DOI 102477jccj2013-0011 105

copy2013 Society of Computer Chemistry Japan

General Paper

A Quantum Chemical Study on Hydration of Ra (II) Comparison with the Other Hydrated Divalent Alkaline

Earth Metal IonsAya MATSUDA and Hirotoshi MORI

Department of Chemistry and Biochemistry Graduate School of Humanities and Sciences Ochanomizu University 2-1-1 Ohtsuka Bunkyo-ku Tokyo 112-8610 Japan

e-mail morihirotoshiochaacjp

(Received July 31 2013 Accepted for publication October 12 2013 Advance publication February 8 2014)

The thermodynamic properties and electronic structure of hydrated Ra2+ have been investigated using ab initio quantum chemical calculations that apply the relativistic model core potential method and compared with those of the other hydrated divalent alkaline earth metal ions (Mg2+ Ca2+ Sr2+ and Ba2+) The solvation free energies calculated for [Ra (H2O)n]2+ (n = 1ndash9) in a continuum dielectric media (semi-continuum model) showed that the hydration number of Ra2+ is in the range of 7ndash9 Natural population analysis (NPA) natural bond orbital (NBO) analysis and localized molecular orbital energy decomposition analysis (LMO-EDA) showed that the dominant interaction between hydrated Ra2+ ions and solvent water molecules is electrostatic interaction to form coordination bonds which have a strong ionic bond character On the other hand not only electrostatic interaction but also covalent interaction accompanying charge-transfer from solvent water molecules to the central ion are important in the interaction between hydrated Mg2+ or Ca2+ (lighter divalent alkaline earth metal ions) and solvent water molecules

Keywords Radium divalent ion Hydration Chemical bond character Relativistic model core potential MCP

1 Introduction

Marie Curie and Pierre Curie discovered the radium element

(Ra) in 1898 [1] Although Ra is the heaviest alkaline earth

metal in the periodic table its chemical and physical properties

are still barely known mainly due to the following two reasons

First Ra is a very rare element the abundance of which in the

earths crust has been estimated to be in the order of 10minus7 ppm

Second Ra is as a highly toxic radioactive element the radio-

activity of which is over one million times higher than that of

the same mass of uranium All isotopes of Ra are highly radio-

active with the most stable isotope being Ra-226 which has a

half-life of 1601 years and decays into the stable radon element

The hydration chemistry of Ra has not been studied due to

the danger associated with the experimental handling as well

as the chemical instabilities of Ra isotopes Although it is com-

monly known that Ra salts dissolve well in water similar to the

other divalent alkaline earth metal ions (Mg2+ Ca2+ Sr2+ and

Ba2+) there has been no experimental report on the hydration

structure of Ra2+

The purpose of the present study is to investigate the hydra-

tion structure of Ra2+ and compare it with those of the other

hydrated divalent alkaline earth metal ions from a theoretical

point of view Hydration structures solvation free energies and

the chemical bonding character in the first hydration shell of

divalent alkaline earth metal ions in water solvent were investi-

gated using ab initio quantum chemical calculations

The absence of previous studies on Ra2+ hydration either ex-

perimental or theoretical compelled us to begin this study from

the most basic steps Although Glendening Feller [2] and Han

[3] have studied the structure of aqua clusters of divalent alka-

line earth metal ions including Ra2+ their studies were those

J Comput Chem Jpn Vol 13 No 1 pp 105ndash113 (2014)

J Comput Chem Jpn Vol 13 No 1 (2014)106

in gas-phase conditions The information that we could obtain

in relation to the hydration of Ra2+ was that for the hydrates

of the other divalent alkaline earth metal ions The hydration

numbers of the divalent alkaline earth metal ions have been ex-

perimentally reported to be 60 [4ndash6] 60ndash80 [7ndash9] 73ndash150

[10ndash13] and 78ndash95 [1415] for Mg2+ Ca2+ Sr2+ and Ba2+

respectively These results have also been well reproduced by

theoretical methods [121416ndash24] Taking into account the hy-

dration numbers for the other alkaline earth metal ions and the

atomic radii of Ra we could expect the hydration number of

Ra2+ to be similar to that of Ba2+ As the use of computational

chemistry allows us to avoid the risks associated with the han-

dling of radioactive Ra2+ it was expected to be the best method

to increase our understanding of the basic physical chemistry

of Ra2+ In this study we studied the first solvation shell of hy-

drated Ra2+ using the relativistic model core potential method

as previously reported [25] In the real hydration of Ra2+ the

hydrolysis reaction accompanying deprotonation of the sol-

vent water is expected to form hydroxide species In this study

however we only focused on the structure of the first solvation

shell of hydrated Ra2+ the first step in understanding Ra2+ ion

hydration

2 Computational Details

First geometry optimizations at the ab initio HF MP2 and

density functional B3LYP [2627] and LC-BLYP [28] levels of

theory were performed for [AE (H2O)n]2+ (AE = Mg Ca Sr

Ba and Ra n = 1ndash9) which are model compounds of hydrated

divalent alkaline earth metal ions In this study we focused on

interactions between the central alkaline earth metal ions and

solvation water molecules in the first hydration shells The ex-

plicit hydration beyond the first shell is out of the scope of this

study Thus only water molecules in the first hydration shell

were explicitly treated in the model systems and the solvent

effects from the outer hydration shells were taken into ac-

count using the conductor-like polarizable continuum (C-PCM

[29ndash32]) method (semi-continuum model [3334]) The static

dielectric permittivity of liquid water (ε = 7839 at 298 K) was

used to define the dielectric medium in C-PCM calculations

The cavity enclosing the hydrates was built using the following

radii 120 152 160 197 215 217 and 223 Aring for H O

Mg Ca Sr Ba and Ra respectively [35] These values were

multiplied with a standard factor of 12 in order to take into ac-

count the fact that the atomic bond or lone pair centers of the

solvent molecules are normally located slightly farther from the

solute atoms than their van der Waals radii [36] We used the

scaled atomic radii in the geometry optimizations with C-PCM

method

Even our scope was limited within first hydration shell to

take into account structural entropy in a proper manner is im-

portant to model hydration shell Prior to performing geometry

optimization at the quantum chemical level we performed clas-

sical molecular dynamics simulations of AE2+ (AE = Mg Ca

Sr Ba and Ra) in small water droplet using MMFF94X force

field [37] which is implemented in MOE program package [38]

(NVT ensemble T = 300 K) Then we performed several geom-

etry optimizations starting from relatively stable arrangements

observed in the molecular dynamics simulations for [AE (H2O)

n]2+ (AE = Mg Ca Sr Ba and Ra n = 1ndash9)

