  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 wavefunction-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 per formula unit. 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
%.
