Cohesive energy curves for noble gas solids calculated by adiabatic connection fluctuation-dissipation theory

We present first-principles calculations for the fcc noble gas solids Ne, Ar, and Kr applying the adiabatic connection fluctuation-dissipation theorem (ACFDT) to evaluate the correlation energy. The ACFDT allows us to describe long-range correlation effects including London dispersion or van der Waals interaction on top of conventional density functional theory calculations. Even within the random phase approximation, the typical $1∕V^2$ volume dependence for the cohesive energy of the noble gas solids is reproduced, and equilibrium cohesive energies and lattice constants are improved compared to density functional theory calculations. Furthermore, we present atomization energies for ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, and ${\mathrm{O}}_2$ within the same post-density-functional-theory framework, finding an excellent agreement with previously published data.

Figure 1

(Color online) Dependence of the ${\mathrm{N}}_2$ correlation energy difference $(\Delta E_c=E_c^{{\mathrm{N}}_2}-2E_c^{\mathrm{N}})$ on the energy $E_{\mathrm{cut}}^{\chi }$, which determines the rank of the response function matrix [${\left(E_{\mathrm{cut}}^{\chi }\right)}^{-3∕2}$ scale]. Shown are results for different supercell volumes (circles) and the fit to $E_{\mathrm{cut}}^{\chi }=350$ and $300\mathrm{eV}$ (solid lines). The volume dependence of the extrapolated values $\Delta E_c^{\infty }$ is displayed in the second panel (${\mathrm{V}}^{-2}$ scale).

Figure 2

(Color online) ACFDT correlation energy based on LDA (circles) and GGA-PBE (squares) wave functions and eigenenergies plotted over $1∕V^2$. Values are given with respect to the extrapolated correlation energy of the isolated atom.

Figure 3

(Color online) Cohesive energies (meV) as a function of the volume of the primitive cell $\left({\mathrm{\AA }}^3\right)$ for the fcc noble gas crystals Ne, Ar, and Kr. Besides the cohesive energies obtained from ACFDT calculations based on LDA (circles) and GGA-PBE (squares) wave functions and eigenvalues, standard DFT results within the LDA (solid line) and the PBE (dashed line) are shown. The experimental values (without zero-point energy) are given by black diamonds.

Figure 4

(Color online) Kr total ACFDT cohesive energies and contributions arising from the HF and the ACFDT correlation energy calculations. Energies based on DFT-LDA (circles) and DFT-PBE (squares) wave functions and eigenenergies are shown.