Next we checked the stabilities of the optimized structures

by performing subsequent vibrational frequency analyses The

results of the frequency analyses were also used to calculate

thermochemical corrections including solvation free energies

Solvation free energies were calculated within the semi-contin-

uum model using the following equation at 29715 K [39ndash42]

ΔGsolv = ΔGcluster + ΔGcont + ΔGcav + ΔGdisp-rep + nΔGvap

(1)

where ΔGcluster is the formation free energy of the cluster ΔGcont

is the solvation energy corresponding to the long-range interac-

tion of the hydrate embedded in a cavity inside a continuum

ΔGcav is the free energy to create the cavity ΔGdisp-rep is the

hydrate-continuum dispersion contribution and nΔGvap is the

free energy needed to bring n water molecules from the liquid

pure solvent to the gas-phase in order to form the hydrate In

this study we used an experimental value of 205 kcal molminus1

for ΔGvap [43]

Finally at the stable minima of [AE (H2O)n]2+ (AE = Mg

Ca Sr Ba and Ra n = 1ndash9) natural population analysis (NPA)

[44] natural bond orbital (NBO) analysis [4546] and local-

ized molecular orbital energy decomposition analysis (LMO-

EDA) [47] were performed to investigate the chemical bonding

character between the central alkaline metals and solvent water

molecules

DOI 102477jccj2013-0011 107

The basis sets used throughout this study were 6-31G (dp)

for OH [4849] and MCPdzp for the central alkaline earth met-

als [25] where MCPs are valence only relativistic model core

potential basis sets that are used to reduce computational costs

arising from chemically inert core electrons and to take into ac-

count scalar relativistic effects The MCP method is one of the

unique pseudo-potential methods which properly reproduces

nodal structures of valence orbitals that are important for ac-

curate treatment of various molecular properties within pseudo-

potential approximations [2550ndash55]

In the MCP method the electronic Hamiltonian H NvMCP ( )1 2 of the Nv valence electrons (in atomic units)

is chosen as follows

(2)

with the one-electron Hamiltonian term defined as

(3)

(4)

where Z is the atomic number of the atom and Nc is the number

of core electrons replaced by MCPs Aj αj Aj αj and Bc (c

= core orbitals) are the MCP parameters and ψc denotes the

core orbital functions while Bc is defined as

(5)

where εc is the orbital energy of the core orbital and F is taken

to be 2 The MCP VMCP in Eq (4) given as a simple spher-

ically-symmetric local potential approximates the local core

Coulomb potential and the non-local core exchange potential as

well as the nuclear attraction potential term The MCP param-

eters in Eq (4) were determined by fitting atomic MCP calcula-

tion results to the corresponding relativistic all-electron calcu-

lations (see Refs [2550ndash55]) The projection operator in Eq

(3) prevents the valence orbitals from collapsing into the core

region and may also be regarded as an energy shift operator By

the use of this operator the energy levels of core electrons are

shifted far above zero energy thus allowing for finding in each

symmetry the lowest valence orbitals with appropriate nodal

structure

In the MCPdzp for alkaline earth metals (ns)2(np)6(n = 2ndash6

for Mg2+ Ca2+ Sr2+ Ba2+ and Ra2+) valence electrons were ex-

plicitly treated The contractions of valence basis sets with a set

of polarization functions were (2111131221) (3111141232)

