Graphite interlayer distance
Description: determine the interlayer distance of graphite in the stacking direction using the method of Tchatchenko and Scheffler to account for van der Waals interactions.
Semilocal DFT at the GGA level underestimates long-range dispersion interactions. This problem causes a bad overestimation of graphite lattice in the stacking direction (8.84 A (PBE) vs. 6.71 A (exp)).
In this example, dispersion correction method of Tchatchenko and Scheffler (PRL 102, 073005 (2009)) is used to cope with this problem.
Optimal length of the lattice vector c normal to the stacking direction is determined in a series of single point calculations with varied value of c (all other degrees of freedom are fixed at their experimental values).
The computed c vs. energy dependence is written in the file results.dat and can be visualized e.g. using xmgrace. The optimal value can be obtained using the attached utility (python with numpy or Numeric is needed):
200 iterations performed Ch-square: 4.30305519481e-09 ---------
E0(eV): -37.433456779 d0(A): 6.65603352689
The computed value of 6.66 A agrees well with experiment (6.71 A).
Details of implementation of TS in VASP + a number of tests: Bucko et al., PRB 87, 064110 (2013).