Quo vadis, quantum crystallography?

In the past few issues of Acta Crystallographica Section B, including the current one, several articles have reported research work on quantum crystallography. Collectively they comprise a virtual special issue on the subject, the first on such an extended concept in the IUCr journals. Previously, a special issue, dedicated to Philip Coppens (1930–2017), was published in Acta Crystallographica Section B (August 2017). It contained many contributions in the field of charge density (as well as photo-crystallography). Originally intended to celebrate his retirement with contributions on two of the main topics developed during his career, the issue appeared just a few weeks after Professor Coppens passed away and became a kind of memorial issue. The occasion of the present special issue is the principal authors’ participation in the first online quantum crystallography meeting (QCrOM2020) held in August 2020. It was organized (and mostly improvised) to replace the sessions on this subject initially programmed for the IUCr Congress in Prague, which, as we know, was postponed to 2021. Its virtual modality (and its subsequent free of charge registration) made it possible to attract attendees from a wider range of expertise. It was the opportunity to present the latest results and reviews on the field and share opinions during fruitful discussion sessions that normally do not take place at large scale and tightly scheduled meetings like those of the IUCr Congress. Despite all the difficulties caused by the pandemic the field is currently blooming, and the community is undergoing a generational turnover with many new young researchers involved and new groups established. The field’s momentum is testified by the rather broad spectrum of studies published in this special issue, with a variety of research themes and many topics analyzed or reviewed in detail. Quantum crystallography is a modern name for a field that started when quantum mechanics itself was put forward, coinciding with the early days of X-ray crystallography. In keeping with Peter Debye’s early intuition (Debye, 1915), the discovery of X-ray diffraction offered a whole new possibility ‘to establish by experiment the particular arrangement of the electrons in the atoms’. Many studies became possible thanks to the interplay between crystallographic techniques and quantum physics. For example, experimental crystallography was used to unveil the nature of electrons (waves and corpuscles; see De Broglie, 1929), to investigate the electronic structures of metals (Weiss & Demarco, 1958), to map the charge density around atoms to form bonds and molecules or solids (Coppens, 1967), and the electron polarization upon application of external stimuli (such as the electric field, see Hansen et al., 2004) or upon temperature changes. Quite remarkably, these kinds of studies are those that originally attracted the interest of quantum physicists for the emerging field of X-ray crystallography in the 1920s. At the same time, chemists also envisaged the exceptional outcome from crystallographic studies and the vast array of details useful in developing theories of chemical bonding (Pauling, 1939). This sentiment has always accompanied studies on accurate charge density, which has become the favourite observable for revealing the nature of chemical bonding and the supramolecular interactions, especially – but not only – within the paradigm of the quantum theory of atoms in molecules (Bader, 1990) that becomes, in the crystallographic framework, the quantum theory of atoms in molecules and crystals (Gatti, 2005). ISSN 2052-5206