(4111151232) (5111161343) and (6111171353) for Mg

Ca Sr Ba and Ra respectively

All the electronic structure calculations were performed us-

ing the GAMESS [5657] quantum chemistry program pack-

age The NBO 50 program package [58] was used for the

NBONPA analyses

3 Results and Discussion

31 Optimized structures of [AE (HO)n]2+ (AE = Mg Ca Sr Ba and Ra n = 1minus9)

The optimized structures the AE-O bond lengths and the aver-

aged AE-H2O binding energies for [AE (H2O)n]2+ (AE = Mg

Ca Sr Ba and Ra n = 1ndash9) are given in Figure 1 and Table 1 As

shown in Figure 1 except for AE = Mg we could observe that

all solvent water molecules coordinate to the central divalent al-

kaline earth ion directly to form the first hydration shell in [AE

(H2O)n]2+ (n = 1ndash9) For [Mg (H2O)n]2+ (n = 1ndash9) we obtained

a hepta-coordinated hydration structure at the maximum due

to the small atomic radii (160 Aring [35]) of Mg2+ compared with

those of the other divalent alkaline earth metal ions For [AE

(H2O)n]2+ (AE = Ca Sr Ba and Ra n = 1ndash9) the structures that

have water molecules in the second solvation shell gave much

higher energies than those in Figure 1 The optimized structures

of [AE (H2O)n]2+ (AE = Mg Ca Sr Ba and Ra n = 1ndash9) and

averaged AE-H2O binding energies were predicted to be very

similar among the HF MP2 and B3LYP levels of theory Even

LC-BLYP level of theory predicted larger binding energies than

these levels the tendency to cluster size (n) is quite similar

The differences of the AE-O bond length among the calculation

methods were within 01 Aring Table 1 shows the elongation of

the AE-O bond length (with the exception of those between n

= 1 and 2 for AE = Ra) and a corresponding monotonic decre-

ment of the averaged AE-H2O binding energy with increased

number of solvent water molecules in each calculation level

A plausible reason for the AE-O bond elongation is the mutual

repulsion of donor orbitals on the water molecules

J Comput Chem Jpn Vol 13 No 1 (2014)108

32 Solvation free energy and hydration numbers of AE2+ (AE = Mg Ca Sr Ba and Ra)

To investigate the hydration structures of alkaline earth metal

ions in finite temperature conditions it is necessary to evalu-

ate the solvation free energies of the ions To do this we have

to take into account two types of solvent effects specific and

long-range solvent effects The former is a solvent effect from

the water molecules that directly coordinate to the central AE2+

to form the first hydration shell and the latter is a solvent ef-

fect from the water molecules in the outer hydration shells We

could not use [AE (H2O)n]2+ (n = 1ndash5) for evaluating solvation

free energies of AE2+ since only a part of the first solvation

shell was described explicitly and the remaining part was treat-

ed via a C-PCM implicit solvation model in the smaller mod-

els To obtain more realistic solvation free energies of AE2+ we

chose a set of larger models [AE (H2O)n]2+ (n = 6ndash9) in which

the water molecules completely surround the central AE2+

Theoretically calculated hydration energies of AE2+ (AE =

Mg Ca Sr Ba and Ra) obtained by the semi-continuum clus-

ter models are given in Table 2 In Table 2 only the LC-BLYP

level results were given as HF MP2 and B3LYP gave similar

structures and binding tendencies as mentioned in the previous

section (See Tables S1-3 in supporting information) Table 2

shows that all divalent alkaline earth metal ions have negative

ΔGsolv values for the [AE (H2O)n]2+ (n = 6ndash9) semi-continuum

model This means that all the [AE (H2O)n]2+ (AE = Mg Ca

Sr Ba and Ra n = 6ndash9) species are thermodynamically stable

Table 2 also shows that the dominant components in ΔGsolv

are ΔGcluster and ΔGcont The remaining terms in Eq (1) ΔGcav

ΔGdisp-rep and nΔGvap make only minor contributions to the

solvation free energies The order of ΔGsolv values for non-

Ra2+ divalent alkaline earth metal ions were experimentally

observed to be Mg2+ gt Ca2+ gt Sr2+ gt Ba2+ [36] Although we

obtained ca 30ndash40 kcal molminus1 errors compared with the experi-

mental ones due to the use of the semi-continuum models we

could theoretically reproduce the experimental order for non-

Ra2+ divalent alkaline earth metal ions in a qualitative manner

(see Table 2) As we could obtain at least qualitative accuracy

with the semi-continuum models we are able to safely discuss

Ra2+ hydration for which there has been no experimental or

theoretical study to date As shown in Table 2 we obtained the

smallest ΔGsolv value for Ra2+ among all divalent alkaline earth

metal ions investigated in this study Thus the theoretical order

of ΔGsolv for divalent alkaline earth metal ions was predicted to

be Mg2+ gt Ca2+ gt Sr2+ gt Ba2+ gt Ra2+ As we could observe no

significant difference in ΔGsolv values among [Ra (H2O)n]2+ (n

= 6ndash9) we could not determine the most likely hydration num-

ber for Ra2+ To determine the hydration number it is necessary

to take into account the dynamical motions of the solvents us-

Figure 1 Optimized structures of [Ra (H2O)n]2+ (n = 1-9) at the HF level of theory (MP2 B3LYP and LC-BLYP levels of theory gave very similar structures and binding of H2O See Table 1) Similar structures were obtained for [AE (H2O)n]2+ (n = 1-9) (AE = Mg2+ Ca2+ Sr2+ and Ba2+)

DOI 102477jccj2013-0011 109

Table 1 AE-O distances and binding energies per water molecule for [AE (H2O)n]2+ (AE = Mg Ca Sr Ba and Ra n = 1-9)

HF MP2 B3LYP LC-BLYPAE2+ n r (AE-O)a BEb r (AE-O)a BEb r (AE-O)a BEb r (AE-O)a BEb

Mg2+ 1 198 minus255 199 minus260 196 minus300 192 minus3762 195 minus254 196 minus263 194 minus298 191 minus3593 197 minus244 197 minus256 196 minus291 193 minus3524 199 minus229 199 minus249 198 minus275 195 minus3375 204 minus217 204 minus235 203 minus255 199 minus3196 208 minus205 208 minus225 207 minus238 203 minus3047 216 minus165 219 minus190 217 minus200 212 minus2658 No structure was obtained without water (s) in the second solvation shell9

Exp Coord Num r (MgndashO) = 60 204 [4] 60 206 [5] 60 minus [6] Previous theory Coord Num r (MgndashO) = 60 203 [16] 60 212 [17] 80 213 [16]

Ca2+ 1 230 minus198 229 minus214 219 minus285 215 minus3462 234 minus187 233 minus203 224 minus257 220 minus3093 234 minus177 233 minus196 227 minus243 223 minus2964 236 minus176 234 minus195 230 minus230 226 minus2825 238 minus168 236 minus187 232 minus220 228 minus2756 241 minus159 240 minus182 235 minus208 235 minus2607 246 minus147 243 minus170 238 minus191 235 minus2518 252 minus129 247 minus159 245 minus179 241 minus2419 257 minus115 254 minus147 250 minus162 248 minus226

Exp Coord Num r (Ca-O) = 60 242 [7] 80 minus [8] 100 246 [9] Previous theory Coord Num r (Ca-O) = 79 248 [19] 83 245 [18] 92 247 [18]

Sr2+ 1 249 minus167 248 minus192 246 minus180 243 minus2342 252 minus164 251 minus170 250 minus187 246 minus2293 253 minus156 252 minus171 250 minus181 246 minus2224 254 minus152 253 minus166 251 minus177 247 minus2185 257 minus145 256 minus161 254 minus171 252 minus2146 260 minus140 257 minus157 256 minus166 255 minus2097 263 minus131 261 minus150 258 minus156 257 minus2068 265 minus122 264 minus143 267 minus148 258 minus2049 270 minus113 269 minus134 269 minus141 261 minus199

Exp Coord Num r (Sr-O) = 73 262 [13] 103 264 [11] 150 265 [10] Previous theory Coord Num r (Sr-O) = 76 260 [21] 90 269 [22] 97 264 [12] 98 263 [20]

Ba2+ 1 274 minus108 271 minus120 267 minus129 261 minus1692 273 minus108 271 minus116 268 minus129 263 minus1683 274 minus100 272 minus110 268 minus124 263 minus1654 275 minus100 273 minus111 269 minus122 265 minus1615 277 minus97 275 minus111 272 minus121 277 minus1626 280 minus94 277 minus106 276 minus118 272 minus1667 282 minus90 278 minus105 282 minus114 275 minus1628 284 minus86 286 minus105 283 minus112 279 minus1699 288 minus81 294 minus100 289 minus109 276 minus167

Exp Coord Num r (Ba-O) = 78 278 [14] 81 282 [14] 95 290 [15] Previous theory Coord Num r (Ba-O) = 78 282 [14] 93 286 [24]

Ra2+ 1 283 minus106 282 minus115 278 minus123 271 minus1602 279 minus99 278 minus108 276 minus119 270 minus1563 282 minus97 279 minus106 277 minus112 272 minus1554 282 minus91 281 minus100 278 minus111 273 minus1505 286 minus90 284 minus103 281 minus110 276 minus1516 289 minus85 286 minus100 284 minus108 280 minus1547 289 minus79 288 minus99 283 minus106 280 minus1558 291 minus79 291 minus98 293 minus106 288 minus1649 296 minus74 293 minus94 295 minus103 291 minus1608 291 minus79 291 minus98 293 minus106 288 minus1649 296 minus74 293 minus94 295 minus103 291 minus160

a AE-O distances in Aring b Binding energies in kcal molminus1 Zero-point energy (ZPE) corrected values are given

