hydration characteristics of ca 2+ and mg 2+ : a density functional theory, polarized continuum...
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Hydration characteristics of Ca2+ and Mg2+: a densityfunctional theory, polarized continuum model andmolecular dynamics investigationGe Bai a , Hai-Bo Yi a , Hui-Ji Li a & Jia-Jia Xu aa State Key Laboratory of Chemo/Biosensing and Chemometrics , College of Chemistry andChemical Engineering, Hunan University , Changsha 410082 , People's Republic of ChinaAccepted author version posted online: 05 Oct 2012.Published online: 24 Oct 2012.
To cite this article: Ge Bai , Hai-Bo Yi , Hui-Ji Li & Jia-Jia Xu (2013) Hydration characteristics of Ca2+ and Mg2+: a densityfunctional theory, polarized continuum model and molecular dynamics investigation, Molecular Physics: An InternationalJournal at the Interface Between Chemistry and Physics, 111:4, 553-568, DOI: 10.1080/00268976.2012.737035
To link to this article: http://dx.doi.org/10.1080/00268976.2012.737035
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4. Conclusion
In order to study the direct impact of a graphenebilayer on protein molecules, we conducted a series ofmolecular dynamics simulations. We chose two proteinmolecules with dissimilar structure characteristics tobuild our simulation systems. The influence of agraphene bilayer can be significantly different ondifferent protein molecules. Our simulations exhibitedsignificant denaturation of a 3-�-helix bundle GAmodule and structure preservation of a �/� hybridprotein G. Additionally, we found a correlationbetween the separation of graphene layers and theextent of GA module denaturation: smaller separationcan cause greater denaturation. Although protein Gbecame slightly more flexible between graphene layersthan in pure water, it retained its native structure quitewell during all of our simulations.
Energetic analysis showed that Van der Waalsinteraction played a greater role in the denaturing ofGA module. Meanwhile, solvation free energy showeda facilitating effect on the denaturing. The Van derWaals interaction between protein G and graphenelayers is also strong. However, protein G showed itsproperty of keeping its integrity under the influence ofgraphene layers.
The influence of graphene on different proteins isdifferent. To construct a relationship between thestability of protein and its structure when interactingwith graphene, further studies should be done, andmore data are needed. We can conclude that Van derWaals interaction should not be overlooked when thegraphene toxicity mechanism is studied. In ourmodeled system, the magnitude of Van der Waalsenergy change between protein molecules and gra-phene layers is several times greater than solvation freeenergy change. This factor should be considered whenone is trying to realize any biological applications ofgraphene and its derivatives.
References
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RESEARCH ARTICLE
Hydration characteristics of Ca2Y and Mg2Y: a density functional theory, polarizedcontinuum model and molecular dynamics investigation
Ge Bai, Hai-Bo Yi*, Hui-Ji Li and Jia-Jia Xu
State Key Laboratory of Chemo/Biosensing and Chemometrics, College of Chemistry and Chemical Engineering,Hunan University, Changsha 410082, People’s Republic of China
(Received 2 August 2012; final version received 28 September 2012)
In this work, density functional theory, Møller–Plesset second-order perturbation theory, and ab initio moleculardynamics (AIMD) were used to investigate hydrated characteristics of Mg2þ and Ca2þ as a function ofcoordination number in the first hydration shell (CN) and cluster size. It is generally accepted that the CNs ofMg2þ and Ca2þ are both six. Calculations show that the hydration of Mg2þ generally prefers six-coordinatedstructures, whereas the CN value of Ca2þ varies from 6 to 8 as the hydration proceeds. Moreover, the firsthydration of Ca2þ is found to be more flexible than that of Mg2þ, as indicated by the results of transition statecalculations and AIMD simulations. In addition, the constraint of Mg2þ on the first hydration shell is obviouslystronger than that of Ca2þ, while the constraint on the inner hydration shells fades slightly faster for Mg2þ thanCa2þ. It is also found that the charge transfer from central cation to water molecules is affected only by the firsthydration shell for Mg2þ, whereas by the first and second hydration shells for Ca2þ. Based on hydrationcharacteristics, approximatively saturated ion hydration shells for the hydration of Mg2þ and Ca2þ wereproposed.
Keywords: magnesium ion; calcium ion; density functional theory; ab initio molecular dynamics; coordinationnumber; hydration shell
1. Introduction
Hydration characteristics of calcium and magnesiumions is of paramount importance since such detailedinformation is essential for understanding the role ofthese ions in chemical and biological processes [1,2].The properties of hydrated calcium and magnesiumions have stimulated intensive investigations on struc-tural parameters (such as coordination number andintermolecular distance) of their nearest environmentby theory and experiment [3–7]. However, detail infor-mation about the first hydration shell of Mg2þand Ca2þ
is still a controversial issue. Diverse of techniques, suchas gas-phase ion-molecule equilibria measurements,high-pressure mass spectrometry (HPMS) and black-body infrared radiative dissociation (BIRD), were used
to explore the coordination numbers in the firsthydration shell (CNs) of the Ca2þ and Mg2þ in thegas phase [8–10]. It seems that the CN value of Ca2þ
may be larger than that of Mg2þ, due to larger ionicsurface for Ca2þ, but all those results indicated that theCNs of Mg2þ and Ca2þ are both six. Recently, theresults of Williams et al. from infrared multiple photondissociation (IRMPD) spectroscopy of [Ca(H2O)n]
2þ
(n¼ 11–69) clusters in the gas phase proposed that the
CN value of Ca2þ may be 8 for clusters with 12 or more
water molecules [11]. Meanwhile, many condensed-
phase experiments and simulations showed that Mg2þ
prefers to bind with six water molecules in aqueous
solution [12–16], but Albright reported that the result of
X-ray diffraction experiment on Mg2þ is hydrated
7.9–8.1 water molecules in concentrated chloride solu-
tion [17]. The results of Jalilehvand and co-workers
both suggested that CN value of Ca2þ is 8 by means of
extended X-ray absorption fine structure spectroscopy
(EXAFS), [18] while the EXAFS results of Simonson
et al proposed that the average hydration number of
water molecules is 7.2� 1.2 in 6mol/L CaCl2 solutions
[19]. Furthermore, little research has been carried out to
compare the hydration characteristics of Mg2þ and
Ca2þ hydrates, and there is still no detailed information
about the transformation among various isomers with
different CN value for the hydration Mg2þ or Ca2þ in
aqueous solution. Therefore, a further insight into the
first hydration shell of Mg2þ and Ca2þ is quite
necessary.It is generally assumed that ions also have a long-
range effect on the structure of liquid water [20,21].
That is, the effect of ions on the structure of water is
*Corresponding author. Email: [email protected]
Molecular Physics, 2013Vol. 111, No. 4, 553–568, http://dx.doi.org/10.1080/00268976.2012.737035
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554 G. Bai et al.
probably not restricted to the formation of the firstand second hydration shells, especially for that ofdications. Markham et al. described the lowest-energy[Mg(H2O)n]
2þ model at present, which 6 water mole-cules are filled in the first hydration shell and 12 watermolecules are arranged in the second hydration shell[22,23]. However, Martinez et al. found the coordina-tion number of the second hydration shell for Mg2þ is13 [24]. In most studies, the number of water moleculesin the second hydration shell of Mg2þ was expected tobe about 12. Recently, result from density functionaltheory (DFT), Lei and Pan considered that the firsthydration shell of Ca2þ is fully occupied by 6 watermolecules, whereas the second hydration shell might beoccupied with 9 water molecules [25]. Since the effect ofdications on the structure of water is probably notrestricted to the formation of first and second hydra-tion shells, it will be interesting to investigate hydrationcharacteristics of Mg2þ and Ca2þ while their secondand third hydration shells explicitly are taken intoaccount as well as their outer hydration shells areinexplicitly considered as polarized continuummedium.
Here, [Mg(H2O)n]2þ (n¼ 6–10, 18–21, 24, 27, 36)
and [Ca(H2O)n]2þ (n¼ 6–10, 18–21, 24, 27) clusters
have been systematically studied using DFT and thepolarized continuum model (PCM) [26,27] to gain aninsight into their hydrated characteristics in detail. Wehave also performed ab initio molecular dynamics(AIMD) simulation of the [Mg(H2O)6,8]
2þ and[Ca(H2O)8,10]
2þ clusters, since it has been proven tobe a suitable alternative to experiments for an accuratedescription of physical and chemical phenomena of ionhydration [28–30]. In this context, the value of CNs ofMg2þ and Ca2þ in solvent water molecules wereexamined by the integration of radial distributionfunction (RDF) obtained from molecular dynamicssimulations. Natural bond orbital (NBO) charge pop-ulation analyses for [Mg(H2O)n]
2þ and [Ca(H2O)n]2þ
clusters were carried out to investigate charge transfereffect of these two ions. Moreover, we especiallyinvestigated the approximatively saturated ion hydra-tion shell of Ca2þ and Mg2þ according to theirstructural characteristics of various hydration shells.
2. Computational details
Previous application of the Becke’s three-parameterfunctional and the correlation function of Lee, Yang,and Parr (B3LYP) [31,32] to model metal ion-watersystems has proved a reasonable success [4,9,33–36].The works of Kim et al. have also investigatedthe hydration of alkali metal ions using B3LYP,
Møller-Plesset second order perturbation theory(MP2), and coupled cluster theory with singles, dou-bles, and perturbative triples excitations (CCSD(T)),but the results obtained using these methods lead to asimilar conclusion on the hydration characteristics[28,37]. Therefore, B3LYP method was chosen to lookfor local minimum energy structures of [Ca(H2O)n]
2þ
and [Mg(H2O)n]2þ clusters in this work. On generating
initial hydrated structures, four-, five-, and six-coordinated conformers were taken into account for[Mg(H2O)n]
2þ clusters, and five-, six-, seven-, andeight-coordinated conformers were considered for[Ca(H2O)n]
2þ clusters. In addition, the possibility ofone water molecule forming four hydrogen bonds(HBs) except those in the first hydration shell, and HBnetwork among hydration shell were considered. A fullgeometry optimization is followed to obtain a localminimum energy structure. DFT calculations wereperformed using B3LYP method employing the aug-cc-pVDZ basis sets for magnesium, hydrogen, andoxygen [38], while for calcium, relativistic effective corepotentials (RECP) according to the Stuttgart groupwith its combined basis set [39]. This basis setcombination is abbreviated as aVDZ. The basis setsuperposition error (BSSE) correction was also takeninto account using counterpoise method [40]. Toconsider the solvation effect of outer hydration shellson ion hydration, PCM calculations were carried outfor various [Ca(H2O)n]
2þ and [Mg(H2O)n]2þ clusters.
