Semilocal Meta-GGA Exchange-Correlation Approximation from Adiabatic Connection Formalism: Extent and Limitations

Abstract

The incorporation of a strong-interaction regime within the approximate semilocal exchange-correlation functionals still remains a very challenging task for density functional theory. One of the promising attempts in this direction is the recently proposed adiabatic connection semilocal correlation (ACSC) approach [Constantin, L. A.; Phys. Rev. B 2019, 99, 085117] allowing one to construct the correlation energy functionals by interpolation of the high and low-density limits for the given semilocal approximation. The current study extends the ACSC method to the meta-generalized gradient approximations (meta-GGA) level of theory, providing some new insights in this context. As an example, we construct the correlation energy functional on the basis of the high- and low-density limits of the Tao-Perdew-Staroverov-Scuseria (TPSS) functional. Arose in this way, the TPSS-ACSC functional is one-electron self-interaction free and accurate for the strictly correlated and quasi-two-dimensional regimes. Based on simple examples, we show the advantages and disadvantages of ACSC semilocal functionals and provide some new guidelines for future developments in this context.

Figure 1

Correlation energy per particle ϵ_c versus the bulk parameter , for the uniform electron gas. See the text for details of the methods and exact reference curve.

Figure 2

Comparison of the leading term of the XC energy (E_xc = W_∞ + 2W_∞^′) in the strong-interaction regime of Hooke’s atom calculated using different models with FCI data.

Figure 3

Comparison of W_∞ (solid line) and W_∞^′ (dashed line) behaviors for an IBM quasi-2D electron gas of fixed 2D electron density (r_s^2D = 4) as a function of the quantum-well thickness L. Also shown is the exact exchange W₀. PC and mPC are obtained from PBE, and results are taken from ref (110). For PBE, the W_∞ and W_∞^′ expressions are from ref (112). For TPSS, W_∞ and W_∞^′ expressions are given in eqs 17 and 18, respectively.

Figure 4

Correlation energy per particle ϵ_c versus the radial distance from the nucleus r, for the Ar atom (computed using Hartree–Fock analytic orbitals and densities⁻). In the inset, we show the reduced gradient .

Figure 5

Relative error on XC energies of harmonium atoms for various values of ω computed at @EXX orbitals for several functionals using the computational setup from ref (128). The errors have been computed with respect to FCI data obtained in the same basis set.^, For all TPSS-like results, the results have been obtained together with the TPSS exchange energy functional. The GL2 and ISI(TPSS) XC correlation results are obtained with the exact GL2 formula combined with EXX energy expression. The ISI formula utilizes W_∞ and W_∞^′ given by eqs 17 and 18. Exact ISI data are taken from ref (108).

Figure 6

Total energy of the stretched H₂ molecule as calculated with the various methods. The insets present the same data around the equilibrium distance (R/R₀ = 1) and large R/R₀ > 10 values.