J Comput Chem Jpn Vol 13 No 1 (2014)110

ing ab initio molecular dynamics simulations

33 Differences in hydration character among divalent alkaline earth metal ions

As discussed in the previous section the ΔGsolv values for the

divalent alkaline metal ion series decrease monotonically with

increasing atomic number As shown in Table 2 the differ-

ence mainly originates from the difference in the ΔGcluster term

which is the formation free energy of the hydrated metal ion

cluster This means that the difference in hydration mechanism

among the divalent alkaline metal ions can be well explained

by the difference in chemical interactions between the metal

ions (AE2+) and solvent water molecules in the first hydration

shell In this section we compare the AE2+minuswater interactions

and discuss the physicochemical differences in hydration using

NPA LMO-EDA and NBO results

We found that the magnitudes of decrements in positive

charge on AE2+ are inversely proportional to the atomic num-

bers of the alkaline earth metal ions (See Table S4 in supporting

information) The tendency can be explained by the difference

in the valence electronic structure of AE2+ Figure 2 shows the

LUMO energy levels of bare AE2+ which are s-type orbitals

Figure 2 An orbital energy diagram by LC-BLYP level of the-ory for AE2+ ions (AE = Mg Ca Sr Ba and Ra) and a water molecule

Table 2 Solvation free energies (ΔGsolv in kcal molminus1) of divalent alkaline earth metal ions calculated for [AE (H2O)n]2+ (AE = Mg Ca Sr Ba and Ra) at the LC-BLYP level of theory

Components of ΔGsolva

AE2+ n ΔGsolv ΔGcluster ΔGcont ΔGcav ΔGdisp-rep nΔGvapc

Mg2+ 6 minus4957 minus3360 minus1802 230 minus148 1237 minus4912 minus3375 minus1776 250 minus155 144

Expb minus4555

Ca2+ 6 minus4003 minus2505 minus1728 260 minus152 1237 minus4060 minus2655 minus1672 283 minus158 1448 minus4138 minus2818 minus1624 313 minus174 1649 minus4202 minus2915 minus1611 326 minus186 185

Expb minus3808

Sr2+ 6 minus3469 minus1949 minus1747 255 minus150 1237 minus3572 minus2124 minus1697 275 minus170 1448 minus3705 minus2331 minus1651 297 minus184 1649 minus3792 minus2498 minus1596 321 minus203 185

Expb minus3459

Ba2+ 6 minus3184 minus1686 minus1724 256 minus153 1237 minus3249 minus1824 minus1687 293 minus175 1448 minus3365 minus2035 minus1600 303 minus197 1649 minus3457 minus2200 minus1576 334 minus201 185

Expb minus3151

Ra2+ 6 minus2960 minus1551 minus1670 289 minus151 1237 minus3111 minus1732 minus1643 294 minus173 1448 minus3064 minus1861 minus1538 353 minus182 1649 minus3143 minus1990 minus1530 383 minus190 185

No experimental result

a Obtained in C-PCM calculations See equation (1) b Ref [39] c An experimental value of 205 kcal molminus1 was used (Ref [43])

DOI 102477jccj2013-0011 111

and work as electron accepting orbitals in the hydration pro-

cess The LUMO energy level becomes higher with increases

in the atomic number of AE2+ with the exception between Ba2+

and Ra2+ due to relativistic stabilization of the 7s orbital of

Ra2+ As Mg2+ has the lowest LUMO energy level Mg2+ can be

easily hydrated to form coordination bonds with covalent char-

acter On the contrary as Ba2+ and Ra2+ have very high LUMO

energy levels these ions are expected to form ionic bonds be-

tween the metals and solvent water molecules

The differences in chemical bonding character between the

divalent alkaline earth metal ions and solvent water molecules

could be further confirmed by LMO-EDA The LMO-EDA re-

sults for gas-phase [AE (H2O)1]2+ (AE = Mg Ca Sr Ba and

Ra) are given in Figure 3 Due to the absence of solvent ef-

fects and structural change upon coordination the interaction

energies predicted by the LMO-EDA were much larger than

the binding energies and solvation free energies predicted with

the semi-continuum models (see Tables 1 and 2) Although the

interaction energies were predicted to be larger we observed

similar metal ion dependencies between the interaction ener-

gies and bindingsolvation free energies Thus we used gas-

phase calculation data to provide a detailed understanding of

the chemical bonding character between the divalent alkaline

earth metal ions and solvent water molecules

As shown in Figure 3 the total chemical interaction between

an alkaline earth metal ion and a water molecule becomes

weaker with increases in the atomic number of the alkaline

metal Figure 3 also shows that the dominant component of the

chemical interaction is the electrostatic interaction term (ΔEES)

for all the divalent alkaline earth metal ions We observed that

the ΔEES terms are also inversely proportional to the atomic

number of the alkaline earth metals This can be simply ex-

plained by the charge density on the ion surface As the diam-

eters of Mg Ca Sr Ba and Ra are 160 197 215 217 and

223 Aring respectively [35] their ratio of surface charge density

is 1 066 055 054 051 which well corresponds to the ratio

for the ΔEES terms (723 596 485 430 394 kcal molminus1 = 1

082 067 059 054)

As the electrostatic interactions (ΔEES) between the central

metal ion and water molecules in the first solvation shell are

effectively screened out by solvent water molecules in the outer

solvation shells to analyze the second largest component of the

chemical bonding interaction in the gas-phase is also impor-

tant to understand the chemical hydration character of the metal

ions The LMO-EDA results in Figure 3 show that the ΔEpol

terms which include not only polarization interaction (POL)

but also charge-transfer interaction (CT) terms are the second

largest energy component for chemical bonding between the

divalent alkaline earth metal ions and water molecules Figure

3 also shows that ΔEpol is larger for lighter alkaline earth met-

als However the CT interaction terms were not well separated

from the POL terms in the LMO-EDA scheme reported by Li

et al [44] Thus to clarify the importance of CT interaction

ie covalent interaction in the coordination process we per-

formed second-order perturbation theory analyses of the Fock

matrix in natural bond orbital (NBO) basis [45] Donor-accep-

tor (AE2+-Owater) interaction energies for [AE (H2O)n]2+ (AE =

Mg Ca Sr Ba and Ra n = 1ndash9) obtained by this analysis at

the LC-BLYP level are given in Table 3 We could find larger

donor-acceptor CT interactions in [Mg (H2O)n]2+ On the other

hand we could find no significant CT interaction in [Ba (H2O)

n]2+ and [Ra (H2O)n]2+ In these heavy alkaline earth metal ion

Figure 3 The LMO-EDA results for [AE (H2O)1]2+ (AE = Mg Ca Sr Ba and Ra) at the LC-BLYP level of theory

