Interplanar binding and lattice relaxation in a graphite dilayer

Abstract

High-precision, large-basis-set calculations, in the local-density approximation (LDA) (using the allelectron, 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%%uo expansion relative to one calculation, 2.5%%uo 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 allelectron 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. The dilayer uniaxial compressibility is much larger than calculated for the crystal, apparently another manifestation of weak interplanar binding. Dilayer Kohn-Sham eigenvalues are largely consistent with those calculated self-consistently for the crystal using the same LDA model. Both differ substantially from the non-self-consistent band structure commonly used to parametrize graphite optical properties of interest in astrophysics. Calculated values of the dilayer work function are larger by about 0.6-0.7 eV than the crystalline experimental results. The dilayer density of states at the Fermi level is predicted to be much smaller than for the crystal, while the occupied bandwidth is in reasonable agreement with crystalline experimental results.

Semiempirical approach to the energetics of interlayer binding in graphite

“…[4][5][6][7][8] The DFT-LDA calculations for graphite have repeatedly given excellent results for the in-plane and even the c-axis lattice constants of graphite. [9][10][11][12][13][14][15][16] Some of these authors have also claimed that their predictions for the interlayer binding energy are reasonably well compared to experiments. [11][12][13]16 However, there has been confusion in quoting the experimental data given by Girifalco and Lad 17 and some corrections such as that due to thermal effect have been ignored in comparisons between theoretical predictions and experiments.…”

“…[9][10][11][12][13][14][15][16] Some of these authors have also claimed that their predictions for the interlayer binding energy are reasonably well compared to experiments. [11][12][13]16 However, there has been confusion in quoting the experimental data given by Girifalco and Lad 17 and some corrections such as that due to thermal effect have been ignored in comparisons between theoretical predictions and experiments. [17][18][19] The apparent success of the LDA for the interlayer binding in graphite has obscured its ability to describe the vdW interaction, and thereby diminished motivation for further work.…”

Interlayer cohesive energy of graphite from thermal desorption of polyaromatic hydrocarbons

“…[1][2][3][4][5][6] These large discrepancies are partly due to the inherent difficulties encountered in the calculation of long-range dispersion forces. Even advanced calculations using nonlocal density functional theory, 6 which account for vdW interactions, with reported values for a single pair of graphene sheets of only 35 meV/atom tend to underestimate the interlayer cohesive energies.…”

“…Not too surprisingly, one finds that values calculated from semiempirical or ab initio methods for the interlayer cohesive or exfoliation energy of graphite range from as little as 8 meV/atom up to 170 meV/atom. [1][2][3][4][5][6] Experimental determinations of the interlayer cohesive energy of graphite have been comparatively rare and are restricted to a heat of wetting experiment by Girifalco which yields an exfoliation energy of 43 meV/atom 7,8 and a measurement by Benedict et al based on radial deformations of multiwall carbon nanotubes which yields 35 meV/atom. 9 At this point it seems that not only the agreement between theory and experiment leaves room for improvement but that the experimental evidence for such comparisons should also be put on a firmer basis.…”

Quantum Hall effect in bilayer graphene: Disorder effect and quantum phase transition

“…The two layers are arranged in the AB ͑Bernal͒ stacking, 16,17 as shown in Fig. 1, where B atoms are located directly below à atoms, and A atoms are the centers of the hexagons in the other layer.…”