We present the first derivation of explicit analytic expressions for the environmental dependence of the $\sigma$, $\pi$, and $\delta$ bond integrals within the orthogonal two-center tight-binding approximation by using the recently developed bond-order potential theory to invert the nonorthogonality matrix. We illustrate the power of this new formalism by showing that it not only captures the transferability of the bond integrals between elemental bcc Mo and Si and binary ${C11\mathrm{}}_b$ ${\mathrm{MoSi}}_2$ but also predicts the absence of any discontinuity between first and second nearest neighbors for the $\mathrm{dd}\sigma$ bond integral even though large discontinuities exist for $\mathrm{pp}\sigma$, $\mathrm{pp}\pi$, and $\mathrm{dd}\pi$.

• Received 31 January 2000

DOI:https://doi.org/10.1103/PhysRevLett.85.4136