Metal surface energy: Persistent cancellation of short-range correlation effects beyond the random phase approximation

The role that nonlocal short-range correlation plays at metal surfaces is investigated by analyzing the correlation surface-energy into contributions from dynamical density fluctuations of various two-dimensional wave vectors. Although short-range correlation is known to yield considerable correction to the ground-state energy of both uniform and nonuniform systems, short-range correlation effects on intermediate and short-wavelength contributions to the surface formation energy are found to compensate one another. As a result, our calculated surface energies, which are based on a nonlocal exchange-correlation kernel that provides accurate total energies of a uniform electron gas, are found to be very close to those obtained in the random-phase approximation, and support the conclusion that the error introduced by the local-density approximation is small.