Reworking the Tao-Mo exchange-correlation functional. I. Reconsideration and simplification

Reworking the Tao-Mo Exchange-Correlation Functional. III. Improved Deorbitalization Strategy and Faithful Deorbitalization

We present a deorbitalization of the recent simplified, regularized Tao-Mo exchange functional ( J. Chem. Phys. 2023, 159, 214102) that is faithful to the parent functional. That is a major gain relative to our earlier deorbitalization which did poorly on molecular heats of formation ( J. Chem. Phys. 2023, 159, 214103). The improvement arises from augmentation of the Mejía-Rodríguez and Trickey deorbitalization strategy ( Phys. Rev. A 2017, 96, 052512) to use a smoothed replacement for the reduced density Laplacian (conventionally denoted q) obtained from that Laplacian itself. The augmentation also rationalizes the improvement obtained from the cutoff of q < 0 that was poorly understood at the time of the previous paper. The new scheme yields deorbitalized chemical region indicators that are much closer to those from the parent, orbital-dependent functional than were obtainable from the previous deorbitalization. It also replicates the good 3d elemental magnetization of the parent functional reasonably well.

Perdew Festschrift editorial

This Special Issue of the Journal of Chemical Physics is dedicated to the work and life of John P. Perdew. A short bio is available within the issue [J. P. Perdew, J. Chem. Phys. 160, 010402 (2024)]. Here, we briefly summarize key publications in density functional theory by Perdew and his collaborators, followed by a structured guide to the papers contributed to this Special Issue.

Reworking the Tao-Mo exchange-correlation functional. II. De-orbitalization

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 order-of-limits problem in the original Tao-Mo form and also eliminates the unphysical behavior introduced by an earlier regularization while essentially preserving compliance with the second-order 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 de-orbitalization of that new sregTM into a pure density functional. We summarize the failures of the Mejía-Rodríguez and Trickey de-orbitalization strategy [Phys. Rev. A 96, 052512 (2017)] when used with both versions. We discuss how those failures apparently arise in the so-called z' indicator function and in substitutes for the reduced density Laplacian in the parent functionals. Then, we show that the sregTM functional can be de-orbitalized somewhat well with a rather peculiarly parameterized version of the previously used deorbitalizer. We discuss, briefly, a de-orbitalization that works in the sense of reproducing error patterns but that apparently succeeds by cancelation of major qualitative errors associated with the de-orbitalized 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 de-orbitalized Tao-Perdew-Staroverov-Scuseri functional. Our work demonstrates that the intricacy of such two-indicator functionals magnifies the errors introduced by the Mejía-Rodríguez and Trickey de-orbitalization approach in ways that are extremely difficult to analyze and correct.