Supplementary information
Computational details
To investigate performance of the RI-PBE/6-31+g* method for the purpose of
dynamical study of the sodium-water clusters, RI-MP2/6-31+g* molecular dynamics was
performed for the smaller Na.(H2O)n, n = 1-4, 7, clusters. For n = 1-4, these runs lasted
15 ps, with initial equilibration period of 2 ps. For n = 7, eight independent trajectories
were run from the initial geometries taken from the RI-PBE trajectories, with initial
equilibration period of 1.5 ps for each trajectory and total duration of production runs of
20 ps. As documented in Figure S1 and Table S1, spectra and spin density characteristics
(Na-e- distances, radius of gyration) are essentially the same as when the RI-PBE/631+g* molecular dynamics is employed for sampling the ground state density.
For n = 1, 4, 7, the agreement with the RI-PBE/6-31+g* sampling is fully
satisfactory. Broad photoionization spectra for n = 2, 3 are present due to the fact that the
inter-water hydrogen bonds are preferentially formed in the RI-MP2/6-31+g* simulation
of these clusters while the O-Na interactions prevail in the RI-PBE/6-31+g* dynamics.
Therefore, sodium electron is unable to spread among higher number of water molecules
and photoionization spectra are extended to higher IP values. These differences are also
documented in Table S1 where smaller Na-e- distances, radii of gyration and smaller
standard deviations thereof are observed, compared to the RI-PBE/6-31+g* results in
Table 1. However, the spectral features discussed in the main text (shift of the spectra to
lower values of ionization potential, saturation of IP for n = 4 and increasing Na-edistance and gyration radius) are all reproduced.
1
Figure S1 – Ionization spectra of the Na.(H2O)n (n = 1-4, 7) clusters as calculated from
the RI-MP2/6-31+g* dynamics trajectories. Ionization potentials were calculated at the
PMP2/6-31++g**(dp.) level of theory.
2
Table S1 – Mean Na-e- distance and radius of gyration rg for the Na.(H2O)n (n = 1-4, 7,
15) clusters, as obtained from the RI-MP2/6-31+g* molecular dynamics trajectories.
Calculated at the PMP2/6-31++g**(dp.) level of theory.
Cluster
Na.H2O
Na.(H2O)2
Na.(H2O)3
Na.(H2O)4
Na.(H2O)7
r(Na-e-) / Å
0.524 ± -0.018
0.797 ± 0.121
1.17 ± 0.22
2.24 ± 0.36
3.11 ± 0.27
rg / Å
2.60 ± 0.04
2.72 ± 0.19
2.83 ± 0.33
3.59 ± 0.33
3.35 ± 0.28
3
Figure S2 – Spin densities of Na.(H2O)n, n = 1-7, 15, clusters. Geometries of MP2/631+g* local minima were employed for the calculations (PBE/631+g* minima in case of
n = 15). Calculated at the MP2/6-31++g** level of theory.
Electron center of density rCOD and radius of gyration rg were calculated from the
discretized electron spin density s(r) on a grid of 803 points obtained at the MP2 level in
the following way:
4
Spin densities calculated in the local minima of sodium-water clusters are shown in
Figure S2.
To analyze basis set effect on the values of calculated ionization potential and spin
density distribution of the Na.(H2O)n clusters, PMP2 calculations with gradually
increasing basis set were performed (Table S2). In addition to standard 6-31+g* and 631++g** basis sets, we performed calculations with “doped” basis sets 6-31+g*(dp.) and
6-31++g**(dp.). For these, additional sodium basis functions were placed onto the
electron center of density calculated in the preceding step for basis set without doping.
From the results in Table S2, 6-31+g* basis set is seen to be able to reproduce the
sodium-water ionization potentials until n = 7, 15. Here, 6-31++g** basis set increases
the ionization potential because of stabilization of the non-ionized state by supplying the
basis set functions for description of the delocalized electron. Na-e- distance and radius of
gyration are also affected by placing of the polarization and diffuse functions on
hydrogen atom only for n = 7, 15. In these cases, Na-e- distance is increased as more
distant parts of the phase space are spanned. At the same time, electron spin distribution
becomes more compact, as seen from lowering of the radius of gyration.