J Comput Chem Jpn Vol 13 No 1 (2014)112

hydrates CT interactions were predicted to be smaller than

10 kcal molminus1 From the NPA LMO-EDA and NBO results

we concluded that the light divalent alkaline earth metal ions

(Mg2+ Ca2+) form more covalent coordination bonds and the

heavy divalent alkaline earth metal ions (Ba2+ Ra2+) form more

ionic coordination bonds

4 Concluding Remarks

The geometries thermodynamic stabilities and electronic

structures of hydrated divalent alkaline earth metal ions (AE2+

AE = Mg Ca Sr Ba and Ra) were theoretically investigated us-

ing quantum chemical calculations at the HF MP2 B3LYP and

LC-BLYP levels of theory through the application of a relativ-

istic model core potential (MCP) method We observed reason-

able agreement between our results and previous experimental

results for hydrated non-Ra2+ metal ions The heaviest divalent

alkaline earth metal ion the Ra2+ ion the hydration number of

which has not been observed experimentally was predicted to

be in the range of 6ndash9 The solvation free energy of hydrated

Ra2+ was calculated to be ca minus310 kcal molminus1 which was the

weakest among the hydrated divalent alkaline metal ions The

chemical interaction between hydrated Ra2+ and solvent water

molecules mainly consists of electrostatic interaction to form

ionic bonds Unlike the hydration of the light divalent alkaline

earth metal ions (Mg2+ Ca2+) CT interactions ie covalent in-

teractions to form coordination bond do not play an important

role in the hydration of Ra2+

This study was supported by JSPS KAKENHI Grant Number

25810002 and Yamada Science Foundation AM is also grate-

ful to JSPS for the Research Fellowships for Young Scientists

Some of the calculations reported here were performed using

computing resources in the Research Center for Computational

Science Okazaki Japan

References

[1] M P Curie P Curie Comptes Rendus 127 175 (1898) [2] E D Glendening D Feller J Phys Chem 100 4790

(1996) [CrossRef] [3] Y-K Han H Y Jeong J Phys Chem 100 18004

(1996) [CrossRef] [4] R Caminiti G Licheri G Piccaluga G Pinna Chem

Phys Lett 47 275 (1977) [CrossRef] [5] H Ohtaki T Radnai Chem Rev 93 1157 (1993)

[CrossRef] [6] N A Matwiyoff H Taube J Am Chem Soc 90 2796

(1968) [CrossRef] [7] G Licheri G Piccaluga G Pinna J Chem Phys 64

2437 (1976) [CrossRef] [8] A K Katz J P Glusker S A Beebe C W Bock J Am

Chem Soc 118 5752 (1996) [CrossRef] [9] N A Hewish G W Neilson J E Enderby Nature 297

138 (1982) [CrossRef] [10] G W Neilson R D Broadbent Chem Phys Lett 167

429 (1990) [CrossRef] [11] P DrsquoAngelo H Nolting N V Pavel Phys Rev A 53

798 (1996) [Medline] [CrossRef] [12] T Driesner P T Cummings J Chem Phys 111 5141

(1999) [CrossRef] [13] D M Pfund J G Darab J L Fulton Y Ma J Phys

Chem 98 13102 (1994) [CrossRef] [14] P DAngelo N V Pavel D Roccatano H-F Nolting

Phys Rev B 54 12129 (1996) [CrossRef] [15] J N Albright J Chem Phys 56 3783 (1972) [CrossRef] [16] A Tongraar B M Rode Chem Phys Lett 346 485

(2001) [CrossRef]

Table 3 Donor-acceptor (AE2+-Owater) interaction energies for [AE (H2O)n]2+ (AE = Mg Ca Sr Ba and Ra n = 1-9) obtained by second-order perturbation theory analyses of Fock matrix in natural bond orbital (NBO) basis at the LC-BLYP level of theory The averaged energies per a AE2+-Owater bond are given in kcal molminus1

AE2+

n Mg2+ Ca2+ Sr2+ Ba2+ Ra2+

1 130 62 54 32 152 242 78 68 35 183 308 90 81 50 254 399 133 102 61 345 405 152 123 69 416 408 196 146 72 507 367 242 158 83 628 minus 276 159 92 619 minus 279 157 87 62

DOI 102477jccj2013-0011 107

The basis sets used throughout this study were 6-31G (dp)

for OH [4849] and MCPdzp for the central alkaline earth met-

als [25] where MCPs are valence only relativistic model core

potential basis sets that are used to reduce computational costs

arising from chemically inert core electrons and to take into ac-

count scalar relativistic effects The MCP method is one of the

unique pseudo-potential methods which properly reproduces

nodal structures of valence orbitals that are important for ac-

curate treatment of various molecular properties within pseudo-

potential approximations [2550ndash55]

In the MCP method the electronic Hamiltonian H NvMCP ( )1 2 of the Nv valence electrons (in atomic units)

is chosen as follows

(2)

with the one-electron Hamiltonian term defined as

(3)

(4)

where Z is the atomic number of the atom and Nc is the number

of core electrons replaced by MCPs Aj αj Aj αj and Bc (c

= core orbitals) are the MCP parameters and ψc denotes the

core orbital functions while Bc is defined as

(5)

where εc is the orbital energy of the core orbital and F is taken

to be 2 The MCP VMCP in Eq (4) given as a simple spher-

ically-symmetric local potential approximates the local core

Coulomb potential and the non-local core exchange potential as

well as the nuclear attraction potential term The MCP param-

eters in Eq (4) were determined by fitting atomic MCP calcula-

tion results to the corresponding relativistic all-electron calcu-

lations (see Refs [2550ndash55]) The projection operator in Eq

(3) prevents the valence orbitals from collapsing into the core

region and may also be regarded as an energy shift operator By

the use of this operator the energy levels of core electrons are

shifted far above zero energy thus allowing for finding in each

symmetry the lowest valence orbitals with appropriate nodal

structure

In the MCPdzp for alkaline earth metals (ns)2(np)6(n = 2ndash6

for Mg2+ Ca2+ Sr2+ Ba2+ and Ra2+) valence electrons were ex-

plicitly treated The contractions of valence basis sets with a set

of polarization functions were (2111131221) (3111141232)

