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Liu ZK. Quantitative predictive theories through integrating quantum, statistical, equilibrium, and nonequilibrium thermodynamics. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:343003. [PMID: 38701831 DOI: 10.1088/1361-648x/ad4762] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2024] [Accepted: 05/03/2024] [Indexed: 05/05/2024]
Abstract
Today's thermodynamics is largely based on the combined law for equilibrium systems and statistical mechanics derived by Gibbs in 1873 and 1901, respectively, while irreversible thermodynamics for nonequilibrium systems resides essentially on the Onsager Theorem as a separate branch of thermodynamics developed in 1930s. Between them, quantum mechanics was invented and quantitatively solved in terms of density functional theory (DFT) in 1960s. These three scientific domains operate based on different principles and are very much separated from each other. In analogy to the parable of the blind men and the elephant articulated by Perdew, they individually represent different portions of a complex system and thus are incomplete by themselves alone, resulting in the lack of quantitative agreement between their predictions and experimental observations. Over the last two decades, the author's group has developed a multiscale entropy approach (recently termed as zentropy theory) that integrates DFT-based quantum mechanics and Gibbs statistical mechanics and is capable of accurately predicting entropy and free energy of complex systems. Furthermore, in combination with the combined law for nonequilibrium systems presented by Hillert, the author developed the theory of cross phenomena beyond the phenomenological Onsager Theorem. The zentropy theory and theory of cross phenomena jointly provide quantitative predictive theories for systems from electronic to any observable scales as reviewed in the present work.
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Affiliation(s)
- Zi-Kui Liu
- Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, United States of America
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2
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Maniar R, Withanage KPK, Shahi C, Kaplan AD, Perdew JP, Pederson MR. Symmetry breaking and self-interaction correction in the chromium atom and dimer. J Chem Phys 2024; 160:144301. [PMID: 38587222 DOI: 10.1063/5.0180863] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2023] [Accepted: 03/21/2024] [Indexed: 04/09/2024] Open
Abstract
Density functional approximations to the exchange-correlation energy can often identify strongly correlated systems and estimate their energetics through energy-minimizing symmetry-breaking. In particular, the binding energy curve of the strongly correlated chromium dimer is described qualitatively by the local spin density approximation (LSDA) and almost quantitatively by the Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA), where the symmetry breaking is antiferromagnetic for both. Here, we show that a full Perdew-Zunger self-interaction-correction (SIC) to LSDA seems to go too far by creating an unphysical symmetry-broken state, with effectively zero magnetic moment but non-zero spin density on each atom, which lies ∼4 eV below the antiferromagnetic solution. A similar symmetry-breaking, observed in the atom, better corresponds to the 3d↑↑4s↑3d↓↓4s↓ configuration than to the standard 3d↑↑↑↑↑4s↑. For this new solution, the total energy of the dimer at its observed bond length is higher than that of the separated atoms. These results can be regarded as qualitative evidence that the SIC needs to be scaled down in many-electron regions.
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Affiliation(s)
- Rohan Maniar
- Department of Physics and Engineering Physics, Tulane University, 6400 Freret St., New Orleans, Louisiana 70118, USA
| | - Kushantha P K Withanage
- Department of Physics, The University of Texas at El Paso, 500 West University Ave., El Paso, Texas 79968, USA
| | - Chandra Shahi
- Department of Physics and Engineering Physics, Tulane University, 6400 Freret St., New Orleans, Louisiana 70118, USA
| | - Aaron D Kaplan
- Materials Project, Lawrence Berkeley National Laboratory, 1 Cyclotron Rd., B33-141B, Berkeley, California 94720, USA
| | - John P Perdew
- Department of Physics and Engineering Physics, Tulane University, 6400 Freret St., New Orleans, Louisiana 70118, USA
| | - Mark R Pederson
- Department of Physics, The University of Texas at El Paso, 500 West University Ave., El Paso, Texas 79968, USA
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Zhang Y, Ke D, Wu J, Zhang C, Hou L, Lin B, Chen Z, Perdew JP, Sun J. Challenges for density functional theory in simulating metal-metal singlet bonding: A case study of dimerized VO2. J Chem Phys 2024; 160:134101. [PMID: 38557836 DOI: 10.1063/5.0180315] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2023] [Accepted: 03/03/2024] [Indexed: 04/04/2024] Open
Abstract
VO2 is renowned for its electric transition from an insulating monoclinic (M1) phase, characterized by V-V dimerized structures, to a metallic rutile (R) phase above 340 K. This transition is accompanied by a magnetic change: the M1 phase exhibits a non-magnetic spin-singlet state, while the R phase exhibits a state with local magnetic moments. Simultaneous simulation of the structural, electric, and magnetic properties of this compound is of fundamental importance, but the M1 phase alone has posed a significant challenge to the density functional theory (DFT). In this study, we show none of the commonly used DFT functionals, including those combined with on-site Hubbard U to treat 3d electrons better, can accurately predict the V-V dimer length. The spin-restricted method tends to overestimate the strength of the V-V bonds, resulting in a small V-V bond length. Conversely, the spin-symmetry-breaking method exhibits the opposite trends. Each of these two bond-calculation methods underscores one of the two contentious mechanisms, i.e., Peierls lattice distortion or Mott localization due to electron-electron repulsion, involved in the metal-insulator transition in VO2. To elucidate the challenges encountered in DFT, we also employ an effective Hamiltonian that integrates one-dimensional magnetic sites, thereby revealing the inherent difficulties linked with the DFT computations.
