Analysis of over-magnetization of elemental transition metal solids from the SCAN density functional

Recent investigations have found that the strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation exchange-correlation functional significantly over-magnetizes elemental Fe, Co, and Ni solids. For the paradigmatic case, bcc Fe, the error relative to experiment is greater than or similar to 20%. A comparative analysis of magnetization results from SCAN and its deorbitalized counterpart, SCAN-L, leads to identification of the source of the discrepancy. It is not from the difference between Kohn-Sham (SCAN-L) and generalized Kohn-Sham (SCAN) procedures. The key is the iso-orbital indicator alpha (the ratio of the local Pauli and Thomas-Fermi kinetic energy densities). Its deorbitalized counterpart alpha(L) has more dispersion in both spin channels with respect to magnetization in an approximate region between 0.6 and 1.2 bohrs around an Fe nucleus. The overall effect is that the SCAN switching function evaluated with alpha(L) reduces the energetic disadvantage of the down channel with respect to up compared to the original alpha, which in turn reduces the magnetization. This identifies the cause of the SCAN magnetization error as insensitivity of the SCAN switching function to alpha values in the approximate range 0.5 less than or similar to alpha less than or similar to 0.8 and oversensitivity for alpha greater than or similar to 0.8.