DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Free-energy orbital-free density functional theory: recent developments, perspective, and outlook

Journal Article · · Electronic Structure

By summarizing the constraint-based development of orbital-free free-energy density functional approximations, we provide a perspective on progress over the last 15 years, the limitations of existing functionals, and the challenges awaiting resolution. We outline the chronology of the development of noninteracting and exchange-correlation free-energy orbital-free functionals and summarize the theoretical basis of existing local density approximation, second-order approximation, generalized gradient approximation (GGA), and meta-GGAs. We discuss limitations and challenges such as problems with thermodynamic derivatives, free-energy nonadditivity and the closely related issue of all-electron versus valence-only local pseudo-potential performance.

Research Organization:
University of Rochester, NY (United States)
Sponsoring Organization:
National Energy Research Scientific Computing Center (NERSC); U.S. National Science Foundation (NSF); USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities (SUF)
Grant/Contract Number:
AC02-05CH11231; NA0004144
OSTI ID:
2513926
Journal Information:
Electronic Structure, Journal Name: Electronic Structure Journal Issue: 1 Vol. 7; ISSN 2516-1075
Publisher:
IOP ScienceCopyright Statement
Country of Publication:
United States
Language:
English

References (90)

On the eigenfunctions of many-particle systems in quantum mechanics journal January 1957
Density functionals for coulomb systems journal September 1983
Coupled-cluster theory and its equation-of-motion extensions: Coupled-cluster theory journal July 2011
Extended Thomas-Fermi theory at finite temperature journal November 1985
Fourth order gradient corrections to the free energy of noninteracting many-electron systems at finite temperature journal March 1985
Issues and challenges in orbital-free density functional calculations journal December 2012
Finite-temperature orbital-free DFT molecular dynamics: Coupling Profess and Quantum Espresso journal December 2014
Improved analytical representation of combinations of Fermi–Dirac integrals for finite-temperature density functional calculations journal July 2015
TFmix: A high-precision implementation of the finite-temperature Thomas–Fermi model for a mixture of atoms journal February 2019
Extended first-principles molecular dynamics model for high temperature simulations in the Abinit code: Application to warm dense aluminum journal February 2022
The uniform electron gas at warm dense matter conditions journal May 2018
Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations journal October 2023
Bound-State Breaking and the Importance of Thermal Exchange–Correlation Effects in Warm Dense Hydrogen journal December 2023
Reworking the Tao–Mo Exchange–Correlation Functional. III. Improved Deorbitalization Strategy and Faithful Deorbitalization journal July 2024
Accurate and Numerically Efficient r 2 SCAN Meta-Generalized Gradient Approximation journal September 2020
Framework for Laplacian-Level Noninteracting Free-Energy Density Functionals journal August 2024
Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields journal November 1994
Nonlocal pseudopotential energy density functional for orbital-free density functional theory journal March 2022
DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science journal January 2022
Jacob’s ladder of density functional approximations for the exchange-correlation energy conference January 2001
Orbital-free density functional theory implementation with the projector augmented-wave method journal December 2014
Extended application of Kohn-Sham first-principles molecular dynamics method with plane wave approximation at high energy—From cold materials to hot dense plasmas journal April 2016
First-principles equation-of-state table of beryllium based on density-functional theory calculations journal June 2017
Regularized SCAN functional journal April 2019
Comment on “Regularized SCAN functional” [J. Chem. Phys. 150, 161101 (2019)] journal November 2019
Many recent density functionals are numerically ill-behaved journal November 2022
Reworking the Tao–Mo exchange-correlation functional. I. Reconsideration and simplification journal December 2023
Tunable noninteracting free-energy density functionals for high-energy-density physics applications journal July 2024
Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem journal December 1979
The history and evolution of configuration interaction journal May 1998
Inhomogeneous Electron Gas journal November 1964
Thermal Properties of the Inhomogeneous Electron Gas journal March 1965
Self-Consistent Equations Including Exchange and Correlation Effects journal November 1965
Equations of State of Elements Based on the Generalized Fermi-Thomas Theory journal May 1949
Gradient correction to the statistical electronic free energy at nonzero temperatures: Application to equation-of-state calculations journal August 1979
Thomas-Fermi molecular dynamics journal October 1992
Deorbitalization strategies for meta-generalized-gradient-approximation exchange-correlation functionals journal November 2017
Towards accurate orbital-free simulations: A generalized gradient approximation for the noninteracting free energy density functional journal February 2020
Meta-GGA performance in solids at almost GGA cost journal September 2020
