affiliation(s)
- Yuechen Gao
- School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Guangdong518172, People's Republic of China
| | - Yihua Lu
- Fine-Fanta Technology, No. 527 Xixi Road, Qianjiang Zhejiang Merch Venture Capital Center, Xihu District, Hangzhou310013, People's Republic of China
| | - Xi Zhu
- School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Guangdong518172, People's Republic of China
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Kirkpatrick J, McMorrow B, Turban DHP, Gaunt AL, Spencer JS, Matthews AGDG, Obika A, Thiry L, Fortunato M, Pfau D, Román Castellanos L, Petersen S, Nelson AWR, Kohli P, Mori-Sánchez P, Hassabis D, Cohen AJ. Response to Comment on "Pushing the frontiers of density functionals by solving the fractional electron problem". Science 2022; 377:eabq4282. [PMID: 35926047 DOI: 10.1126/science.abq4282] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Gerasimov et al. claim that the ability of DM21 to respect fractional charge (FC) and fractional spin (FS) conditions outside of the training set has not been demonstrated in our paper. This is based on (i) asserting that the training set has a ~50% overlap with our bond-breaking benchmark (BBB) and (ii) questioning the validity and accuracy of our other generalization examples. We disagree with their analysis and believe that the points raised are either incorrect or not relevant to the main conclusions of the paper and to the assessment of general quality of DM21.
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Affiliation(s)
| | | | | | | | | | | | | | - Louis Thiry
- Département d'informatique, ENS, CNRS, PSL University, Paris, France
| | | | - David Pfau
- DeepMind, 6 Pancras Square, London N1C 4AG, UK
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