Cohesive Energies

The cohesive energy of a solid is the energy required to break the atoms of the solid into isolated atomic species, i.e,

$$E_{\hbox{{coh}}} = E_{\hbox{{solid}}} - \sum_{\hbox{{A}}} E_{\hbox{{A}}}^{\hbox{{isolated}}}$$ (3.26)

where A represents the different atoms that constitute the solid. The cohesive energy is important, not only because it probes the energetic quality of a functional, but also because of the range of densities tested, namely infinite and finite corresponding to the solid and atomic systems respectively. Calculated values of the cohesive energy are compared with experimental results which can be obtained by measuring the latent heat of sublimation at various low temperatures, and extrapolating to zero Kelvin.

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 $1$ meV/atom.

Table 3.3: Cohesive energies (in eV/atom) calculated using the LDA, PW91 and HCTH.

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$91$ 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.