Ab initio temperature dependence of EXAFS : multiple scattering and configurational averaging for a biologically significant model compound (zinc tetraimidazole complex)

An ab initio calculation of the temperature dependence of the EXAFS spectrum of the zinc (II) tetraimidazole complex has been made and compared to low noise, energy calibrated EXAFS spectra at seven temperatures. The ab initio calculation was based on the MSXAS package, (122), and was adapted to incorporate a full configurational average to account for the temperature dependent damping of the EXAFS spectra due to thermal atomic disorder and it did not involve the fitting of free parameters. The information about the atomic disorder was obtained from two sources: (i) a TLS analysis of x-ray crystallography data which yielded estimates of total atomic displacements and (ii) a full normal mode analysis based on the refinement of a model force field which reproduces the hydrogen-weighted vibrational density of states measured via inelastic neutron scattering. In the latter, a vibrational force field for solid state imidazole was determined which is shown to be a significant improvement over existing force fields, mainly obtained via ab initio methods, since it more accurately reproduces both the eigenvalues and the eigenvectors of the force field ( the eigenvectors correspond to the atomic displacements in the normal vibrations and are frequently not checked for consistency with experiment ). The imidazole force field was subsequently incorporated into the much larger force field for zinc (II) tetraimidazole. This latter force field was shown to be consistent with inelastic neutron scattering measurements of zinc (II) tetraimidazole borofluorate ( boron-11 enriched ), zinc (II) tetraimidazole perchlorate and two deuterated states of the perchlorate compound; this demonstrates the validity of the isolated molecule approach used to model the force field for this case. The mean discrepancy in the rms atomic displacements derived from the normal mode analysis and the TLS analysis is shown to be ±50%. The 105 normal modes modes of the zinc (II) tetraimidazole complex are interpreted in terms of their effect on the damping of the individual multiple scattering paths in the EXAFS spectrum. The Zn-N pair correlation function is found to be dominant in causing damping of the most significant partial signals from both single and multiple scattering paths but it is shown that the cumulative damping effect of other intramolecular motions cannot be neglected. The total configurationally averaged theoretical EXAFS spectra exhibit an underestimate of the amplitude compared to experiment. The magnitude of this underestimate is not uniform through the spectrum and it is shown that the Muffin-Tin energy discontinuity in the modelling of the emitter optical potential causes a significant oscillatory modulation of the theoretical amplitude up to ±25% which persists strongly in the high wavevector regime. The implications of the underestimate and oscillatory modulation of the theoretical amplitude for the EXAFS method as an analytical tool are an impairment of the structural determination beyond the first coordination shell and in particular an underestimate of the values determined for atomic disorder