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a
b
Z
μ
lp
lp
O
X
Y
H
bp
bp
H
Fig. 3 (a) Pictorial representation of the projections of the charge vectors along the molecular
axis. O-lp is the vector with origin at the oxygen which identifies the Wannier center for the
electrons of the lone pair orbitals; this vector is indicated by lp. Analogously bp, for bonding pair,
and OH, for the protons.
m
represents the total dipole vector. (b) Projection of the oxygen-
Wannier-center vectors (times the charge) along the molecular axis of water (in Debye) measured
w.r.t. the isolated molecule. Figure adapted from [
45
]
These results basically show, at electronic level, what was already speculated on
a larger scale in the previous section: as the number of water molecule increases,
the repulsion of the electronic clouds of the lone pair electrons increases and thus
the corresponding contribution decreases. This in turn leads to a partial charge
redistribution of the electrons of the bonding pair. In fact, these electrons are also
polarized by the presence of the ions and their orbitals are shifted from the
hydrogens towards the oxygen in the oxygen-ion direction; however, since the
repulsion increases as the number of molecules increases, the electrons are shifted
back towards the hydrogens. Moreover, the rapid increase of the bonding pair
contribution for larger clusters is due to the formation of hydrogen bonds that
shift the bonding pair electron distribution further towards the hydrogen as in the
case of bulk water. These conclusions can be pictorially described by Fig.
4
for the
case of Mg
2
þ
where the focus is on one specific molecule of the system, represented
together with its corresponding electron density map. The latter is determined by
subtracting the electron density of an isolated water molecule with the same
geometry of the molecule in the water-ion system.
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