Moreover, to gain a better understanding, principallywith regard to possible charge-transfer effects of thecentral metal ion to ligands, NBO charge populationanalyses [41,42] were performed. In addition to quan-tum mechanical DFT calculations, we have performedatom-centered density matrix propagation (ADMP)AIMD simulations [43] for the magnesium and calciumions water system in order to investigate the firsthydration shell of Mg2þ and Ca2þ ions. Since AIMDsimulations require a lot of computing time, and thuswe used the B3LYP method with a moderate basis set(6-31þG**), which is slightly smaller than the aVDZbasis set. For each conformer, 3.0 ps simulation wasperformed, and the time step employed in eachsimulation is 0.2 fs. All the calculations were doneusing the Gaussian package [44].
In the hydration process of Mxþ, one may considerthere is an approximate boundary between innersolvation shells that should be considered using quan-tum mechanics methods, and outer solvation shellsmainly having polarization effects on ions that can beconsidered as polarized continuum medium usingPCM. A simple approximation to a saturated ionsolvation shell around Mxþ in infinitely dilute aqueoussolution is that the sequential water binding energy
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Molecular Physics 555
probably not restricted to the formation of the firstand second hydration shells, especially for that ofdications. Markham et al. described the lowest-energy[Mg(H2O)n]
2þ model at present, which 6 water mole-cules are filled in the first hydration shell and 12 watermolecules are arranged in the second hydration shell[22,23]. However, Martinez et al. found the coordina-tion number of the second hydration shell for Mg2þ is13 [24]. In most studies, the number of water moleculesin the second hydration shell of Mg2þ was expected tobe about 12. Recently, result from density functionaltheory (DFT), Lei and Pan considered that the firsthydration shell of Ca2þ is fully occupied by 6 watermolecules, whereas the second hydration shell might beoccupied with 9 water molecules [25]. Since the effect ofdications on the structure of water is probably notrestricted to the formation of first and second hydra-tion shells, it will be interesting to investigate hydrationcharacteristics of Mg2þ and Ca2þ while their secondand third hydration shells explicitly are taken intoaccount as well as their outer hydration shells areinexplicitly considered as polarized continuummedium.
Here, [Mg(H2O)n]2þ (n¼ 6–10, 18–21, 24, 27, 36)
and [Ca(H2O)n]2þ (n¼ 6–10, 18–21, 24, 27) clusters
have been systematically studied using DFT and thepolarized continuum model (PCM) [26,27] to gain aninsight into their hydrated characteristics in detail. Wehave also performed ab initio molecular dynamics(AIMD) simulation of the [Mg(H2O)6,8]
2þ and[Ca(H2O)8,10]
2þ clusters, since it has been proven tobe a suitable alternative to experiments for an accuratedescription of physical and chemical phenomena of ionhydration [28–30]. In this context, the value of CNs ofMg2þ and Ca2þ in solvent water molecules wereexamined by the integration of radial distributionfunction (RDF) obtained from molecular dynamicssimulations. Natural bond orbital (NBO) charge pop-ulation analyses for [Mg(H2O)n]
2þ and [Ca(H2O)n]2þ
clusters were carried out to investigate charge transfereffect of these two ions. Moreover, we especiallyinvestigated the approximatively saturated ion hydra-tion shell of Ca2þ and Mg2þ according to theirstructural characteristics of various hydration shells.
2. Computational details
Previous application of the Becke’s three-parameterfunctional and the correlation function of Lee, Yang,and Parr (B3LYP) [31,32] to model metal ion-watersystems has proved a reasonable success [4,9,33–36].The works of Kim et al. have also investigatedthe hydration of alkali metal ions using B3LYP,
Møller-Plesset second order perturbation theory(MP2), and coupled cluster theory with singles, dou-bles, and perturbative triples excitations (CCSD(T)),but the results obtained using these methods lead to asimilar conclusion on the hydration characteristics[28,37]. Therefore, B3LYP method was chosen to lookfor local minimum energy structures of [Ca(H2O)n]
2þ
and [Mg(H2O)n]2þ clusters in this work. On generating
initial hydrated structures, four-, five-, and six-coordinated conformers were taken into account for[Mg(H2O)n]
2þ clusters, and five-, six-, seven-, andeight-coordinated conformers were considered for[Ca(H2O)n]
2þ clusters. In addition, the possibility ofone water molecule forming four hydrogen bonds(HBs) except those in the first hydration shell, and HBnetwork among hydration shell were considered. A fullgeometry optimization is followed to obtain a localminimum energy structure. DFT calculations wereperformed using B3LYP method employing the aug-cc-pVDZ basis sets for magnesium, hydrogen, andoxygen [38], while for calcium, relativistic effective corepotentials (RECP) according to the Stuttgart groupwith its combined basis set [39]. This basis setcombination is abbreviated as aVDZ. The basis setsuperposition error (BSSE) correction was also takeninto account using counterpoise method [40]. Toconsider the solvation effect of outer hydration shellson ion hydration, PCM calculations were carried outfor various [Ca(H2O)n]
2þ and [Mg(H2O)n]2þ clusters.
Moreover, to gain a better understanding, principallywith regard to possible charge-transfer effects of thecentral metal ion to ligands, NBO charge populationanalyses [41,42] were performed. In addition to quan-tum mechanical DFT calculations, we have performedatom-centered density matrix propagation (ADMP)AIMD simulations [43] for the magnesium and calciumions water system in order to investigate the firsthydration shell of Mg2þ and Ca2þ ions. Since AIMDsimulations require a lot of computing time, and thuswe used the B3LYP method with a moderate basis set(6-31þG**), which is slightly smaller than the aVDZbasis set. For each conformer, 3.0 ps simulation wasperformed, and the time step employed in eachsimulation is 0.2 fs. All the calculations were doneusing the Gaussian package [44].
In the hydration process of Mxþ, one may considerthere is an approximate boundary between innersolvation shells that should be considered using quan-tum mechanics methods, and outer solvation shellsmainly having polarization effects on ions that can beconsidered as polarized continuum medium usingPCM. A simple approximation to a saturated ionsolvation shell around Mxþ in infinitely dilute aqueoussolution is that the sequential water binding energy
DEseq,n of the nth water molecule in [M(H2O)n]xþ (n is
the undetermined number) cluster is close to theestimated dissociation energy of one water molecule
from liquid water or water clusters calculation inabsolute value (Figure 1) [36].
The sequential water binding energy for the addi-
tive water molecule in [M(H2O)m]2þ cluster is defined
as
DEseq,m ¼ EM H2Oð Þm½ �2þ � E
M H2Oð Þm�1½ �2þ � EH2O ð1Þ
DEseq,m is the sequential water binding energy of themth water molecule. The dissociation energy DED of
one water molecule from bulk liquid water is�10.5 kcal/mol estimated from the evaporation
energy of liquid water [45,46], and the averageddissociation energy of one water molecule is
�10.7 kcal/mol estimated from water clusters (H2O)21[46,47]. Generally, the binding energy of the mth water
molecule binding with water molecules in the outersolvation shell, DEout
seq,m is not greater than the sequen-
tial water binding energy DEinseq,m of the mth water
molecule binding with water molecules of the inner
solvation shell. DEinseq,m can be calculated using
Equation (1), while DEoutseq,m does not really need to be
calculated due to the inequality relation. Such inequal-ity relation is generally reasonable when one or two
hydration shells are considered in the inner solvationshell. Therefore, if the sequential water binding energy
DEinseq,m of the mth water molecule, binding with water
molecules of the inner solvation shell, is close to the
evaporation energy of liquid water (�10.5 kcal/mol),and then DEseq,m is also �10.5 kcal/mol, and thus this
water molecule can be approximated as a watermolecule in the outer solvation shell or bulk water.
Furthermore, it can probably be concluded that nomore water molecule needs to be considered in the
inner solvation shell, while only inexplicitly considered
in the outer solvation shell as polarized continuum
medium.The binding energy (DE) was computed using the
following equation:
M2þ þ nH2O DE �!½MðH2OÞn�2þ M ¼ Mg,Cað ÞDE ¼ E½MðH2OÞn�
2þ � EðH2OÞn � EM2þð2Þ
We can compare the stabilities of [M(H2O)n]2þ
(M¼Mg or Ca) in the gas phase through Equation (2).Thermodynamic values for DGsolv were obtained
using PCM within the context of
DGsolv ¼X
Gprod �X
Greact ð3Þ
The free energy of a species is expressed as
G ¼ E0gas þ Gcorr þ Gscrf þ Gss ð4Þ
where
Gcorr ¼ PV� TS ð5Þ
E0gas is the binding energy of standard state (298.15K,
1 atm) in the gas phase, and
Gscrf ¼ Gelectrostatic þ Gcavitation þ Gdispersion þ Grepulsion
ð6Þ
In the case of water [35]
Gss ¼ RT ln pw=p�� �=n ð7Þ
where pw is the pressure of liquid water assuming that
it is an ideal gas, p� is the pressure of the gas-phase
standard state, R is the universal gas constant, and T is
the room temperature in Kelvin. Water molecule is
present in liquid at a concentration of 55.56mol/kg or
about 1350 atm. This corresponds to 4.3/n, where n is
the number of water molecules in the cluster [35].
the mth water molecule inininer solvation shell
Mx+( H2O)x
OH
H
O
H
H
O
H H
outer solvation shell
free water
comparable
DEΔ
approximatively saturated ion hydration shell
mth
(m-1)th
liquid water
Bulk
free waterDEΔ
inseq,mΔE
outseq,mΔE
(m-2)th seq,mΔE2
outseq,mΔE+in
seq,mΔE
seq,mΔE
inner solvation shell
Figure 1. Approximative saturated ion hydration shell which should be treated using quantum mechanics (QM) method.
