Abstract
Abstract
Atomic partial charges, integral to understanding molecular structure, interactions and reactivity, remain an ambiguous concept lacking a precise quantum-mechanical definition1,2. The accurate determination of atomic partial charges has far-reaching implications in fields such as chemical synthesis, applied materials science and theoretical chemistry, to name a few3. They play essential parts in molecular dynamics simulations, which can act as a computational microscope for chemical processes4. Until now, no general experimental method has quantified the partial charges of individual atoms in a chemical compound. Here we introduce an experimental method that assigns partial charges based on crystal structure determination through electron diffraction, applicable to any crystalline compound. Seamlessly integrated into standard electron crystallography workflows, this approach requires no specialized software or advanced expertise. Furthermore, it is not limited to specific classes of compounds. The versatility of this method is demonstrated by its application to a wide array of compounds, including the antibiotic ciprofloxacin, the amino acids histidine and tyrosine, and the inorganic zeolite ZSM-5. We refer to this new concept as ionic scattering factors modelling. It fosters a more comprehensive and precise understanding of molecular structures, providing opportunities for applications across numerous fields in the chemical and materials sciences.
Topics

No keywords indexed for this article. Browse by subject →

References
74
[1]
Marenich, A. V., Jerome, S. V., Cramer, C. J. & Truhlar, D. G. Charge model 5: an extension of Hirshfeld population analysis for the accurate description of molecular interactions in gaseous and condensed phases. J. Chem. Theory Comput. 8, 527–541 (2012). 10.1021/ct200866d
[2]
Cho, M., Sylvetsky, N., Eshafi, S., Santra, G., Efremenko, I. & Martin, J. M. L. The atomic partial charges arboretum: trying to see the forest for the trees. ChemPhysChem 21, 688–696 (2020). 10.1002/cphc.202000040
[3]
Hamad, S., Balestra, S. R. G., Bueno-Perez, R., Calero, S. & Ruiz-Salvador, A. R. Atomic charges for modeling metal-organic frameworks: why and how. J. Solid State Chem. 223, 144–151 (2015). 10.1016/j.jssc.2014.08.004
[4]
Leach, A. R. Molecular Modelling: Principles and Applications 2nd edn (Prentice Hall, 2006).
[5]
Brutiu, B. R., Iannelli, G., Riomet, M., Kaiser, D. & Maulide, N. Stereodivergent 1,3-difunctionalization of alkenes by charge relocation. Nature 626, 92–97 (2024). 10.1038/s41586-023-06938-0
[6]
Copper-catalysed asymmetric hydroboration of alkenes with 1,2-benzazaborines to access chiral naphthalene isosteres

Wanlan Su, Jide Zhu, Yu Chen et al.

Nature Chemistry 2024 10.1038/s41557-024-01505-0
[7]
Edelmann, S. & Lumb, J.-P. A para- to meta-isomerization of phenols. Nat. Chem. 16, 1193–1199 (2024). 10.1038/s41557-024-01512-1
[8]
Chan, H. S. S., Lu, Y. & Yu, J.-Q. Palladium-catalysed methylene C(sp3)-H lactamization and cycloamination enabled by chlorinated pyridine-pyridone ligands. Nat. Synth 3, 752–762 (2024). 10.1038/s44160-024-00517-5
[9]
Racioppi, S. & Rahm, M. In-situ electronegativity and the bridging of chemical bonding concepts. Chem. Eur. J. 27, 18156–18167 (2021). 10.1002/chem.202103477
[10]
A quantum theory of molecular structure and its applications

Richard F. W. Bader

Chemical Reviews 1991 10.1021/cr00005a013
[11]
McGrady, G. S. et al. Nature of the bonding in metal-silane σ-complexes. Inorg. Chem. 48, 1588–1598 (2009). 10.1021/ic8019777
[12]
Wall, M. E. Quantum crystallographic charge density of urea. IUCrJ 3, 237–246 (2016). 10.1107/s2052252516006242
[13]
Zagorac, D., Müller, H., Ruehl, S., Zagorac, J. & Rehme, S. Recent developments in the Inorganic Crystal Structure Database: theoretical crystal structure data and related features. J. Appl. Crystallogr. 52, 918–925 (2019). 10.1107/s160057671900997x
[14]
Vaitkus, A., Merkys, A. & Gražulis, S. Validation of the crystallography open database using the crystallographic information framework. J. Appl. Crystallogr. 54, 661–672 (2021). 10.1107/s1600576720016532
[15]
The Cambridge Structural Database

Colin R. Groom, Ian J. Bruno, Matthew P. Lightfoot et al.

