In Paper I [H. Francisco, A. C. Cancio, and S. B. Trickey, J. Chem. Phys. 159, 214102 (2023)], we gave a regularization of the Tao–Mo exchange functional that removes the orderoflimits problem in the original Tao–Mo form and also eliminates the unphysical behavior introduced by an earlier regularization while essentially preserving compliance with the secondorder gradient expansion. The resulting simplified, regularized (sregTM) functional delivers performance on standard molecular and solid state test sets equal to that of the earlier revised, regularized Tao–Mo functional. Here, we address deorbitalization of that new sregTM into a pure density functional. We summarize the failures of the MejíaRodríguez and Trickey deorbitalization strategy [Phys. Rev. A 96, 052512 (2017)] when used with both versions. We discuss how those failures apparently arise in the socalled z′ indicator function and in substitutes for the reduced density Laplacian in the parent functionals. Then, we show that the sregTM functional can be deorbitalized somewhat well with a rather peculiarly parameterized version of the previously used deorbitalizer. We discuss, briefly, a deorbitalization that works in the sense of reproducing error patterns but that apparently succeeds by cancelation of major qualitative errors associated with the deorbitalized indicator functions α and z, hence, is not recommended. We suggest that the same issue underlies the earlier finding of comparatively mediocre performance of the deorbitalized Tao–Perdew–Staroverov–Scuseri functional. Our work demonstrates that the intricacy of such twoindicator functionals magnifies the errors introduced by the MejíaRodríguez and Trickey deorbitalization approach in ways that are extremely difficult to analyze and correct.
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The revised, regularized Tao–Mo (rregTM) exchangecorrelation 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 orderoflimits 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 metageneralizedgradientapproximation DFAs (SCAN and r2SCAN) while also providing superior performance on elemental solid magnetization. Puzzlingly however, rregTM proved to be intractable for deorbitalization via the approach of MejíaRodríguez 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 vonWeizsäcker and Kohn–Sham kinetic energy densities) leads to nonphysical 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 deorbitalization.
more » « less Award ID(s):
 1912618
 NSFPAR ID:
 10496518
 Publisher / Repository:
 American Institute of Physics
 Date Published:
 Journal Name:
 The Journal of Chemical Physics
 Volume:
 159
 Issue:
 21
 ISSN:
 00219606
 Subject(s) / Keyword(s):
 density functional theory metaGGA
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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