Supporting Material
S1. A test calculation using B3LYP method with the all-electron
basis set
To confirm the reliability of the used effective core potential (ECP) basis set
(LANL2DZ) on the Fe atom in our calculation, we performed an additional test
calculation by using the all-electron basis set (6-311+G(d,p)) on the Fe atom. The
6-311+G(d,p) basis set and the LANL2DZ basis set were employed respectively to
calculate the [Fe(H2O)n]2+ clusters with up to n=6, and the obtained average hydration
energies are displayed in figure S1. As can be seen from figure S1, the trend of the
average hydration energy obtained at the level of the LANL2DZ basis set is quite
similar to that at the level of the 6-311+G(d,p) basis set. When n=6, the average
hydration energy, 2.288 eV, from the calculation of the 6-311+G(d,p) basis set is very
close to the value, 2.285 eV, from the calculation of the lanl2dz basis set. The
exceptional case at n=1 does not affect the whole trend of the energy curve. So, with
consideration of the time-consuming, it is reasonable to use the ECP basis set for our
The average hydration energies (eV)
calculations.
4.0
3.8
3.6
3.4
3.2
3.0
2.8
2.6
2.4
2.2
the 6-311+G(d,p) basis set
the lanl2dz basis set
1
2
3
4
5
6
The number of water molecules (n)
Figure S1. The average hydration energy calculated at the level of the 6-311+G(d,p)
1
basis set and the LANL2DZ basis set respectively
S2. The average Fe-O distances evaluated by using B3LYP, MP2,
B3PW91, and HF methods
Since the structural feature including the bond lengths is also a factor to reflect the
suitability of the used computational method, we thus summarized the average Fe-O
distances obtained at the levels of B3LYP, MP2, B3PW91 and HF. As displayed in
figure S2, the difference of the average Fe-O distances resulted from B3LYP and
B3PW91 levels is tiny, just within 0.003-0.009 Å only. Meanwhile, the trend of the
average Fe-O distances with the cluster size, obtained at the levels of B3LYP and
B3PW91 respectively, are nearly same too. This also implies that both the B3LYP
functional and the B3PW91 functional are reliable to describe the interactions in the
current studies of the hydrated ferrous ion clusters. So, it is suitable to handle the
The average distances of Fe-O (Ang)
concerned systems by using the B3LYP functional.
2.20
B3LYP
MP2
B3PW91
HF
2.15
2.10
2.05
2.00
1.95
1.90
1
2
3
4
5
6
The number of water molecules (n)
Figure S2. The average Fe-O distances obtained at the levels of B3LYP, MP2,
B3PW91, and HF, respectively.
S3. The spin contaminations
The disadvantage of unrestricted calculations is that the wave function is no longer
an eigenfunction of the total spin, <S2>, thus some error may be introduced into the
2
calculation. This error is called spin contamination. If there is no spin contamination,
the expectation value of the total spin, <S2>, should equal s(s+1), where s is 1/2 times
the number of unpaired electrons. One rule of thumb which was derived from
experience with organic molecule calculations is that the spin contamination is
negligible if the value of <S2> differs from s(s+1) by less than 10%. The values of
<s2> and s(s+1) in the calculations are displayed table S1. As can be seen from table
S1, these spin contaminations are very weak for our investigated system and can be
negligible.
Table S1. The values of spin contaminations for the [Fe(H2O)1-19]2+ complexes.
n
1
2
3
4
5
6
7
8
9
10
s(s+1)
6
6
6
6
6
6
6
6
6
6
<S2>
6.0036 6.0039 6.0038 6.004 6.0037 6.0034 6.0037 6.0037 6.0037 6.0038
n
11
12
13
14
15
16
17
18
19
s(s+1)
6
6
6
6
6
6
6
6
6
6.004
6.004
6.004
6.004
<S2>
6.0039
6.004
6.004
6.004
6.004
3