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Affiliation(s)
- Yubo Zhang
- Minjiang Collaborative Center for Theoretical Physics, College of Physics and Electronic Information Engineering, Minjiang University, Fuzhou, China
| | - Da Ke
- Minjiang Collaborative Center for Theoretical Physics, College of Physics and Electronic Information Engineering, Minjiang University, Fuzhou, China
| | - Junxiong Wu
- Minjiang Collaborative Center for Theoretical Physics, College of Physics and Electronic Information Engineering, Minjiang University, Fuzhou, China
| | - Chutong Zhang
- Minjiang Collaborative Center for Theoretical Physics, College of Physics and Electronic Information Engineering, Minjiang University, Fuzhou, China
| | - Lin Hou
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA
| | - Baichen Lin
- School of Materials Science and Engineering, Nanyang Technological University, Singapore 639798, Republic of Singapore
- Institute of Materials Research and Engineering (IMRE), Agency for Science, Technology and Research (A*STAR), Singapore 138634, Republic of Singapore
| | - Zuhuang Chen
- School of Materials Science and Engineering, Harbin Institute of Technology, Shenzhen, Shenzhen 518055, China
- Flexible Printed Electronics Technology Center, Harbin Institute of Technology, Shenzhen, Shenzhen 518055, China
| | - John P Perdew
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA
| | - Jianwei Sun
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA
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Shi Y, Shi Y, Wasserman A. Stretching Bonds without Breaking Symmetries in Density Functional Theory. J Phys Chem Lett 2024; 15:826-833. [PMID: 38232318 DOI: 10.1021/acs.jpclett.3c03073] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2024]
Abstract
Kohn-Sham density functional theory (KS-DFT) stands out among electronic structure methods due to its balance of accuracy and computational efficiency. However, to achieve chemically accurate energies, standard density functional approximations in KS-DFT often need to break underlying symmetries, a long-standing "symmetry dilemma". By employing fragment spin densities as the main variables in calculations (rather than total molecular densities, as in KS-DFT), we present an embedding framework in which this symmetry dilemma is understood and partially resolved. The spatial overlap between fragment densities is used as the main ingredient to construct a simple, physically motivated approximation to a universal functional of the fragment densities. This "overlap approximation" is shown to significantly improve semilocal KS-DFT binding energies of molecules without artificially breaking either charge or spin symmetries. The approach is shown to be applicable to covalently bonded molecules and to systems of the "strongly correlated" type.
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Affiliation(s)
- Yuming Shi
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, United States
| | - Yi Shi
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
| | - Adam Wasserman
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, United States
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
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Trushin E, Görling A. Avoiding spin contamination and spatial symmetry breaking by exact-exchange-only optimized-effective-potential methods within the symmetrized Kohn-Sham framework. J Chem Phys 2023; 159:244109. [PMID: 38149736 DOI: 10.1063/5.0171546] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2023] [Accepted: 11/16/2023] [Indexed: 12/28/2023] Open
Abstract
For open-shell atoms and molecules, Kohn-Sham (KS) methods typically resort to spin-polarized approaches that exhibit spin-contamination and often break spatial symmetries. As a result, the KS Hamiltonian operator and the KS orbitals do not exhibit the space and spin symmetry of the physical electron system. The KS formalism can be symmetrized in a rigorous way only in real space, only in spin space, or both in real and spin space. Within such symmetrized KS frameworks, we present exact-exchange-only optimized-effective-potential (OEP) methods that are free of spin contamination and/or spatial symmetry breaking. The effect of symmetrizations on the total energy and its parts and on the exchange potential is analyzed. The presented exact-exchange-only OEP methods may serve as a starting point for high-level symmetrized KS methods based, e.g., on the adiabatic-connection fluctuation-dissipation theorem.
