Reactivity Analysis in Diamond Surfaces with a Density Functional Calculation

The surface states of different diamond surfaces are studied using total and partial density of states (DOS) curves, and are related qualitatively to the reactivity of these surfaces, which are important in the process of diamond growth. The calculations combined atomic and functional density approaches with MARVIN and LMTO–ASA codes, respectively. In the atomic calculation, the interatomic potentials are as follows: the b parameter in the Morse potential is 0.5523 Å, the A and B parameters in the nonbonding Lennards–Jonnes potential are 639.6258 eV Ź² and 3.632 eV Å⁶, and the three-body bending potential K₃, is 0.7797 eV rad². To validate these results, the elastic constants were evaluated, finding a good agreement with the experiment. With these potentials, a slab, for each of the diamond surfaces, of 40 carbon atoms with periodic conditions in two dimensions was optimized. The output coordinates were used for DOS calculations. These results were later verified with a surface-cluster calculation of HOMO and LUMO frontier orbitals. These were calculated using a 9-carbon cluster with the DGauss code. In a nonrelaxed surface, two surface states are identified: the first is an occupied state placed at the center of the gap, and the other, adjacent to a valence band maximum, is an empty state of p character and, therefore, potentially able to participate in chemical interactions. In the relaxation process of the surface, the surface states become narrower as the valences of the surface carbons are saturated; in this case the isolated p state participates in dangling bonds. With the monohydrogenation, the surface state placed at the center of the gap of the relaxed surface, becomes a subsurface state, that is, the highest density is not at the surface layer, but in inner layers. As a consequence, the reactivity diminishes. Therefore, it is possible to conclude that the study of surface states could give predictive information about the reactivity of surfaces.