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Kumar S, Jing X, Pask JE, Medford AJ, Suryanarayana P. Kohn-Sham accuracy from orbital-free density functional theory via Δ-machine learning. J Chem Phys 2023; 159:244106. [PMID: 38147461 DOI: 10.1063/5.0180541] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2023] [Accepted: 11/30/2023] [Indexed: 12/28/2023] Open
Abstract
We present a Δ-machine learning model for obtaining Kohn-Sham accuracy from orbital-free density functional theory (DFT) calculations. In particular, we employ a machine-learned force field (MLFF) scheme based on the kernel method to capture the difference between Kohn-Sham and orbital-free DFT energies/forces. We implement this model in the context of on-the-fly molecular dynamics simulations and study its accuracy, performance, and sensitivity to parameters for representative systems. We find that the formalism not only improves the accuracy of Thomas-Fermi-von Weizsäcker orbital-free energies and forces by more than two orders of magnitude but is also more accurate than MLFFs based solely on Kohn-Sham DFT while being more efficient and less sensitive to model parameters. We apply the framework to study the structure of molten Al0.88Si0.12, the results suggesting no aggregation of Si atoms, in agreement with a previous Kohn-Sham study performed at an order of magnitude smaller length and time scales.
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Affiliation(s)
- Shashikant Kumar
- College of Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Xin Jing
- College of Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
- College of Computing, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - John E Pask
- Physics Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Andrew J Medford
- College of Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Phanish Suryanarayana
- College of Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
- College of Computing, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
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2
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Mi W, Luo K, Trickey SB, Pavanello M. Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations. Chem Rev 2023; 123:12039-12104. [PMID: 37870767 DOI: 10.1021/acs.chemrev.2c00758] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2023]
Abstract
Kohn-Sham Density Functional Theory (KSDFT) is the most widely used electronic structure method in chemistry, physics, and materials science, with thousands of calculations cited annually. This ubiquity is rooted in the favorable accuracy vs cost balance of KSDFT. Nonetheless, the ambitions and expectations of researchers for use of KSDFT in predictive simulations of large, complicated molecular systems are confronted with an intrinsic computational cost-scaling challenge. Particularly evident in the context of first-principles molecular dynamics, the challenge is the high cost-scaling associated with the computation of the Kohn-Sham orbitals. Orbital-free DFT (OFDFT), as the name suggests, circumvents entirely the explicit use of those orbitals. Without them, the structural and algorithmic complexity of KSDFT simplifies dramatically and near-linear scaling with system size irrespective of system state is achievable. Thus, much larger system sizes and longer simulation time scales (compared to conventional KSDFT) become accessible; hence, new chemical phenomena and new materials can be explored. In this review, we introduce the historical contexts of OFDFT, its theoretical basis, and the challenge of realizing its promise via approximate kinetic energy density functionals (KEDFs). We review recent progress on that challenge for an array of KEDFs, such as one-point, two-point, and machine-learnt, as well as some less explored forms. We emphasize use of exact constraints and the inevitability of design choices. Then, we survey the associated numerical techniques and implemented algorithms specific to OFDFT. We conclude with an illustrative sample of applications to showcase the power of OFDFT in materials science, chemistry, and physics.
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Affiliation(s)
- Wenhui Mi
- Key Laboratory of Material Simulation Methods & Software of Ministry of Education, College of Physics, Jilin University, Changchun 130012, PR China
- State Key Laboratory of Superhard Materials, Jilin University, Changchun 130012, PR China
- International Center of Future Science, Jilin University, Changchun 130012, PR China
| | - Kai Luo
- Department of Applied Physics, Nanjing University of Science and Technology, Nanjing 210094, PR China
| | - S B Trickey
- Quantum Theory Project, Department of Physics and Department of Chemistry, University of Florida, Gainesville, Florida 32611, United States
| | - Michele Pavanello
- Department of Physics and Department of Chemistry, Rutgers University, Newark, New Jersey 07102, United States
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3
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Shao X, Lopez AC, Khan Musa MR, Nouri MR, Pavanello M. Adaptive Subsystem Density Functional Theory. J Chem Theory Comput 2022; 18:6646-6655. [PMID: 36179128 DOI: 10.1021/acs.jctc.2c00698] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Subsystem density functional theory (DFT) is emerging as a powerful electronic structure method for large-scale simulations of molecular condensed phases and interfaces. Key to its computational efficiency is the use of approximate nonadditive noninteracting kinetic energy functionals. Unfortunately, currently available nonadditive functionals lead to inaccurate results when the subsystems interact strongly such as when they engage in chemical reactions. This work disrupts the status quo by devising a workflow that extends subsystem DFT's applicability also to strongly interacting subsystems. This is achieved by implementing a fully automated adaptive definition of subsystems which is realized during geometry optimizations or ab initio molecular dynamics simulations. The new method prescribes subsystem merging and splitting events redistributing the resources (both for work and data) in an efficient way making use of modern parallelization strategies and object-oriented programming. We showcase the method with examples probing from moderate-to-strong inter-subsystem interactions, opening the door to using subsystem DFT for modeling chemical reactions in molecular condensed phases with a black box computational tool.
