Removing Orbital-Dependence to Improve Exchange-Correlation Functional Accuracy

Deorbitalization (replacement of orbital dependence by an explicit density functional) of a meta-generalized gradient approximation for exchange and correlation has been deemed successful if the deorbitalized functional delivers simple error bounds comparable to those from the parent functional on standard data sets. Tacitly, it has been assumed that deorbitalization will not improve on those errors. One counter-example is known; at least on molecular data sets, the meta-GGA made very simple (MVS) functional; see <i>Phys. Rev. A</i> <b>2017</b>, 96, 052512. On the basis of post-SCF calculations [<i>J. Chem. Phys.</i> <b>2018</b>, 149, 144105], it was argued that the unexpected betterment of molecules provided by that one specific deorbitalizer does not occur in solids. Some other deorbitalizers considered in that later work did show performance betterment of MVS on solids; however, molecules were not treated, nor was the issue of ambiguous betterment pursued. We revisit the issue and show that the betterment of MVS for that particular deorbitalizer does occur in solids when the calculations are done self-consistently and with the same computational techniques as used in other deorbitalizations. For systems without <i>d</i> states or without transition metals, that betterment is improved. Imposition of second-order gradient expansion compliance as a constraint upon the deorbitalizer refines (rather than degrades) the improvement relative to the parent MVS functional and provides insight as to why deorbitalized MVS behaves differently from other deorbitalized meta-GGA functionals.