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556 G. Bai et al.
3. Results and discussion
In this work, a variety of Mg2þ and Ca2þ hydratedclusters with water molecules in the first, second, andeven third hydration shells were studied. Discussionsabout hydration nature of Mg2þ and Ca2þ werearranged as: (1) hydration characteristics based oncomparison of the binding energies, and bond param-eters; (2) comparison of sequential binding energy andNBO charge on metal cation during hydrationproceeds, and transformation among various isomers;(3) comparison of AIMD simulations.
3.1. Hydrated structures and energetics
The major information of the water binding energiesand M�O bond distances within the first hydrationshell for [Mg(H2O)n]
2þ and [Ca(H2O)n]2þ clusters are
gathered in Tables 1–4. M�O bond distances andNBO charge on Mg2þ of [Mg(H2O)27]
2þ clusterobtained from B3LYP/aVDZ and PCM B3LYP/aVDZ geometry optimizations are almost the same[see Supplementary Material]. Therefore, only gasphase structures were included in this work. Thebinding energies in the gas phase (DE) and in thedilute aqueous solution (DEsolv) in Tables 1–4 wereobtained according to Equations (2)–(7). Hydrationcharacteristics about the first hydration shell of Mg2þ
and Ca2þ were discussed based on binding energies,bond parameters, and charge transfer effects of centralcation.
3.1.1. [Mg(H2O)n]2þ clusters
For [Mg(H2O)6]2þ cluster, there is a debate as to the
number of water molecules in the first hydration shell[6,7,10,48]. Pavlov’s calculations [6] as well as those ofRao [7] indicated that the six-coordinated structure isthe most stable one. However, Williams et al. [10,48]reported that for [Mg(H2O)6]
2þ cluster, the twoisomers most likely correspond to a six-coordination(6, 0) structure at low temperature, and either afive-coordination (5, 1) or a four-coordination (4, 2)structure at high temperature. Since the transformationfrom a six-coordination (6, 0) structure to either afive-coordination (5, 1) or a four-coordination (4, 2)structure will lead an increase of entropy, and thussix-coordinated structures will be favorable at lowtemperature while five- or four-coordinated confor-mers at high temperature, as suggested by Williamset al. [10,48]. However, B3LYP/aVDZ calculationsshow that the six-coordinated conformer of[Mg(H2O)n]
2þ cluster is slightly preferred in energy,except [Mg(H2O)7]
2þ and [Mg(H2O)8]2þcluster,
and MP2/aVDZ results also show that the six-coordinated conformer of [Mg(H2O)n]
2þ cluster is
Table 1. Bond and energy parametersa of [Mg(H2O)n]2þ (n¼ 6–10) clusters in the gas phase at B3LYP/
aVDZ and MP2/aVDZ levels.
B3LYP MP2
Geometries HBb rMg-O qMg DE rMg-O qMg DE
W6-4L 4 199.2 1.63 �311.2 200.6 1.71 �303.9W6-5L 2 205.6 1.57 �312.9 206.4 1.65 �307.2W6-6L 0 210.5 1.50 Z314.4 210.7 1.60 Z310.8W7-4L 5 198.8 1.62 �332.3 200.2 1.70 �325.2W7-5L 4 205.0 1.56 Z337.9 205.8 1.65 Z333.2W7-6L 2 210.7 1.50 �335.4 210.9 1.60 Z332.9W8-5L 6 204.7 1.55 Z359.1 205.5 1.64 �355.7W8-6L 4 210.2 1.50 �357.4 210.3 1.59 Z356.2W9-5L 8 204.0 1.54 Z378.6 204.7 1.63 �376.7W9-6L 6 210.0 1.49 Z378.8 210.1 1.58 Z378.8W10-5L 9 203.9 1.54 Z395.5 204.5 1.63 �394.3W10-6L 8 210.4 1.50 �394.8 210.5 1.59 Z396.0
Note: aW and L are the abbreviations of water molecule and direct coordinated ligand, and CN value of Mg2þ
is added before L. rMg-O is the mean Mg–O distance between Mg2þ with oxygen atoms of water molecules inthe first hydrated shell, qMg is the charge obtained from NBO charge population analyses, DE is the bindingenergy calculated using Equation (2). All the energies are in kcal/mol at room temperature (298K and 1 atm),NBO charge and bond distance are given in au/e and pm correspondingly. For [Mg(H2O)n]
2þ clusters, themost stable conformers with the cluster size n increase are marked in bold.bNumber of hydrogen bond (HB) formed among water molecules. W6-4L is a four-coordination (4, 2)structure, W6-5L is a five-coordination (5, 1) structure, and W6-6L is a six-coordination (6, 0) structure.
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Molecular Physics 557
3. Results and discussion
In this work, a variety of Mg2þ and Ca2þ hydratedclusters with water molecules in the first, second, andeven third hydration shells were studied. Discussionsabout hydration nature of Mg2þ and Ca2þ werearranged as: (1) hydration characteristics based oncomparison of the binding energies, and bond param-eters; (2) comparison of sequential binding energy andNBO charge on metal cation during hydrationproceeds, and transformation among various isomers;(3) comparison of AIMD simulations.
3.1. Hydrated structures and energetics
The major information of the water binding energiesand M�O bond distances within the first hydrationshell for [Mg(H2O)n]
2þ and [Ca(H2O)n]2þ clusters are
gathered in Tables 1–4. M�O bond distances andNBO charge on Mg2þ of [Mg(H2O)27]
2þ clusterobtained from B3LYP/aVDZ and PCM B3LYP/aVDZ geometry optimizations are almost the same[see Supplementary Material]. Therefore, only gasphase structures were included in this work. Thebinding energies in the gas phase (DE) and in thedilute aqueous solution (DEsolv) in Tables 1–4 wereobtained according to Equations (2)–(7). Hydrationcharacteristics about the first hydration shell of Mg2þ
and Ca2þ were discussed based on binding energies,bond parameters, and charge transfer effects of centralcation.
3.1.1. [Mg(H2O)n]2þ clusters
For [Mg(H2O)6]2þ cluster, there is a debate as to the
number of water molecules in the first hydration shell[6,7,10,48]. Pavlov’s calculations [6] as well as those ofRao [7] indicated that the six-coordinated structure isthe most stable one. However, Williams et al. [10,48]reported that for [Mg(H2O)6]
2þ cluster, the twoisomers most likely correspond to a six-coordination(6, 0) structure at low temperature, and either afive-coordination (5, 1) or a four-coordination (4, 2)structure at high temperature. Since the transformationfrom a six-coordination (6, 0) structure to either afive-coordination (5, 1) or a four-coordination (4, 2)structure will lead an increase of entropy, and thussix-coordinated structures will be favorable at lowtemperature while five- or four-coordinated confor-mers at high temperature, as suggested by Williamset al. [10,48]. However, B3LYP/aVDZ calculationsshow that the six-coordinated conformer of[Mg(H2O)n]
2þ cluster is slightly preferred in energy,except [Mg(H2O)7]
2þ and [Mg(H2O)8]2þcluster,
and MP2/aVDZ results also show that the six-coordinated conformer of [Mg(H2O)n]
2þ cluster is
Table 1. Bond and energy parametersa of [Mg(H2O)n]2þ (n¼ 6–10) clusters in the gas phase at B3LYP/
aVDZ and MP2/aVDZ levels.
B3LYP MP2
Geometries HBb rMg-O qMg DE rMg-O qMg DE
W6-4L 4 199.2 1.63 �311.2 200.6 1.71 �303.9W6-5L 2 205.6 1.57 �312.9 206.4 1.65 �307.2W6-6L 0 210.5 1.50 Z314.4 210.7 1.60 Z310.8W7-4L 5 198.8 1.62 �332.3 200.2 1.70 �325.2W7-5L 4 205.0 1.56 Z337.9 205.8 1.65 Z333.2W7-6L 2 210.7 1.50 �335.4 210.9 1.60 Z332.9W8-5L 6 204.7 1.55 Z359.1 205.5 1.64 �355.7W8-6L 4 210.2 1.50 �357.4 210.3 1.59 Z356.2W9-5L 8 204.0 1.54 Z378.6 204.7 1.63 �376.7W9-6L 6 210.0 1.49 Z378.8 210.1 1.58 Z378.8W10-5L 9 203.9 1.54 Z395.5 204.5 1.63 �394.3W10-6L 8 210.4 1.50 �394.8 210.5 1.59 Z396.0
Note: aW and L are the abbreviations of water molecule and direct coordinated ligand, and CN value of Mg2þ
is added before L. rMg-O is the mean Mg–O distance between Mg2þ with oxygen atoms of water molecules inthe first hydrated shell, qMg is the charge obtained from NBO charge population analyses, DE is the bindingenergy calculated using Equation (2). All the energies are in kcal/mol at room temperature (298K and 1 atm),NBO charge and bond distance are given in au/e and pm correspondingly. For [Mg(H2O)n]
2þ clusters, themost stable conformers with the cluster size n increase are marked in bold.bNumber of hydrogen bond (HB) formed among water molecules. W6-4L is a four-coordination (4, 2)structure, W6-5L is a five-coordination (5, 1) structure, and W6-6L is a six-coordination (6, 0) structure.
slightly preferred, except for [Mg(H2O)7]2þ cluster
which slightly prefers five-coordinated structures, asshown in Table 1. Four-coordinated structures areobviously less stable than their five-, and six-coordi-nated isomers. Moreover, our calculated results indi-cate that all [Mg(H2O)n]
2þ clusters prefer6-coordinated conformers if solvation effect of outersolvation shells is taken into account, and its four-coordinated structure much less stable at the PCM-B3LYP/aVDZ level [see Supplementary Material].