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Affiliation(s)
- Xuecheng Shao
- Department of Chemistry, Rutgers University, Newark, New Jersey07102, United States
| | | | - Md Rajib Khan Musa
- Department of Chemistry, Rutgers University, Newark, New Jersey07102, United States
| | - Mohammad Reza Nouri
- Department of Chemistry, Rutgers University, Newark, New Jersey07102, United States
| | - Michele Pavanello
- Department of Physics, Rutgers University, Newark, New Jersey07102, United States
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4
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Della Sala F. Orbital-Free Methods for Plasmonics: Linear Response. J Chem Phys 2022; 157:104101. [DOI: 10.1063/5.0100797] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Plasmonic systems, such as metal nanoparticles, are widely used in different application areas, going from biology to photovoltaics.The modeling of the optical response of such systems is of fundamental importance to analyze their behavior and to design new systems with required properties.When the characteristic sizes/distances reach a few nanometers, non-local and spill-out effects become relevant and conventional classical electrodynamics models are no more appropriate. Methods based on the Time-Dependent Density-Functional Theory (TD-DFT) represent the current reference for the description of quantum effects. However, TD-DFT is based on knowledge of all occupied orbitals whose calculation is computationally prohibitive to model large plasmonic systems of interest for applications.On the other hand, methods based on the Orbital-Free (OF) formulation of TD-DFT, can scale linearly with the system size.In this Review, OF methods ranging from semiclassical models to the quantum hydrodynamic theory, will be derived from the linear response TD-DFT, so that the key approximations and properties of each method can be clearly highlighted. The accuracy of the various approximations will be then validated for the linear optical properties of jellium nanoparticles, the most relevant model system in plasmonics. OF methods can describe the collective excitations in plasmonic systems with great accuracy andwithout system-tuned parameters. The accuracy on these methods depends only on the accuracy on the (universal) kinetic energy functional of the ground-state electronic density. Current approximations and future development directions will be indicated.
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Affiliation(s)
- Fabio Della Sala
- CNR-IMM, IMM CNR Lecce, Italy
- Istituto Italiano di Tecnologia Center for Biomolecular Nanotechnologies
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5
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Kinetic Energy Density Functionals Based on a Generalized Screened Coulomb Potential: Linear Response and Future Perspectives. COMPUTATION 2022. [DOI: 10.3390/computation10020030] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
We consider kinetic energy functionals that depend, beside the usual semilocal quantities (density, gradient, Laplacian of the density), on a generalized Yukawa potential, that is the screened Coulomb potential of the density raised to some power. These functionals, named Yukawa generalized gradient approximations (yGGA), are potentially efficient real-space semilocal methods that include significant non-local effects and can describe different important exact properties of the kinetic energy. In this work, we focus in particular on the linear response behavior for the homogeneous electron gas (HEG). We show that such functionals are able to reproduce the exact Lindhard function behavior with a very good accuracy, outperforming all other semilocal kinetic functionals. These theoretical advances allow us to perform a detailed analysis of a special class of yGGAs, namely the linear yGGA functionals. Thus, we show how the present approach can generalize the yGGA functionals improving the HEG linear behavior and leading to an extended formula for the kinetic functional. Moreover, testing on several jellium cluster model systems allows highlighting advantages and limitations of the linear yGGA functionals and future perspectives for the development of yGGA kinetic functionals.
