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  • 1
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 57 (2001), S. 87-100 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A wavefunction has been derived for the oxalic acid dihydrate molecule using accurate low-temperature X-ray electron-density structure-factor data. The electron density from this constrained theoretical wavefunction is compared to those of unconstrained theoretical wavefunctions. Fitted electron densities around hydrogen atoms show significant deviation compared to Hartree–Fock calculations. In particular, hydrogen bonding appears enhanced in the crystal over theoretical predictions, while the density usually attributed to lone-pair electrons of the oxalic acid oxygen atoms is decreased. The constrained fitting procedure improves the overall agreement of the calculated structure factors even for structure factors that were not used as input to the fitting procedure. The pictures obtained from the constrained fitting procedure are insensitive to random errors introduced into the data. Similarly, the fitting procedure is able to reproduce features that arise from more accurate theoretical calculations. However, we are unable to fit our wavefunction to within the experimentally quoted error bounds without allowing an unreasonably large change in the energy of the constrained wavefunction. Large Hartree–Fock and density functional theory (DFT) cluster calculations involving up to 86 atoms in size also do not show significantly improved agreement with the experimentally observed structure factors. Derived properties from the constrained wavefunction fragments, such as the kinetic energy, electrostatic potential and the electron localization function, are also presented. In general, there are no difficulties in extracting experimental wavefunctions and the associated derived properties from elastic X-ray scattering data for crystal fragments of the order of 20 atoms.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 57 (2001), S. 76-86 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An experimental wavefunction is one that has an assumed form and that is also fitted to experimental measurements according to some well defined procedure. In this paper, the concept of extracting wavefunctions from experimental data is critically examined and past efforts are reviewed. In particular, the importance of scattering experiments for wavefunction fitting schemes is highlighted in relation to the more familiar model, the Hamiltonian paradigm. A general and systematically improvable method for fitting a wavefunction to experimental data is proposed. In this method, the parameters in a model wavefunction are determined according to the variational theorem but subject to an imposed constraint that an agreement statistic between the calculated and observed experimental data has a certain acceptable value. Advantages of the method include the fact that any amount of experimental data can be used in the fitting procedure irrespective of the number of parameters in the model wavefunction, the fact that a unique answer is obtained for a given choice of the model wavefunction, and the fact that the method can be used to model different experiments simultaneously. The wavefunction fitting method is illustrated by developing the theory for extracting a single-determinant wavefunction for a fragment of a molecular crystal, using data obtained from elastic X-ray scattering data. Effects due to thermal motion of the nuclei, secondary extinction of the X-ray scattering and different choices for the crystal fragment are treated.
    Type of Medium: Electronic Resource
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