EXAFS structure refinement supplemented by computational chemistry

We present a method that combines structure determination using extended x-ray absorption fine structure (EXAFS) measurements and computational chemistry (CC) calculations, EXAFS/CC. Using such an approach, it is possible to obtain a full structure of model complexes or protein metal active sites, although the EXAFS data primarily give radial distance information about the metal ion’s nearest neighbors. In essence, CC provides a formalism within which chemical knowledge can be introduced to EXAFS modeling. In this sense, the method is analogous to the use of molecular mechanics in standard crystallographic or NMR structure refinement. In addition, the method provides structures that are a compromise between EXAFS data and the CC calculations. Therefore, they can be used directly to obtain energies or study reaction mechanisms. The method is implemented for both density functional theory and molecular mechanics calculations. It is applied to five Ni(II) (both low- and high-spin) and Cu(I/II) complexes with known crystal structures and it is shown to perform well. We also show that the method can be successfully combined with the calculation of ab initio Debye-Waller factors for all paths using the equation-of-motion method and force constants obtained from the CC calculations.

Figure 1

A flowchart of the EXAFS/CC approach (top) compared to that of standard EXAFS refinement (bottom).

Figure 2

(Color online) Comparative EXAFS fit results for $\mathrm{Ni}{\left(\mathrm{en}\right)}_3^{2+}$ (structure in inset), displayed as calculated (dashed line) vs observed (full line) $k^3\chi \left(k\right)$ vs $k$ (a), (b), (c) and Fourier-transformed magnitude ($k^3$-weighted, no phase correction) vs ${\mathrm{R}}^{\prime }$ (d), (e), (f). Results are compared for a two-shell single-scattering fit [(a) and (d); fit 3 in Table ], a full MS analysis using calculated DWFs [(b) and (e); fit 8], and an EXAFS/QM analysis [(c) and (f); fit 29B in Table ]. The fitting range in terms of photoelectron wave number was $2–13{\mathrm{\AA }}^{-1}$ and $1–5\mathrm{\AA }$ in terms of the radial distance from the metal center. The spectrum was collected at $4\mathrm{K}$.

Figure 3

(Color online) Comparative EXAFS fit results for the TMACC complex (structure in inset), displayed as calculated (dashed line) vs observed (full line) $k^3\chi \left(k\right)$ vs $k$ [(a), (b), (c)] and Fourier-transformed magnitude ($k^3$-weighted, no phase correction) vs ${\mathrm{R}}^{\prime }$ [(d), (e), (f)]. Results are compared for a three-shell single-scattering fit [(a) and (d); fit 33 in Table ], a full MS analysis using calculated DWFs [(b) and (e); fit 39], and an EXAFS/QM analysis [(c) and (f); fit 49B in Table ]. The fitting range in terms of photoelectron wave number was $2–16.25{\mathrm{\AA }}^{-1}$ and $1–6\mathrm{\AA }$ in terms of the radial distance from the metal center. The spectrum was collected at $296\mathrm{K}$.

Figure 4

(Color online) Comparative EXAFS fit results for the NiTPP complex (structure in inset), displayed as calculated (dashed line) vs observed (full line) $k^3\chi \left(k\right)$ vs $k$ [(a), (b), (c)] and Fourier-transformed magnitude ($k^3$-weighted, no phase correction) vs ${\mathrm{R}}^{\prime }$ [(d), (e), (f)]. Results are compared for a three-shell single-scattering fit [(a) and (d); fit 56C in Table ], a full MS analysis using calculated DWFs [(b) and (e); fit 59B], and an EXAFS/QM analysis [(c) and (f); fit 71B in Table ]. The fitting range in terms of photoelectron wave number was $2–16{\mathrm{\AA }}^{-1}$ and $1–6\mathrm{\AA }$ in terms of the radial distance from the metal center. The spectrum was collected at $10\mathrm{K}$.

Figure 5

(Color online) Comparative EXAFS fit results for the reduced Bite1 complex (structure in inset), displayed as calculated (dashed line) vs observed (full line) $k^3\chi \left(k\right)$ vs $k$ [(a), (b), (c)] and Fourier-transformed magnitude ($k^3$-weighted, no phase correction) vs ${\mathrm{R}}^{\prime }$ [(d), (e), (f)]. Results are compared for a three-shell single-scattering fit [(a) and (d); fit 78C in Table A2 in the auxiliary material[46]], a full MS analysis using calculated DWFs [(b) and (e); fit 81B], and an EXAFS/QM analysis [(c) and (f); fit 88B]. The fitting range in terms of photoelectron wave number was $2–12.8{\mathrm{\AA }}^{-1}$ and $1–4.5\mathrm{\AA }$ in terms of the radial distance from the metal center. The spectrum was collected at $30\mathrm{K}$.

Figure 6

(Color online) Comparative EXAFS fit results for the oxidized Bite2 complex (structure in inset), displayed as calculated (dashed line) vs observed (full line) $k^3\chi \left(k\right)$ vs $k$ [(a), (b), (c)] and Fourier-transformed magnitude ($k^3$-weighted, no phase correction) vs ${\mathrm{R}}^{\prime }$ [(d), (e), (f)]. Results are compared for a three-shell single-scattering fit [(a) and (d); fit 95C in Table A4 in the auxiliary material (Ref. 46)], a full MS analysis using calculated DWFs [(b) and (e); fit 98B], and an EXAFS/QM analysis [(c) and (f); fit 110B]. The fitting range in terms of photoelectron wave number was $2–12.8{\mathrm{\AA }}^{-1}$ and $1–4.5\mathrm{\AA }$ in terms of the radial distance from the metal center. The spectrum was collected at $30\mathrm{K}$.