B3LYP/aVDZ results of larger hydrated clusters[Mg(H2O)n]
2þ (n¼ 18–21, 24, 27, 36) are listed inTable 2 and Figure 2. For n¼ 18, we have consideredthe conformers of [Mg(H2O)6(H2O)12]
2þ reportedby Pavlov et al. (denoted by PSS) [6], the PCRconformer showed by Pye and Rudolph [49], theMGB conformer reported by Markham et al. [22].Recently, the [Ca(H2O)6(H2O)9(H2O)3]
2þ conformer,with the first hydration shell occupied by 6 water
molecules whereas 9 water molecules in the secondhydration shell, was considered in the DFT work ofLei and Pan (denoted by LP) [25]. In this work, the LPtype conformer was also considered for [Mg(H2O)18]
2þ
clusters. The coordination numbers of the secondhydration shell are 9 and 12 for LP type, and MGBtype conformers of [Mg(H2O)18]
2þ clusters, respec-tively. Except those six-coordinated conformers for the[Mg(H2O)18]
2þ cluster, we have also considered a five-coordinated conformer, W18-5L. B3LYP/aVDZ cal-culations point out that for [Mg(H2O)18]
2þ cluster, thesix-coordinated MGB-type conformer is the moststable configuration among those obtained confor-mers, the five-coordinated conformer is �13.9 kcal/molfar less stable than the most stable configuration, andthus the five-coordinated structures were notconsidered for [Mg(H2O)19-21,24,27,36]
2þ clusters.The third hydration shell of Mg2þ hydrated clusters
were also considered on the basis of MGB-type,
Table 2. B3LYP/aVDZ bond and energy parametersa of [Mg(H2O)n]2þ clusters in the gas and aqueous phasesb.
Gas phase Aqueous phase
Geometriesc rMg-O qMg DE DE0 DHr DGr DEsolv DE0,solv DHr,solv DGr,solv
W18-5L 203.2 1.53 �494.8 �450.6 �463.1 �289.3 �572.5 �528.3 �540.8 �367.0W18-6LA 209.3 1.49 �513.0 Z464.5 �480.0 �294.3 �592.5 Z543.9 �559.5 �373.8W18-6LB 210.0 1.49 �505.6 �461.6 �473.8 �300.5 �582.4 �538.4 �550.7 �377.3W18-6LC 209.4 1.48 �504.9 �458.8 �472.8 �291.9 �581.3 �535.2 �549.2 �368.2W19-6LA 209.3 1.49 �525.4 Z475.0 �490.8 �296.9 �598.4 Z548.0 �563.8 �369.8W19-6LB 209.6 1.49 �522.4 �472.2 �487.9 �293.8 �597.1 �546.9 �562.6 �368.4W19-6LC 210.1 1.49 �517.0 �471.4 �483.7 �302.7 �588.5 �542.9 �555.2 �374.2W20-6LA 209.4 1.49 �536.9 �483.8 �500.5 �295.8 �604.4 �551.3 �568.0 �363.4W20-6LB 209.3 1.49 �536.3 Z484.1 �500.3 �298.3 �604.2 Z552.0 �568.2 �366.2W20-6LC 210.0 1.49 �528.5 �481.1 �493.6 �304.8 �594.8 �547.4 �559.9 �371.0W21-6LA 209.3 1.49 �549.6 Z495.1 �511.9 �299.8 �611.7 Z557.1 �573.9 �361.9W21-6LB 209.2 1.49 �549.4 �494.2 �511.3 �297.6 �611.2 �555.9 �573.0 �359.4W21-6LC 209.4 1.49 �548.6 �494.7 �510.7 �301.0 �609.8 �556.0 �572.0 �362.2W24-6LA 209.3 1.49 �585.1 Z523.4 �541.8 �301.5 �631.4 �569.7 �588.1 �347.8W24-6LB 209.4 1.49 �584.3 �523.2 �541.3 �302.6 �631.1 Z570.0 �588.1 �349.4W24-6LC 209.4 1.49 �583.6 �522.0 �540.3 �300.3 �630.8 �569.2 �587.5 �347.5W27-6LA 209.5 1.49 �616.8 Z549.4 �568.6 �303.9 �650.2 Z582.8 �602.0 �337.3W27-6LB 209.4 1.49 �616.7 �548.9 �568.3 �302.3 �650.1 �582.4 �601.8 �335.8W27-6LC 210.3 1.48 �592.3 �534.7 �546.2 �308.9 �630.3 �572.7 �584.2 �346.9W36-6L 209.7 1.49 �700.7 Z613.7 �636.5 �291.5 �705.2 Z618.3 �641.0 �296.0
Note: aW and L are the abbreviations of water molecule and direct coordinated ligand, and CN value of Mg2þ is added before L.Binding energy (DE) were obtained according to Equation (2), DE0 is zero-point corrected binding energy, DHr and DGr areenthalpy and free energy in the gas phase. rMg�O is the average distance between Mg and O of water molecules in the firsthydration shell. All the energies are in kcal/mol at room temperature (298K and 1 atm), NBO charge and bond distance are givenin au/e and pm correspondingly. For [Mg(H2O)n]
2þ clusters, the most stable conformers with the cluster size n increase aremarked in bold.bDEsolv, DE0,solv, DHr,solv and DGr,solv are binding energy, zero-point corrected binding energy, enthalpy, and free energy in theaqueous phase, respectively, which were obtained using the PCM-B3LYP/aVDZ method.cW18-6LA is the MBG type conformer, W18-6LB is the LP type conformer ([Mg(H2O)6(H2O)9(H2O)3]
2þ), and W18-6LC is thePCR type conformer. W19-6LA and W19-6LB are MBG type conformers, W19-6LC is the LP type conformer. W20-6LA andW20-6LB are MBG type conformers, W20-6LC is the LP type conformer. W27-6LC is the LP type conformer. The coordinationnumber of the second hydration shell is 12 and 9 for MBG type and LP type conformers, respectively.
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558 G. Bai et al.
PSS-type, and PCR-type structures of [Mg(H2O)18]2þ
cluster, and an extensive searching for the low-lyingconformer of [Mg(H2O)n]
2þ (n¼ 19–21, 24, 27, 36) clus-ters was carried out at the B3LYP/aVDZ level.The low-lying conformers are presented in Figure 2.As n¼ 19 or 20, the MGB-type conformer is still morestable than other conformers, as shown in Table 2.With the proceeding of the third hydration shell theenergy difference between the conformers of MGB-type and other conformers becomes larger, that is, theMGB-type conformer is probably the most stableconfiguration for [Mg(H2O)n]
2þ (n¼ 18–36) clusters.However, LP conformers may be more favorable dueto its large entropy, even at room temperature. Theresults of free energy indicate that the constraint ofMg2þ on the second hydration shell is less definitive,and the coordination number of the second hydrationshell may vary at range of 9–12, and is more likely tobe 9 especially at high temperature, as shown inTable 2. Recent results of vibrational spectra and MDsimulations by Callahan and Allen et al. [50] suggestthat Mg2þ preferentially forms a [Mg(H2O)6]
2þ com-plex of a nearly octahedral symmetry, even in concen-trated solutions. Our B3LYP/aVDZ calculations ofvarious hydrated clusters also show that the hydrationof Mg2þ generally prefers six-coordinated structures in
the gas phase, or in the aqueous solution whensolvation effect of outer hydration shells is consideredusing PCM.
3.1.2. [Ca(H2O)n]2þ clusters
Selected low-lying energy structures of [Ca(H2O)n]2þ
(n¼ 6–10) clusters in the gas phase are shown inTable 3. Calcium has much larger ionic surface, sothe Ca2þ can accommodate more water molecules inthe first hydration shell than Mg2þ as n� 7. Five-,six-, seven-, and eight-coordinated conformers wereconsidered for [Ca(H2O)n]
2þ clusters. It should benoted that we have attempted to find a stablestructure with nine water molecules in the firsthydration shell around Ca2þ, but all calculatedresults are that one water molecule migrates to thesecond hydration shell. Binding energies of[Ca(H2O)n]
2þ (n¼ 7–10) clusters obtained atB3LYP/aVDZ and MP2/aVDZ levels also showthat six-coordinated conformers are more stable inthe gas phase, as shown in Table 3. It was alsofound that hydrogen atoms of one water molecule inthe first hydration shell, which does not yet form aHB with water molecules in the second hydrationshell, will clearly point towards the oxygen atoms on
Table 3. Bond and energy parametersa of [Ca (H2O)n]2þ (n¼ 6–10) clusters in the gas phase at B3LYP/
aVDZ and MP2/aVDZ levels.
HBb
B3LYP MP2
rCa-O qCa DE rCa-O qCa DE
W6-5L 2 235.3 1.60 �240.6 235.6 1.71 �240.4W6-6L 0 239.2 1.49 Z243.3 238.7 1.60 Z245.1W7-5L 4 234.5 1.59 �263.7 234.8 1.69 �264.6W7-6L 2 239.1 1.48 Z263.9 238.5 1.59 Z266.9W7-7L 0 244.6 1.41 �258.4 243.1 1.52 �264.1W8-5L 6 234.0 1.58 �283.4 234.3 1.68 �285.7W8-6L 4 238.5 1.48 Z285.0 237.9 1.58 Z289.2W8-7L 2 244.2 1.39 �279.0 242.7 1.51 �286.0W8-8L 0 249.1 1.32 �272.8 246.6 1.42 �282.8W9-6L 6 238.1 1.46 Z305.2 237.4 1.57 Z310.7W9-7L 4 243.8 1.38 �299.2 242.2 1.49 �307.4W9-8L 2 249.2 1.31 �291.3 246.7 1.42 �302.5W10-6L 8 238.1 1.45 Z321.6 237.6 1.57 Z328.7W10-7L 6 243.7 1.37 �316.7 242.1 1.49 �326.4W10-8L 4 249.3 1.30 �309.6 246.9 1.41 �327.0
Note: aW and L are the abbreviations of water molecule and direct coordinated ligand, and CN value ofCa2þ is added before L. rCa-O is the mean CaZO distance between Ca2þ with oxygen atoms of watermolecules in the first hydrated shell, qCa is the charge obtained from NBO charge population analyses,DE is the binding energy calculated using Equation (2). All the energies are in kcal/mol at roomtemperature (298K and 1 atm), NBO charge and bond distance are given in au/e and pmcorrespondingly. For [Ca(H2O)n]
2þ clusters, the most stable conformers with the cluster size n increaseare marked in bold.bNumber of hydrogen bonds formed among water molecules.
