The measurement of X-ray diffraction from crystals of (ND4)2Cu(SO4)2 . 6D2O at 9 K gives a set of Bragg intensities as the basic observable. It is shown that ab initio quantum-mechanical calculations on individual isolated ions, near the Hartree-Fock limit, based on nuclear positions from a neutron diffraction experiment, when assembled into the crystal unit cell, reproduce the data set for the complex at a level close to the experimental error limits. This is accomplished using only four adjustable parameters related to the experimental details. Our procedure avoids the biasing effects of multipole models, of which a typical one used one hundred and eighty four parameters.