Evaluation of Coulombic lattice sums for vibrational calculations in crystals: An extension of Bertaut's method

The well known general method due to Bertaut for calculating the Coulombic lattice sums in crystals has been extended to evaluating the Coulombic contribution to the dynamical matrices in harmonic lattice-dynamical calculations. The procedure is particularly simple and close to usual crystallographic routines, in line with Bertaut's treatment of the general problem. It involves the evaluation of first derivatives of structure factors for two satellite reflexions of indices h0+q and h0-q for each reflexion of indices h0, with respect to the primitive lattice, where q is the wave vector; the 'self' contribution can be directly evaluated from the second derivatives of F(h0)'s. A particularly interesting feature is that the contribution of the macroscopic field is already included, and it derives from the two satellites of F(000). (orig.)