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6
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Finzel K. Approximate Analytical Solutions for the Euler Equation for Second-Row Homonuclear Dimers. J Chem Theory Comput 2021; 17:6832-6840. [PMID: 34407616 DOI: 10.1021/acs.jctc.1c00435] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Abstract
This work presents a new method how to obtain approximate analytical solutions for the Euler equation for second-row homonuclear dimers. In contrast to the well-known Kohn-Sham method where a system of N nonlinear coupled differential equations must be solved iteratively, orbital-free density functional theory allows to access the minimizing electron density directly via the Euler equation. For simplified models, here, an atom-centered monopole expansion with one free parameter, solutions of the electron density can be obtained analytically by solving the Euler equation at the bond critical point. The procedure is exemplarily carried out for N2, C2, and B2, yielding bound molecules with an internuclear distance of 2.01, 2.43, and 3.07 bohr, respectively.
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Affiliation(s)
- Kati Finzel
- Technische Universität Dresden, Bergstrasse 66c, Dresden 01069, Germany
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Deformation Potentials: Towards a Systematic Way beyond the Atomic Fragment Approach in Orbital-Free Density Functional Theory. Molecules 2021; 26:molecules26061539. [PMID: 33799716 PMCID: PMC8000561 DOI: 10.3390/molecules26061539] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2021] [Revised: 03/01/2021] [Accepted: 03/05/2021] [Indexed: 11/25/2022] Open
Abstract
This work presents a method to move beyond the recently introduced atomic fragment approximation. Like the bare atomic fragment approach, the new method is an ab initio, parameter-free, orbital-free implementation of density functional theory based on the bifunctional formalism that treats the potential and the electron density as two separate variables, and provides access to the Kohn–Sham Pauli kinetic energy for an appropriately chosen Pauli potential. In the present ansatz, the molecular Pauli potential is approximated by the sum of the bare atomic fragment approach, and a so-called deformation potential that takes the interaction between the atoms into account. It is shown that this model can reproduce the bond-length contraction due to multiple bonding within the list of second-row homonuclear dimers. The present model only relies on the electron densities of the participating atoms, which themselves are represented by a simple monopole expansion. Thus, the bond-length contraction can be rationalized without referring to the angular quantum numbers of the participating atoms.
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8
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Francisco HI, Carmona-Espíndola J, Gázquez JL. Analysis of the kinetic energy functional in the generalized gradient approximation. J Chem Phys 2021; 154:084107. [PMID: 33639771 DOI: 10.1063/5.0040973] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A new density functional for the total kinetic energy in the generalized gradient approximation is developed through an enhancement factor that leads to the correct behavior in the limits when the reduced density gradient tends to 0 and to infinity and by making use of the conjoint conjecture for the interpolation between these two limits, through the incorporation, in the intermediate region of constraints that are associated with the exchange energy functional. The resulting functional leads to a reasonable description of the kinetic energies of atoms and molecules when it is used in combination with Hartree-Fock densities. Additionally, in order to improve the behavior of the kinetic energy density, a new enhancement factor for the Pauli kinetic energy is proposed by incorporating the correct behavior into the limits when the reduced density gradient tends to 0 and to infinity, together with the positivity condition, and imposing through the interpolation function that the sum of its integral over the whole space and the Weiszacker energy must be equal to the value obtained with the enhancement factor developed for the total kinetic energy.
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Affiliation(s)
- Héctor I Francisco
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, México, Ciudad de México 09340, Mexico
| | - Javier Carmona-Espíndola
- Departamento de Química, CONACYT-Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Ciudad de México 09340, Mexico
| | - José L Gázquez
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, México, Ciudad de México 09340, Mexico
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9
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Ghasemi SA, Kühne TD. Artificial neural networks for the kinetic energy functional of non-interacting fermions. J Chem Phys 2021; 154:074107. [PMID: 33607906 DOI: 10.1063/5.0037319] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Abstract
A novel approach to find the fermionic non-interacting kinetic energy functional with chemical accuracy using machine learning techniques is presented. To that extent, we apply machine learning to an intermediate quantity rather than targeting the kinetic energy directly. We demonstrate the performance of the method for three model systems containing three and four electrons. The resulting kinetic energy functional remarkably accurately reproduces self-consistently the ground state electron density and total energy of reference Kohn-Sham calculations with an error of less than 5 mHa. This development opens a new avenue to advance orbital-free density functional theory by means of machine learning.
