Ab initio molecular dynamics: Theory and Implementation

¢¢¢¢¢¢¢¢¢c i (G) n c (G) ∆V local (G)densitymodulen(R)fw FT ¤n tot (G) = n(G) + n c (G)inv FTXCmodulePoissonsolverV xc (R) V H (R) ∆V local (R)V loc (R)Figure 9. Flow chart for the calculation of the local potential from the Kohn–Sham orbitals.This module calculates also the charge density in real and Fourier space and the exchange andcorrelation energy, Hartree energy, and local pseudopotential energy.3.6.1 Initial GuessThe initial guess of the Kohn–Sham orbitals is the first step to a successful calculation.One would like to introduce as much knowledge as possible into the firststep of the calculation, but at the same time the procedure should be general androbust. One should also take care not to introduce artifical symmetries that maybe preserved during the optimization and lead to false results. The most generalinitialization might be, choosing the wavefunction coefficients from a random distribution.It makes sense to weight the random numbers by a function reflectingthe relative importance of different basis functions. A good choice is a Gaussiandistribution in G 2 . This initialization scheme avoids symmetry problems but leadsto energies far off the final results and especially highly tuned optimization methodsmight have problems.A more educated guess is to use a superposition of atomic densities and thendiagonalize the Kohn–Sham matrix in an appropriate basis. This basis can be thefull plane wave basis or just a part of it, or any other reasonable choice. Themost natural choice of atomic densities and basis sets for a plane wave calculationare the pseudo atomic density and the pseudo atomic wavefunction of the atomicreference state used in the generation of the pseudopotential. In the CPMD code thisis one possibility, but often the data needed are not available. For this case thedefault option is to generate a minimal basis out of Slater functions (see Eq. (98) inSect. 2.8) and combine them with the help of atomic occupation numbers (gatheredusing the Aufbau principle) to an atomic density. From the superposition of thesedensities a Kohn–Sham potential is constructed. The Slater orbitals are expanded64