Po(IV) hydration: a quantum chemical study.

Abstract

This work presents a theoretical study on the hydration of Po(IV) in solution. Three points have been addressed: (i) the level of calculation needed to properly describe the system under study, (ii) the hydration number of Po(IV), and (iii) the nature of the polonium-water bonding. The condensed medium effects have been included by means of a continuum solvation model, thus different [Po(H(2)O)(n)](4+) hydrates were embedded in a cavity surrounded by a polarizable dielectric medium. Among the quantum-mechanical calculation levels here considered, the MPW1PW91 functional was shown to be the most suitable, allowing a proper description of the Po-H(2)O interactions at affordable cost. The hydration number of Po(IV) was found to be between 8 and 9. This value is ruled by a dynamic equilibrium involving the octa- and ennea-hydrates, although the 7-fold coordination cannot be completely excluded. The hydration free energy of Po(IV) is estimated to be around -1480 kcal/mol. The Po-H(2)O bonding is dominated by strong electrostatic contributions although a small covalent contribution is responsible for the peculiar arrangement adopted by the smaller hydrates (n < or = 5). A natural bond order (NBO) analysis of the hydrate wave functions shows that the covalent bond involves the empty 6p orbitals of the polonium ion and one lone pair on the oxygen atom of the water molecule. A parallel investigation to the hydrate study, where the polonium ion was replaced by a tetravalent point charge plus a repulsion potential, was carried out. These results allowed a detailed examination of the electrostatic and nonelectrostatic contributions to the polonium hydrate formation.

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Po(IV) Hydration: A Quantum Chemical Study
Regla Ayala,†Jose Manuel Martinez,‡Rafael R. Pappalardo,‡A. Mun ˜oz-Paez,†and
Enrique Sanchez Marcos*,‡
Departamento de Quimica Inorganica, CSIC, ICMSE, UniVersity of SeVilla, SeVille 41092, Spain, and
Departamento de Quimica Fisica, UniVersity of SeVilla, E-41012 SeVille, Spain
ReceiVed: July 30, 2007; In Final Form: NoVember 27, 2007
This work presents a theoretical study on the hydration of Po(IV) in solution. Three points have been
addressed: (i) the level of calculation needed to properly describe the system under study, (ii) the hydration
number of Po(IV), and (iii) the nature of the polonium-water bonding. The condensed medium effects have
been included by means of a continuum solvation model, thus different [Po(H2O)n]4+hydrates were embedded
in a cavity surrounded by a polarizable dielectric medium. Among the quantum-mechanical calculation levels
here considered, the MPW1PW91 functional was shown to be the most suitable, allowing a proper description
of the Po-H2O interactions at affordable cost. The hydration number of Po(IV) was found to be between 8
and 9. This value is ruled by a dynamic equilibrium involving the octa- and ennea-hydrates, although the
7-fold coordination cannot be completely excluded. The hydration free energy of Po(IV) is estimated to be
around -1480 kcal/mol. The Po-H2O bonding is dominated by strong electrostatic contributions although a
small covalent contribution is responsible for the peculiar arrangement adopted by the smaller hydrates (n e
5). A natural bond order (NBO) analysis of the hydrate wave functions shows that the covalent bond involves
the empty 6p orbitals of the polonium ion and one lone pair on the oxygen atom of the water molecule. A
parallel investigation to the hydrate study, where the polonium ion was replaced by a tetravalent point charge
plus a repulsion potential, was carried out. These results allowed a detailed examination of the electrostatic
and nonelectrostatic contributions to the polonium hydrate formation.
1. Introduction
Although the discovery of the polonium element was made
by Marie Curie1more than one century ago, the chemistry and
properties of this element and its complexes are still barely
known, primarily because of two reasons. First, polonium is a
very rare element in nature, being found in uranium ores at about
100 micrograms per metric ton. Second is that polonium is
highly toxic,2the main hazard being its intense radioactivity
(as an R emitter), which makes it very difficult to handle safely.
Polonium has 25 known isotopes, all of them being radioactive.
