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The reduced partition function ratio (RPFR) of lithium in lithium-graphite intercalation compounds (Li-GICs) was evaluated at the UB3LYP=6-311G(d) level of theory. The partition functions were written in the usual rigid-rotor harmonic oscillator approximation.With a C 24 H 12  coronene molecule as the model of graphene, lithium-coronene sandwich, and club sandwich compounds were considered as models of Li-GICs. The estimated value of the  6 Li-to- 7 Li RPFR was 1.0402 at 25 °C, which yielded 1.034 as the value of the equilibrium constant, K, of the lithium isotope exchange reaction between a lithium ion in an ethylene carbonate=ethylmethyl carbonate mixed solvent and a lithium atom in interlayer space of graphite. The estimated value of K was larger than the experimental value of 1.025. The unsatisfactory agreement between the estimated and experimental K values suggested that larger molecules should be used as models of graphene and that the vibrational anharmonicity should also be taken into consideration.

Estimation of Reduced Partition Function Ratios of Lithium-Graphite Intercalation Compounds by Density Functional Theory