Bulk and surface energetics of crystalline lithium hydride: Benchmarks from quantum Monte Carlo and quantum chemistry

We show how accurate benchmark values of the surface formation energy of crystalline lithium hydride can be computed by the complementary techniques of quantum Monte Carlo (QMC) and wave-function-based molecular quantum chemistry. To demonstrate the high accuracy of the QMC techniques, we present a detailed study of the energetics of the bulk LiH crystal, using both pseudopotential and all-electron approaches. We show that the equilibrium lattice parameter agrees with experiment to within 0.03%, which is around the experimental uncertainty, and the cohesive energy agrees to within around 10 meV/f.u. QMC in periodic slab geometry is used to compute the formation energy of the LiH (001) surface, and we show that the value can be accurately converged with respect to slab thickness and other technical parameters. The quantum chemistry calculations build on the recently developed hierarchical scheme for computing the correlation energy of a crystal to high precision. We show that the hierarchical scheme allows the accurate calculation of the surface formation energy, and we present results that are well converged with respect to basis set and with respect to the level of correlation treatment. The QMC and hierarchical results for the surface formation energy agree to within about 1%.

Figure 1

(Color online) Cohesive energy as a function of primitive cell volume for the extrapolated pp-DMC calculations and the quantum chemistry calculations with and without core-valence correlation effects. DMC calculations on finite supercells are included to show convergence. The lines indicate a Birch-Murnaghan fit to the data.

Figure 2

(Color online) Total energy vs time step. This shows the convergence of the ae-DMC calculations with respect to time step and is for a $3\times 3\times 3$ supercell. A linear extrapolation to zero time step is included.

Figure 3

(Color online) Cohesive energy vs primitive cell volume. Here the DMC energy differences have been calculated using a $3\times 3\times 3$ supercell and time step of 0.004 a.u. and the point at $17.03{\text{A}}^3$ calculated using the extrapolation procedure in the text.

Figure 4

(Color online) The convergence of $E^{011}$ (red circles) and $E^{111}$ (blue squares) with respect to maximum cluster size $N$ using MP2/cc-pVTZ for LiH $a=4.084\text{Å}$.