Interplanar binding and lattice relaxation in a graphite dilayer

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Abstract
High-precision, large-basis-set calculations, in the local-density approximation (LDA) (using the all-electron, full-potential, linear combination of Gaussian orbitals, fitting-function technique), of the cohesive properties and electronic states (bare Kohn-Sham energies) of the isolated AB dilayer of graphite are reported. They show that the dilayer interplanar spacing (c axis) differs little from the value for ABABAB... crystalline graphite (0.7% expansion relative to one calculation, 2.5% contraction relative to another, 2% expansion relative to experiment). This result, which differs significantly from a preliminary report of strong c-axis contraction, is related to the weak interplanar binding. The intraplanar lattice spacing (a axis) is virtually identical with the crystalline value for both the graphite dilayer and monolayer. The interplanar binding energy (obtained directly via optimization of the monolayer ground state with the same techniques) is in excellent (perhaps fortuitous) agreement with the experimental value for the crystal, in contrast with crystalline calculations, which are too large (in magnitude) by 40–100 % or more. The dilayer cohesive energy agrees well with the crystalline value from an all-electron calculation. Both exceed the experimental value in magnitude by over 1 eV/atom, a problem already known to arise from inadequacies in the LDA treatment of the multiplet structure of the isolated C atom.