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Affiliation(s)
- S Alireza Ghasemi
- Dynamics of Condensed Matter and Center for Sustainable Systems Design, Chair of Theoretical Chemistry, Paderborn University, Warburger Str. 100, D-33098 Paderborn, Germany
| | - Thomas D Kühne
- Dynamics of Condensed Matter and Center for Sustainable Systems Design, Chair of Theoretical Chemistry, Paderborn University, Warburger Str. 100, D-33098 Paderborn, Germany
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10
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Lüder J, Manzhos S. Nonparametric Local Pseudopotentials with Machine Learning: A Tin Pseudopotential Built Using Gaussian Process Regression. J Phys Chem A 2020; 124:11111-11124. [DOI: 10.1021/acs.jpca.0c05723] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Johann Lüder
- Department of Materials and Optoelectronic Science, National Sun Yat-sen University, 80424, No. 70, Lien-Hai Road, Kaohsiung, Taiwan, R.O.C
- Center for Crystal Research, National Sun Yat-sen University, 70 Lien-Hai Road, Kaohsiung 80424, Taiwan, R.O.C
| | - Sergei Manzhos
- Centre Énergie Matériaux Télécommunications, Institut National de la Recherche Scientifique, 1650 boulevard Lionel-Boulet, Varennes QC J3X1S2, Canada
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11
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Equilibrium Bond Lengths from Orbital-Free Density Functional Theory. Molecules 2020; 25:molecules25081771. [PMID: 32294892 PMCID: PMC7221999 DOI: 10.3390/molecules25081771] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2020] [Revised: 03/31/2020] [Accepted: 04/03/2020] [Indexed: 11/17/2022] Open
Abstract
This work presents an investigation to model chemical bonding in various dimers based on the atomic fragment approach. The atomic fragment approach is an ab-initio, parameter-free implementation of orbital-free density functional theory which is based on the bifunctional formalism, i.e., it uses both the density and the Pauli potential as two separate variables. While providing the exact Kohn-Sham Pauli kinetic energy when the orbital-based Kohn-Sham data are used, the bifunctional formalism allows for approximations of the functional derivative which are orbital-free. In its first implementation, the atomic fragment approach uses atoms in their ground state to model the Pauli potential. Here, it is tested how artificial closed-shell fragments with non-integer electron occupation perform regarding the prediction of bond lengths of diatomics. Such fragments can sometimes mimic the electronic structure of a molecule better than groundstate fragments. It is found that bond lengths may indeed be considerably improved in some of the tested diatomics, in accord with predictions based on the electronic structure.
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12
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Finzel K. The first order atomic fragment approach-An orbital-free implementation of density functional theory. J Chem Phys 2019; 151:024109. [PMID: 31301700 DOI: 10.1063/1.5099217] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An orbital-free implementation of the original Hohenberg-Kohn theorems is presented, making use of the scaling properties from a fictitious Kohn-Sham system, but without reintroducing orbitals. The first order fragment approach does not contain data or parameters that are fitted to the final outcome of the molecular orbital-free calculation and thus represents a parameter-free implementation of orbital-free density functional theory, although it requires the precalculation of atomic data. Consequently, the proposed method is not limited to a specific type of molecule or chemical bonding. The different approximation levels arise from including (first order) or neglecting (zeroth order) the dependency between the potential and the electron density, which in the bifunctional approach are formally treated as independent variables.
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Affiliation(s)
- K Finzel
- Faculty of Chemistry and Food Chemistry, Technische Universität Dresden, Bergstraße 66, 01069 Dresden, Germany
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13
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Abstract
A generating function σ is defined for spherically symmetric systems. Compared to the density, the generating functional has two extra variables and reduces to the density if these variables are equal to zero. It is proved that σ satisfies a differential equation that contains only the derivatives of σ and the Kohn-Sham potential. A Schrödinger-like equation for the square root of σ is also derived. The effective potential of this equation is the sum of the Kohn-Sham potential and a term that is expressed with an integral containing the derivatives of σ. The noninteracting kinetic energy can be calculated in the knowledge of σ. The theory is valid in case of zero and nonzero temperatures as well. For nonspherically symmetric systems, the muffin-tin approximation can be applied.