The half-life of210Po, the most widely available, is 138.376
days. Even at trace concentrations, this isotope is lethal by
ingestion or inhalation. In the case of individual or environ-
mental contamination, the nature of chemical species that are
present are far from being understood. Therefore, characteriza-
tion and understanding of polonium complexes can help to
develop protocols and strategies to minimize its lethal effects
on living beings, and to control its diffusion in natural
environments.
Although it is known that polonium metal salts dissolve
readily in dilute acids and are only slightly soluble in alkalis,3
their chemistry in solution has scarcely been studied. In this
work, we have focused on the theoretical study of the hydration
of Po(IV). The absence of previous studies on this subject, either
experimental or theoretical, compelled us to begin this study
with the most basic of steps, the only information having been
reported so far being that the hydration number of the Po(IV)
in solution is between 6 and 8.4The use of computational
chemistry can increase our understanding of these systems while
avoiding the difficulties of experimental methods. Since a
standard methodology to achieve an accurate description of ionic
solvation phenomena has not been established, the first chemical
candidates to be thoroughly examined were the aquaion forms,
[Po(H2O)n]4+. These species should be present in highly acidic
aqueous solutions, as reported for other tetravalent cations in
similar media.5,6
Taking into account the high charge of this radioactive cation,
several species such as aquaions, hydrolyzed forms or oligomers,
may be expected in aqueous solutions as a function of the
medium acidity, ionic strength, the presence of counterions, and
other factors. Therefore, considering this complex scenario, we
have focused exclusively on the aquaion forms.
To unveil the nature of ionic solutions from the computational
point of view, it is essential to gain knowledge of the structural,
thermodynamic, and dynamical properties of the system under
study. Considering first the structural and thermodynamic
properties, the study of small clusters [M(H2O)n]m+/-(n typically
between 1 and 10) in gas phase and the a posteriori inclusion
of bulk solvent effects via the polarizable continuum model
(PCM)7can give us an initial guide to the behavior of the system
in solution.8-10To get further insight into the system it is
necessary to perform computer simulations, e.g., Monte Carlo
or molecular dynamics. These methods require the availability
of reliable interaction potentials for classical simulations or
pseudopotentials and/or basis sets for ab initio simulations.
This work focuses on the structural and thermodynamic
properties of the Po(IV) in aqueous solution. The strategy
applied has been the analysis of both the specific Po-H2O
* Corresponding author.E-mail: sanchez@us.es.
†Departamento de Quimica Inorganica.
‡Departamento de Quimica Fisica.
5416
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interactions in [Po(H2O)n]4+clusters with an increasing number
of water molecules, as well as the analysis of long-range
interactions with the bulk by including a dielectric continuum
surrounding the aquaions.
The aim of this work is centered on three points. The first
one is to find a reasonable quantum mechanical level involving
the inclusion of solvent effects to tackle the Po(IV) hydration.
The second is the determination of the most stable structure
for the aquaion, while the third is the description of the bonding
nature of the polonium hydrates.
2. Methodology
Ab initio (HF, MP2, and CCSD(T)) and density functional
theory (DFT) (B3LYP,11,12G96LYP13-16and MPW1PW9117)
methods were used to optimize [Po(H2O)n]4+clusters in gas
phase for n ) 1-9, and for CCSD(T) n ) 1-3. Calculations
were carried out with the Gaussian 03 program,18except for
the CCSD(T) calculations, which were performed with the
NWCHEM program.19Although hybrid functionals are gener-
ally considered more suitable for transition metal chemistry,20,21
G96LYP was also included in this work on the basis of Truhlar
and co-workers results.22,23The Dunning aug-cc-pVDZ24basis
sets were used for O and H. For Po, the relativistic small core
pseudopotential (60 core electrons) developed by Dolg and co-
workers25was used for the core electrons, while the valence
electrons were described with the aug-cc-pVDZ basis set.25The
choice of Dunning basis sets was motivated by the desire for
consistency with the limited availability of high quality small
core pseudopotentials and basis sets for the polonium atom.
