  Graphite has been reported to have anion as well as cation intercalation
capacities as both cathode and anode host materials for the dual ion battery.
In this work, we study the intercalation of bis(trifluoromethanesulfonyl) imide
(TFSI) anion from ionic liquid electrolyte into graphite with first-principles
calculations. We build models for TFSI-C$_n$ compounds with systematically
increasing unit cell sizes of graphene sheet and investigate their stabilities
by calculating the formation energy, resulting in the linear decrease and
arriving at the limit of stability. With identified unit cell sizes for stable
compound formation, we reveal that the interlayer distance and relative volume
expansion ratio of TFSI-C$_n$ increase as increasing the concentration of TFSI
intercalate during the charge process. The electrode voltage is determined to
be ranged from 3.8 V to 3.0 V at the specific capacity ranging from 30 mAh
g$^{-1}$ to 54 mAh g$^{-1}$ in agreement with experiment. Moreover, a very low
activation barrier of under 50 meV for TFSI migration and good electronic
conductivity give a proof of using these compounds as a promising cathode.
Through the analysis of charge transfer, we clarify the mechanism of TFSI-C$_n$
formation, and reveal new prospects for developing graphite based cathode.