(4111151232) (5111161343) and (6111171353) for Mg

Ca Sr Ba and Ra respectively

All the electronic structure calculations were performed us-

ing the GAMESS [5657] quantum chemistry program pack-

age The NBO 50 program package [58] was used for the

NBONPA analyses

3 Results and Discussion

31 Optimized structures of [AE (HO)n]2+ (AE = Mg Ca Sr Ba and Ra n = 1minus9)

The optimized structures the AE-O bond lengths and the aver-

aged AE-H2O binding energies for [AE (H2O)n]2+ (AE = Mg

Ca Sr Ba and Ra n = 1ndash9) are given in Figure 1 and Table 1 As

shown in Figure 1 except for AE = Mg we could observe that

all solvent water molecules coordinate to the central divalent al-

kaline earth ion directly to form the first hydration shell in [AE

(H2O)n]2+ (n = 1ndash9) For [Mg (H2O)n]2+ (n = 1ndash9) we obtained

a hepta-coordinated hydration structure at the maximum due

to the small atomic radii (160 Aring [35]) of Mg2+ compared with

those of the other divalent alkaline earth metal ions For [AE

(H2O)n]2+ (AE = Ca Sr Ba and Ra n = 1ndash9) the structures that

have water molecules in the second solvation shell gave much

higher energies than those in Figure 1 The optimized structures

of [AE (H2O)n]2+ (AE = Mg Ca Sr Ba and Ra n = 1ndash9) and

averaged AE-H2O binding energies were predicted to be very

similar among the HF MP2 and B3LYP levels of theory Even

LC-BLYP level of theory predicted larger binding energies than

these levels the tendency to cluster size (n) is quite similar

The differences of the AE-O bond length among the calculation

methods were within 01 Aring Table 1 shows the elongation of

the AE-O bond length (with the exception of those between n

= 1 and 2 for AE = Ra) and a corresponding monotonic decre-

ment of the averaged AE-H2O binding energy with increased

number of solvent water molecules in each calculation level

A plausible reason for the AE-O bond elongation is the mutual

repulsion of donor orbitals on the water molecules

J Comput Chem Jpn Vol 13 No 1 (2014)108

32 Solvation free energy and hydration numbers of AE2+ (AE = Mg Ca Sr Ba and Ra)

To investigate the hydration structures of alkaline earth metal

ions in finite temperature conditions it is necessary to evalu-

ate the solvation free energies of the ions To do this we have

to take into account two types of solvent effects specific and

long-range solvent effects The former is a solvent effect from

the water molecules that directly coordinate to the central AE2+

to form the first hydration shell and the latter is a solvent ef-

fect from the water molecules in the outer hydration shells We

could not use [AE (H2O)n]2+ (n = 1ndash5) for evaluating solvation

free energies of AE2+ since only a part of the first solvation

shell was described explicitly and the remaining part was treat-

ed via a C-PCM implicit solvation model in the smaller mod-

els To obtain more realistic solvation free energies of AE2+ we

chose a set of larger models [AE (H2O)n]2+ (n = 6ndash9) in which

the water molecules completely surround the central AE2+

Theoretically calculated hydration energies of AE2+ (AE =

Mg Ca Sr Ba and Ra) obtained by the semi-continuum clus-

ter models are given in Table 2 In Table 2 only the LC-BLYP

level results were given as HF MP2 and B3LYP gave similar

structures and binding tendencies as mentioned in the previous

section (See Tables S1-3 in supporting information) Table 2

shows that all divalent alkaline earth metal ions have negative

ΔGsolv values for the [AE (H2O)n]2+ (n = 6ndash9) semi-continuum

model This means that all the [AE (H2O)n]2+ (AE = Mg Ca

Sr Ba and Ra n = 6ndash9) species are thermodynamically stable

Table 2 also shows that the dominant components in ΔGsolv

are ΔGcluster and ΔGcont The remaining terms in Eq (1) ΔGcav

ΔGdisp-rep and nΔGvap make only minor contributions to the

solvation free energies The order of ΔGsolv values for non-

Ra2+ divalent alkaline earth metal ions were experimentally

observed to be Mg2+ gt Ca2+ gt Sr2+ gt Ba2+ [36] Although we

obtained ca 30ndash40 kcal molminus1 errors compared with the experi-

mental ones due to the use of the semi-continuum models we

could theoretically reproduce the experimental order for non-

Ra2+ divalent alkaline earth metal ions in a qualitative manner

(see Table 2) As we could obtain at least qualitative accuracy

with the semi-continuum models we are able to safely discuss

Ra2+ hydration for which there has been no experimental or

theoretical study to date As shown in Table 2 we obtained the

smallest ΔGsolv value for Ra2+ among all divalent alkaline earth

metal ions investigated in this study Thus the theoretical order

of ΔGsolv for divalent alkaline earth metal ions was predicted to

be Mg2+ gt Ca2+ gt Sr2+ gt Ba2+ gt Ra2+ As we could observe no

significant difference in ΔGsolv values among [Ra (H2O)n]2+ (n

= 6ndash9) we could not determine the most likely hydration num-

ber for Ra2+ To determine the hydration number it is necessary

to take into account the dynamical motions of the solvents us-

Figure 1 Optimized structures of [Ra (H2O)n]2+ (n = 1-9) at the HF level of theory (MP2 B3LYP and LC-BLYP levels of theory gave very similar structures and binding of H2O See Table 1) Similar structures were obtained for [AE (H2O)n]2+ (n = 1-9) (AE = Mg2+ Ca2+ Sr2+ and Ba2+)

DOI 102477jccj2013-0011 109

Table 1 AE-O distances and binding energies per water molecule for [AE (H2O)n]2+ (AE = Mg Ca Sr Ba and Ra n = 1-9)

HF MP2 B3LYP LC-BLYPAE2+ n r (AE-O)a BEb r (AE-O)a BEb r (AE-O)a BEb r (AE-O)a BEb

Mg2+ 1 198 minus255 199 minus260 196 minus300 192 minus3762 195 minus254 196 minus263 194 minus298 191 minus3593 197 minus244 197 minus256 196 minus291 193 minus3524 199 minus229 199 minus249 198 minus275 195 minus3375 204 minus217 204 minus235 203 minus255 199 minus3196 208 minus205 208 minus225 207 minus238 203 minus3047 216 minus165 219 minus190 217 minus200 212 minus2658 No structure was obtained without water (s) in the second solvation shell9

Exp Coord Num r (MgndashO) = 60 204 [4] 60 206 [5] 60 minus [6] Previous theory Coord Num r (MgndashO) = 60 203 [16] 60 212 [17] 80 213 [16]

Ca2+ 1 230 minus198 229 minus214 219 minus285 215 minus3462 234 minus187 233 minus203 224 minus257 220 minus3093 234 minus177 233 minus196 227 minus243 223 minus2964 236 minus176 234 minus195 230 minus230 226 minus2825 238 minus168 236 minus187 232 minus220 228 minus2756 241 minus159 240 minus182 235 minus208 235 minus2607 246 minus147 243 minus170 238 minus191 235 minus2518 252 minus129 247 minus159 245 minus179 241 minus2419 257 minus115 254 minus147 250 minus162 248 minus226

Exp Coord Num r (Ca-O) = 60 242 [7] 80 minus [8] 100 246 [9] Previous theory Coord Num r (Ca-O) = 79 248 [19] 83 245 [18] 92 247 [18]

