Revisiting the hydration structure of aqueous Na

A combination of theory, X-ray diffraction (XRD) and extended x-ray absorption fine structure (EXAFS) are used to probe the hydration structure of aqueous Na⁺. The high spatial resolution of the XRD measurements corresponds to Q_max = 24 Å^-1 while the first-reported Na K-edge EXAFS measurements have a spatial resolution corresponding to 2k = Q_max = 16 Å^-1. Both provide an accurate measure of the shape and position of the first peak in the Na-O pair distribution function, g_NaO(r). The measured Na-O distances of 2.384 ± 0.003 Å (XRD) and 2.37 ± 0.024 Å (EXAFS) are in excellent agreement. These measurements show a much shorter Na-O distance than generally reported in the experimental literature (Na-O_avg ∼ 2.44 Å) although the current measurements are in agreement with recent neutron diffraction measurements. The measured Na-O coordination number from XRD is 5.5 ± 0.3. The measured structure is compared with both classical and first-principles density functional theory (DFT) simulations. Both of the DFT-based methods, revPBE and BLYP, predict a Na-O distance that is too long by about 0.05 Å with respect to the experimental data (EXAFS and XRD). The inclusion of dispersion interactions (-D3 and -D2) significantly worsens the agreement with experiment by further increasing the Na-O distance by 0.07 Å. In contrast, the use of a classical Na-O Lennard-Jones potential with SPC/E water accurately predicts the Na-O distance as 2.39 Å although the Na-O peak is over-structured with respect to experiment.