Titolo presentazione The connubiumsottotitolo between quantum mechanicsMilano, XX andmese 20XXcrystallography Piero Macchi Department of Chemistry, Materials, Chemical Engineering, «Giulio Natta», Politecnico di Milano, Milano, Italy The connubium between quantum mechanics and crystallography Macchi P. Cryst. Rev. 2020, 26, 209-268 https://www.tandfonline.com/doi/full/10.1080/0889311X.2020.1853712
1. Historical Background: Who, What, When, Where, Why? 1. the atomic model and the electronic structure 2. the chemical bonding 3. supramolecular interactions 4. wavefunction from experiments 5. modelling electron charge and spin densities
2. State of the Art 1. standard models and beyond 2. chemical bonding analysis 3. molecules and beyond Historical Background The Solvay Conference 1927: Crystallographers & Quantum Physicists
AH Comton WL Bragg L. Brillouin
L De Broglie 1. The atomic model
1803 1897 1911 1913 1926 Rontgen 1896 Laue 1912 It seems to me that the experimental study of the scattered radiation, in particular from light atoms, should get more attention, since along this way it should be possible to determine the arrangement of the electrons in the atoms. Debye P. Zerstreuung von Röntgenstrahlen. Ann. Phys. 1915; 351: 809–823. 1 The atomic model. Was X-ray diffraction able to shed light?
The elastic scattering (Thomson) A distribution which fits Bragg's data acceptably is an arrangement of the electrons in equally-spaced, concentric rings, each ring having the same 4휋푠푖푛휗 퐤 퐤 = number of electrons, and the diameter of the outer ring being about 0.7 of the 휆 distance between the successive planes of atoms. Compton AH. The Distribution of the Electrons in Atoms. Nature. 1915; 95: 343-344.
퐤퐬 퐤ퟎ 휗 휗 2휗 electron r dhkl
2휋 퐤 = 퐤 = 퐬 휆 hkl
Bragg WH, Bragg WL. The Reflexion of X-rays by Crystals. Proc. R. Soc. Lond. A. 1913; 88: 428–38 1 The atomic model. What we gain with a crystal?
No second spectacular crystallographic discovery has since been made of Diffraction image consequences comparable with those of the Lens original discovery of X-ray diffraction. Crystal structure
Ewald PP. Editorial Preface. Acta Cryst. 1948; 1: 1-2. Crystal
X-ray
1 nm
100 nm the crystal is a periodically homogeneous object, a special tool that enables the magnification of a given functionality 1 The atomic model. What we gain with a crystal?
…although calculation, and not a lens, is used in the final stages of its Diffraction image formation, and although Lens Crystal structure certain essential data, used automatically by a lens, Crystal namely the relative phases of the spectra, have to be inferred by means other than optical before the X-ray calculation can be carried out, the [Fourier] 1 nm projection is nevertheless formally an optical image.
James RW. The optical principles of the diffraction of X-rays, G. Bell and 100 nm Sons, London, 1958, page 385. the crystal is a periodically homogeneous object, a special tool that enables the magnification of a given functionality 1 The atomic model. Bragg experiment and the radial electron density distribution
4휋푟 휌 푟
Bragg WL, James RW, Bosanquet CH. The distributions of electrons around the nucleus in the sodium and chlorine atoms. Phil Mag. 1922; 44: 433-449. 1 The atomic model. Bragg experiment and the radial electron density distribution
From experiment (1921)
From experiment (1921)
From theory (>1930) From theory (>1930) 1 The atomic model. Bragg experiment and the radial electron density distribution
25 K Na form factor Na 8 20 L 7푓 ] 6