General expressions for three-centre integrals in crystals

One-electron three-centre integrals between localized functions appearing in calculations of electronic states are expressed as combinations of integrals involving only the relative distances of centres. The explicit dependence of the coefficients on the relative orientations of centres is given in closed general form. When only two centres remain distinct the previous expressions for two-centre integrals are recovered. The case of a simple cubic lattice is explicitly worked out as an illustrative example