In the first instance, the [Po(H2O)n]4+(n ) 1-9) clusters
were fully optimized in gas phase. Different optimizations
starting from usual arrangements corresponding to each coor-
dination number were performed. In the case of clusters with n
) 1-6, the final structures are shown in Figure 1. For larger
clusters (n ) 7-9), depending on the starting geometry, we
obtained either the optimized geometries given in Figure 1 or
structures where a rearrangement of the first hydration shell had
taken place, in conjunction with the migration of some water
molecules to the second hydration shell. The explicit hydration
beyond the first shell is out of the scope of this study and would
need a different methodological framework.33
The basis set superposition error (BSSE) was computed using
the counter-poise method26,27for [Po(H2O)n]4+clusters with n
) 1 and 2. For the DFT methods, the estimation of the BSSE
was smaller than 0.2% of the total energy, whereas values below
2% were obtained for the MP2 and CCSD(T) methods. The
[Po(H2O)n]4+(n ) 1-9) clusters that were characterized as
minima (no negative frequencies) were taken as the starting point
for the optimizations in solution via the polarizable continuum
method in the integral equation formalism (IEFPCM).28-31The
continuum-discrete model used in this study takes into account
the cavity containing the Po(IV) ion and its first hydration shell,
and the dielectric continuum surrounding the cavity.8,10The
static dielectric permittivity of liquid water at 298 K (? ) 78.39)
was used for the dielectric continuum. With the reoptimization
in solution, bulk solvent effects were taken into account on both
energies and geometries. As shown in a number of previous
studies of monatomic cations, the inclusion of explicit solvent
molecules in the first hydration shell is necessary to obtain
reliable values of the free energy of solvation.8,32The second
or outer solvation shells are rarely included due to the rapid
increase of computational cost, as well as methodological
concerns associated with proper inclusion of statistical contribu-
tions in the quantum mechanical calculations.33,32The cavity
enclosing the hydrates was built using the following radii: 1.520
Å for O, 1.200 Å for H, and 2.354 Å for Po.34,35These radii
have been multiplied by a standard factor of 1.2 in order to
take into account the fact that atomic bond or lone pair centers
of the solvent molecules are normally located slightly further
from the solute atoms than their van der Waals radii.7Free
energies of the clusters in gas phase and in solution were
calculated.
Solvation free energies were calculated within the semi-
continuum model33,36,37as
where ∆Gclusteris the free energy of formation of the cluster;
∆Gcontis the solvation energy corresponding to the long-range
Figure 1. MPW1PW91 optimized structures of [Po(H2O)n]4+clusters
(n ) 1-9).
∆Gsolv) ∆Gcluster+ ∆Gcont+ ∆Gcav+ ∆Gdisp-rep+
n∆Gvap(1)
Po(IV) Hydration
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interactions of the hydrated cluster embedded in a cavity inside
a continuum; ∆Gcav is the free energy needed to create the
cavity; ∆Gdisp-repis a term that collects the hydrate-continuum
dispersion and repulsion contributions; and n∆Gvapis the free
energy needed to evaporate n water molecules from the liquid
pure solvent to the gas phase, in order to form the hydrate. A
temperature of 298 K was assumed. As previously re-
ported,9,10,33,38the standard application of the PCM method using
the interlocked spheres procedure to define the solute cavity
predicts a shortening of the Po-O distance in the [Po(H2O)n]4+
hydrate compared to the gas-phase geometry. In our case, this
shortening is about 0.05 Å. However, ∆Gclusterwas computed
from the gas-phase geometries because the shortening due to
solvent effects has an almost negligible energetic effect (less
than 5 kcal/mol in all cases). The polonium contribution to the
dispersion and repulsion term was neglected, as no parameters
are currently available for that element. Nevertheless, the
dispersion-repulsion term of the hydrate is largely dominated
by the first hydration shell where water molecules roughly
enclose the polonium cation, making its contribution negligible.
∆Gvapwas taken from experimental data (2.05 kcal/mol).39
3. Results and Discussion
3.1. Choice of Calculation Level. In order to ascertain the
most convenient computational methods to properly describe
[Po(H2O)n]4+clusters, different ab initio (HF, MP2, CCSD(T))
and DFT (B3LYP, G96LYP, MPW1PW91) methods were
tested. In the absence of experimental data, we assumed that
an accurate description of energetics and structural properties
of the Po-H2O clusters would be given by high-level ab initio
calculations such as CCSD(T). This method is generally
regarded as the most accurate among the electronic structure
methods practically applicable.40The excellent agreement
between CCSD(T) and experimental results for other molecular
systems supports the hypothesis that this level of theory will
predict accurate properties such as bonding distances and
interaction energies.41,42However, while CCSD(T) calculations
are highly accurate, they are computationally too expensive and
cannot be used for full geometry optimizations of clusters with
n > 3. This is mainly due to the fact that the gradients required
for the optimization have to be computed numerically. For
instance, the full geometry optimization of the [Po(H2O)3]4+
cluster at CCSD(T) level took 20 days using 8 Itanium 2 1.6
GHz CPUs. Nevertheless, results for the small clusters optimized
at the CCSD(T) level can be used as a reference to calibrate
the other methods included in this study.
