A unified formulation of the constant temperature molecular dynamics methods

TL;DR: In this article, the authors compared the canonical distribution in both momentum and coordinate space with three recently proposed constant temperature molecular dynamics methods by: (i) Nose (Mol. Phys., to be published); (ii) Hoover et al. [Phys. Rev. Lett. 77, 63 (1983); and (iii) Haile and Gupta [J. Chem. Phys. 79, 3067 (1983).

Abstract: Three recently proposed constant temperature molecular dynamics methods by: (i) Nose (Mol. Phys., to be published); (ii) Hoover et al. [Phys. Rev. Lett. 48, 1818 (1982)], and Evans and Morriss [Chem. Phys. 77, 63 (1983)]; and (iii) Haile and Gupta [J. Chem. Phys. 79, 3067 (1983)] are examined analytically via calculating the equilibrium distribution functions and comparing them with that of the canonical ensemble. Except for effects due to momentum and angular momentum conservation, method (1) yields the rigorous canonical distribution in both momentum and coordinate space. Method (2) can be made rigorous in coordinate space, and can be derived from method (1) by imposing a specific constraint. Method (3) is not rigorous and gives a deviation of order N−1/2 from the canonical distribution (N the number of particles). The results for the constant temperature–constant pressure ensemble are similar to the canonical ensemble case.

Summary

A. Basis sets and electronic structure methods

• A systematic study by stepwise hydration of CdCl2 was carried out at the DFT level, i.e., water molecules were added to previously optimized CdCl2-(H2O)n structures for n = 1– 24.
• Incremental water binding free energies and optimized structures have been computed.
• As previously done for HgCl2 and Hg(OH)2, the oxygen and hydrogen atoms have been described with the 6- 31G** basis sets.
• Full geometry optimizations were carried out at B3PW91 level without any symmetry restrictions.
• All the calculations were carried out with the Gaussian03 program.

B. DFT molecular dynamics

• The thermal stability of the largest cluster studied here, CdCl2-(H2O)24, has been tested using Born-Oppenheimer molecular dynamics (BO-MD) simulations at the B3PW91 level.
• The simulations were carried out with the Geraldyn2.1 code based on the method developed by Raynaud et al.,27 which uses the velocity-Verlet integration scheme.
• The electronic structure DFT calculations (done with Gaussian09) involve 669 molecular orbitals and the 10 ps BO-MD simulation took 26 CPU days on 32 processors@2.8 GHz running the Linux versions of Geraldyn2.1Gaussian09.

A. The isolated CdCl2 molecule and calibration of the Cd,Cl valence basis sets

• For bare CdCl2, at the MP2/RECP(Cd)+cc-pVTZ(Cl) level, the Cd-Cl bond distance is 2.254 Å, to be compared with the experimental value of 2.266 Å.31, 32 We emphasize that the corresponding B3PW91 optimized distance (2.273 Å) is in excellent agreement with these values.the authors.the authors.
• Here the authors note that while the Cl-Hg-Cl angle is 178.6◦ for bare HgCl2, 33 for CdCl2 the Cl-Cd-Cl angle is perfectly linear.
• The authors shall later make this comparison in the context of the water binding energies.
• The authors proceed now to address the water-microsolvated species.

B. Geometries of the CdCl2-(H2O)n optimized complexes

• The interaction of CdCl2 with water was studied via stepwise solvation by adding a number (n) of water molecules to the system, with n = 1–24.
• Special care was taken in order to insure that all the Cl-Cd-Cl–Ow (Ow stands for water oxygens) and Cd-Cl-Ow-Ow dihedral angles were properly sampled with each additional water molecule.
• Note that the Cl-Cd-Cl angle goes back to being almost linear at 176◦.
• Therefore, the authors report here only the lowest energy structure without the assurance that it is the absolute minimum at 0 K in each case.