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Affiliation(s)
- Á Nagy
- Department of Theoretical Physics, University of Debrecen, H-4002 Debrecen, Hungary
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14
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A study of the basis set dependence of the bifunctional expression of the non-interacting kinetic energy for atomic systems. COMPUT THEOR CHEM 2019. [DOI: 10.1016/j.comptc.2019.03.022] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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15
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Constantin LA, Fabiano E, Della Sala F. Performance of Semilocal Kinetic Energy Functionals for Orbital-Free Density Functional Theory. J Chem Theory Comput 2019; 15:3044-3055. [DOI: 10.1021/acs.jctc.9b00183] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Lucian A. Constantin
- Center for Biomolecular Nanotechnologies @UNILE, Istituto Italiano di Tecnologia, Via Barsanti, I-73010 Arnesano, Italy
| | - Eduardo Fabiano
- Center for Biomolecular Nanotechnologies @UNILE, Istituto Italiano di Tecnologia, Via Barsanti, I-73010 Arnesano, Italy
- Institute for Microelectronics and Microsystems (CNR-IMM), Campus Unisalento, Via Monteroni, 73100 Lecce, Italy
| | - Fabio Della Sala
- Center for Biomolecular Nanotechnologies @UNILE, Istituto Italiano di Tecnologia, Via Barsanti, I-73010 Arnesano, Italy
- Institute for Microelectronics and Microsystems (CNR-IMM), Campus Unisalento, Via Monteroni, 73100 Lecce, Italy
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17
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18
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Constantin LA, Fabiano E, Della Sala F. Semilocal Pauli-Gaussian Kinetic Functionals for Orbital-Free Density Functional Theory Calculations of Solids. J Phys Chem Lett 2018; 9:4385-4390. [PMID: 30019904 DOI: 10.1021/acs.jpclett.8b01926] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Kinetic energy (KE) approximations are key elements in orbital-free density functional theory. To date, the use of nonlocal functionals, possibly employing system-dependent parameters, has been considered mandatory in order to obtain satisfactory accuracy for different solid-state systems, whereas semilocal approximations are generally regarded as unfit to this aim. Here, we show that, instead, properly constructed semilocal approximations, the Pauli-Gaussian (PG) KE functionals, especially at the Laplacian level of theory, can indeed achieve similar accuracy as nonlocal functionals and can be accurate for both metals and semiconductors, without the need for system-dependent parameters.
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Affiliation(s)
- Lucian A Constantin
- Center for Biomolecular Nanotechnologies @UNILE , Istituto Italiano di Tecnologia , Via Barsanti , I-73010 Arnesano , Italy
| | - Eduardo Fabiano
- Center for Biomolecular Nanotechnologies @UNILE , Istituto Italiano di Tecnologia , Via Barsanti , I-73010 Arnesano , Italy
- Institute for Microelectronics and Microsystems (CNR-IMM) , Via Monteroni, Campus Unisalento , 73100 Lecce , Italy
| | - Fabio Della Sala
- Center for Biomolecular Nanotechnologies @UNILE , Istituto Italiano di Tecnologia , Via Barsanti , I-73010 Arnesano , Italy
- Institute for Microelectronics and Microsystems (CNR-IMM) , Via Monteroni, Campus Unisalento , 73100 Lecce , Italy
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19
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Mi W, Genova A, Pavanello M. Nonlocal kinetic energy functionals by functional integration. J Chem Phys 2018; 148:184107. [PMID: 29764156 DOI: 10.1063/1.5023926] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Since the seminal studies of Thomas and Fermi, researchers in the Density-Functional Theory (DFT) community are searching for accurate electron density functionals. Arguably, the toughest functional to approximate is the noninteracting kinetic energy, Ts[ρ], the subject of this work. The typical paradigm is to first approximate the energy functional and then take its functional derivative, δTs[ρ]δρ(r), yielding a potential that can be used in orbital-free DFT or subsystem DFT simulations. Here, this paradigm is challenged by constructing the potential from the second-functional derivative via functional integration. A new nonlocal functional for Ts[ρ] is prescribed [which we dub Mi-Genova-Pavanello (MGP)] having a density independent kernel. MGP is constructed to satisfy three exact conditions: (1) a nonzero "Kinetic electron" arising from a nonzero exchange hole; (2) the second functional derivative must reduce to the inverse Lindhard function in the limit of homogenous densities; (3) the potential is derived from functional integration of the second functional derivative. Pilot calculations show that MGP is capable of reproducing accurate equilibrium volumes, bulk moduli, total energy, and electron densities for metallic (body-centered cubic, face-centered cubic) and semiconducting (crystal diamond) phases of silicon as well as of III-V semiconductors. The MGP functional is found to be numerically stable typically reaching self-consistency within 12 iterations of a truncated Newton minimization algorithm. MGP's computational cost and memory requirements are low and comparable to the Wang-Teter nonlocal functional or any generalized gradient approximation functional.