Acta Crystallographica Section B Structural Scienc... 2016 10.1107/s2052520616003954
[16]
Spence, J. C. H. Quantitative electron microdiffraction. J. Electron Microsc. 45, 19–26 (1996). 10.1093/oxfordjournals.jmicro.a023407
[17]
Avilov, A., Lepeshov, G., Pietsch, U. & Tsirelson, V. Multipole analysis of the electron density and electrostatic potential in germanium by high-resolution electron diffraction. J. Phys. Chem. Solids 62, 2135–2142 (2001). 10.1016/s0022-3697(01)00170-6
[18]
Tsirelson, V. G. et al. Quantitative analysis of the electrostatic potential in rock-salt crystals using accurate electron diffraction data. J. Phys. Chem. B 105, 5068–5074 (2001). 10.1021/jp0015729
[19]
Suresh, A. et al. Ionisation of atoms determined by kappa refinement against 3D electron diffraction data. Nat. Commun. 15, 9066 (2024). 10.1038/s41467-024-53448-2
[20]
Yonekura, K., Kato, K., Ogasawara, M., Tomita, M. & Toyoshima, C. Electron crystallography of ultrathin 3D protein crystals: atomic model with charges. Proc. Natl Acad. Sci. USA 112, 3368–3373 (2015). 10.1073/pnas.1500724112
[21]
Yonekura, K. & Maki-Yonekura, S. Refinement of cryo-EM structures using scattering factors of charged atoms. J. Appl. Crystallogr. 49, 1517–1523 (2016). 10.1107/s1600576716011274
[22]
Yonekura, K. et al. Ionic scattering factors of atoms that compose biological molecules. IUCrJ 5, 348–353 (2018). 10.1107/s2052252518005237
[23]
Klar, P. B. et al. Accurate structure models and absolute configuration determination using dynamical effects in continuous-rotation 3D electron diffraction data. Nat. Chem. 15, 848–855 (2023). 10.1038/s41557-023-01186-1
[24]
Zhang, G.-F., Liu, X., Zhang, S., Pan, B. & Liu, M.-L. Ciprofloxacin derivatives and their antibacterial activities. Eur. J. Med. Chem. 146, 599–612 (2018). 10.1016/j.ejmech.2018.01.078
[25]
Ito, S. et al. Structure determination of small molecule compounds by an electron diffractometer for 3D ED/MicroED. CrystEngComm 23, 8622–8630 (2021). 10.1039/d1ce01172c
[26]
Guzmán-Afonso, C. et al. Understanding hydrogen-bonding structures of molecular crystals via electron and NMR nanocrystallography. Nat. Commun. 10, 3537 (2019). 10.1038/s41467-019-11469-2
[27]
Crystal Structure Refinement

Peter Müller, Regine Herbst-Irmer, Anthony L. Spek et al.

10.1093/acprof:oso/9780198570769.001.0001
[28]
Frisch, J. M. Gaussian 16 Revision C.01 (Gaussian, 2016).
[29]
Baerlocher, C. & McCusker, L. Database of Zeolite Structures www.iza-structure.org/databases (2017).
[30]
Morris, R. J. & Bricogne, G. Sheldrick’s 1.2 Å rule and beyond. Acta Crystallogr. D59, 615–617 (2003).
[31]
Dauter, Z. Carrying out an optimal experiment. Acta Crystallogr. D66, 389–392 (2010).
[32]
Luebben, J. & Gruene, T. New method to compute Rcomplete enables maximum likelihood refinement for small datasets. Proc. Natl Acad. Sci. USA 112, 8999–9003 (2015). 10.1073/pnas.1502136112
[33]
Authier, A. Dynamical Theory of X-Ray Diffraction (Oxford Univ. Press, 2001).
[34]
Xu, H. et al. A rare lysozyme crystal form solved using highly redundant multiple electron diffraction datasets from micron-sized crystals. Structure 26, 667–675 (2018). 10.1016/j.str.2018.02.015
[35]
Novelli, G., Maynard-Casely, H. E., McIntyre, G. J., Warren, M. R. & Parsons, S. Effect of high pressure on the crystal structures of polymorphs of l-histidine. Cryst. Growth Des. 20, 7788–7804 (2020). 10.1021/acs.cgd.0c01085
[36]
Bruce, P., Bruce, A. & Gedeck, P. Practical Statistics for Data Scientists 2nd edn (O’Reilly Media, 2020).
[37]
Bonded-atom fragments for describing molecular charge densities