C. Continous solvent models

• In order to address the possible effects of the polar aqueous medium on the geometry of the optimized structures including explicit water molecules, for selected values of n the authors performed calculations using the Polarizable Continuum Model (PCM) of Tomasi et al.34 and the implicit solvation (SMD) method of Marenich et al.35 as implemented in Gaussian09.
• The authors find that for these cases the PCM scheme leads to similar optimized geometries as those obtained in vacuo, with Cd-Cl and Cd-Ow distances slightly longer (∼0.1 Å) than those obtained in vacuo.
• Note that changes to the Cl-H distances are smaller, except for n = 12.
• In the case with large n (n = 21), the “internal” water molecules directly interacting with CdCl2 already show hydrogen bonding with “external” second solvation shell waters; therefore the different solvation schemes of these external water molecules do not appreciably affect their bonding pattern with the solute and, thus, the optimized structures are very similar with both methods.

D. Water binding energies

• At this stage it is interesting to compare these water binding energies with those previously reported for the HgCl2 case.
• Second, note the presence of three regimes for both solutes; each curve has, grosso modo, two growth regions (where the slope of the second region is smaller than the slope of the first region) separated by a plateau.
• This has been achieved by performing a single-point calculation for the solute with the geometry it attains in each microsolvated system.
• Table III shows the evolution of the total and incremental deformation energies at the B3PW91/6-31G** level as functions of n.

E. Solute-water bonding analysis

• The bonding situation in the CdCl2-(H2O)n hydrated complexes was studied by means of the Natural Bond Orbital scheme.
• Apart from the polarized covalent bond between Cd and the two Cl, it has been possible to identify four donor-acceptor interactions, i.e., bonds, between four water molecules and the cadmium center, all of them in equatorial positions with respect to the axial Cl atoms.
• This is further highlighted by scrutinizing the WIberg Bond Indexes (WBI).
• Indeed, for the latter only two bonds were found between the water molecules and HgCl2 in the pentahydrated complex; even with six solvating water molecules, the water hydrogen bond network expands but no other Hg–Ow interaction was found.
• Thus, the magnitude of the microsolvation energy is clearly associated with the strength of the bonding interaction between the metal center and the closest water molecules, Cd being more covalent than Hg.

F. DFT Born-Oppenheimer molecular dynamics

• To address the role of thermal effects on the largest solvated structure, several of Born–Oppenheimer MD simulations (B3PW91/6-31G**) at 700 K were carried out.
• At this point the authors recall that the Gibbs free energy of the hexacoordinated-Cd structure is only 5 kcal/mol lower than that of the pentacoordinated-Cd species, so that these simulations reveal the greater dynamic stability of the latter structures at higher temperatures.
• Note also that, during the hexacoordination, no water-exchange was observed as it is the same water molecule that gets into the first coordination sphere and that is expulsed after a few hundredths of femtoseconds.
• The shape of the radial distribution function is in line with very little exchange between the two solvation spheres, at least during the 10 ps of the longest simulation the authors performed, in line with the analysis of the Cd-Ow bond distance evolution.

IV. CONCLUSIONS AND PERSPECTIVES

• Aqueous solvation of CdCl2 is crucial in the context of the transmembrane passage of this species into the cellular environment.
• The hybrid DFT method was calibrated against MP2 energetic and structural results for small n.
• The first solvation shell is shown to consist of 12 water molecules (eight of them not coordinated to Cd), in sharp contrast with the much bulkier HgCl2 case, where ∼24 molecules are needed to fully form the first solvation sphere.
• Several BO molecular dynamics simulations at high temperature of the largest cluster, CdCl2–(H2O)24, were done.
• The authors best estimate of the free energy difference between the pentacoordinatedCd and the statically more stable hexacoordinated-Cd is 5.6 kcal/mol, corresponding to the largest cluster CdCl2(H2O)24.

Figures

FIG. 4. The optimized penta- and hexacoordinated-Cd structures with 24 water molecules. The Gibbs free energy of the latter is only 5.6 kcal/mol lower than that of the former.

FIG. 3. The optimized structure with 12 water molecules. Note the nearly linear Cl-Cd-Cl (176.6◦) angle and the nearly flat Ow-Ow-Ow-Ow (4.8 ◦) dihedral angle of the equatorial waters around Cd.