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Affiliation(s)
- Wenhui Mi
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, USA
| | - Alessandro Genova
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, USA
| | - Michele Pavanello
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, USA
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20
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Seino J, Kageyama R, Fujinami M, Ikabata Y, Nakai H. Semi-local machine-learned kinetic energy density functional with third-order gradients of electron density. J Chem Phys 2018; 148:241705. [DOI: 10.1063/1.5007230] [Citation(s) in RCA: 47] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Junji Seino
- Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| | - Ryo Kageyama
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| | - Mikito Fujinami
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| | - Yasuhiro Ikabata
- Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| | - Hiromi Nakai
- Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
- Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Katsura, Kyoto 615-8520, Japan
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21
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Modified Fourth-Order Kinetic Energy Gradient Expansion with Hartree Potential-Dependent Coefficients. J Chem Theory Comput 2017; 13:4228-4239. [DOI: 10.1021/acs.jctc.7b00705] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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22
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del Rio BG, Dieterich JM, Carter EA. Globally-Optimized Local Pseudopotentials for (Orbital-Free) Density Functional Theory Simulations of Liquids and Solids. J Chem Theory Comput 2017; 13:3684-3695. [DOI: 10.1021/acs.jctc.7b00565] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Beatriz G. del Rio
- Departamento
de Física Teórica, Facultad de Ciencias, Universidad de Valladolid, 47002 Valladolid, Spain
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Dieterich JM, Witt WC, Carter EA. libKEDF: An accelerated library of kinetic energy density functionals. J Comput Chem 2017; 38:1552-1559. [DOI: 10.1002/jcc.24806] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2017] [Revised: 03/22/2017] [Accepted: 03/24/2017] [Indexed: 01/09/2023]
Affiliation(s)
- Johannes M. Dieterich
- Department of Mechanical and Aerospace EngineeringPrinceton UniversityPrinceton New Jersey08544‐5263
| | - William C. Witt
- Department of Mechanical and Aerospace EngineeringPrinceton UniversityPrinceton New Jersey08544‐5263
| | - Emily A. Carter
- School of Engineering and Applied SciencePrinceton UniversityPrinceton New Jersey08544‐5263
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Ratcliff LE, Mohr S, Huhs G, Deutsch T, Masella M, Genovese L. Challenges in large scale quantum mechanical calculations. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2016. [DOI: 10.1002/wcms.1290] [Citation(s) in RCA: 70] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Laura E. Ratcliff
- Argonne Leadership Computing Facility Argonne National Laboratory Lemon IL USA
| | - Stephan Mohr
- Department of Computer Applications in Science and Engineering Barcelona Supercomputing Center (BSC‐CNS) Barcelona Spain
| | - Georg Huhs
- Department of Computer Applications in Science and Engineering Barcelona Supercomputing Center (BSC‐CNS) Barcelona Spain
| | - Thierry Deutsch
- University Grenoble Alpes INAC‐MEM Grenoble France
- CEA, INAC‐MEM Grenoble France
| | - Michel Masella
- Laboratoire de Biologie Structurale et Radiologie, Service de Bioénergétique, Biologie Structurale et Mécanisme Institut de Biologie et de Technologie de Saclay, CEA Saclay Gif‐sur‐Yvette Cedex France
| | - Luigi Genovese
- University Grenoble Alpes INAC‐MEM Grenoble France
- CEA, INAC‐MEM Grenoble France
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Yu HS, Li SL, Truhlar DG. Perspective: Kohn-Sham density functional theory descending a staircase. J Chem Phys 2016; 145:130901. [DOI: 10.1063/1.4963168] [Citation(s) in RCA: 204] [Impact Index Per Article: 25.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Haoyu S. Yu
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, USA
| | - Shaohong L. Li
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, USA
| | - Donald G. Truhlar
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, USA
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Chen M, Jiang XW, Zhuang H, Wang LW, Carter EA. Petascale Orbital-Free Density Functional Theory Enabled by Small-Box Algorithms. J Chem Theory Comput 2016; 12:2950-63. [DOI: 10.1021/acs.jctc.6b00326] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Mohan Chen
- Department