F. L. Hirshfeld

Theoretica Chimica Acta 1977 10.1007/bf00549096
[38]
A well-behaved electrostatic potential based method using charge restraints for deriving atomic charges: the RESP model

Christopher I. Bayly, Piotr Cieplak, Wendy Cornell et al.

The Journal of Physical Chemistry 1993 10.1021/j100142a004
[39]
Verstraelen, T., Ayers, P. W., Van Speybroeck, V. & Waroquier, M. Hirshfeld-E partitioning: AIM charges with an improved trade-off between robustness and accurate electrostatics. J. Chem. Theory Comput. 9, 2221–2225 (2013). 10.1021/ct4000923
[40]
Maisriml, J. & Gruene, T. SinglaGUI - a graphical user interface for the SINGLA detector and TEM. Zenodo https://doi.org/10.5281/zenodo.15688376 (2024). 10.5281/zenodo.15688376
[41]
Ferjaoui, K., Fröjdh, E., Takaba, K. & Gruene, T. epocGUI. Zenodo https://doi.org/10.5281/zenodo.15688506 (2024). 10.5281/zenodo.15688506
[42]
XDS

Wolfgang Kabsch

Acta Crystallographica Section D Biological Crysta... 10.1107/s0907444909047337
[43]
SHELXT– Integrated space-group and crystal-structure determination

George M. Sheldrick

Acta Crystallographica Section A Foundations and A... 2015 10.1107/s2053273314026370
[44]
Crystal structure refinement withSHELXL

George M. Sheldrick

Acta Crystallographica Section C Structural Chemis... 2015 10.1107/s2053229614024218
[45]
Hübschle, C. B., Sheldrick, G. M. & Dittrich, B. ShelXle: a Qt graphical user interface for SHELXL. J. Appl. Crystallogr. 44, 1281–1284 (2011). 10.1107/s0021889811043202
[46]
Bamberg, G., Baur, F. & Krapp, M. Statistik Ch. 3 (De Gruyter Oldenbourg, 2012). 10.1524/9783486717471
[47]
Olukayode, S., Froese Fischer, C. & Volkov, A. Revisited relativistic Dirac–Hartree–Fock X-ray scattering factors. I. Neutral atoms with Z = 2–118. Acta Crystallogr. A Found. Adv. 79, 59–79 (2023). 10.1107/s2053273322010944
[48]
Williams, T. & Kelley, C. Gnuplot 4.6: an interactive plotting program. http://gnuplot.sourceforge.net/ (2013).
[49]
Pacoste, L., Ignat’ev, V. M., Dominiak, P. M. & Zou, X. On the structure refinement of metal complexes against 3D electron diffraction data using multipolar scattering factors. IUCrJ 11, 878–890 (2024). 10.1107/s2052252524006730
[50]
Accurate crystal structures and chemical properties from NoSpherA2

Florian Kleemiss, Oleg V. Dolomanov, Michael Bodensteiner et al.

Chemical Science 2021 10.1039/d0sc05526c

Showing 50 of 74 references

Related

You May Also Like

Deep learning

Yann LeCun, Yoshua Bengio · 2015

78,982 citations

Highly accurate protein structure prediction with AlphaFold

John Jumper, Richard Evans · 2021

42,787 citations

Helical microtubules of graphitic carbon

Sumio Iijima · 1991

38,201 citations

Collective dynamics of ‘small-world’ networks

Duncan J. Watts, Steven H. Strogatz · 1998

33,426 citations