Quantum crystallography is a branch of crystallography that investigates crystalline materials within the framework of quantum mechanics, with analysis and representation, in position or in momentum space, of quantities like wave function, electron charge and spin density, density matrices and all properties related to them. Quantum crystallography involves both experimental and computational work. The theoretical part of quantum crystallography is based on quantum mechanical calculations of atomic/molecular/crystal wave functions, density matrices or density models, used to simulate the electronic structure of a crystalline material. Experimental works mainly rely on scattering techniques, although spectroscopy as well as atomic microscopy are also sources of information. The connection between crystallography and quantum chemistry has always been very tight, after X-ray diffraction techniques became available in crystallography. In fact, the scattering of radiation enables mapping the one-electron distribution or the elements of a density matrix. The kind of radiation and scattering determines the quantity which is represented and the space in which it is represented. Although the wave function is typically assumed not to be directly measurable, recent advances enable also to compute wave functions that are restrained to some experimentally measurable observable. The term Quantum Crystallography was first introduced in revisitation articles by L. Huang, L. Massa and Nobel Prize winner Jerome Karle, who associated it with two mainstreams: a) crystallographic information that enhances quantum mechanical calculations and b) quantum mechanical approaches to improve crystallography information. This definition mainly refers to studies started in the 1960s and 1970s, when first attempts to obtain wave functions from scattering experiments appeared. This field has been recently reviewed, within the context of this definition. Parallel to studies on wave function determination, R. F. Stewart and P. Coppens investigated the possibilities to compute models for one-electron charge density from X-ray scattering, and later of spin density from polarized neutron diffraction, that originated the scientific community of charge, spin and momentum density. In a recent review article, gave a more general definition: "Quantum crystallography is a research area exploiting the fact that parameters of quantum-mechanically valid electronic model of a crystal can be derived from the accurately measured set of X-ray coherent diffraction structure factors". The book Modern Charge Density Analysis offers a survey of the research involving Quantum Crystallography and of the most adopted experimental or theoretical methodologies. The International Union of Crystallography has recently established a , as extension of the previous commission on Charge, Spin and Momentum density, with the purpose of coordinating research activities in this field.