Sr2+ 1 249 minus167 248 minus192 246 minus180 243 minus2342 252 minus164 251 minus170 250 minus187 246 minus2293 253 minus156 252 minus171 250 minus181 246 minus2224 254 minus152 253 minus166 251 minus177 247 minus2185 257 minus145 256 minus161 254 minus171 252 minus2146 260 minus140 257 minus157 256 minus166 255 minus2097 263 minus131 261 minus150 258 minus156 257 minus2068 265 minus122 264 minus143 267 minus148 258 minus2049 270 minus113 269 minus134 269 minus141 261 minus199

Exp Coord Num r (Sr-O) = 73 262 [13] 103 264 [11] 150 265 [10] Previous theory Coord Num r (Sr-O) = 76 260 [21] 90 269 [22] 97 264 [12] 98 263 [20]

Ba2+ 1 274 minus108 271 minus120 267 minus129 261 minus1692 273 minus108 271 minus116 268 minus129 263 minus1683 274 minus100 272 minus110 268 minus124 263 minus1654 275 minus100 273 minus111 269 minus122 265 minus1615 277 minus97 275 minus111 272 minus121 277 minus1626 280 minus94 277 minus106 276 minus118 272 minus1667 282 minus90 278 minus105 282 minus114 275 minus1628 284 minus86 286 minus105 283 minus112 279 minus1699 288 minus81 294 minus100 289 minus109 276 minus167

Exp Coord Num r (Ba-O) = 78 278 [14] 81 282 [14] 95 290 [15] Previous theory Coord Num r (Ba-O) = 78 282 [14] 93 286 [24]

Ra2+ 1 283 minus106 282 minus115 278 minus123 271 minus1602 279 minus99 278 minus108 276 minus119 270 minus1563 282 minus97 279 minus106 277 minus112 272 minus1554 282 minus91 281 minus100 278 minus111 273 minus1505 286 minus90 284 minus103 281 minus110 276 minus1516 289 minus85 286 minus100 284 minus108 280 minus1547 289 minus79 288 minus99 283 minus106 280 minus1558 291 minus79 291 minus98 293 minus106 288 minus1649 296 minus74 293 minus94 295 minus103 291 minus1608 291 minus79 291 minus98 293 minus106 288 minus1649 296 minus74 293 minus94 295 minus103 291 minus160

a AE-O distances in Aring b Binding energies in kcal molminus1 Zero-point energy (ZPE) corrected values are given

J Comput Chem Jpn Vol 13 No 1 (2014)110

ing ab initio molecular dynamics simulations

33 Differences in hydration character among divalent alkaline earth metal ions

As discussed in the previous section the ΔGsolv values for the

divalent alkaline metal ion series decrease monotonically with

increasing atomic number As shown in Table 2 the differ-

ence mainly originates from the difference in the ΔGcluster term

which is the formation free energy of the hydrated metal ion

cluster This means that the difference in hydration mechanism

among the divalent alkaline metal ions can be well explained

by the difference in chemical interactions between the metal

ions (AE2+) and solvent water molecules in the first hydration

shell In this section we compare the AE2+minuswater interactions

and discuss the physicochemical differences in hydration using

NPA LMO-EDA and NBO results

We found that the magnitudes of decrements in positive

charge on AE2+ are inversely proportional to the atomic num-

bers of the alkaline earth metal ions (See Table S4 in supporting

information) The tendency can be explained by the difference

in the valence electronic structure of AE2+ Figure 2 shows the

LUMO energy levels of bare AE2+ which are s-type orbitals

Figure 2 An orbital energy diagram by LC-BLYP level of the-ory for AE2+ ions (AE = Mg Ca Sr Ba and Ra) and a water molecule

Table 2 Solvation free energies (ΔGsolv in kcal molminus1) of divalent alkaline earth metal ions calculated for [AE (H2O)n]2+ (AE = Mg Ca Sr Ba and Ra) at the LC-BLYP level of theory

Components of ΔGsolva

AE2+ n ΔGsolv ΔGcluster ΔGcont ΔGcav ΔGdisp-rep nΔGvapc

Mg2+ 6 minus4957 minus3360 minus1802 230 minus148 1237 minus4912 minus3375 minus1776 250 minus155 144

Expb minus4555

Ca2+ 6 minus4003 minus2505 minus1728 260 minus152 1237 minus4060 minus2655 minus1672 283 minus158 1448 minus4138 minus2818 minus1624 313 minus174 1649 minus4202 minus2915 minus1611 326 minus186 185

Expb minus3808

Sr2+ 6 minus3469 minus1949 minus1747 255 minus150 1237 minus3572 minus2124 minus1697 275 minus170 1448 minus3705 minus2331 minus1651 297 minus184 1649 minus3792 minus2498 minus1596 321 minus203 185

Expb minus3459

Ba2+ 6 minus3184 minus1686 minus1724 256 minus153 1237 minus3249 minus1824 minus1687 293 minus175 1448 minus3365 minus2035 minus1600 303 minus197 1649 minus3457 minus2200 minus1576 334 minus201 185

Expb minus3151

Ra2+ 6 minus2960 minus1551 minus1670 289 minus151 1237 minus3111 minus1732 minus1643 294 minus173 1448 minus3064 minus1861 minus1538 353 minus182 1649 minus3143 minus1990 minus1530 383 minus190 185

No experimental result

a Obtained in C-PCM calculations See equation (1) b Ref [39] c An experimental value of 205 kcal molminus1 was used (Ref [43])

DOI 102477jccj2013-0011 111

and work as electron accepting orbitals in the hydration pro-

cess The LUMO energy level becomes higher with increases

in the atomic number of AE2+ with the exception between Ba2+

and Ra2+ due to relativistic stabilization of the 7s orbital of

Ra2+ As Mg2+ has the lowest LUMO energy level Mg2+ can be

easily hydrated to form coordination bonds with covalent char-

acter On the contrary as Ba2+ and Ra2+ have very high LUMO

energy levels these ions are expected to form ionic bonds be-

tween the metals and solvent water molecules

The differences in chemical bonding character between the

divalent alkaline earth metal ions and solvent water molecules

could be further confirmed by LMO-EDA The LMO-EDA re-

sults for gas-phase [AE (H2O)1]2+ (AE = Mg Ca Sr Ba and

Ra) are given in Figure 3 Due to the absence of solvent ef-

fects and structural change upon coordination the interaction

energies predicted by the LMO-EDA were much larger than

the binding energies and solvation free energies predicted with

the semi-continuum models (see Tables 1 and 2) Although the

interaction energies were predicted to be larger we observed

similar metal ion dependencies between the interaction ener-

gies and bindingsolvation free energies Thus we used gas-

phase calculation data to provide a detailed understanding of

the chemical bonding character between the divalent alkaline

earth metal ions and solvent water molecules

As shown in Figure 3 the total chemical interaction between

an alkaline earth metal ion and a water molecule becomes

weaker with increases in the atomic number of the alkaline

metal Figure 3 also shows that the dominant component of the

chemical interaction is the electrostatic interaction term (ΔEES)

for all the divalent alkaline earth metal ions We observed that

the ΔEES terms are also inversely proportional to the atomic

number of the alkaline earth metals This can be simply ex-

plained by the charge density on the ion surface As the diam-

eters of Mg Ca Sr Ba and Ra are 160 197 215 217 and

223 Aring respectively [35] their ratio of surface charge density

is 1 066 055 054 051 which well corresponds to the ratio

for the ΔEES terms (723 596 485 430 394 kcal molminus1 = 1

082 067 059 054)

