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

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