The cohesive energy of a solid is the energy required to break the atoms
of the solid into isolated atomic species, i.e,
The calculated cohesive energies are presented in Table 3.3. For the atomic calculations spin-dependent forms of all three functionals are employed, with the atoms in their ground-state spin configurations. The energy associated with the bulk solid is evaluated at the optimised lattice constant given in Table 3.1. Convergence tests show that a 10 Å supercell is sufficiently large to converge the total energy of each atom to better than meV/atom.
Again, the LDA and PW91 values are in good agreement with the calculations reported in Refs. [114,115,118,119]. The serious overbinding of LDA is clearly evident. While PW and HCTH go someway to correcting this overbinding, HCTH overcompensates, giving cohesive energies that are systematically lower than experiment. As with the lattice constants, the HCTH error increases as the periodic table is descended, from 0.20 eV (3%) in C to 1.25 eV (19%) in GaAs. The HCTH underbinding is consistent with the overestimated lattice constants in Table 3.1 and the underestimated bulk moduli in Table 3.2.