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Affiliation(s)
- Egor Trushin
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany and Erlangen National High Performance Computing Center (NHR@FAU), Martensstr. 1, D-91058 Erlangen, Germany
| | - Andreas Görling
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany and Erlangen National High Performance Computing Center (NHR@FAU), Martensstr. 1, D-91058 Erlangen, Germany
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Yu H, Song S, Nam S, Burke K, Sim E. Density-Corrected Density Functional Theory for Open Shells: How to Deal with Spin Contamination. J Phys Chem Lett 2023; 14:9230-9237. [PMID: 37811877 DOI: 10.1021/acs.jpclett.3c02017] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/10/2023]
Abstract
Density functional theory (DFT) is usually used self-consistently to predict chemical properties, but the use of the Hartree-Fock (HF) density improves energetics in certain, well-characterized cases. Density-corrected (DC) DFT provides the theory behind this, but unrestricted Hartree-Fock (UHF) densities yield poor energetics in cases of strong spin contamination. Here we compare with restricted open-shell HF (ROHF) across 13 different functionals and two DC-DFT methods. For significant spin contamination, ROHF densities outperform UHF densities by as much as a factor of 3, depending on the energy functional, and ROHF-DFT improves over self-consistent DFT for most of the tested functionals. We refine the DC(HF)-DFT algorithm to use ROHF densities in cases of severe spin contamination.
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Affiliation(s)
- Hayoung Yu
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, Korea
| | - Suhwan Song
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, Korea
| | - Seungsoo Nam
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, Korea
| | - Kieron Burke
- Department of Chemistry, University of California, Irvine, California 92697, United States
| | - Eunji Sim
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, Korea
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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
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Roy PO, Cuierrier E, Ernzerhof M. Generating Exchange-Correlation Functionals with a Simplified, Self-Consistent Correlation Factor Model. J Phys Chem A 2023; 127:2026-2033. [PMID: 36802604 DOI: 10.1021/acs.jpca.2c08397] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/22/2023]
Abstract
We focus on the spherically averaged exchange-correlation hole ρXC(r, u) of density functional theory, which describes the reduction in the electron density at a distance u due to the reference electron localized at position r. The correlation factor (CF) approach, where the model exchange hole ρXmodel(r, u) is multiplied by a CF (fC(r, u)) to yield an approximation to the exchange-correlation hole ρXC(r, u) = fC(r, u) ρXmodel(r, u), has proven to be a powerful tool for the development of new approximations. One of the remaining challenges within the CF approach is the self-consistent implementation of the resulting functionals. To address this issue, here we propose a simplification of the previously developed CFs such that self-consistent implementations become feasible. As an illustration of the simplified CF model, we develop a new meta-GGA functional, and using only a minimum of empiricism, we provide an easy derivation of an approximation that is of an accuracy similar to more involved meta-GGA functionals.
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Affiliation(s)
- Pierre-Olivier Roy
- Département de Chimie, Université de Montréal, C.P. 6128 Succursale A, Montréal, Québec H3C 3J7, Canada
| | - Etienne Cuierrier
- Département de Chimie, Université de Montréal, C.P. 6128 Succursale A, Montréal, Québec H3C 3J7, Canada
| | - Matthias Ernzerhof
- Département de Chimie, Université de Montréal, C.P. 6128 Succursale A, Montréal, Québec H3C 3J7, Canada
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Pederson MR, Johnson AI, Withanage KPK, Dolma S, Flores GB, Hooshmand Z, Khandal K, Lasode PO, Baruah T, Jackson KA. Downward quantum learning from element 118: Automated generation of Fermi-Löwdin orbitals for all atoms. J Chem Phys 2023; 158:084101. [PMID: 36859080 DOI: 10.1063/5.0135089] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/09/2023] Open
Abstract
A new algorithm based on a rigorous theorem and quantum data computationally mined from element 118 guarantees automated construction of initial Fermi-Löwdin-Orbital (FLO) starting points for all elements in the Periodic Table. It defines a means for constructing a small library of scalable FLOs for universal use in molecular and solid-state calculations. The method can be systematically improved for greater efficiency and for applications to excited states such as x-ray excitations and optically silent excitations. FLOs were introduced to recast the Perdew-Zunger self-interaction correction (PZSIC) into an explicit unitarily invariant form. The FLOs are generated from a set of N quasi-classical electron positions, referred to as Fermi-Orbital descriptors (FODs), and a set of N-orthonormal single-electron orbitals. FOD positions, when optimized, minimize the PZSIC total energy. However, creating sets of starting FODs that lead to a positive definite Fermi orbital overlap matrix has proven to be challenging for systems composed of open-shell atoms and ions. The proof herein guarantees the existence of a FLOSIC solution and further guarantees that if a solution for N electrons is found, it can be used to generate a minimum of N - 1 and a maximum of 2N - 2 initial starting points for systems composed of a smaller number of electrons. Applications to heavy and super-heavy atoms are presented. All starting solutions reported here were obtained from a solution for element 118, Oganesson.
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Affiliation(s)
- Mark R Pederson
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Alexander I Johnson
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA
| | | | - Sherab Dolma
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Gustavo Bravo Flores
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Zahra Hooshmand
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Kusal Khandal
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Peter O Lasode
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Tunna Baruah
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Koblar A Jackson
- Department of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, USA
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