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Molecular Physics 559
PSS-type, and PCR-type structures of [Mg(H2O)18]2þ
cluster, and an extensive searching for the low-lyingconformer of [Mg(H2O)n]
2þ (n¼ 19–21, 24, 27, 36) clus-ters was carried out at the B3LYP/aVDZ level.The low-lying conformers are presented in Figure 2.As n¼ 19 or 20, the MGB-type conformer is still morestable than other conformers, as shown in Table 2.With the proceeding of the third hydration shell theenergy difference between the conformers of MGB-type and other conformers becomes larger, that is, theMGB-type conformer is probably the most stableconfiguration for [Mg(H2O)n]
2þ (n¼ 18–36) clusters.However, LP conformers may be more favorable dueto its large entropy, even at room temperature. Theresults of free energy indicate that the constraint ofMg2þ on the second hydration shell is less definitive,and the coordination number of the second hydrationshell may vary at range of 9–12, and is more likely tobe 9 especially at high temperature, as shown inTable 2. Recent results of vibrational spectra and MDsimulations by Callahan and Allen et al. [50] suggestthat Mg2þ preferentially forms a [Mg(H2O)6]
2þ com-plex of a nearly octahedral symmetry, even in concen-trated solutions. Our B3LYP/aVDZ calculations ofvarious hydrated clusters also show that the hydrationof Mg2þ generally prefers six-coordinated structures in
the gas phase, or in the aqueous solution whensolvation effect of outer hydration shells is consideredusing PCM.
3.1.2. [Ca(H2O)n]2þ clusters
Selected low-lying energy structures of [Ca(H2O)n]2þ
(n¼ 6–10) clusters in the gas phase are shown inTable 3. Calcium has much larger ionic surface, sothe Ca2þ can accommodate more water molecules inthe first hydration shell than Mg2þ as n� 7. Five-,six-, seven-, and eight-coordinated conformers wereconsidered for [Ca(H2O)n]
2þ clusters. It should benoted that we have attempted to find a stablestructure with nine water molecules in the firsthydration shell around Ca2þ, but all calculatedresults are that one water molecule migrates to thesecond hydration shell. Binding energies of[Ca(H2O)n]
2þ (n¼ 7–10) clusters obtained atB3LYP/aVDZ and MP2/aVDZ levels also showthat six-coordinated conformers are more stable inthe gas phase, as shown in Table 3. It was alsofound that hydrogen atoms of one water molecule inthe first hydration shell, which does not yet form aHB with water molecules in the second hydrationshell, will clearly point towards the oxygen atoms on
Table 3. Bond and energy parametersa of [Ca (H2O)n]2þ (n¼ 6–10) clusters in the gas phase at B3LYP/
aVDZ and MP2/aVDZ levels.
HBb
B3LYP MP2
rCa-O qCa DE rCa-O qCa DE
W6-5L 2 235.3 1.60 �240.6 235.6 1.71 �240.4W6-6L 0 239.2 1.49 Z243.3 238.7 1.60 Z245.1W7-5L 4 234.5 1.59 �263.7 234.8 1.69 �264.6W7-6L 2 239.1 1.48 Z263.9 238.5 1.59 Z266.9W7-7L 0 244.6 1.41 �258.4 243.1 1.52 �264.1W8-5L 6 234.0 1.58 �283.4 234.3 1.68 �285.7W8-6L 4 238.5 1.48 Z285.0 237.9 1.58 Z289.2W8-7L 2 244.2 1.39 �279.0 242.7 1.51 �286.0W8-8L 0 249.1 1.32 �272.8 246.6 1.42 �282.8W9-6L 6 238.1 1.46 Z305.2 237.4 1.57 Z310.7W9-7L 4 243.8 1.38 �299.2 242.2 1.49 �307.4W9-8L 2 249.2 1.31 �291.3 246.7 1.42 �302.5W10-6L 8 238.1 1.45 Z321.6 237.6 1.57 Z328.7W10-7L 6 243.7 1.37 �316.7 242.1 1.49 �326.4W10-8L 4 249.3 1.30 �309.6 246.9 1.41 �327.0
Note: aW and L are the abbreviations of water molecule and direct coordinated ligand, and CN value ofCa2þ is added before L. rCa-O is the mean CaZO distance between Ca2þ with oxygen atoms of watermolecules in the first hydrated shell, qCa is the charge obtained from NBO charge population analyses,DE is the binding energy calculated using Equation (2). All the energies are in kcal/mol at roomtemperature (298K and 1 atm), NBO charge and bond distance are given in au/e and pmcorrespondingly. For [Ca(H2O)n]
2þ clusters, the most stable conformers with the cluster size n increaseare marked in bold.bNumber of hydrogen bonds formed among water molecules.
adjacent water molecules in the first hydrationshell both for the six-coordinated hydrated struc-tures, [Mg(H2O)n]
2þ and [Ca(H2O)n]2þ (n¼ 6–10)
clusters, as proposed in the experimental work ofArmentrout [3].
B3LYP/aVDZ calculations of [Ca(H2O)n]2þ
(n¼ 18–27) show that six-coordinated conformers arestill slightly more stable in the gas phase, even forlarger hydrated clusters. However, PCM/B3LYP/aVDZ calculations of [Ca(H2O)20,21,24,27]
2þ clustersindicate that seven- and eight-coordinated structuresbecome more stable than their six-coordinated struc-tures in the dilute aqueous solution. Detail informationabout the hydration characteristics were provided asshown in Table 4 and Figure 3. It should be noted thatthe binding energy of Mg2þ is obviously larger than
that of Ca2þ with the hydration proceeds, and thedifference of binding energies is always greater than60 kcal/mol as the hydration proceeds (n¼ 6–27), asshown in Tables 1–4. It suggests that the constraint ofMg2þ on the first hydration shell is obviously strongerthan that of Ca2þ.
The experimental results of Radnai [51] suggestedthat CN value of Ca2þ may be eight in low concen-tration solution, while six in concentrated solution.The classical MD simulation of Piquemal [52] alsoshowed that Ca2þ prefers eight-coordination for largeclusters or simulation boxes, while six-coordination forsmall ones. Meanwhile, the results of Williams et al.from infrared multiple photon dissociation (IRMPD)spectroscopy of [Ca(H2O)n]
2þ (n¼ 11–69) clusters inthe gas phase proposed that the CN value of Ca2þ may
Table 4. B3LYP/aVDZ bond and energy parametersa of [Ca(H2O)n]2þ clusters in the gas and aqueous phasesb.
Geometries
Gas phase Aqueous phase
rCa-O qCa DE DE0 DHr DGr DEsolv DE0,solv DHr,solv DGr,solv
W18-6LA 235.7 1.38 �433.4 �386.5 �401.2 �217.5 �507.1 Z460.2 �474.9 �291.2W18-6LB 237.0 1.41 �429.6 Z386.9 �398.5 �227.1 �502.2 �459.5 �471.1 �299.7W18-6LC 237.4 1.41 �428.4 �383.5 �397.0 �218.1 �500.0 �455.1 �468.6 �289.7W18-7L 244.7 1.35 �429.4 �383.1 �397.3 �215.4 �506.3 Z460.0 �474.2 �292.3W18-8L 249.0 1.26 �424.0 �380.8 �392.4 �217.7 �503.2 Z460.0 �471.6 �297.0W19-6LA 235.8 1.38 �445.8 Z397.1 �412.0 �220.1 �513.1 Z464.4 �479.3 �287.4W19-6LB 236.1 1.39 �443.5 �394.7 �409.6 �217.3 �513.4 Z464.6 �479.5 �287.2W19-6LC 237.0 1.41 �441.0 Z396.7 �408.4 �229.3 �508.4 Z464.0 �475.7 �296.6W19-7L 243.8 1.33 �438.7 �390.2 �404.9 �212.7 �508.4 �459.9 �474.6 �282.4W19-8L 249.1 1.25 �439.4 �391.7 �405.5 �215.9 �511.8 Z464.1 �477.9 �288.3W20-6LA 235.8 1.38 �457.3 �405.9 �421.7 �219.3 �519.5 �468.1 �483.9 �281.5W20-6LB 236.9 1.41 �452.2 Z406.2 �418.0 �231.2 �514.4 �468.4 �480.2 �293.4W20-7L 243.7 1.33 �455.9 �404.0 �420.1 �215.8 �521.6 Z469.7 �485.7 �281.5W20-8L 249.9 1.27 �448.4 �399.3 �413.2 �215.3 �516.8 �467.7 �481.6 �283.7W21-6LA 235.8 1.38 �470.0 Z416.6 �432.7 �221.8 �526.7 �473.4 �489.5 �278.5W21-6LB 235.5 1.38 �468.8 �415.6 �431.6 �220.7 �525.2 �472.1 �488.1 �277.2W21-6LC 235.8 1.38 �468.6 Z416.6 �431.6 �224.2 �524.1 �472.1 �487.1 �279.7W21-7L 244.4 1.34 �468.8 �414.4 �431.2 �217.4 �529.4 Z475.0 �491.8 �278.1W21-8L 249.7 1.26 �462.8 �409.4 �425.3 �213.5 �526.1 �472.7 �488.6 �276.8W24-6LA 235.8 1.38 �504.9 Z445.1 �462.5 �224.6 �546.3 �486.4 �503.9 �266.0W24-6LB 235.8 1.38 �504.4 �444.6 �462.0 �224.4 �545.5 �485.7 �503.1 �265.4W24-7L 244.1 1.34 �503.9 �442.7 �461.0 �219.0 �548.8 Z487.7 �506.0 �264.0W24-8L 250.6 1.28 �500.5 �439.6 �457.8 �214.7 �548.8 Z487.9 �506.1 �263.0W27-6LA 235.9 1.37 �536.8 Z470.7 �489.2 �224.9 �565.3 Z499.1 �517.7 �253.4W27-6LB 235.9 1.37 �536.5 Z470.5 �488.9 �225.6 �564.8 Z498.8 �517.2 �253.9W27-6LC 236.9 1.40 �515.2 �459.4 �470.0 �235.8 �549.9 �494.1 �504.7 �270.6W27-7L 244.5 1.34 �533.6 �466.4 �485.8 �217.5 �564.5 �497.3 �516.7 �248.4W27-8L 250.6 1.28 �533.2 �465.9 �485.4 �215.6 �567.1 Z499.8 �519.3 �249.5
Note: aW and L are the abbreviations of water molecule and direct coordinated ligand of Ca2þ, and CN value of Ca2þ is addedbefore L. Binding energy (DE) were obtained according to Equation (2), DE0 is zero-point corrected binding energy, DHr andDGr. are enthalpy and free energy in the gas phase, respectively. rCa-O is the average distance between Ca and O of watermolecules in the first hydration shell. All the energies are in kcal/mol at room temperature (298K and 1 atm), NBO charge andbond distance are given in au/e and pm correspondingly. For [Ca(H2O)n]
2þ clusters, the most stable conformers with the clustersize n increase are marked in bold.bDEsolv, DE0,solv, DHr.solv and DGr.solv are binding energy, zero-point corrected binding energy, enthalpy, and free energy in theaqueous phase, respectively, which were obtained using the PCM-B3LYP/aVDZ method.
