skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Investigations of the exchange energy of neutral atoms in the large- Z limit
The non-relativistic large-Z expansion of the exchange energy of neutral atoms provides an important input to modern non-empirical density functional approximations. Recent works report results of fitting the terms beyond the dominant term, given by the local density approximation (LDA), leading to an anomalous Z ln Z term that cannot be predicted from naïve scaling arguments. Here, we provide much more detailed data analysis of the mostly smooth asymptotic trend describing the difference between exact and LDA exchange energy, the nature of oscillations across rows of the Periodic Table, and the behavior of the LDA contribution itself. Special emphasis is given to the successes and difficulties in reproducing the exchange energy and its asymptotics with existing density functional approximations.  more » « less
Award ID(s):
2154371
PAR ID:
10488878
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
AIP
Date Published:
Journal Name:
The Journal of Chemical Physics
Volume:
160
Issue:
4
ISSN:
0021-9606
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Standard approximations for the exchange–correlation functional in Kohn–Sham density functional theory (KS-DFT) typically lead to unacceptably large errors when applied to strongly correlated electronic systems. Partition-DFT (PDFT) is a formally exact reformulation of KS-DFT in which the ground-state density and energy of a system are obtained through self-consistent calculations on isolated fragments, with a partition energy representing inter-fragment interactions. Here, we show how typical errors of the local density approximation (LDA) in KS-DFT can be largely suppressed through a simple approximation, the multi-fragment overlap approximation (MFOA), for the partition energy in PDFT. Our method is illustrated on simple models of one-dimensional strongly correlated linear hydrogen chains. The MFOA, when used in combination with the LDA for the fragments, improves LDA dissociation curves of hydrogen chains and produces results that are comparable to those of spin-unrestricted LDA, but without breaking the spin symmetry. MFOA also induces a correction to the LDA electron density that partially captures the correct density dimerization in strongly correlated hydrogen chains. Moreover, with an additional correction to the partition energy that is specific to the one-dimensional LDA, the approximation is shown to produce dissociation energies in quantitative agreement with calculations based on the density matrix renormalization group method. 
    more » « less
  2. Abstract 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 non-interacting and exchange-correlation free-energy orbital-free functionals and summarize the theoretical basis of existing local density approximation (LDA), 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. 
    more » « less
  3. The large-Z asymptotic expansion of atomic exchange energies has been useful in determining exact conditions for corrections to the local density approximation in density functional theory. We find that the necessary correction is fit well with a leading ZlnZ term, and find its coefficient numerically. The gradient expansion approximation also displays such a term, but with a substantially smaller coefficient. Analytic results in the limit of vanishing interaction with hydrogenic orbitals (a Bohr atom) are given, leading to the conjecture that the true coefficients for all atoms are precisely 2.7 times larger than their gradient expansion counterpart. Combined with the hydrogen atom result, this yields an analytic expression for the exchange-energy correction which is accurate to ∼5% for all Z. 
    more » « less
  4. The revised, regularized Tao–Mo (rregTM) exchange-correlation density functional approximation (DFA) [A. Patra, S. Jana, and P. Samal, J. Chem. Phys. 153, 184112 (2020) and Jana et al., J. Chem. Phys. 155, 024103 (2021)] resolves the order-of-limits problem in the original TM formulation while preserving its valuable essential behaviors. Those include performance on standard thermochemistry and solid data sets that is competitive with that of the most widely explored meta-generalized-gradient-approximation DFAs (SCAN and r2SCAN) while also providing superior performance on elemental solid magnetization. Puzzlingly however, rregTM proved to be intractable for de-orbitalization via the approach of Mejía-Rodríguez and Trickey [Phys. Rev. A 96, 052512 (2017)]. We report investigation that leads to diagnosis of how the regularization in rregTM of the z indicator functions (z = the ratio of the von-Weizsäcker and Kohn–Sham kinetic energy densities) leads to non-physical behavior. We propose a simpler regularization that eliminates those oddities and that can be calibrated to reproduce the good error patterns of rregTM. We denote this version as simplified, regularized Tao–Mo, sregTM. We also show that it is unnecessary to use rregTM correlation with sregTM exchange: Perdew–Burke–Ernzerhof correlation is sufficient. The subsequent paper shows how sregTM enables some progress on de-orbitalization. 
    more » « less
  5. Abstract Time-dependent density functional theory continues to draw a large number of users in a wide range of fields exploring myriad applications involving electronic spectra and dynamics. Although in principle exact, the predictivity of the calculations is limited by the available approximations for the exchange-correlation functional. In particular, it is known that the exact exchange-correlation functional has memory-dependence, but in practise adiabatic approximations are used which ignore this. Here we review the development of non-adiabatic functional approximations, their impact on calculations, and challenges in developing practical and accurate memory-dependent functionals for general purposes. 
    more » « less