FIG. 2. Two stable geometries of CdCl2 solvated by seven water molecules. The pentacoordinated structure is ( G0298 = 2.1 kcal/mol) more stable than the hexacoordinated one. Although stable pentacoordinated structures exist, hexacoordination around Cd was found to be slightly favored with a larger number of water molecules (see text).

TABLE I. Main optimized B3PW91/6-31G** geometrical parameters of gaseous and solvated CdCl2-(H2O)n systems. For comparison MP2/AVTZ optimized values are given in parentheses for small n. For n > 12 only data corresponding to the lowest-energy structure are shown. The water oxygen atoms (Ow) are those directly linked to Cd. Distances in Å and angles in degrees. Ow-Cd-Ow are the angles concerning the water oxygens coordinated to Cd.

FIG. 8. Evolution of the shortest Cd-Ow distances (Å) during the simulation starting from the optimized pentacoordinated Cd structure. Horizontal axis in fs. Note the transient Cd-hexacoordination.

FIG. 7. Time evolution of the shortest Cd-Ow distances (Å) during the simulations starting from the hexacoordinated Cd structure. Horizontal axis in fs.

FIG. 9. Cd-Ow radial distribution function extracted from the BO-MD 10 ps simulation of the CdCl2-(H2O)24 cluster. Horizontal axis in Å.

TABLE II. Optimized B3PW91 main geometrical parameters (Å) of selected CdCl2-(H2O)n structures in vacuo and with continuous solvent models. The optimized PCM structure is a first order transition state for n = 5 with ω = 18i cm−1.

FIG. 5. Optimized CdCl2-(H2O)12 complex with PCM (left) and SMD (right) solvation models. Note the complete Cl dissociation in the latter case (Cd-Cl distance of 4.71 Å).

FIG. 6. Gibbs free water binding energies (kcal/mol) at 298 K vs. the number of solvating water molecules for HgCl2 (black) and CdCl2 (red). Data for HgCl2-(H2O)n taken from Ref. 20.

TABLE III. Single-point B3PW91/6-31G** calculation for CdCl2 with the geometry it attains in the microsolvated system. Total energies in a.u. and deformation energies in kcal/mol. Cl-Cd-Cl angle θ in degrees.

FIG. 1. Optimized geometries of CdCl2 solvated by one to six water molecules.

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Aqueous microsolvation of CdCl 2 : Density functional
theory and Born-Oppenheimer molecular dynamics
studies
A. Ramirez-Solis, Laurent Maron
To cite this version:
A. Ramirez-Solis, Laurent Maron. Aqueous microsolvation of CdCl 2 : Density functional theory and
Born-Oppenheimer molecular dynamics studies. Journal of Chemical Physics, American Institute of
Physics, 2014, 141 (9), pp.094304. �10.1063/1.447334�. �hal-01969513�

