Errors in the calculation of (27)Al nuclear magnetic resonance chemical shifts

Abstract

Computational chemistry is an important tool for signal assignment of 27Al nuclear magnetic resonance spectra in order to elucidate the species of aluminum(III) in aqueous solutions. The accuracy of the popular theoretical models for computing the 27Al chemical shifts was evaluated by comparing the calculated and experimental chemical shifts in more than one hundred aluminum(III) complexes. In order to differentiate the error due to the chemical shielding tensor calculation from that due to the inadequacy of the molecular geometry prediction, single-crystal X-ray diffraction determined structures were used to build the isolated molecule models for calculating the chemical shifts. The results were compared with those obtained using the calculated geometries at the B3LYP/6-31G(d) level. The isotropic chemical shielding constants computed at different levels have strong linear correlations even though the absolute values differ in tens of ppm. The root-mean-square difference between the experimental chemical shifts and the calculated values is approximately 5 ppm for the calculations based on the X-ray structures, but more than 10 ppm for the calculations based on the computed geometries. The result indicates that the popular theoretical models are adequate in calculating the chemical shifts while an accurate molecular geometry is more critical.

Figure 1

Correlation between the calculated isotropic ²⁷Al chemical shielding constants using the X-ray crystallographic geometries at the B3LYP/6-31G(d) (black squares) and the HF/6-311+G(d,p) (red circles) levels versus those obtained at the B3LYP/6-311+G(d,p) level. The black dashed line and the red dashed line are the best-fit linear regression of the two data sets, respectively, and the best-fit equations are given in Equations 1 and 2. The solid black line is the ideal diagonal line (y = x).

Figure 2

Calculated ²⁷Al shielding constants using the GIAO method with the B3LYP functional with different basis sets in optimized geometries of [Al(OH₂)₆]³⁺ (A), [Al(OH)₄]⁻ (B) and other complexes (C). The basis sets were labeled on the graphs. In Panels A and B, there are three data points for each basis set which represent the values calculated in vacuum, in the PCM environment of water and methanol. Twelve geometries in A were obtained at the B3LYP/aug-cc-pVQZ, B3LYP/aug-cc-pVTZ, B3LYP/aug-cc-pVDZ and B3LYP/6-311++G(d,p) levels in vacuum, in the PCM environment of methanol and water, and the data sets are colored in black, red, blue, green, cyan, magenta, yellow, brown, orange, pink, purple and gray, respectively. The last geometry in A, which is in light orange color, was obtained at the B3LYP/6-31G(d) level in the PCM environment of water. Ten geometries in B were obtained at the B3LYP/aug-cc-pVQZ, B3LYP/aug-cc-pVTZ, B3LYP/aug-cc-pVDZ and B3LYP/6-311++G(d,p) levels in vacuum, at the B3LYP/ aug-cc-pVQZ and B3LYP/aug-cc-pVTZ levels in the PCM environment of methanol, and at the B3LYP/aug-cc-pVQZ, B3LYP/aug-cc-pVTZ, B3LYP/aug-cc-pVDZ and B3LYP/ 6-31G(d) levels in the PCM environment of water, and the data sets are colored in black, red, blue, green, cyan, magenta, yellow, brown, orange and pink, respectively. Six complexes in C are [Al(oxalate)₃]³⁻, [AlF₆]³⁻, [Al(EDTA)]⁻, Al(lactate)₃, [Al(malonate)₂(OH₂)₂]⁻ and [Al(N≡CCH₃)₆]³⁺, respectively. All the values obtained with a same geometry are connected with straight lines.

Figure 3

Correlation between the experimental ²⁷Al chemical shifts versus the calculated values using the X-ray crystallographic geometries at the GIAO-B3LYP/6-31G(d) (black squares), the B3LYP/6-311+G(d,p) (red circles) and the HF/6-311+G(d,p) (blue triangles) levels. The black solid line, the red dashed line and the dotted blue lines are the best-fit linear regression of the three data sets, respectively, and the best-fit equations are given in Equations 3–5.

Figure 4

Correlation between the experimental ²⁷Al chemical shifts versus the calculated values at the GIAO-B3LYP/6-31G(d) level using the optimized geometries at the B3LYP/6-31G(d) level. The black solid line is the best-fit linear regression of the data and the best-fit equation is given in Equation 6, while the dashed red line is the ideal diagonal line (y = x).

Figure 5

Difference between the calculated σ_Al for 10 Al(III) complexes. The blue bars are the differences between the values in the PCM environment of water and in vacuum using the X-ray geometries. The red bars are the differences between the values calculated using the geometries optimized at the B3LYP/6-31G(d) level in the PCM environment of water and those calculated using the X-ray geometries in vacuum. All the σ_Al are calculated at the GIAO-B3LYP/6-31G(d) level. The complexes are [Al(OH₂)₆]³⁺, [Al(oxalate)₃]³⁻, [AlF₆]³⁻, Al(8-hydroxyquinoline)₃, [Al(EDTA)]⁻, Al(lactate)₃, [Al(malonate)₂(OH₂)₂]⁻, [Al(H₋₁citrate)₂]⁵⁻, [Al(N≡CCH₃)₆]³⁺ and Al(maltol)₃ for 1–10, respectively.