Meta-GGA exchange-correlation free energy density functional to increase the accuracy of warm dense matter simulations journal February 2022
Exchange and correlation in the electron gas journal January 1975
Nonlocal free-energy density functional for a broad range of warm dense matter simulations journal August 2024
Gradient corrections to the exchange-correlation energy of electrons at metal surfaces journal February 1977
Validity of the frozen-core approximation and pseudopotential theory for cohesive energy calculations journal March 1980
Nonlinear ionic pseudopotentials in spin-density-functional calculations journal August 1982
Fourth-order gradient contributions in extended Thomas-Fermi theory for noninteracting fermions at finite temperature journal December 1985
Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density journal January 1988
Kinetic-energy functional of the electron density journal June 1992
Relativistic separable dual-space Gaussian pseudopotentials from H to Rn journal August 1998
Importance of nonlinear core corrections for density-functional based pseudopotential calculations journal November 1999
Transferable local pseudopotentials derived via inversion of the Kohn-Sham equations in a bulk environment journal March 2004
Laplacian-level density functionals for the kinetic energy density and exchange-correlation energy journal April 2007
First-principles equation-of-state table of deuterium for inertial confinement fusion applications journal December 2011
Toward an orbital-free density functional theory of transition metals based on an electron density decomposition journal January 2012
Generalized-gradient-approximation noninteracting free-energy functionals for orbital-free density functional calculations journal September 2012
Quantum Monte Carlo study of the three-dimensional spin-polarized homogeneous electron gas journal August 2013
Nonempirical generalized gradient approximation free-energy functional for orbital-free simulations journal October 2013
Nonlocal orbital-free noninteracting free-energy functional for warm dense matter journal November 2013
Angular momentum dependent orbital-free density functional theory: Formulation and implementation journal April 2014
Gradient corrections to the exchange-correlation free energy journal October 2014
Stochastic density functional theory at finite temperatures journal March 2018
Nonlocal kinetic energy functional from the jellium-with-gap model: Applications to orbital-free density functional theory journal May 2018
Deorbitalized meta-GGA exchange-correlation functionals in solids journal September 2018
Status of free-energy representations for the homogeneous electron gas journal May 2019
Exchange-correlation thermal effects in shocked deuterium: Softening the principal Hugoniot and thermophysical properties journal June 2019
First-principles equation of state of CHON resin for inertial confinement fusion applications journal October 2022
Spectral-partitioned Kohn-Sham density functional theory journal October 2023
Very-high-temperature molecular dynamics journal January 2006
Ab initio molecular dynamics simulations of dense boron plasmas up to the semiclassical Thomas-Fermi regime journal May 2007
Direct verification of mixing rules in the hot and dense regime journal February 2008
Equation of state of a dense plasma by orbital-free and quantum molecular dynamics: Examination of two isothermal-isobaric mixing rules journal January 2015
First-principles equation of state of polystyrene and its effect on inertial confinement fusion implosions journal October 2015
Importance of finite-temperature exchange correlation for warm dense matter calculations journal June 2016
First-principles equation-of-state table of silicon and its effects on high-energy-density plasma simulations journal April 2017
Angular-Momentum-Dependent Orbital-Free Density Functional Theory journal August 2013
Accurate Homogeneous Electron Gas Exchange-Correlation Free Energy for Local Spin-Density Calculations journal February 2014
Fast and Accurate Quantum Molecular Dynamics of Dense Plasmas Across Temperature Regimes journal October 2014
Strongly Constrained and Appropriately Normed Semilocal Density Functional journal July 2015
Ab Initio Thermodynamic Results for the Degenerate Electron Gas at Finite Temperature journal September 2015
Ab initio Exchange-Correlation Free Energy of the Uniform Electron Gas at Warm Dense Matter Conditions journal September 2017
Nonempirical Semilocal Free-Energy Density Functional for Matter under Extreme Conditions journal February 2018
Thomas-Fermi molecular-dynamics, linear screening, and mean-field theories of plasmas journal July 1992
Generalized Gradient Approximation Made Simple journal October 1996
On the Stability of Molecules in the Thomas-Fermi Theory journal October 1962
Coupled-cluster theory in quantum chemistry journal February 2007
Density functional theory is straying from the path toward the exact functional journal January 2017
Nonlocal exchange contribution to the free energy of inhomogeneous many–fermion systems. I: Formulation of the gradient expansion journal January 1994
Nonlocal exchange contribution to the free energy of inhomogeneous many-fermion systems. II: Second-order gradient coefficient for a Coulomb system journal January 1994
Nonlocal exchange contribution to the free energy of inhomogeneous many-fermion systems. III: Numerical study for screened Coulomb interaction journal January 1994
Material Properties for the Interiors of Massive Giant Planets and Brown Dwarfs journal September 2018