Wavefunctions derived from experiment. III. Topological analysis of crystal fragments

A constrained wavefunction model has been used to extract a Hartree–Fock wavefunction for C₂H₂O₄·4H₂O from both low-angle ( < 0.71 Å⁻¹, 571 reflections) and full ( < 1.00 Å⁻¹, 968 reflections) experimental X-ray diffraction data for crystalline α-oxalic acid dihydrate (α-C₂H₂O₄·2H₂O) using polarized double-ζ and triple-ζ Gaussian basis sets. Properties obtained from the zero-flux partitioning of the total charge-density distribution derived from these wavefunctions, as well as from multipole refinement of the experimental data, are calculated and compared. This work represents the first calculation of integrated atomic properties derived from the fitting of Gaussian density functions to experimental X-ray diffraction data. In particular, atomic kinetic energies derived from experimental data are presented for the first time. The results obtained from the constrained (experimental) charge density show qualitatively similar properties to those obtained from conventional ab initio gas-phase calculations, though the quantitative differences are often substantial. The accuracy of integrated properties calculated using this procedure was established from the analysis of a wavefunction derived from simulated random-error diffraction data; that is, data obtained by adding normally distributed errors to the experimental structure factors. Analysis of this random-error wavefunction indicated that most topological properties are accurate to within approximately 5%, although the error is much larger for those properties that have a steep gradient in the region being evaluated [e.g. the value of ∇²ρ(r_b) at bond critical points] or are very small (e.g. the atomic dipole moment). Calculations of the constrained wavefunction using both the larger basis set and the complete set of experimental data yield results that agree quantitatively with the smaller calculations.