Aqueous microsolvation of CdCl
2
: Density functional theory and Born-Oppenheimer
molecular dynamics studies
A. Ramírez-Solís, and L. Maron
Citation: J. Chem. Phys. 141, 094304 (2014); doi: 10.1063/1.4894286
View online: https://doi.org/10.1063/1.4894286
View Table of Contents: http://aip.scitation.org/toc/jcp/141/9
Published by the American Institute of Physics
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THE JOURNAL OF CHEMICAL PHYSICS 141, 094304 (2014)
Aqueous microsolvation of CdCl
2
: Density functional theory
and Born-Oppenheimer molecular dynamics studies
A. Ramírez-Solís
a)
and L. Maron
Laboratoire de Physicochimie de Nano-Objets, INSA-IRSAMC, Université de Toulouse III,
135, Avenue de Rangueil, Toulouse, F31077, France
(Received 18 March 2014; accepted 18 August 2014; published online 3 September 2014)
We report a systematic study of aqueous microsolvation of CdCl
2
. The optimized structures and
binding energies of the CdCl
2
-(H
2
O)
n
clusters with n = 1–24 have been computed at the B3PW91/
6-31G** level. The solvation patterns obtained at the DFT level are verified at the MP2/AVTZ level
for n < 6. Unlike HgCl
2
-(H
2
O)
n
case, where there are at most three Hg-O
w
orbital interactions,
Cd also establishes four equatorial orbital interactions with water for n > 6 leading to a planar
square bipyramid hexacoordination around Cd. The first solvation shell is fully attained with 12 wa-
ter molecules. At the same level of theory the water binding energies are much larger than those
previously found for HgCl
2
due to the stronger Cd-O
w
interactions arising from the smaller core of
Cd. For the largest system studied, CdCl
2
-(H
2
O)
24
, both penta- and hexa-coordination stable pat-
terns around Cd are found. However, Born-Opphenheimer molecular dynamics simulations starting
from these optimized geometries at 700 K reveal the greater stability of the Cd-pentacoordinated
species, where a CdCl
2
-(H
2
O)
3
trigonal bipyramid effective solute appears. The Cd-O(water) radial
distribution function shows a bimodal distribution with two maxima at 2.4 Å and 4.2 Å, revealing
the different coordination spheres, even with such a small number of solvating water molecules.
© 2014 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4894286]
I. INTRODUCTION
Human activities have contributed to increase heavy
metal levels in soil, sediments, and aquatic ecosystems world-
wide. Pollution by toxic cadmium and mercury species has
become a true environmental problem that plagues nowadays
developed and third-world countries. Both metals are well
known to be at the root of a plethora of diseases. Although
some cadmium-containing products can be recycled, a large
share of the general cadmium pollution is caused by dump-
ing and incinerating cadmium-polluted waste.
1
In Europe, for
example, cadmium concentration in agricultural soil increases
by 0.2% per year. Aquatic cadmium levels have also increased
in the last 30 years worldwide and total global emission of
cadmium amounts to ∼7000 t/year.
2
Cadmium can have many
adverse effects in humans, most notably causing lung, kid-
ney, and testicular damage.
3
Several studies in the last century
showed a connection between cadmium intoxication and bone
damage, demineralization, and osteoporosis.
4
The most envi-
ronmentally abundant Cd containing species is CdCl
2
(cad-
mium dichloride) and it has been shown to induce kidney,
5
prostate,
6
and breast cancer.
7
Very recently it has been shown
that prenatal exposure to very low levels (10 ppm) of CdCl
2
produces persistent changes to thymus and spleen cell pheno-
typic repertoire as well as the acquired immune response.
8
From the biochemical point of view it is still unclear how
CdCl
2
enters the cell. The question of passive vs. active trans-
membrane passage for Cd-containing species is dependent on
the specific type of ligands bonded to the metal atom. The type
a)
On sabbatical leave from Facultad de Ciencias, Universidad Autónoma del
Estado de Morelos, Morelos, Mexico. Electronic mail: alex@uaem.mx.
of ligands critically determines the bioavailability of these
toxic species through the structural and energetic features of
these metallic molecules in aqueous environments. Bioavail-
ability is a pivotal issue for Cd toxicity, for the potential for
intracellular Cd accumulation and for the biochemical pro-
duction of organometallic species such metal-hormones and
metal-peptide complexes. Several relevant experimental and a
few theoretical studies have been reported over the years.
9–13
One previous theoretical study of relevance here is re-
ported in Ref. 11, where the structures of Group 12 dihalides
in their vapor and crystal phases are sought and discussed.
The molecular structures of all monomers and dimers (MX2:
M = Zn, Cd, Hg, and X = F, Cl, Br, I) were obtained at the
DFT-B3PW91 and MP2 levels. Experimentally, the identity
and stability of aqueous species formed by cadmium in H
2
O–
Na/LiCl–HCl–HNO
3
solutions were investigated using X-ray
absorption spectroscopy (XANES and EXAFS) with varying
chloride concentration, temperature and pH.
10
Results show
that aqueous Cd speciation is dominated by the Cd(H
2
O)
6
2+
cation in acidic Cl-free solutions, and by chloride species
CdCl
m
(H
2
O)
n
2−m
over a wide range of temperatures (20
≤ T ≤ 450
◦
C), acidities (1 ≤ pH ≤ 8), and chloride con-
centrations (0.04 ≤ mCl ≤ 18 mol/kg H
2
O). EXAFS spec-
tra from chloride solutions show that with increasing T and
mCl the average number of Cl atoms increases from 1 to ∼3
(±0.6), accompanied by a decrease of the number of O from
6to∼1(±0.7), in the nearest coordination sphere around Cd.
At this point we recall also that Ref. 13 recommends a
formation constant of CdCl
2
is 2.64 which corresponds to
a fairly weak interaction between Cd
2+
and 2Cl
−
of around
−3.6 kcal/mol.
0021-9606/2014/141(9)/094304/10/$30.00 © 2014 AIP Publishing LLC141, 094304-1