Table 1 shows structural data for the methods and clusters
considered in this work. The equilibrium structures for the [Po-
(H2O)n]4+clusters (n ) 1-9) obtained by the MPW1PW91
method are shown in Figure 1. The optimizations carried out
with HF, MP2, CCSD(T), and B3LYP generate similar struc-
tures. G96LYP-optimized structures for n ) 3-5 are slightly
different. The main differences in the results obtained by the
different methods employed are found in the Po-O distances.
As a rule, DFT Po-O distances are longer than ab initio ones,
the gap with HF and MP2 being more pronounced than that for
CCSD(T). The longest distances are obtained with G96LYP,
whereas B3LYP and MPW1PW91 are more similar to each
other and to ab initio methods. As expected, Po-O distances
lengthen with the increase of the hydration number for all
computational levels. A closer analysis of Table 1 shows that
there is not a simple pattern defining the Po-O distance in terms
of the number of water molecules, n, and the method employed.
For n ) 1 CCSD(T), the Po-O distance is closer to the B3LYP
distance than to those of the other two DFT methods
(MPW1PW91 and G96LYP), while it is longer than both the
HF and MP2 distances. For n ) 2, CCSD(T) Po-O distances
are more similar to those of MPW1PW91 than to those of the
other methods. HF and MP2 Po-O distances reduce their
discrepancies with CCSD(T). B3LYP Po-O distances are
slightly longer than those obtained from CCSD(T), while the
G96LYP distances are too long. The results for n ) 3 follow
the trend shown for n ) 2, that is, CCSD(T) and MPW1PW91
distances are similar, HF and MP2 results evolve to resemble
CCSD(T) ones, B3LYP Po-O distances are slightly longer than
CCSD(T) results, and G96LYP results are too long.
The previous analysis of the results obtained for [Po(H2O)n]4+
clusters (n ) 1-3) highlights a difference in the results of the
methods between G96LYP, where the results diverge from
CCSD(T), and the other methods, HF, MP2, MPW1PW91, and
B3LYP, where results resemble those from CCSD(T) to a certain
extent. Although CCSD(T) results are not available for n g 4,
results from the other methods can be compared to each other,
and they show that the trend observed in the small clusters (n
) 1-3) is maintained. HF, MP2, MPW1PW91, and B3LYP
results are more similar as n increases, especially in the case of
the first three methods, while G96LYP distances are consistently
longer.
Not only does G96LYP overestimate Po-O distances, but
also the structures for clusters with n )3-5 were observed to
be slightly different. As shown in Figure 1c, in other cases the
[Po(H2O)3]4+cluster is not flat but adopts a trigonal pyramid
arrangement. This pyramidalization is less marked in the case
of G96LYP. For n ) 4, the cluster optimized at G96LYP can
be described as a distorted tetrahedron centered on the polonium
atom, while the remaining structures followed the arrangement
shown in Figure 1d. This structure (Figure 1d) is peculiar since
it is rather different from the typical arrangements for this
coordination, either tetrahedral or square planar coordination
with the cation in the center. The origin of this peculiar structure
(Figure 1d) and the nature of the Po-H2O bonding will be
discussed in section 3.3. A singular behavior of G96LYP in
the structural pattern of the water molecules around the polonium
ion is again found for n ) 5. In this sense, whereas [Po(H2O)5]4+
structures optimized by HF, MP2, MPW1PW91, and B3LYP
methods can be defined as distorted tetragonal pyramids centered
on the metal cation (Figure 1e), the G96LYP structure is a
distorted trigonal bipyramid in which the ion is at the center.
