Biomedical Engineering Reference
In-Depth Information
optimization calculations have been performed by the Dacapo code
[18, 19], which implements DFT in a supercell approach, using
ultrasoft pseudopotentials for the frozen atom cores. We used a
400 eV cutoff for the expansion of one-electron wave functions, and
the generalized gradient approximation (GGA) for the electronic
exchange-correlation term. The Brillouin zone was sampled by a 4 ×
4 × 1 grid through the Monkhorst and Pack scheme [20]. In general,
we expect hydrogen on the solid surfaces to have nonnegligible
magnetic properties, and hence we have used spin-polarized
calculations in this chapter. A pair of hydrogen atoms on 32-
substrate carbon atoms comprise the unit cell (“isolated” adsorbed
atoms have been treated at half of the coverage), using a single,
isolated graphene sheet with C-C nearest neighbor distances of
1.42 Å and a 15 Å vacuum separating sheets in the periodic supercell
scheme. While surface reconstruction was extensive in terms of the
affected substrate area, it is most prominent within the immediate
vicinity of the adsorbed hydrogen atoms. The carbon atoms closest
to the attached hydrogen expectedly pucker up most, moving to
positions up to 0.8 Å above the lowest-lying substrate atoms. Note
that pairs p1, p2, and p6 are similar to the T-B-T, T-H-T, and T-C-T
final geometries of Ref. [7], respectively. The pairs have been labeled
in a decreasing order of the adsorption strength. Stable hydrogen
pair positions, obtained after geometry optimization only slightly
differ (<0.1 Å increase in H-H separation) from the exact on-top
positions shown in the figure, with the exception of pair p1, where
the repulsion is much stronger.
Hydrogen trimer stabilities were studied for clearer cluster
trending. For the trimer stabilities, stable hydrogen adsorption
configurations have been determined through geometry optimization
calculations using the VASP code [21], which implements the
projector augmented-wave method [22] for DFT-based electronic
structure calculations. All calculations were also spin-polarized and
used the GGA-PBE exchange-correlation functional [23]. We have
applied a 400 eV cutoff to limit the plane wave basis set without
compromising computational accuracy, and a 4 × 4 × 1 Monkhorst-
Pack special k point grid for Brillouin zone sampling. Three H atoms
on a 48-C atom single sheet comprise the unit cell with C-C nearest-
neighbor distances of 1.42 Å before relaxation. All atoms have been
completely unrestricted in the geometry optimization. Similarly,
a 15.0 Å vacuum separating adjacent sheets have been used. We
