  Motivated by experimental suggestions of anionic redox processes helping to
design higher energy lithium ion-battery cathode materials, we investigate this
effect using first-principles electronic structure calculations for Li-rich
layered sulfides. We identify the determination of the energetic contribution
of intra-atomic Hund's exchange coupling as a major obstacle to a reliable
theoretical description. We overcome this challenge by developing a
particularly efficient flavor of charge-self-consistent combined density
functional + dynamical mean-field theory (DFT+DMFT) calculations. Our scheme
allows us to describe the spin ground states of the transition metal d shell,
the electronic structure of the materials, and its energetics. As a result of
the high-spin to low-spin transition the average intercalation voltage shows
intriguing non-monotonic behavior. We rationalize these findings by an analysis
of the fluctuations of spin and charge degrees of freedom. Our work
demonstrates the relevance of most recent insights into correlated electron
materials for the physics of functional materials such as Li-ion battery
compounds.
