DOI:10.1002/chem.201705952 Concept & Physical Chemistry Quantum Crystallography:CurrentDevelopments and Future Perspectives Alessandro Genoni,*[a] Lukas Bucˇinsky´,[b] NicolasClaiser,[c] JuliaContreras-García,[d] Birger Dittrich,[e] PaulinaM.Dominiak,[f] Enrique Espinosa,[c] Carlo Gatti,[g] Paolo Giannozzi,[h] Jean-Michel Gillet,[i] Dylan Jayatilaka,[j] Piero Macchi,[k] AndersØ.Madsen,[l] Lou Massa,[m] ChØrifF.Matta,[n] Kenneth M. Merz,Jr. ,[o] Philip N. H. Nakashima,[p] Holger Ott,[q] Ulf Ryde,[r] Karlheinz Schwarz,[s] Marek Sierka,[t] and SimonGrabowsky*[u] Chem. Eur.J.2018, 24,10881 –10905 10881 2018 Wiley-VCH Verlag GmbH &Co. KGaA, Weinheim Concept Abstract: Crystallographyand quantum mechanics have Nevertheless, many other active andemerging research always been tightly connected because reliable quantum areas involving quantum mechanics andscattering experi- mechanical models are neededtodetermine crystal struc- ments are not covered by the originaldefinition although tures. Due to this natural synergy,nowadays accurate distri- they enable to observeand explain quantum phenomenaas butions of electrons in space can be obtained from diffrac- accurately and successfully as theoriginalstrategies. There- tion and scattering experiments.Inthe original definition of fore, we give an overview over current research that is relat- quantum crystallography (QCr) given by Massa,Karle and ed to abroader notion of QCr,and discuss optionshow QCr Huang, direct extraction of wavefunctions or density matri- can evolve to become acomplete and independent domain ces from measured intensities of reflectionsor, conversely, of natural sciences. The goal of this paper is to initiate dis- ad hoc quantum mechanical calculations to enhancethe ac- cussionsaround QCr,but not to find afinal definition of the curacy of the crystallographic refinement are implicated. field. [a] A. Genoni [m] L. Massa UniversitØ de Lorraine,CNRS, LaboratoireLPCT HunterCollege&the Ph.D. Programofthe Graduate Center 1Boulevard Arago, F-57078, Metz (France) City University of New York, New York (USA) E-mail:[email protected] [n] C. F. Matta [b] L. Bucˇinsky´ Department of Chemistry and Physics, MountSaint Vincent University Institute of Physical Chemistryand Chemical Physics Halifax, Nova Scotia B3M 2J6 (Canada) Slovak University of Technology, FCHPT SUT and RadlinskØho 9, SK-812 37 Bratislava(Slovakia) Department of Chemistry,Dalhousie University [c] N. Claiser,E.Espinosa Halifax, Nova Scotia B3H 4J3 (Canada) UniversitØ de Lorraine,CNRS, LaboratoireCRM2 and Boulevard des Aiguillettes, BP 70239,F-54506, Vandoeuvre-ls-Nancy Department of Chemistry,Saint Mary’s University (France) Halifax, Nova Scotia B3H 3C3 (Canada) and [d] J. Contreras-García DØpartement de Chimie, UniversitØ Laval Sorbonne UniversitØs, UPMC UniversitØ Paris 06 QuØbec, QC G1V 0A6 (Canada) CNRS, Laboratoire de ChimieThØorique (LCT) 4Place Jussieu, F-75252 Paris Cedex 05 (France) [o] K. M. Merz,Jr. Department of Chemistry and Department of Biochemistry and Molecular [e] B. Dittrich Biology,Michigan State University Anorganische und StrukturchemieII, Heinrich-Heine-UniversitätDüsseldorf 578 South Shaw Lane, East Lansing, Michigan 48824(USA) Universitätsstraße 1, 40225 Düsseldorf (Germany) and [f] P. M. Dominiak Institute for Cyber Enabled Research, Michigan State University Biological and Chemical Research Centre,Department of Chemistry 567 WilsonRoad, Room 1440, East Lansing, Michigan 48824(USA) University of Warsaw [p] P. N. H. Nakashima ul. Z˙wirki iWigury 101, 02-089, Warszawa (Poland) Department of Materials Science and Engineering, Monash University [g] C. Gatti Victoria 3800 (Australia) CNR-ISTMIstituto di ScienzeeTecnologie Molecolari [q] H. Ott via Golgi 19, Milano, I-20133 (Italy) Bruker AXS GmbH and ÖstlicheRheinbrückenstraße 49,76187 Karlsruhe (Germany) Istituto Lombardo Accademia di ScienzeeLettere via Brera 28, 20121Milano (Italy) [r] U. Ryde Department of Theoretical Chemistry,Lund University [h] P. Giannozzi Chemical Centre, P.O. Box 124, SE-22100Lund (Sweden) Department of Mathematics, ComputerScience and Physics University of Udine [s] K. Schwarz Via delle Scienze 208, I-33100 Udine (Italy) Technische UniversitätWien, Institut fürMaterialwissenschaften Getreidemarkt 9, A-1060 Vienna (Austria) [i] J.