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W18-5L W18-6LA W18-6LB W18-6LC
W19-6LA W19-6LB W19-6LC W20-6LA
W20-6LB W20-6LC W21-6LA W21-6LB
W21-6LC W24-6LA W24-6LB W24-6LC
W27-6LA W27-6LB W27-6LC W36-6L
Figure 2. Selected optimized geometries of [Mg(H2O)n]2þ (n¼ 18–21, 24, 27, 36) at the B3LYP/aVDZ level. W and L are the
abbreviations of water and direct coordinated ligand, and CN value of Mg2þ is added before L. W18-6LA is the MBG typeconformer, W18-6LB is the LB type conformer, and W18-6LC is the PCR type conformer. PSS type conformers of [Mg(H2O)n]
2þ
clusters were not obtained in our B3LYP/aVDZ calculations. W19-6LA and W20-6LA are MBG type conformers, W19-6LC andW20-6LC are LP type conformers. W27-6LC is also the LP type conformer. The coordination number of the second hydrationshell is 12 and 9 for MBG type and LB type conformers, respectively.
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W18-5L W18-6LA W18-6LB W18-6LC
W19-6LA W19-6LB W19-6LC W20-6LA
W20-6LB W20-6LC W21-6LA W21-6LB
W21-6LC W24-6LA W24-6LB W24-6LC
W27-6LA W27-6LB W27-6LC W36-6L
Figure 2. Selected optimized geometries of [Mg(H2O)n]2þ (n¼ 18–21, 24, 27, 36) at the B3LYP/aVDZ level. W and L are the
abbreviations of water and direct coordinated ligand, and CN value of Mg2þ is added before L. W18-6LA is the MBG typeconformer, W18-6LB is the LB type conformer, and W18-6LC is the PCR type conformer. PSS type conformers of [Mg(H2O)n]
2þ
clusters were not obtained in our B3LYP/aVDZ calculations. W19-6LA and W20-6LA are MBG type conformers, W19-6LC andW20-6LC are LP type conformers. W27-6LC is also the LP type conformer. The coordination number of the second hydrationshell is 12 and 9 for MBG type and LB type conformers, respectively.
W18-6LA W18-6LB W18-6LC W18-7L
W18-8L W19-6LA W19-6LB W19-6LC
W19-7L W19-8L W20-6LA W20-6LB
W20-7L W20-8L W21-6LA W21-6LB
W21-6LC W21-7L W21-8L W24-6LA
Figure 3. Selected optimized geometries of [Ca(H2O)n]2þ (n¼ 18–21, 24, 27) at the B3LYP/aVDZ level. W and L are the
abbreviations of water molecule and direct coordinated ligand, and CN value of Ca2þ is added before L.
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562 G. Bai et al.
be 8 for clusters with 12 or more water molecules [11].However, our B3LYP/aVDZ calculations show that theenergy differences among six-, seven-, and eight-coordinated conformers of Ca2þ hydrates are verysmall for [Ca(H2O)n]
2þ (n� 20) clusters. Therefore, six-,seven-, and eight-coordinated structures for the hydra-tion of Ca2þmay be all possible when solvation effect ofouter hydration shells are considered using PCM.
3.2. Hydration shells for Mg2þ and Ca2þ hydrates
The mean Ca–O bond distance between Ca and oxygenatoms of water molecules in the first hydration shellincreases steadily from n¼ 1 to 8, and is almostunchanged when n� 18, as shown in Figure 4.It indicates that the mean Ca–O bond distance isalmost unchanged when the first and second hydrationshells are saturated, while the mean Mg–O bonddistance is almost unchanged when the first hydrationshell is saturated. NBO charge population analyses of[Ca(H2O)n]
2þ clusters show that the charge on six-,seven-, or eight-coordinated Ca2þ is essentiallyunchanged when n� 18, which is slightly differentfrom the situation of Mg2þ hydration, as shown inTables 2 and 4, and Figure 5. The comparison of NBOcharge indicates that the charge transfer from centralcation to water molecules is nearly affected by the firstand second hydration shells for Ca2þ, whereas only bythe first hydration shell for Mg2þ. Meanwhile, theresults of mean metal–oxygen bond length and NBO
charge population show that the constraint of Mg2þ on
the first hydration shell is very strong, while that on thesecond hydration shell is less definitive, as shown in
Figures 4 and 5. Since the constraint of Mg2þ on the
first hydration shell is very strong but nearly limited to
the first hydration shell, and thus this characteristicsmay lead to its limited ability to form contact ion pair
with anions, such as chloride, as also proposed by
some recent works [50,53]. Comparison with that ofMg2þ, the first hydration shell of Ca2þ is still more
flexible, but the constraint on the second hydration
shell is still obvious for the hydration of Ca2þ, asshown in Figures 4 and 5.
The sequential water binding energies (DEseq) were
calculated according to Equation (1) in Section 2. As
shown in Figure 6, the sequential water bindingenergies of M2þ(H2O)n (M¼Mg or Ca, n¼ 6–27)
clusters vary slowly in the case of occupying the second
hydration shell, and followed by a smooth trend in the
case of water molecules locating in the third hydrationshell, which have also been partially noted in some
previous work [6,25]. The sequential water binding
energy of the 27th water molecule is about 10.6 kcal/mol for the [Mg(H2O)27]
2þ cluster, which is very close
to the dissociation energy of one water molecule from
bulk liquid water is �10.5 kcal/mol estimated from the
evaporate energy of liquid water [45,46]. Similarly,B3LYP/aVDZ calculation also indicates that the
sequential water binding energy of the 27th water
molecule is about 10.5 kcal/mol for six-, seven or eight-
W24-6LB W24-7L W24-8L W27-6LA
W27-6LB W27-6LC W27-7L W27-8L
Figure 3. Continued.
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Molecular Physics 563
be 8 for clusters with 12 or more water molecules [11].However, our B3LYP/aVDZ calculations show that theenergy differences among six-, seven-, and eight-coordinated conformers of Ca2þ hydrates are verysmall for [Ca(H2O)n]
2þ (n� 20) clusters. Therefore, six-,seven-, and eight-coordinated structures for the hydra-tion of Ca2þmay be all possible when solvation effect ofouter hydration shells are considered using PCM.
3.2. Hydration shells for Mg2þ and Ca2þ hydrates
The mean Ca–O bond distance between Ca and oxygenatoms of water molecules in the first hydration shellincreases steadily from n¼ 1 to 8, and is almostunchanged when n� 18, as shown in Figure 4.It indicates that the mean Ca–O bond distance isalmost unchanged when the first and second hydrationshells are saturated, while the mean Mg–O bonddistance is almost unchanged when the first hydrationshell is saturated. NBO charge population analyses of[Ca(H2O)n]
2þ clusters show that the charge on six-,seven-, or eight-coordinated Ca2þ is essentiallyunchanged when n� 18, which is slightly differentfrom the situation of Mg2þ hydration, as shown inTables 2 and 4, and Figure 5. The comparison of NBOcharge indicates that the charge transfer from centralcation to water molecules is nearly affected by the firstand second hydration shells for Ca2þ, whereas only bythe first hydration shell for Mg2þ. Meanwhile, theresults of mean metal–oxygen bond length and NBO
charge population show that the constraint of Mg2þ on
the first hydration shell is very strong, while that on thesecond hydration shell is less definitive, as shown in
Figures 4 and 5. Since the constraint of Mg2þ on the
first hydration shell is very strong but nearly limited to
the first hydration shell, and thus this characteristicsmay lead to its limited ability to form contact ion pair
with anions, such as chloride, as also proposed by
some recent works [50,53]. Comparison with that ofMg2þ, the first hydration shell of Ca2þ is still more
flexible, but the constraint on the second hydration
shell is still obvious for the hydration of Ca2þ, asshown in Figures 4 and 5.
The sequential water binding energies (DEseq) were
calculated according to Equation (1) in Section 2. As
shown in Figure 6, the sequential water bindingenergies of M2þ(H2O)n (M¼Mg or Ca, n¼ 6–27)
clusters vary slowly in the case of occupying the second
hydration shell, and followed by a smooth trend in the
case of water molecules locating in the third hydrationshell, which have also been partially noted in some
previous work [6,25]. The sequential water binding
energy of the 27th water molecule is about 10.6 kcal/mol for the [Mg(H2O)27]
2þ cluster, which is very close
to the dissociation energy of one water molecule from
bulk liquid water is �10.5 kcal/mol estimated from the
evaporate energy of liquid water [45,46]. Similarly,B3LYP/aVDZ calculation also indicates that the
sequential water binding energy of the 27th water
molecule is about 10.5 kcal/mol for six-, seven or eight-
W24-6LB W24-7L W24-8L W27-6LA
W27-6LB W27-6LC W27-7L W27-8L
Figure 3. Continued.
coordinated conformers of the [Ca(H2O)27]2þ cluster.
