Quantum crystallography: From the intersection to the union of crystallography and quantum mechanics

There has been a recent dramatic surge in interest in the emerging field of Quantum Crystallography (QCr), the topic of this special issue of the Journal of Computational Chemistry. During its General Assembly in Hyderabad in August 2017, the International Union of Crystallography (IUCr) approved renaming its “Commission on Charge, Spin, and Momentum Densities” to its new name “Commission on Quantum Crystallography” to reflect the shift of the consensus of opinion to this direction. There are (or were) at least three international meetings devoted to Quantum Crystallography in 2018-2017. A Wikipedia article on the topic has also been recently published. Finally and significantly, the journal Structural Chemistry has devoted its October 2017 to a special issue titled “Honoring Professor Lou Massa: A Path through Quantum Crystallography”, to give tribute to the principal founder and driver of the field. Quantum Crystallography has its roots in the seminal work of Clinton and Massa, in the sense of constraining the refinement of experimentally-determined crystallographic X-ray structure factors to quantum mechanical requirements such as N-representability and the generation of density matrices or of wavefunctions. The term itself, “Quantum Crystallography”, has been coined in 1995 by Lulu Huang, Lou Massa, and Jerome Karle who fleshed it out with extensive applications subsequently. Possibly because of this history, Quantum Crystallography has been traditionally viewed as the intersection of X-Ray diffraction and quantum mechanics in the original meaning imparted to the term by Huang, Massa, and Karle. This use of the term can be captured in a Venn diagram where QCr is represented by the intersection of two distinct disciplines, that is, X-ray diffraction crystallography on one side and quantum mechanics at the other (Fig. 1). In the CECAM Meeting and in the deliberations among the members of the IUCr’s Commission on QCr regarding the programme of the upcoming Sagamore 2018 Conference in Halifax (Canada), there has been an opinion trend of widening the definition of QCr. A broader definition of QCr is expected to engage communities from neighbouring fields of research that have not as yet interacted much with the Commission’s community. Furthermore, and since the term “Quantum Crystallography” is adopted now to designate the IUCr’s old “Commission on Charge Spin and Momentum Densities”, it is necessary indeed to widen the definition to accommodate the various approaches under the umbrella of the old title under the new one. The view of a larger and more universal definition of QCr may be viewed as the union, rather than just the intersection, of quantum mechanics and crystallography or at least the intersection of these two fields but with fuzzy diffuse boundaries (Fig 1). The diversity of the topics included in this issue of the Journal of Computational Chemistry, by extending thematically from crystallography to quantum mechanics, theory and/or its computational-implementations to specific problems, and passing by the more restricted classical definition of the term, espouses the emerging “union” view of Quantum Crystallography. All the articles included in this issue have been invited. After accepting our invitation, Professor Robert G. Parr (1921–2017) has sadly passed away. The closing comments of the review of one of the anonymous Reviewers of Professor Parr’s paper, Figure 1. A Venn diagram representing the position of “Quantum Crystallography” between the two extremes of its definition as either (a) a clearly delimited and distinct area or research, that of obtaining wavefunctions or density matrices consistent with experiment (the “intersection (\) view”), or (b) a continuum, with fuzzy or no boundaries, that extends from traditional X-ray diffraction crystallography to quantum mechanics which can be viewed as their union ([). View (a) is indicated by the demarcation of the regions and view (b) by the gradually changing color. Both views are valid and are in some sense in a state of superposition. [Color figure can be viewed at wileyonlinelibrary.com]