Semiempirical approach to the energetics of interlayer binding in graphite

Abstract

The interlayer binding energy of graphite is obtained by a semiempirical method in which ab initio calculations based on the density functional theory (DFT) are supplemented with an empirical van der Waals (vdW) interaction. The local density approximation (LDA) and generalized gradient approximation (GGA) are used in the DFT calculations, and the damping (or interpolation) function used to combine these DFT results with an empirical vdW interaction is fitted to the observed interlayer spacing and c-axis elastic constant. The interlayer binding energies calculated in the LDA and GGA are quite different, but the combined results are nearly the same, which may be a necessary condition and provide reinforcements for validating the method. The present results are also consistent with those obtained by the empirical method based on the Lennard-Jones potential, and both are in reasonable agreement with the recent experimental data. These results indicate that, in contrast to the prevailing belief, the LDA underestimates the interlayer binding energy of graphite.

Radial deformation and stability of single-wall carbon nanotubes under hydrostatic pressure

“…In fact, the contribution of the vdW interaction to the interlayer cohesive energy of graphite is substantial. 47 This is also true for other graphitic systems such as fullerenes and carbon nanotubes. Hence, the above results for E DFT based on the conventional DFT calculations are insufficient for our purpose of calculating the strain energy.…”

“…47 In Eq. ͑3͒, the integrations in the first line over the conformal surface of a SWNT are written in the second line as those along the circumference and the z axis taken to be in the axial direction, and r and rЈ are the atomic positions on the circumferences specified by the variables s and sЈ, respectively.…”

“…Such an extra contribution to the strain energy of a deformed SWNT may be taken into account by the method similar to that used to study interlayer interaction in graphite. 47 By modifying that method, we may write the extra contribution as…”

“…In the previous work, we found that V DFT ͑ld͒ itself can be well represented by a Morse potential. 47 Here, we take a different …”

“…͑4͒ we follow the previous work 47 and assume that the interlayer interaction energy ͑per atom͒ of graphite obtained by the DFT calculations can be written as…”