of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, United States
| | - Xiang-Wei Jiang
- State
Key Laboratory of Superlattices and Microstructures, Institute of
Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, China
| | - Houlong Zhuang
- Department
of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, United States
| | - Lin-Wang Wang
- Material
Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Emily A. Carter
- Department
of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, United States
- Program
in Applied and Computational Mathematics and the Andlinger Center
for Energy and the Environment, Princeton University, Princeton, New Jersey 08544, United States
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28
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Yao K, Parkhill J. Kinetic Energy of Hydrocarbons as a Function of Electron Density and Convolutional Neural Networks. J Chem Theory Comput 2016; 12:1139-47. [PMID: 26812530 DOI: 10.1021/acs.jctc.5b01011] [Citation(s) in RCA: 73] [Impact Index Per Article: 9.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We demonstrate a convolutional neural network trained to reproduce the Kohn-Sham kinetic energy of hydrocarbons from an input electron density. The output of the network is used as a nonlocal correction to conventional local and semilocal kinetic functionals. We show that this approximation qualitatively reproduces Kohn-Sham potential energy surfaces when used with conventional exchange correlation functionals. The density which minimizes the total energy given by the functional is examined in detail. We identify several avenues to improve on this exploratory work, by reducing numerical noise and changing the structure of our functional. Finally we examine the features in the density learned by the neural network to anticipate the prospects of generalizing these models.
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Affiliation(s)
- Kun Yao
- Department of Chemistry, University of Notre Dame , 251 Nieuwland Science Hall, Notre Dame, Indiana 46556, United States
| | - John Parkhill
- Department of Chemistry, University of Notre Dame , 251 Nieuwland Science Hall, Notre Dame, Indiana 46556, United States
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Finzel K. Local conditions for the Pauli potential in order to yield self-consistent electron densities exhibiting proper atomic shell structure. J Chem Phys 2016; 144:034108. [PMID: 26801021 DOI: 10.1063/1.4940035] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The local conditions for the Pauli potential that are necessary in order to yield self-consistent electron densities from orbital-free calculations are investigated for approximations that are expressed with the help of a local position variable. It is shown that those local conditions also apply when the Pauli potential is given in terms of the electron density. An explicit formula for the Ne atom is given, preserving the local conditions during the iterative procedure. The resulting orbital-free electron density exhibits proper shell structure behavior and is in close agreement with the Kohn-Sham electron density. This study demonstrates that it is possible to obtain self-consistent orbital-free electron densities with proper atomic shell structure from simple one-point approximations for the Pauli potential at local density level.
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Affiliation(s)
- Kati Finzel
- Linköpings University, IFM Department of Physics, 58183 Linköping, Sweden
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Akimov AV, Prezhdo OV. Large-Scale Computations in Chemistry: A Bird’s Eye View of a Vibrant Field. Chem Rev 2015; 115:5797-890. [DOI: 10.1021/cr500524c] [Citation(s) in RCA: 159] [Impact Index Per Article: 17.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Affiliation(s)
- Alexey V. Akimov
- Department
of Chemistry, University of South California, Los Angeles, California 90089, United States
| | - Oleg V. Prezhdo
- Department
of Chemistry, University of South California, Los Angeles, California 90089, United States
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Beck TL. A real-space stochastic density matrix approach for density functional electronic structure. Phys Chem Chem Phys 2015; 17:31472-9. [DOI: 10.1039/c5cp01222h] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A novel stochastic approach aimed at solving for the ground-state one-particle density matrix in density functional theory is developed.
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Affiliation(s)
- Thomas L. Beck
- Departments of Chemistry and Physics
- University of Cincinnati
- Cincinnati
- USA
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