The Role of the Lone Pairs in Hydrogen Bonding

Tuesday, February 6 12:00-13:00
ON THE DIFFICULTIES OF JOINT REFINEMENT OF 1-
MATRICES FROM DIFFERENT EXPERIMENTAL DATA
JEAN-MICHEL GILLET
Ecole Centrale Paris ” Laboratoire SPMS, UMR CNRS 8580 ” 92295 Chatenay-Malabry Cedex, France,
jean-michel.gillet@ecp.fr
High resolution x-ray diffraction, convergent beam electron diffraction, deep in- elastic x-ray scattering
(Compton scattering), e-2e and ◦ -e- ◦ spectroscopies have in common to be directly related to the Oneelectron
Reduced Density Matrix (1- RDM)[13]. On the other hand, it is well known [7][3] that the
1-RDM contains all the information about the electronic structure available at the one-electron level.
Unfortunately, and to our best knowledge, few attempts for refining 1-RDM models have been carried out
[2][8][5][12][6] [1]. With the exceptions of Schmider [9][10] for atomic systems, and Schulke and co-workers
[11] only x-ray diffraction data were employed as experimental references. The purpose of this talk is
to discuss to what extent the successfull decomposi- tion of the electron density into aspherical pseudoatomic
contributions [4] can be adapted to the 1-RDM case. Furthermore, we intend to show that, with
such a model, the complementarity between very different experiments can be better ex- ploited through
a joint refinement. Emphasis will be made on the diffculties which are specific to a joint refinement of
1- matrices from different experimental data as opposed to usual ”mono-experimental”refinements.
References
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A 34 (1978), 909-913. 5. S.T. Howard, J.P. Hulke, P.R. Mallinson, and C.S. Frampton, Density matrix
refinement for molecular crystals, Phys. Rev. B 49 (1994), no. 11, 7124-7136. 6. D. Jayatilaka and D.J.
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and S.J. La Placa, Wavefunctions derived by quantum modeling of the electron density from coherent
x-ray diffraction: Beryllium metal., Phys. Rev. Lett. 55 (85), no. 6, 622-625. 9. H. Schmider, K.E.
Edgecombe, V. H. Smith, and W. Weyrich, One-particle density matrix along the molecular bonds in
linear molecules, J. Chem. Phys. 96 (1992), no. 11, 8411-8419. 10. H. Schmider, V. H. Smith, and W.
Weyrich, Z. Naturforsch. A 48 (1993), 211-220. 11. W. Schulke, U. Bonse, and S. Mourikis, Phys. Rev.
Lett. 47 (1981), no. 17, 12091212. 12. J.A. Snyder and E.D. Stevens, A wavefunction and energy of
the azyde ion in potassium azide obtained by a quantum-mechanically constrained fit to x-ray diffraction
data., Chem. Phys. Lett. 313 (1999), 293-298. 13. W. Weyrich, One-electron density matrices and related
observables, Quantum Mechanical Ab- initio Calculation of the Properties of Crystalline Matrials (C.
Pisani, ed.), Springer-Verlag, 1996, pp. 245-272.
I wish to express my warm gratitude to N. Ghermani and Y. Sakurai for essential exchanges on experimental
issues. P.J. Becker, B. Courcot and P. Cortona are greatly thanked for stimulated discussions as
well as the SSpin, Charge and Momentum DensitiesSSagamore community for inspiring this work.
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