For n ) 6-9, the structures are pretty similar, regardless of the
TABLE 1: Po-O Distances (Å) of the [Po(H2O)n]4+Clusters
(n ) 1-9) Optimized by Different Quantum Mechanical
Methods
n
1 2.05
2 2.08
3 2.12
4 2.13
2.14
2.23 × 2 2.25 × 2
5 2.13
2.26 × 4 2.27 × 4
6 2.30
7 2.31
2.32 × 2 2.35 × 3
2.35 × 2 2.36
2.39
8 2.38
9 2.40 × 6 2.39 × 6
2.47 × 3 2.45 × 3
HF MP2
2.08
2.11
2.14
2.15
2.16
MPW1PW91
2.10
2.12
2.15
2.17
2.18
2.26 × 2
2.17
2.28 × 4
2.31
2.32 × 2
2.36 × 2
2.37
2.38 × 2
2.38
2.40 × 6
2.46 × 3
B3LYP
2.12
2.15
2.18
2.19
2.21
2.28 × 2
2.20
2.30 × 4 2.33 × 3
2.33
2.34 × 2 2.37 × 2
2.35
2.38 × 2 2.41 × 2
2.40 × 2 2.43 × 2
2.40
2.42 × 6 2.45 × 3
2.49 × 3 2.47 × 3
G96LYP CCSD(T)
2.18
2.19
2.21
2.30
2.13
2.12
2.15
2.152.30
2.34
2.362.30
2.31 × 3
2.38
2.372.44
2.54 × 3
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method, although G96LYP distances are in all cases longer than
those obtained with the other methods. A cluster for n ) 10
bearing all the water molecules in the first hydration shell cannot
be optimized. Irrespective of the starting structure or method,
one or more water molecules were expelled from the first
hydration shell of the Po(IV), leading to octa- or ennea-hydrates.
Table 2 shows the interaction energies, Eint, for the [Po-
(H2O)n]4+clusters (n ) 1-9) at different levels of calculation.
The interaction energy increases with the number of water
molecules, but, because of many body effects, the energy per
water molecule is reduced when going from small to large
clusters. This behavior runs parallel to the elongation of the
Po-O distance with n as observed in Table 1. For n ) 1, CCSD-
(T) Eint(-239.1 kcal/mol) is close to the MP2 one (-238.8
kcal/mol), while DFT methods over-stabilize the polonium-
water interaction (Eint is -249.7, -253.1, and -261.5 kcal/
mol for MPW1PW91, B3LYP, and G96LYP, respectively). The
value of Eint for the HF method (-218.3 kcal/mol) is an
underestimate of the value obtained through CCSD(T) methods.
For n ) 2-3, MP2 provides interaction energies very similar
to the CCSD(T) ones, followed closely by G96LYP, MPW1PW91
and B3LYP. HF again underestimates CCSD(T) results. On the
basis of these results, HF can be ruled out for the purpose of
this study. As n increases, the interaction energy per water
molecule and, consequently, the total interaction energy is very
similar for the MP2, MPW1PW91, and B3LYP methods. In
the case of MP2 and MPW1PW91, they are almost identical
for larger values of n. However, G96LYP begins with the most
attractive interaction per water molecule and ends up with the
least attractive character. It seems that many body effects are
more important with G96LYP than in the other methods. On
the basis of the structural and energetic results of this study, it
seems that the larger n is, the more similar MP2 and MPW1PW91
results are. Recalling that CCSD(T) results are our reference,
we have on one hand that MPW1PW91 structures resemble the
CCSD(T) ones, and on the other hand, MP2 interaction energies
are similar to the CCSD(T) values. MPW1PW91 appears to be
the most suitable method since it is less CPU time demanding
than MP2, and a compromise between accuracy and feasibility
is desirable.
3.2. Semi-continuum Solvation Model. To study the com-
bined effect of specific and long-range solvent effects, we have
selected a set of larger clusters, with a number of water
molecules high enough to completely surround the central cation.