094304-2 A. Ramírez-Solís and L. Maron J. Chem. Phys. 141, 094304 (2014)
Another issue related to this problem is the speciation and
transformation of the Cd
2+
in biological environments since,
once Cd-containing species cross the cellular membrane, they
will chemically interact with one or many complex biological
agents. Indeed, if a fully comprehensive biochemical study
is to be performed, one must take into account the role of
specific enzymes such as metallothionein (MT). MT is a fam-
ily of cysteine-rich, low molecular weight proteins which are
mainly found in the membrane of the Golgi apparatus. MTs
have the capacity to bind both physiological (such as zinc,
copper, selenium) and xenobiotic (such as cadmium, mercury,
silver, arsenic) heavy metals through the thiol group of its cys-
teine residues, which represents nearly the 30% of its amino
acidic residues. MTs function is not completely clear, but ex-
perimental data suggest MTs provide protection against metal
toxicity (in particular against Cd(II)), that they are involved in
the regulation of physiological metals (Zn and Cu) and pro-
vide protection against oxidative stress.
14
However, this much
more complex issue is clearly out of the scope of the present
study.
Another important aspect is the comparison between Cd-
and Hg-containing species in solution. Indeed, since Cd and
Hg belong to the same group in the periodic table, it is
useful to recall what is known about the similar mercury-
containing species. Since there are clear parallels to draw
between Cd(II) and Hg(II), we highlight recent quantum
chemical work on ligand binding free energies and group 12
hydration by the Mercury Science Focus Area at the Oak
Ridge National Laboratory.
15
In this context we note that the
neutral HgCl
2
, HgOHCl and Hg(OH)
2
species are found to be
the most abundant toxic species in aqueous environments.
16,17
Gutknecht
18
addressed the permeability of HgCl
2
,HgCl
3
−
,
HgCl
4
2−
, Hg(OH)
2
, and HgClOH through lipid bilayer mem-
branes. This classic study revealed that these membranes are
20 times more permeable to HgCl
2
than to water and more
than a million times more permeable to HgCl
2
than to Na
+
,
K
+
,orCl
−
. In a more recent study similar conclusions were
found by Barkay et al.
19
A fundamental question related to the bioavailability is-
sue is whether HgCl
2
and CdCl
2
can be considered as water-
dressed molecules or not during the transmembrane transport
process making them available to the cell interior. In this re-
gard we recently addressed the solvation of HgCl
2
through
a DFT study using stepwise cluster solvation,
20
and through
Monte Carlo simulations of the aqueous solution.
21
We found
that the hydrogen bond network is crucial to allow orbital-
driven interactions between Hg(II) and the water molecules.
In order to study HgCl
2
in the aqueous phase we performed
extensive Monte Carlo (MC) simulations including ∼1000
water molecules and taking into account up to 10
10
con-
figurations. The MC simulations were done using very re-
fined MP2 derived interaction potentials which are polariz-
able, flexible, and include non-additive effects. The MC sim-
ulations of the solution revealed that HgCl
2
behaves like a
hydrophobic solute, which explains the rather easy passage
of HgCl
2
through the cell membrane; these simulations of
the solution also showed that one to three water molecules
establish Hg-O
w
interactions in the fashion of a hydrophilic
solute.
21
In this context some natural questions arise concerning
CdCl
2
: does the aqueous solvation environment of CdCl
2
re-
semble that of HgCl
2
? Are the water binding energies of
CdCl
2
, both in the gas phase and in the condensed phase, as
low as those found for HgCl
2
?
Since to best of our knowledge no information, theo-
retical or experimental, concerning these issues is available,
we aim at providing answers to these questions. Therefore,
we report here some structural and energetic results for the
aqueous microsolvation of CdCl
2
using cluster models. We
shall also address some key structural aspects and the ther-
mal stability of the largest water-solvated systems through
Born-Oppenheimer molecular dynamics. As previously done
for HgCl
2
, these cluster results will serve as references for
further solvation studies in the condensed liquid phase.
21
Sec. II presents the methodological details, while in Sec. III
we present the results and discuss them in the light of previ-
ous microsolvation studies of HgCl
2
. Finally, in Sec. IV we
present some conclusions and perspectives.
II. COMPUTATIONAL DETAILS
A. Basis sets and electronic structure methods
A systematic study by stepwise hydration of CdCl
2
was
carried out at the DFT level, i.e., water molecules were added
to previously optimized CdCl
2
-(H
2
O)
n
structures for n = 1–
24. As it will be shown later, 24 is twice the number of water
molecules needed to form the first solvation shell of CdCl
2
.
Incremental water binding free energies and optimized struc-
tures have been computed. The core electrons of cadmium
were substituted by the small core Stuttgart-Dresden relativis-
tic effective core potentials (RECP) and augmented versions
of their associated basis sets.
22,23
Since Hargittai and Hoffman have shown that the Cd-
Cl distance is very well reproduced at the B3PW91 level
(2.273 Å vs. 2.28 Å exp.) with the cc-pVTZ basis for Cl
10
we used here the same approach. In order to more accurately
deal with the molecular flexibility of CdCl
2
upon solvaton, the
Cd RECP basis set has been augmented by a set of polariza-
tion and diffuse even-tempered (α = 1/3) functions: 0.0190
and 0.0066 s exponents, 0.0012 p exponent, 0.075 and 0.025
d exponents. As previously done for HgCl
2
and Hg(OH)
2
,the
oxygen and hydrogen atoms have been described with the 6-
31G** basis sets. Full geometry optimizations were carried
out at B3PW91 level without any symmetry restrictions. An-
alytical frequency calculations were done to verify the stable
nature of the stationary points (all minima) and the Gibbs free
energies were computed at 298 K within the harmonic ap-
proximation. All the calculations were carried out with the
Gaussian03 program.
24
In order to assess the accuracy and reliability of the DFT
results, the structures of the CdCl
2
-(H
2
O)
n
systems for small
n(n< 6) were also optimized at the MP2 level using the
large aug-cc-pV(D,T)Z basis sets for O and H.
25
Thus, opti-
mized geometries at the MP2/AVTZ level and frequency cal-
culations at the MP2/AVDZ level are also reported for these
systems. The reliability of the MP2 single reference method
was determined by the calculation of the T1Diagnostic at the
CCSD/AVDZ level for the n = 0, 1, 2, and 3 cases using the