-M. Gillet Structure, Properties and Modeling of Solids Laboratory,CentraleSupelec [t] M. Sierka Paris-Saclay University Otto Schott Institute of Materials Research 3rue Joliot-Curie, 91191 Gif-sur-Yvette (France) FriedrichSchiller University Jena Lçbdergraben 32, 07743 Jena (Germany) [j] D. Jayatilaka SchoolofMolecular Sciences, University of Western Australia [u] S. Grabowsky 35 Stirling Highway,Perth,WA6009 (Australia) Fachbereich 2—Biologie/Chemie Institut fürAnorganische Chemieund Kristallographie, UniversitätBremen [k] P. Macchi LeobenerStr.3,28359 Bremen(Germany) Department of Chemistry and Biochemistry,University of Bern E-mail:[email protected] Freiestrasse 3, CH-3012 Bern (Switzerland) The ORCID identification number(s) for the author(s) of this articlecan be [l] A. Ø. Madsen found under:https://doi.org/10.1002/chem.201705952. Department of Pharmacy,University of Copenhagen Universitetsparken2,2100 Copenhagen(Denmark) Chem. Eur.J.2018, 24,10881 –10905 www.chemeurj.org 10882 2018 Wiley-VCH Verlag GmbH &Co. KGaA, Weinheim Concept 1. Introduction of molecules, which represents akind of magnifying lens of the scatteringofindividual objects. Properties of materials as well as modes of action of drugs are Thus, theoreticalcalculations and scattering experiments are directly related to their electronic structure. Therefore, one of complementary approaches to gain insightinto the electronic the most importantchallenges in modernscience is the accu- structure of compounds. Actually,X-ray diffraction and wave- rate determination of the electronic structure, from which functions have alwaysbeen intimately related, because model- structure–functionrelationships can be derived. One way of ing crystal structures requires atheoretical framework to inter- obtaining information on electronic structure is by calculating pret the measured data, that is, chargedensity is an “observa- wavefunctions of the materials or compounds under investiga- ble” available by means of modeling. The simplest model as- tion using quantum mechanics. Wavefunctions are mathemati- sumesthat diffraction is caused by acombination of non-inter- cal objects that intrinsically contain all the information of acting atoms, each of them represented by aspherically quantum mechanical systems in specific pure states. They can averaged ground-state electron density.[1] This model,univer- be obtained as approximate solutions of the Schrçdinger sally known as Independent AtomModel (IAM),implies calcula- equation(e.g.,through numerical calculations) and allow to tion of atomicwavefunctions, thus relyingonquantum me- determine variousexpectationvalues that can be directly mea- chanics(QM).[2] The vast majority of moderncrystal structure sured through experiments. Another class of experimental “ob- refinementsadopts this model to obtain comparably accurate servables” are availableonly by means of modeling, namely atomic positions and displacement parameters for non-hydro- through optimizations of some parameters that replicate a gen atoms.[3,4] However,already in 1915, Debye pointed out physicalquantity within the assumptionsofagiven theoretical that there is more information in the measuredX-ray diffrac- framework (for example, electron density,magnetization, etc.). tion pattern than the atomic positions. In particular,herecog- At the same time, some modelsbased on electron density nized that “it should be possible to experimentally determine functions may return partial information also on the wavefunc- the special arrangements of the electrons inside an atom”.1[5] tion:for example, an approximate form of the spin part of the More than half acenturylater,this proposal became reality.[6] wavefunctionoranapproximate partofthe atomic or molecu- Today,more accurate crystallographic models are available, lar orbitals. Due to the increasing computational powerand which allow to obtain apicture of the “special arrangements the continuing development of sophisticatedmethods and of the electrons” (namely,the electron density) from X-ray dif- software, wavefunctions can provide profound insights into fractionmeasurements.[7] electronic distributionsand are becoming increasingly impor- In this context, besidesmaximum entropy methods,[8–10] the tant. most populartechnique is the atomic multipolar expansion of Althoughquantum chemistry has reached great maturity the electron density,based on the projection of the electron and abroad base of applications,itisworth bearing in mind density in atomicterms.[11–15] The multipole model is the result that even the most rigorous first-principle calculations for sys- of necessary approximations. In fact, arigorous treatment of tems with more than one electron depend on approximations. two-center scattering would be quite complicated even for Therefore, their predictions must find validations. In quantum simplecompounds,although reported for some diatomic mol- chemistry,this is particularly cogent because the uncertainty ecules.[16] Furthermore, the modeling of atomicdisplacements intrinsically associated with the approximationchosen forthe initially led to additional problems in case of two-center elec- calculation is unknown. Onecan only evaluate the per- tron density functions.[17,18]