Competition between crystal-field, overlap, and three-center contributions in HN eigenspectra

The environment dependence of the on-site energy levels and intersite bond integrals within an orthogonal tight-binding (OTB) model for s-valent systems is determined by the competition between the attractive crystal-field and three-center terms and the repulsive overlap contribution. This is demonstrated explicitly for the case of symmetric HN clusters, where the OTB parameters can be expressed analytically in terms of the nonorthogonal tight-binding (NOTB) on-site, intersite, and overlap matrix elements. The values of the OTB parameters are obtained directly from the density-functional theory eigenspectra of the HN clusters with the on-site energy levels being found to be very sensitive to the local atomic environment but the intersite bond integrals much less so. This different behavior is shown to result from the large cancellations between the crystal-field, overlap, and three-center contributions. The common first-order expression for the OTB on-site energy level as the sum of the NOTB crystal field and a two-body overlap repulsion is found to be a poor approximation due to the sizable values of the overlap in these HN clusters around equilibrium.