When passing from the 6-31+g* and 6-31++g** to the doped basis sets 631+g*(dp.) and 6-31++g**(dp.), ionization potentials are not significantly affected.
However, characteristics of the spin distribution are altered markedly, with the largest
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effect for n = 15. Similarly to the transition from 6-31+g* to 6-31++g** basis set, Na-edistance is further increased and radius of gyration decreases.
Table S2 – Ionization potentials, Na-e- distances and radii of gyration calculated in the
PMP2/6-31+g* local minima of the respective sodium-water clusters (PBE/631+g*
minima in case of n = 15). “Doped” basis sets 6-31+g*(dp.) and 6-31++g**(dp.) are
augmented by sodium basis functions positioned on the electron center of density
calculated in the respective basis set without augmentation.
cluster
Na
Na.H2O
Na.(H2O)2
Na.(H2O)3
Na.(H 2O)4
Na.(H2O)5
Na.(H2O)6
Na.(H2O)7
Na.(H2O)15 inner
Property
IP / eV
r(Na-e-) / Å
rg / Å
IP / eV
r(Na-e-) / Å
rg / Å
IP / eV
r(Na-e-) / Å
rg / Å
IP / eV
r(Na-e-) / Å
rg / Å
IP / eV
r(Na-e-) / Å
rg / Å
IP / eV
r(Na-e-) / Å
rg / Å
IP / eV
r(Na-e-) / Å
rg / Å
IP / eV
r(Na-e-) / Å
rg / Å
IP / eV
r(Na-e-) / Å
rg / Å
6-31+g*
4.96
0.00
2.41
4.16
0.53
2.62
3.80
0.92
2.78
3.56
1.32
2.96
3.26
2.10
3.64
3.52
2.05
3.30
3.27
2.40
3.54
3.29
2.54
3.53
2.68
3.43
4.55
6-31+g* (dp.)
4.16
0.52
2.60
3.80
0.92
2.78
3.58
1.39
2.92
3.31
2.53
3.39
3.58
2.38
3.09
3.33
2.91
3.20
3.37
3.06
3.13
2.81
4.63
3.88
6-31++g**
4.17
0.52
2.62
3.82
0.91
2.79
3.59
1.35
2.97
3.31
2.38
3.48
3.57
2.28
3.19
3.33
2.77
3.29
3.37
2.93
3.24
2.83
4.31
3.88
6-31++g** (dp.)
4.18
0.52
2.60
3.83
0.92
2.76
3.61
1.38
2.76
3.33
2.53
3.39
3.59
2.41
3.07
3.35
2.93
3.18
3.38
3.07
3.13
2.84
4.75
3.85
6
Na.(H2O)15 surface IP / eV
r(Na-e-) / Å
rg / Å
3.07
2.88
3.29
3.15
3.36
2.90
3.17
3.29
2.89
3.18
3.36
2.88
Further details on the influence of method and basis set on the calculation of the
ionization potential are provided in Table S3. It is obvious that the DFT/B3LYP method
is not suitable for quantitative reproduction of the ionization potential, overestimating
both experimental value and results of better electronic structure methods (MP2,
CCSD(T)) by about 0.5 eV.
Table S3 – Ionization potentials of the Na(H2O)4 cluster in the geometry optimized at the
PMP2/6-31+g* level.
method
B3LYP
basis set
6-31+g*
6-31++g**
aug-cc-pVTZ
MP2
6-31+g*
6-31++g**
aug-cc-pVTZ
CCSD(T) 6-31+g*
6-31++g**
experiment
IP [eV]
3.81
3.84
3.82
3.26
3.31
3.37
3.30
3.36
3.17
7