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Table 1 Calculated and observed Cr–O and Cr–Fe distances relevant to chromate adsorption onto Fe-oxides and Fe-hydroxides. Experiment data from other studies on goethite [22] and hematite [46] are shown

From: Density functional theory modeling of chromate adsorption onto ferrihydrite nanoparticles

  Cr–O Cr–O(Fe) Cr–O(H) Cr–Fe
Experiment (this study) 1.67    3.35–3.58
Experiment [22, 46] 1.64–1.68 3.30–3.60
Outer-sphere
 Periodic 1.64 1.77 5.27
 M06-2x/6-31G(d) 1.57 1.80 4.17
 M06-2x/6-311+G(d,p) 1.57 1.82 4.95
 B3LYP/6-31G(d) 1.60 1.80 4.42
 B3LYP/6-311+G(d,p) 1.60 1.83 4.54
 PBE0/6-311+G(d,p) 1.59 1.81 5.80
Mono(A)
 Periodic 1.66 1.70 3.54
 M06-2x/6-31G(d) 1.60 1.66 3.39
 M06-2x/6-311 + G(d) 1.61 1.67 3.37
 B3LYP/6-31G(d) 1.63 1.69 3.44
 B3LYP/6-311+G(d,p) 1.63 1.69 3.40
 PBE0/6-311+G(d,p) 1.61 1.68 3.35
Mono(B)
 Periodic 1.66 1.70 3.43
Bi(A)
 Periodic 1.65 1.70 3.29
 M06-2x/6-31G(d) 1.57 1.68 3.19
 M06-2x/6-311+G(d,p) 1.57 1.68 3.23
 B3LYP/6-31G(d) 1.60 1.68 3.23
 B3LYP/6-311+G(d,p) 1.60 1.69 3.26
 PBE0/6-311+G(d,p) 1.59 1.68 3.22
Bi(B)
 Periodic 1.65 1.69 3.26
 M06-2x/6-311+G(d,p) 1.59 1.66 3.40
 B3LYP/6-311+G(d,p) 1.62 1.68 3.48
 PBE0/6-311+G(d,p) 1.61 1.66 3.44
  1. The Mono(B) configuration was not calculated as a cluster due to the prediction of a high total energy in the periodic model—see Table 2