Ab initio study of the autocorrelation function for lithium nitride

The autocorrelation function B(r→) is the convolution of the density matrix ρ(r→’, r→’+r→), and can be obtained experimentally by taking the Fourier transform of directional Compton profiles. The different terms that contribute to B(r→) are discussed here in general and carefully analyzed in the case of hexagonal lithium nitride (${\mathrm{Li}}_3$N). The results of different Hartree-Fock calculations are compared with recent very detailed experimental data in the basal plane of lithium nitride. It is shown that, while a minimal basis set gives quite wrong results, satisfactory agreement with experiment is obtained with the use of an extended basis set, comprising 28 atomic orbitals per unit cell, and that there is room for further improvements within the Hartree-Fock approximation. Overcoming some limitations of the present experimental technique would make the autocorrelation function a most valuable means for checking the accuracy of calculated wave functions for crystalline systems, and for assessing the adequacy of the employed basis set.