Thus, the semi-continuum model treats each hydration region
at the same methodological level. This would not be the case if
clusters with a smaller number of molecules were considered
(the extreme case would be n ) 1) because part of the first
hydration shell would have been described by the discrete model
and the rest by the continuum one. Examination of the solvation
data given in Table 3 reveals that the solvation energy
contribution depends on cluster size. Although the nonelectro-
static contributions ∆Gcavand ∆Gdisp-repdepend on the cluster
volume, their sum is a minor contribution to ∆Gsolv because
there is a significant cancellation between them. The formation
energy of the cluster, ∆Gcluster, and the continuum contribution,
∆Gcont, present more significant changes, although, as expected,
the trend with the increase in the cluster size is in the opposite
direction. ∆Gclusterbecomes more stabilizing (more negative)
when the number of water molecules directly attached to the
metal cation increases, while ∆Gcont is less stabilizing (less
negative) when the cavity size increases, i.e., when the cluster
is larger.
The lack of experimental data precludes the direct validation
of our results. However, the comparison of our results with
experimental data of other tetravalent cations such as Zr4+, Sn4+,
Ce4+, Hf4+, Th4+, Pa4+, U4+, Np4+, and Pu4+indicates that
our estimation for the hydration free energy (-1479.5 kcal/
mol) is within the range of values obtained for this set of cations
[1380-1800] kcal/mol.5Moreover, Po-O distances (2.1-2.5
Å) are also in agreement with the experimental results of
tetravalent cations in aqueous solutions [2.22-2.51 Å].4,6,43
The [Po(H2O)9]4+cluster seems to be the most stable one in
solution. However, the energy difference with the [Po(H2O)8]4+
one is negligible, especially taking into account that the
uncertainty associated with this theoretical procedure of estimat-
ing ∆Gsolv may be quantified as a 5-7% of the absolute
value.33,44When comparing ∆Gsolvwithin a series, the uncer-
tainty associated with the energy gap (∆∆Gsolv) ∆Gsolv,1-
∆Gsolv,2) decreases because there is cancellation of common
contributions. Then, ∆∆Gsolvvalues of the hydrates are affected
roughly by 1.5%, that is, ∼20 kcal/mol. We can conclude that
on the basis of our study, the hydration number of the Po(IV)
is ruled by a dynamic equilibrium involving the octa- and ennea-
hydrates, although a 7-fold coordination cannot be completely
excluded. This indicates the existence of a region in the potential
energy surface with several minima close in energy. The intrinsic
dynamic behavior of this equilibrium implies, for a complete
description, the use of further computer simulations where an
appropriate statistical average is accounted for.
3.3. Bond Analysis and Point Charge Calculations. To
complete the description of ion hydration, in addition to the
estimation of solvation free energies and hydration numbers, a
detailed description of the nature of the ion-solvent bonding
must be supplied. In Figure 1, the five smaller [Po(H2O)n]4+(n
e 5) clusters can be labeled as surface clusters, denoting that
the ion is exposed and not completely buried in the center of
the cluster. In the case of clusters with n e 3, this could be
understood because the number of water molecules is not large
enough to completely surround the ion. Nevertheless, for n )
4-5, the distribution pattern of water molecules around the ion
is not that expected for a tetravalent cation, that is, the water
molecules symmetrically distributed around the ion, maximizing
the ion-solvent interactions and minimizing solvent-solvent
repulsions at the same time. Obviously, the distribution of water
TABLE 2: Interaction Energies, Eint(kcal/mol), of the
Optimized [Po(H2O)n]4+Structures (n ) 1-9) Obtained by
Different Quantum Mechanical Methods
n
1
2
3
4
5
6
7
8
9
HFMP2
-238.8
-417.7
-554.1
-650.7
-735.6
-807.4
-860.2
-910.9
-946.6
MPW1PW91
-249.7
-434.9
-572.4
-669.6
-753.6
-825.8
-874.5
-920.4
-951.0
B3LYP
-253.1
-437.9
-572.8
-669.2
-751.9
-823.8
-870.8
-885.5
-944.7
G96LYP
-261.5
-426.1
-545.2
-631.4
-697.9
-754.6
-784.3
-811.6
-823.9
CCSD(T)
-239.1
-415.7
-550.1
-218.3
-388.1
-522.7
-614.7
-694.7
-759.5
-808.9
-855.2
-915.2
-
-
-
-
-
-
TABLE 3: Solvation Free Energy ∆Gsolv(kcal/mol) and Its
Components for the MPW1PW91 Clusters Including Solvent
Effects via PCM Modela
n
6
7
8
9
cavity
volumeb
190.6
209.5
230.4
248.9
∆Gcluster
-762.9
-800.8
-831.9
-851.5
∆Gcont
-708.7
-691.3
-674.8
-660.6
n∆Gvapc
12.3
14.4
16.4
18.4
∆Gcav+dis-rep
10.4
11.9
14.2
14.2
∆Gsolv
-1448.9
-1465.8
-1476.1
-1479.5
a∆Gcluster was computed from the gas-phase structure.bCavity
volume in Å3.cExperimental value of ∆Gvapwas taken from ref 39.
