Kohn-Sham density functional theory is the workhorse computational method in materials and surface science. Unfortunately, most semilocal density functionals predict surfaces to be more stable than they are experimentally. Naively, we would expect that consequently adsorption energies on surfaces are too small as well, but the contrary is often found: chemisorption energies are usually overestimated. Modifying the functional improves either the adsorption energy or the surface energy but always worsens the other aspect. This suggests that semilocal density functionals possess a fundamental flaw that is difficult to cure, and alternative methods are urgently needed. Here we show that a computationally fairly efficient many-electron approach, the random phase approximation to the correlation energy, resolves this dilemma and yields at the same time excellent lattice constants, surface energies and adsorption energies for carbon monoxide and benzene on transition-metal surfaces.

We present lattice constants, bulk moduli, and atomization energies of solids using the correlation energy evaluated within the adiabatic connection fluctuation-dissipation framework and applying the random-phase approximation. Recently, we have shown ͓Phys. Rev. Lett. 103, 056401 ͑2009͔͒ that geometrical properties and heats of formation are well described within this approximation. We extend this study to a larger set of materials and focus on the treatment of metals and the effect introduced by the frozen-core approximation.

We introduce the hybrid functional HSEsol. It is based on PBEsol, a revised Perdew-Burke-Ernzerhof functional, designed to yield accurate equilibrium properties for solids and their surfaces. We present lattice constants, bulk moduli, atomization energies, heats of formation, and band gaps for extended systems, as well as atomization energies for the molecular G2-1 test set. Compared to HSE, significant improvements are found for lattice constants and atomization energies of solids, but atomization energies of molecules are slightly worse than for HSE. Additionally, we present zero-point anharmonic expansion corrections to the lattice constants and bulk moduli, evaluated from ab initio phonon calculations.

Water monomer adsorption on graphene is examined with state-of-the-art electronic structure approaches. The adsorption energy determinations on this system from quantum Monte Carlo and the random-phase approximation yield small values of <100 meV. These benchmarks provide a deeper understanding of the reactivity of graphene that may underpin the development of improved more approximate methods enabling the accurate treatment of more complex processes at wet-carbon interfaces. As an example, we show how dispersion-corrected density functional theory, which we show gives a satisfactory description of this adsorption system, predicts that water undergoes ultra-fast diffusion on graphene at low temperatures.

We show that the inclusion of second-order screened exchange to the random phase approximation allows for an accurate description of electronic correlation in atoms and solids clearly surpassing the random phase approximation, but not yet approaching chemical accuracy. From a fundamental point of view, the method is self-correlation free for one-electron systems. From a practical point of view, the approach yields correlation energies for atoms, as well as for the jellium electron gas within a few kcal/mol of exact values, atomization energies within typically 2-3 kcal/mol of experiment, and excellent lattice constants for ionic and covalently bonded solids (0.2% error). The computational complexity is only O(N(5)), comparable to canonical second-order Møller-Plesset perturbation theory, which should allow for routine calculations on many systems.