First-principles-based calculation of branching ratio for 5$\boldsymbol{d}$, 4$\boldsymbol{d}$, and 3$\boldsymbol{d}$ transition metal systems

A new first-principles computation scheme to calculate `branching ratio' has been applied to various $5d$, $4d$, and $3d$ transition metal elements and compounds. This recently suggested method is based on a theory which assumes the atomic core hole interacting barely with valence electrons. While it provides an efficient way to calculate the experimentally measurable quantity without generating spectrum itself, its reliability and applicability should be carefully examined especially for the light transition metal systems. Here we select 36 different materials and compare the calculation results with experimental data. It is found that our scheme well describes 5$d$ and 4$d$ transition metal systems whereas, for 3$d$ materials, the difference between the calculation and experiment is quite significant. It is attributed to the neglect of core-valence interaction whose energy scale is comparable with the spin-orbit coupling of core $p$ orbitals.