Improving Performance by Removing Orbitals

De-orbitalization of meta-GGA  for exchange and correlation replaces the orbital-dependent Kohn-Sham KE density τ with a function of the density n(r), its reduced gradient s(r), and Laplacian  q(r). A de-orbitalized functional typically has been deemed successful if it has error bounds on standard molecular and crystalline data sets akin to those from the parent functional.  Tacitly de-orbitalization has been assumed not improve on the parent functional errors. For molecules, one counter-example is known, meta-GGA made very simple (MVS) functional de-orbitalized with “CRopt”, Phys. Rev. A 96, 052512 (2017). Post-SCF calculations on solids [J. Chem. Phys. 149, 144105 (2018)] showed that MVS(CRopt) did not better performance on standard solid test sets. Some other de-orbitalizers did show MVS betterment for solids, but molecular performance was not studied. The issue of ambiguous betterment thus was unresolved. We have revisited the issue and find that MVS(CRopt) does better than MVS for both solids and molecues if the calculations are self-consistent and done with the same computational techniques as used to test other de-orbitalizations. For systems without d states or without transition metals, the betterment is greater. Imposition of 2nd-order gradient expansion compliance as a de-orbitalization constraint improves performance relative to the parent MVS functional and provides insight as to why de-orbitalized MVS behaves differently from other de-orbitalized meta-GGA functionals.