Tight-Binding Calculation of Structure Amplitudes in LiH

The x-ray structure amplitudes in LiH are calculated from tight-binding Bloch functions using the first-order density-matrix formalism of Löwdin, a technique employed previously in calculations of the Compton profile of LiH. The Kunz localized atomic orbitals, which take into account overlaps to first order, are used in the calculations. The symmetric orthonormalization procedure of Löwdin is used to construct atomic orbitals which are orthonormalized over the entire crystal and in which the overlaps of the Kunz wave functions are included exactly. The present calculations are in much better agreement with experiment than (i) previous calculations which used the Kunz wave functions but neglected the overlaps, (ii) the overlap treatment of Waller et al., which used simple screened-hydrogenic wave functions. In the present formalism, reflection planes which have different hkl indices but the same value of $\frac{\left(sin\theta \right)}{\lambda }$ have different structure factors, as is indeed observed experimentally.