Po(IV) Hydration
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molecules in these clusters is not the optimum from the point
of view of water-water repulsions. In order to understand the
reasons of this unusual structural arrangement, it is necessary
to analyze the driving force of the Po-H2O interaction. A
natural bond order (NBO) analysis45of the [Po(H2O)n]4+clusters
with n ) 1-7 shows that there is covalent bond formation
between the 6p orbitals of polonium ion and the water
molecules, without a significant participation of the 6s orbital
of the polonium ion in the bonding. For n ) 8 and 9, the NBO
analysis indicates the participation of the 6d orbitals of the
polonium ion in the bonding, but not of the 6s orbital. In
practice, the polonium 6s orbital may be considered a core
orbital. Figure 3 shows a 3D plot of the three localized natural
Po-O bonding molecular orbital in [Po(H2O)3]4+, as derived
from an NBO analysis. It is seen that the O-Po-O angle is
∼90° in all cases. Figure 4 illustrates how the increase in the
number of water molecules involved in the Po(IV) cluster
formation leads to the saturation of the bonding capability of
the 6p Po orbital, this bonding behavior being responsible for
the observed final structures. This way, O-Po-O angles in the
[Po(H2O)n]4+cluster (n ) 2-6) are around 90 or 180° as a
result of the interaction of the water molecules with the 6p
orbitals of the polonium ion. The lack of hybridization between
the 6p and 6s polonium orbitals precludes the formation of small
clusters with water molecules symmetrically distributed around
the ion. This simple model is capable of explaining water
arrangements in the polonium hydrates and underlines the
importance of the directionality imposed by the covalent
contribution of the ion-solvent interactions in the final [Po-
(H2O)n]4+(n ) 1-5) structures. Despite the fact that there is a
certain covalent bonding between the polonium ion and the
water molecules, the natural population analysis indicates that
the electron donation from a water molecule of the cluster to
the positively charged ion is between 0.48e (n ) 1) and 0.16e
(n ) 9). Bearing in mind that we are dealing with a tetravalent
cation, the charge transfer from water molecules to the ion is
small. This suggests that electrostatic attraction should play a
major role in the total stabilization of complex formation for
the Po-H2O clusters.
To quantify the electrostatic and its associated long-range
contributions to Po-H2O interaction, we compared the results
of the [Po(H2O)n]4+clusters with those resulting from the
optimization of n water molecules plus a 4+ point charge (q4+)
at the MPW1PW91 level. In these calculations, the diffuse
functions on the O and H were eliminated due to convergence
difficulties of the SCF process. To avoid the collapse of the
water molecules with the point charge, a classical pair potential
of the form A‚e-r/B(A ) 530 a.u., B ) 0.47 Å, and r is the q
4+-O and q4+-H distances in Å) was applied at the charge
site. These parameters were chosen in such a way that the Po-O
distances of the optimized [Po(H2O)6]4+hydrate were repro-
duced. By this procedure, the size of the polonium ion was to
Figure 2. MPW1PW91 optimized structures of [q-(H2O)n]4+clusters
(n ) 1-9).
Figure 3. 3D representation of the three natural Po-O bond molecular
orbitals of the [Po(H2O)3]4+cluster obtained with NBOView.
Figure 4. Schematic representation of how the Po(IV) cation and water
molecules interact through the 6p Po orbitals for the n ) 1-4 clusters.
5420 J. Phys. Chem. B, Vol. 112, No. 17, 2008
Ayala et al.
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Published on April 9, 2008 on http://pubs.acs.org | doi: 10.1021/jp076032r