  Constructing a quantum description of crystals from scattering experiments is
of paramount importance to explain their macroscopic properties and to evaluate
the pertinence of theoretical ab-initio models. While reconstruction methods of
the one-electron reduced density matrix have already been proposed, they are
usually tied to strong assumptions that limit and may introduce bias in the
model. The goal of this paper is to infer a one-electron reduced density matrix
(1-RDM) with minimal assumptions. We have found that the mathematical framework
of Semidefinite Programming can achieve this goal. Additionally, it
conveniently addresses the nontrivial constraints on the 1-RDM which were major
hindrances for the existing models. The framework established in this work can
be used as a reference to interpret experimental results. This method has been
applied to the crystal of dry ice and provides very satisfactory results when
compared with periodic ab-initio calculations.