094304-3 A. Ramírez-Solís and L. Maron J. Chem. Phys. 141, 094304 (2014)
corresponding MP2/AVTZ optimized geometries. As could
be expected, in all cases the T1Diagnostic was found to be
quite small (T1Diag < 0.0142). These results are in agree-
ment with the previous report by Shepler et al.
26
where they
used the MP2 and B3LYP methods to study the microsol-
vation of several mercury-mono and -dihalide species. Thus,
as in our previous studies of HgCl
2
and Hg(OH)
2
,theMP2
method also provides reliable structural and energetic refer-
ences for the CdCl
2
-(H
2
O)
n
clusters.
B. DFT molecular dynamics
The thermal stability of the largest cluster studied here,
CdCl
2
-(H
2
O)
24
, has been tested using Born-Oppenheimer
molecular dynamics (BO-MD) simulations at the B3PW91
level. The simulations were carried out with the Geraldyn2.1
code based on the method developed by Raynaud et al.,
27
which uses the velocity-Verlet integration scheme.
28
For the
integration of the equations of motion a time step of 0.5 fs
was used. A Nosé–Hoover chain of four thermostats
29,30
was
used to control the temperature at 700 K during the 10 ps
of the simulation. The electronic structure DFT calculations
(done with Gaussian09) involve 669 molecular orbitals and
the 10 ps BO-MD simulation took 26 CPU days on 32 pro-
cessors@2.8 GHz running the Linux versions of Geraldyn2.1-
Gaussian09.
III. RESULTS AND DISCUSSION
A. The isolated CdCl
2
molecule and calibration
of the Cd,Cl valence basis sets
For bare CdCl
2,
at the MP2/RECP(Cd)+cc-pVTZ(Cl)
level, the Cd-Cl bond distance is 2.254 Å, to be compared
with the experimental value of 2.266 Å.
31,32
We emphasize
that the corresponding B3PW91 optimized distance (2.273 Å)
is in excellent agreement with these values. Here we note
that while the Cl-Hg-Cl angle is 178.6
◦
for bare HgCl
2
,
33
for
CdCl
2
the Cl-Cd-Cl angle is perfectly linear. The atomic NPA
charges are −0.675 for Cl and +1.35 for Cd. Since the dipole
moment of CdCl
2
is zero due to its linear geometry, in an
aqueous environment it could be expected that CdCl
2
interacts
roughly as strongly as HgCl
2
with the dipole moments of the
solvating water molecules. We shall later make this compari-
son in the context of the water binding energies. We proceed
now to address the water-microsolvated species.
B. Geometries of the CdCl
2
-(H
2
O)
n
optimized
complexes
The interaction of CdCl
2
with water was studied via step-
wise solvation by adding a number (n) of water molecules to
the system, with n = 1–24. Special care was taken in order
to insure that all the Cl-Cd-Cl–O
w
(O
w
stands for water oxy-
gens) and Cd-Cl-O
w
-O
w
dihedral angles were properly sam-
pled with each additional water molecule. The stability of the
optimized structures with varying number of water molecules
(Figures 1 and 2) was verified by the absence of imaginary
frequencies at the MP2 level with the various basis sets used
here. A detailed analysis of the geometries of the optimized
complexes with one to six water molecules is given in the
supplementary material.
43
Note that the optimized structures
with three, four, and five water molecules all belong to the C
s
point group and their geometries are similar to those obtained
for the HgCl
2
case.
20
However, a particularly interesting case
arises when a seventh water molecule is considered, since two
different stable structures are found (Figure 2). The first one
is directly related to the optimized hexa-hydrated structure,
since the new water molecule does not alter the pentacoor-
dination pattern around Cd. The second, slightly more stable
FIG. 1. Optimized geometries of CdCl
2
solvated by one to six water molecules.

