Abhirup Patra

Properties of real metallic surfaces: Effects of density functional semilocality and van der Waals nonlocality

Significance It is primarily at their surfaces that solids interact with their environments. What is the physics behind the measurable properties of clean metallic surfaces? To answer this question, we calculate surface energies, work functions, and surface interlayer relaxations for aluminum and seven d-electron metals, using a sequence of exchange-correlation density functionals of increasing sophistication. While the simplest one, the local density approximation, works well through error cancellation, the usually more realistic Perdew–Burke–Ernzerhof functional underestimates both surface energies and work functions. The more advanced functionals, including the new strongly constrained and appropriately normed (SCAN) and SCAN+rVV10, demonstrate the unexpected importance of intermediate and long-range van der Waals attraction (seamlessly included in the random phase approximation). We have computed the surface energies, work functions, and interlayer surface relaxations of clean (111), (100), and (110) surfaces of Al, Cu, Ru, Rh, Pd, Ag, Pt, and Au. We interpret the surface energy from liquid metal measurements as the mean of the solid-state surface energies over these three lowest-index crystal faces. We compare experimental (and random phase approximation) reference values to those of a family of nonempirical semilocal density functionals, from the basic local density approximation (LDA) to our most advanced general purpose meta-generalized gradient approximation, strongly constrained and appropriately normed (SCAN). The closest agreement is achieved by the simplest density functional LDA, and by the most sophisticated one, SCAN+rVV10 (Vydrov–Van Voorhis 2010). The long-range van der Waals interaction, incorporated through rVV10, increases the surface energies by about 10%, and increases the work functions by about 3%. LDA works for metal surfaces through two known error cancellations. The Perdew–Burke–Ernzerhof generalized gradient approximation tends to underestimate both surface energies (by about 24%) and work functions (by about 4%), yielding the least-accurate results. The amount by which a functional underestimates these surface properties correlates with the extent to which it neglects van der Waals attraction at intermediate and long range. Qualitative arguments are given for the signs of the van der Waals contributions to the surface energy and work function. A standard expression for the work function in Kohn–Sham (KS) theory is shown to be valid in generalized KS theory. Interlayer relaxations from different functionals are in reasonable agreement with one another, and usually with experiment.

Short-Range Cut-Off of the Summed-Up van der Waals Series: Rare-Gas Dimers

van der Waals interactions are important in typical van der Waals-bound systems such as noble gas, hydrocarbon, and alkaline earth dimers. The summed-up van der Waals series of Perdew et al. 2012 works well and is asymptotically correct at large separation between two atoms. However, as with the Hamaker 1937 expression, it has a strong singularity at short non-zero separation, where the two atoms touch. In this work we remove that singularity (and most of the short-range contribution) by evaluating the summed-up series at an effective distance between the atom centers. Only one fitting parameter is introduced for this short-range cut-off. The parameter in our model is optimized for each system, and a system-averaged value is used to make the final binding energy curves. This method is applied to different noble gas dimers such as Ar–Ar, Kr–Kr, Ar–Kr, Ar–Xe, Kr–Xe, Xe–Xe, Ne–Ne, He–He, and also to the Be2 dimer. When this correction is added to the binding energy curve from the semilocal density functional meta-GGA-MS2, we get a vdW-corrected binding energy curve. These curves are compared with the results of other vdW-corrected methods such as PBE-D2 and vdW-DF2, and found to be typically better. Binding energy curves are in reasonable agreement with those from experiment.