The results of sequential binding energies indicate thatthe constraint of Mg2þ or Ca2þ on the third hydrationshell is quite weak. In addition, changes of rM-O
(M¼Mg, Ca) and charges on Mg or Ca atom for[M(H2O)n]
2þ clusters as n� 18 are negligible. Resultsof sequential water binding energy, NBO charge andM–O bond length show that 27 water molecules areenough to form an approximatively saturated ionhydration shells for Mg2þ hydrates in the diluteaqueous solution. The situation is similar for six-,seven-, and eight-coordinated conformers of the[Ca(H2O)27]
2þ cluster, which indicates that 27 watermolecules are enough to form an approximativelysaturated ion hydration shells for Ca2þ hydrates in thedilute aqueous solution. For six-coordinated[Mg(H2O)27]
2þ or [Ca(H2O)27]2þ clusters, the HB
network around the second hydration shell is stillunsaturated or unsymmetrical, while for six-
coordinated [Mg(H2O)36]2þ or [Ca(H2O)36]
2þ clusters,the water molecules in the second hydration shellcannot form HB any more. Therefore, based on theapproximatively saturated ion hydration shell of Mg2þ
or Ca2þ ions, [Mg(H2O)n]2þ or [Ca(H2O)n]
2þ (n� 36)cluster with nearly spherical symmetry combined withPCM calculation may be appropriate to model thehydration of Mg2þ or Ca2þ in the infinitely diluteaqueous solution.
Generally, the CN value of Mg2þ is 6, while forCa2þ, having larger ionic surface, the CN value may belarger than that of Mg2þ. Our calculations also supportsuch trend. In the gas phase, Ca2þ(H2O)n (n¼ 6–20)clusters may still prefer low coordination, that is six-coordination, while for Ca2þ(H2O)n (n� 20) clusters,their seven-, and eight-coordinated structures alsobecome stable. To examine how the transformationoccurs among different coordinated structures for M2þ
(M¼Mg, Ca), transition state (TS) has also beenlocated using transit-guided quasi-Newton method[54]. The calculated energy barriers obtained atB3LYP/aVDZ level indicate that the transformationamong the isomers of Mg2þ hydrates with differentCNs are relatively difficult and slow, as shown inFigure 7. For [Ca(H2O)n]
2þ clusters, low energybarriers (1.1–2.1 kcal/mol) were obtained for the tran-sition from high-coordination to low-coordinationstructures whereas larger energy barriers were obtainedfor the transition from low-coordination to high-coordination structures, as shown in Figure 7.Therefore, the transition from high-coordination tolow-coordination structures for [Ca(H2O)n]
2þ clustersis easier as temperature increases. Meanwhile thetransformation among isomers with six- and five
2 4 6 8 10 12 14 16 18 20 22 24 26 28
-40
-30
-20
-10
ΔEse
q (k
cal/m
ol)
n /H2O
Mg-6L
Ca-6L
Ca-7L
Ca-8L
Figure 6. Sequential water binding energies (DEseq) for stable[M(H2O)n]
2þ clusters (M¼Mg, Ca). Sequential water bind-ing energies were obtained according to Equation (1). L is theabbreviation of direct coordinated ligand, and CN value ofMg2þ or Ca2þ is added before L.
0 2 4 6 8 10 12 14 16 18 20 22 24 26 281.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
q M/e
-
n/H2O
Mg-6L Ca-6L Ca-7L Ca-8L
Figure 5. NBO charge of M2þ (qM) for [M(H2O)n]2þ
(M¼Mg, Ca) clusters. L is the abbreviation of directcoordinated ligand, and CN value of Mg2þ or Ca2þ isadded before L.
0 2 4 6 8 10 12 14 16 18 20 22 24 26 281.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
n/H2O
r M-O
/Å Mg-6L
Ca-6L
Ca-7L
Ca-8L
Figure 4. Mean metal-oxygen bond lengths (rM�O) for[M(H2O)n]
2þ (M¼Mg, Ca) clusters. L is the abbreviationof direct coordinated ligand, and CN value of Mg2þ or Ca2þ
is added before L.
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564 G. Bai et al.
coordination is found to be more difficult due to highenergy barriers for [Mg(H2O)n]
2þ clusters, as shown inFigure 7.
3.3. Ab initio molecular dynamic simulations
From the above quantum electronic structure calcula-tion for hydrated magnesium and calcium clusters, itcan be seen that the CN of magnesium ion is around 6,while for calcium ion, the CN value may be 6, 7 or 8.To collaborate with this finding, AIMD simulationshave been performed for [Mg(H2O)6,8]
2þ and[Ca(H2O)8,10]
2þ clusters to get a qualitative ideaabout different coordination of calcium and magne-sium ions. The partial radial distribution function,g��(r) and the average coordination number, n��, wereemployed to investigate the variation of the firsthydration shell for [Mg(H2O)6,8]
2þ and[Ca(H2O)8,10]
2þ clusters. The Ca�O and Mg�ORDF and the running CNs for [Mg(H2O)8]
2þ and[Ca(H2O)10]
2þ clusters at different temperatures(100K, 200K, 300K) have been shown in Figure 8and Figure 9.
The first peak in the RDF is very sharp, and thepeak height is reduced as temperature increases,indicating a higher disorder or lower CNs.Integration over the first maximum of the Ca�O andMg�O RDF correspond to the CNs for Mg2þ andCa2þ. With temperature increasing, the CN of Ca2þ
reduces from 8 to 6 or 7 for [Ca(H2O)7(H2O)1,3]2þ and
[Ca(H2O)8(H2O)0,2]2þ clusters, respectively. For Ca2þ,
the CN reducing from 8 to 6 or 7 is easy at 200 and300K, which is consistent with low energy barriersobtained for those transformations from high-coordi-nation structures to low-coordination structures(as shown in Figure 7), while the CN transformationof Ca2þ from 6 or 7 to 8 is much more difficult and
slow in AIMD simulations. However, at all simulationtemperatures the [Mg(H2O)6(H2O)2]
2þ cluster theoctahedral surroundings of Mg2þ are predominantduring 3 ps simulations, even though five-coordinatedstructures occasionally present in the simulation at300K. Those transformations between those isomersamong different CNs are more difficult and slow forMg2þ hydrates, due to higher energy barriers as shownin Figure 7. Inaddition, the first RDF peak of Mg2þ issharper than that of Ca2þ, which indicates that Mg2þ
imposes stronger orientational constraints to the firsthydration shell, while the first hydration of Ca2þ seemsto be more flexible, as also suggested by a recentlywork based Monte Carlo simulations and neutrondiffraction results [55]. The binding energy of Mg2þ isalso obviously larger than that of Ca2þ with thehydration proceeds, as shown in Tables 1–4. Thehydration structures of Ca2þ and Mg2þ are by nomeans static, i.e. the CNs are not constant during asimulation. This may be already inferred from therunning integration numbers of Figure 8 and Figure 9.The AIMD results about CNs of Mg2þ and Ca2þ
hydrates show that the CN of Mg2þ hydrates stillprefers six-coordination during 3 ps and 6 ps simula-tions at the temperature of 373K, as shown inFigure 10. Meanwhile, the CN of [Ca(H2O)10]
2þ
hydrate changes from eight-coordination to six-coor-dination during 3 ps and 6 ps ADMP simulation at thetemperature 373K (Figure 10). It indicates that thefirst hydration shell and CN of Ca2þ are easier tofluctuate as temperature changes, compared with thoseof Mg2þ.
4. Conclusion
An exhaustive and systematic theoretical investigationabout hydrated characteristics of Mg2þ and Ca2þ were
Figure 7. The structural transitions between different coordinated structures of [Mg(H2O)6]2þ clusters and those of [Ca(H2O)8]
2þ
clusters calculated at B3LYP/aVDZ level. Bond distance and energies are given in pm and kcal/mol, respectively. W and L arethe abbreviations of water molecule and direct coordinated ligand, and CN value of Mg2þ or Ca2þ is added before L.
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Molecular Physics 565
coordination is found to be more difficult due to highenergy barriers for [Mg(H2O)n]
2þ clusters, as shown inFigure 7.
3.3. Ab initio molecular dynamic simulations
From the above quantum electronic structure calcula-tion for hydrated magnesium and calcium clusters, itcan be seen that the CN of magnesium ion is around 6,while for calcium ion, the CN value may be 6, 7 or 8.To collaborate with this finding, AIMD simulationshave been performed for [Mg(H2O)6,8]
2þ and[Ca(H2O)8,10]
2þ clusters to get a qualitative ideaabout different coordination of calcium and magne-sium ions. The partial radial distribution function,g��(r) and the average coordination number, n��, wereemployed to investigate the variation of the firsthydration shell for [Mg(H2O)6,8]
2þ and[Ca(H2O)8,10]
2þ clusters. The Ca�O and Mg�ORDF and the running CNs for [Mg(H2O)8]
2þ and[Ca(H2O)10]
2þ clusters at different temperatures(100K, 200K, 300K) have been shown in Figure 8and Figure 9.
The first peak in the RDF is very sharp, and thepeak height is reduced as temperature increases,indicating a higher disorder or lower CNs.Integration over the first maximum of the Ca�O andMg�O RDF correspond to the CNs for Mg2þ andCa2þ. With temperature increasing, the CN of Ca2þ
reduces from 8 to 6 or 7 for [Ca(H2O)7(H2O)1,3]2þ and
[Ca(H2O)8(H2O)0,2]2þ clusters, respectively. For Ca2þ,
the CN reducing from 8 to 6 or 7 is easy at 200 and300K, which is consistent with low energy barriersobtained for those transformations from high-coordi-nation structures to low-coordination structures(as shown in Figure 7), while the CN transformationof Ca2þ from 6 or 7 to 8 is much more difficult and
slow in AIMD simulations. However, at all simulationtemperatures the [Mg(H2O)6(H2O)2]
2þ cluster theoctahedral surroundings of Mg2þ are predominantduring 3 ps simulations, even though five-coordinatedstructures occasionally present in the simulation at300K. Those transformations between those isomersamong different CNs are more difficult and slow forMg2þ hydrates, due to higher energy barriers as shownin Figure 7. Inaddition, the first RDF peak of Mg2þ issharper than that of Ca2þ, which indicates that Mg2þ
imposes stronger orientational constraints to the firsthydration shell, while the first hydration of Ca2þ seemsto be more flexible, as also suggested by a recentlywork based Monte Carlo simulations and neutrondiffraction results [55]. The binding energy of Mg2þ isalso obviously larger than that of Ca2þ with thehydration proceeds, as shown in Tables 1–4. Thehydration structures of Ca2þ and Mg2þ are by nomeans static, i.e. the CNs are not constant during asimulation. This may be already inferred from therunning integration numbers of Figure 8 and Figure 9.The AIMD results about CNs of Mg2þ and Ca2þ
hydrates show that the CN of Mg2þ hydrates stillprefers six-coordination during 3 ps and 6 ps simula-tions at the temperature of 373K, as shown inFigure 10. Meanwhile, the CN of [Ca(H2O)10]
2þ
hydrate changes from eight-coordination to six-coor-dination during 3 ps and 6 ps ADMP simulation at thetemperature 373K (Figure 10). It indicates that thefirst hydration shell and CN of Ca2þ are easier tofluctuate as temperature changes, compared with thoseof Mg2þ.
