Investigations within the local spin density functional theory (LSDF) of the intermetallic hydride system $ {rm CeRhSnH_x} $ were carried out for discrete model compositions in the range $ 0.33 leq x_H leq 1.33 $. The aim of this study is to assess the change of the cerium valence state in the neighborhood of the experimental hydride composition, $ {rm CeRhSnH_{0.8}} $. In agreement with experiment, the analyses of the electronic and magnetic structures and of the chemical bonding properties point to trivalent cerium for $ 1 leq x_H leq 1.33 $. In contrast, for lower hydrogen amounts the hydride system stays in an intermediate-valent state for cerium, like in $ {rm CeRhSn} $. The influence of the insertion of hydrogen is addressed from both the volume expansion and chemical bonding effects. The latter are found to have the main influence on the change of Ce valence character. Spin polarized calculations point to a finite magnetic moment carried by the Ce $ 4f $ states; its magnitude increases with $ x_H $ in the range $ 1 leq x_H leq 1.33 $.
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