Frequently asked questions

Q1. What are the contributions mentioned in the paper "Aqueous microsolvation of cdcl 2 : density functional theory and born-oppenheimer molecular dynamics studies" ?

Ramirez-Solis et al. this paper reported a systematic quantum chemical study of the structures, vibrational frequencies and the water binding energies of the CdCl2-H2O ) n ( n = 1-24 ) microsolvated species. 

Q2. What future works have the authors mentioned in the paper "Aqueous microsolvation of cdcl 2 : density functional theory and born-oppenheimer molecular dynamics studies" ?

However, the authors stress that the conclusions ( especially those concerning the penta vs. hexacoordination around Cd ) extracted from these simulations pertain only to gas-phase hydration since the dynamic many-body effects arising from the third and subsequent shells of solvation are missing, therefore, further studies must be done to accurately address the solvation in the liquid medium. 21 In particular when the authors consider the full liquid solvation they wish to answer if, as they found for HgCl2, there exists an CdCl2– ( H2O ) k effective solute, what is the number k and what are its symmetry properties, i. e., the local coordination environment of the Cd atom in the liquid phase. Their final goal will be to study the structural and energetic properties of CdCl2 in the condensed liquid phase through classical MC simulations and applying the quasi-chemical theory of Pratt et al. using refined ab initio derived interaction potentials. The understanding of the solvation of CdCl2 in the condensed aqueous phase requires the use of sophisticated classical Cd ( II ) -water, Cl-water and CdCl2water-water non-additive interaction potentials in conjunction with Monte Carlo or molecular dynamics simulations for the solution.