4. Conclusion
An exhaustive and systematic theoretical investigationabout hydrated characteristics of Mg2þ and Ca2þ were
Figure 7. The structural transitions between different coordinated structures of [Mg(H2O)6]2þ clusters and those of [Ca(H2O)8]
2þ
clusters calculated at B3LYP/aVDZ level. Bond distance and energies are given in pm and kcal/mol, respectively. W and L arethe abbreviations of water molecule and direct coordinated ligand, and CN value of Mg2þ or Ca2þ is added before L.
carried out using B3LYP/aVDZ and MP2/aVDZ
methods, and the transformation among their isomers
with different coordination were also investigated
using transition state method and ADMP simulations
in this work. Among the conclusions that can be
drawn, the following arise:
(1) Six-coordinated structures are slightly more
stable than its five-coordinated structures for
the hydrates of Mg2þ in the gas phase, even
when more than two hydration shells are
considered. Six-coordinated structures for
[Ca(H2O)n]2þ (n¼ 6–27) clusters is more stable
in the gas phase, whereas their seven-, and
eight-coordinated structures also become stable
for n� 18 in the aqueous solution as more
hydration shells considered as polarized con-
tinuum medium using PCM.(2) The charge transfer from central cation to
water molecules is affected by the first and
second hydration shells for Ca2þ, whereas only
by the first hydration shell for Mg2þ. The mean
Ca–O bond distance is almost unchanged when
the first and second hydration shells are
saturated, while the mean Mg–O bond distanceis almost unchanged when only the firsthydration shell is saturated. Inaddition, theconstraint of Mg2þ on the first hydration shellis obviously stronger than that of Ca2þ, whilethe constraint on the inner hydration shellsfades slightly faster for Mg2þ than Ca2þ. Theresults of sequential water binding energies alsoindicate that the constraint of Mg2þ or Ca2þ onthe third hydration shell is quite weak, and willbe negligible when the third hydration shell ispartially saturated.
(3) The first hydration shell of Mg2þ is generallystable and prefers six-coordinated structures attemperature range of 100–373K. That is, theCN value of Mg2þ remains six for the hydra-tion of Mg2þ in dilute aqueous solution.However, the first hydration of Ca2þ is foundto be more flexible, especially at high temper-ature. Low energy barriers (1.1–2.1 kcal/mol) ofthe transition from high-coordination to low-coordination structures for [Ca(H2O)n]
2þ clus-ters indicate that those transitions are easier astemperature increases. That is, the CN value of
0
1
2
r(Å) r(Å)
100k
0
2
4
6
80
1
2
g Mg-
O(r
)
n Mg-
O(r
)
0
2
4
6
8200k0
1
2300k
gMg-O(r)
n(r)
0
2
4
6
8
0 1 2 3 4 5 6 0 1 2 3 4 5 60
1
2100k
0
2
4
6
80
1
2200k
g Mg-
O(r
)
n Mg-
O(r
)
0
2
4
6
80
1
2 gMg-O(r)
n(r)
300k
0
2
4
6
8
W8-6L W8-5L
Figure 8. Mg�O radial distribution functions and running integration numbers at the various temperatures obtained fromthe ADMP simulation: the solid line represents the radial distribution function gMg�O(r) and corresponds to the axis on the left;the dashed line is the oxygen coordination number, n(r).
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566 G. Bai et al.
0
1
2
0
2
4
6
8
10100k
r(Å) r(Å) r(Å)
0
1
2
0
2
4
6
8
10200k
g Ca-
O (r
)
n Ca-
O(r
)
0
1
2
0
2
4
6
8
10gCa-O(r)
n(r)
300k
0
1
2
0
2
4
6
8
10100k0
1
2
n Ca-
O(r
)
n Ca-
O(r
)
g Ca-
O(r
)
g Ca-
O(r
)0
2
4
6
8
10200k0
1
2300k
gCa-O(r)n(r)
0
2
4
6
8
10
0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 60
1
2100k
0
2
4
6
8
100
1
2
0
2
4
6
8
10200k0
1
2
0
2
4
6
8
10300k
gCa-O(r)n(r)
W10-8L W10-7L W10-6L
Figure 9. Ca�O radial distribution functions and running integration numbers at the various temperatures obtained from theADMP simulation: the solid line represents the radial distribution function gCa�O(r) and corresponds to the axis on the left; thedashed line is the oxygen coordination number, n(r).
0
1
2
n Mg-
O (r
)
n Mg-
O (r
)
gMg-O(r)
n(r)
0
2
4
6
8
r(Å) r(Å)
r(Å)
g Mg-
O (r
)
g Mg-
O (r
)
373k
0
1
2373k
0
2
4
6
8
gMg-O (r)
n(r)
(a) (b)
0
1
2
r(Å)
gCa-O (r)
n(r)
373k
0
2
4
6
8
10
0 1 2 3 4 5 6 0 1 2 3 4 5 6
0 1 2 3 4 5 6 0 1 2 3 4 5 60
1
2
0
2
4
6
8
10
gCa-O(r)
n(r)g Ca-
O(r
)
g Ca-
O(r
)
n Ca-
O (r
)
n Ca-
O (r
)
373k(c) (d)
3ps
3ps
6ps
6ps
Figure 10. ADMP simulations for [Mg(H2O)8]2þ cluster (a, b) and [Ca(H2O)10]
2þ cluster (c, d) at the temperature of 373Kobtained from the ADMP simulations (3 ps and 6 ps): the solid line represents the radial distribution function gM�O(r) andcorresponds to the axis on the left; the dashed line is the oxygen coordination number, n(r).
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Molecular Physics 567
0
1
2
0
2
4
6
8
10100k
r(Å) r(Å) r(Å)
0
1
2
0
2
4
6
8
10200k
g Ca-
O (r
)
n Ca-
O(r
)
0
1
2
0
2
4
6
8
10gCa-O(r)
n(r)
300k
0
1
2
0
2
4
6
8
10100k0
1
2
n Ca-
O(r
)
n Ca-
O(r
)
g Ca-
O(r
)
g Ca-
O(r
)
0
2
4
6
8
10200k0
1
2300k
gCa-O(r)n(r)
0
2
4
6
8
10
0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 60
1
2100k
0
2
4
6
8
100
1
2
0
2
4
6
8
10200k0
1
2
0
2
4
6
8
10300k
gCa-O(r)n(r)
W10-8L W10-7L W10-6L
Figure 9. Ca�O radial distribution functions and running integration numbers at the various temperatures obtained from theADMP simulation: the solid line represents the radial distribution function gCa�O(r) and corresponds to the axis on the left; thedashed line is the oxygen coordination number, n(r).
0
1
2
n Mg-
O (r
)
n Mg-
O (r
)
gMg-O(r)
n(r)
0
2
4
6
8
r(Å) r(Å)
r(Å)
g Mg-
O (r
)
g Mg-
O (r
)
373k
0
1
2373k
0
2
4
6
8
gMg-O (r)
n(r)
(a) (b)
0
1
2
r(Å)
gCa-O (r)
n(r)
373k
0
2
4
6
8
10
0 1 2 3 4 5 6 0 1 2 3 4 5 6
0 1 2 3 4 5 6 0 1 2 3 4 5 60
1
2
0
2
4
6
8
10
gCa-O(r)
n(r)g Ca-
O(r
)
g Ca-
O(r
)
n Ca-
O (r
)
n Ca-
O (r
)
373k(c) (d)
3ps
3ps
6ps
6ps
Figure 10. ADMP simulations for [Mg(H2O)8]2þ cluster (a, b) and [Ca(H2O)10]
2þ cluster (c, d) at the temperature of 373Kobtained from the ADMP simulations (3 ps and 6 ps): the solid line represents the radial distribution function gM�O(r) andcorresponds to the axis on the left; the dashed line is the oxygen coordination number, n(r).
Ca2þ could not be a regular number, six oreight, while its averaged CN value may vary inthe range 6–8 with water molecule activity andtemperature fluctuations. And thus an expla-nation about the changing CN value of Ca2þ inthe aqueous solution as reported before [18,19]could be that the averaged CN value of Ca2þ
may prefer low coordination, or six in concen-trated solution as water molecule activity isrelatively low, or at high temperature, whilehigh coordination, seven or eight in diluteaqueous solution and at low temperature.
(4) Based on hydration characteristics and sequen-tial water binding energy, [Mg(H2O)n]
2þ or[Ca(H2O)n]
2þ (n� 36) clusters combined withPCM calculation may be appropriate to modelthe hydration of Mg2þ or Ca2þ in the diluteaqueous solution.
Supplementary material
Supplementary data associated with this article can befound in the online version. Supplementary materialincludes supporting information for Mg2þ and Ca2þ
hydrated structures and thermodynamics results,scheme for saturated ion hydration shell, AIMDsimulations of Mg2þ and Ca2þ hydrates, and theeffect of OH IR spectra of various hydration shells forMg2þ and Ca2þ.
Acknowledgements
This work was supported financially by the National NaturalScience Foundation of China under Contract Number21073056, and partially supported by enhancement projectfor young faculty of Hunan University.
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