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We present a comparative analysis of 1$s$ and 2$p$ core-level hard X-rayphotoemission spectroscopy (HAXPES) spectra in metallic VO$_2$ and CrO$_2$.Even though the V 1$s$ and 2$p$ spectra in VO$_2$ display similar line shapesexcept the absence or presence of a spin-orbit coupling splitting, the Cr 1$s$and 2$p$ spectra exhibit distinct main-line shapes. The experimental HAXPESspectra are analyzed by the Anderson impurity model based on the densityfunctional theory + dynamical mean-field theory and a conventional MO$_6$cluster model. We elucidate the complex interplay between formation of theintra-atomic multiplet and charge transfer effect on the chemical bondingfollowed by the 1$s$ and 2$p$ core electron excitations. We demonstrate theadvantage of the 1$s$ excitations to the routinely-employed 2$p$ excitationsfor distinguishing between metal-ligand and metal-metal charge transfercontributions in early 3$d$ transition-metal oxides.

Atomic multiplet and charge-transfer screening effects in 1$s$ and 2$p$ core-level X-ray photoemission spectra of early 3$d$ transition-metal oxides