Modeling the Partial Atomic Charges in Inorganometallic Molecules and Solids and Charge Redistribution in Lithium-Ion Cathodes

Partial atomic charges are widely used for the description of charge distributions of molecules and solids. These charges are useful to indicate the extent of charge transfer and charge flow during chemical reactions in batteries, fuel cells, and catalysts and to characterize charge distributions in capacitors, liquid-phase electrolytes, and solids and at electrochemical interfaces. However, partial atomic charges given by various charge models differ significantly, especially for systems containing metal atoms. In the present study, we have compared various charge models on both molecular systems and extended systems, including Hirshfeld, CM5, MK, ChElPG, Mulliken, MBS, NPA, DDEC, LoProp, and Bader charges. Their merits and drawbacks are compared. The CM5 charge model is found to perform well on the molecular systems, with a mean unsigned percentage deviation of only 9% for the dipole moments. We therefore formulated it for extended systems and applied it to study charge flow during the delithiation process in lithium-containing oxides used as cathodes. Our calculations show that the charges given by the CM5 charge model are reasonable and that during the delithiation process, the charge flow can occur not only on the transition metal but also on the anions. The oxygen atoms can lose a significant density of electrons, especially for deeply delithiated materials. We also discuss other methods in current use to analyze the charge transfer and charge flow in batteries, in particular the use of formal charge, spin density, and orbital occupancy. We conclude that CM5 charges provide useful information in describing charge distributions in various materials and are very promising for the study of charge transfer and charge flows in both molecules and solids.