As the electrostatic interactions (ΔEES) between the central

metal ion and water molecules in the first solvation shell are

effectively screened out by solvent water molecules in the outer

solvation shells to analyze the second largest component of the

chemical bonding interaction in the gas-phase is also impor-

tant to understand the chemical hydration character of the metal

ions The LMO-EDA results in Figure 3 show that the ΔEpol

terms which include not only polarization interaction (POL)

but also charge-transfer interaction (CT) terms are the second

largest energy component for chemical bonding between the

divalent alkaline earth metal ions and water molecules Figure

3 also shows that ΔEpol is larger for lighter alkaline earth met-

als However the CT interaction terms were not well separated

from the POL terms in the LMO-EDA scheme reported by Li

et al [44] Thus to clarify the importance of CT interaction

ie covalent interaction in the coordination process we per-

formed second-order perturbation theory analyses of the Fock

matrix in natural bond orbital (NBO) basis [45] Donor-accep-

tor (AE2+-Owater) interaction energies for [AE (H2O)n]2+ (AE =

Mg Ca Sr Ba and Ra n = 1ndash9) obtained by this analysis at

the LC-BLYP level are given in Table 3 We could find larger

donor-acceptor CT interactions in [Mg (H2O)n]2+ On the other

hand we could find no significant CT interaction in [Ba (H2O)

n]2+ and [Ra (H2O)n]2+ In these heavy alkaline earth metal ion

Figure 3 The LMO-EDA results for [AE (H2O)1]2+ (AE = Mg Ca Sr Ba and Ra) at the LC-BLYP level of theory

J Comput Chem Jpn Vol 13 No 1 (2014)112

hydrates CT interactions were predicted to be smaller than

10 kcal molminus1 From the NPA LMO-EDA and NBO results

we concluded that the light divalent alkaline earth metal ions

(Mg2+ Ca2+) form more covalent coordination bonds and the

heavy divalent alkaline earth metal ions (Ba2+ Ra2+) form more

ionic coordination bonds

4 Concluding Remarks

The geometries thermodynamic stabilities and electronic

structures of hydrated divalent alkaline earth metal ions (AE2+

AE = Mg Ca Sr Ba and Ra) were theoretically investigated us-

ing quantum chemical calculations at the HF MP2 B3LYP and

LC-BLYP levels of theory through the application of a relativ-

istic model core potential (MCP) method We observed reason-

able agreement between our results and previous experimental

results for hydrated non-Ra2+ metal ions The heaviest divalent

alkaline earth metal ion the Ra2+ ion the hydration number of

which has not been observed experimentally was predicted to

be in the range of 6ndash9 The solvation free energy of hydrated

Ra2+ was calculated to be ca minus310 kcal molminus1 which was the

weakest among the hydrated divalent alkaline metal ions The

chemical interaction between hydrated Ra2+ and solvent water

molecules mainly consists of electrostatic interaction to form

ionic bonds Unlike the hydration of the light divalent alkaline

earth metal ions (Mg2+ Ca2+) CT interactions ie covalent in-

teractions to form coordination bond do not play an important

role in the hydration of Ra2+

This study was supported by JSPS KAKENHI Grant Number

25810002 and Yamada Science Foundation AM is also grate-

ful to JSPS for the Research Fellowships for Young Scientists

Some of the calculations reported here were performed using

computing resources in the Research Center for Computational

Science Okazaki Japan

References

[1] M P Curie P Curie Comptes Rendus 127 175 (1898) [2] E D Glendening D Feller J Phys Chem 100 4790

(1996) [CrossRef] [3] Y-K Han H Y Jeong J Phys Chem 100 18004

(1996) [CrossRef] [4] R Caminiti G Licheri G Piccaluga G Pinna Chem

Phys Lett 47 275 (1977) [CrossRef] [5] H Ohtaki T Radnai Chem Rev 93 1157 (1993)

[CrossRef] [6] N A Matwiyoff H Taube J Am Chem Soc 90 2796

(1968) [CrossRef] [7] G Licheri G Piccaluga G Pinna J Chem Phys 64

2437 (1976) [CrossRef] [8] A K Katz J P Glusker S A Beebe C W Bock J Am

Chem Soc 118 5752 (1996) [CrossRef] [9] N A Hewish G W Neilson J E Enderby Nature 297

138 (1982) [CrossRef] [10] G W Neilson R D Broadbent Chem Phys Lett 167

429 (1990) [CrossRef] [11] P DrsquoAngelo H Nolting N V Pavel Phys Rev A 53

798 (1996) [Medline] [CrossRef] [12] T Driesner P T Cummings J Chem Phys 111 5141

(1999) [CrossRef] [13] D M Pfund J G Darab J L Fulton Y Ma J Phys

Chem 98 13102 (1994) [CrossRef] [14] P DAngelo N V Pavel D Roccatano H-F Nolting

Phys Rev B 54 12129 (1996) [CrossRef] [15] J N Albright J Chem Phys 56 3783 (1972) [CrossRef] [16] A Tongraar B M Rode Chem Phys Lett 346 485

(2001) [CrossRef]

Table 3 Donor-acceptor (AE2+-Owater) interaction energies for [AE (H2O)n]2+ (AE = Mg Ca Sr Ba and Ra n = 1-9) obtained by second-order perturbation theory analyses of Fock matrix in natural bond orbital (NBO) basis at the LC-BLYP level of theory The averaged energies per a AE2+-Owater bond are given in kcal molminus1

AE2+

n Mg2+ Ca2+ Sr2+ Ba2+ Ra2+

1 130 62 54 32 152 242 78 68 35 183 308 90 81 50 254 399 133 102 61 345 405 152 123 69 416 408 196 146 72 507 367 242 158 83 628 minus 276 159 92 619 minus 279 157 87 62

J Comput Chem Jpn Vol 13 No 1 (2014)108

32 Solvation free energy and hydration numbers of AE2+ (AE = Mg Ca Sr Ba and Ra)

To investigate the hydration structures of alkaline earth metal

ions in finite temperature conditions it is necessary to evalu-

ate the solvation free energies of the ions To do this we have

to take into account two types of solvent effects specific and

long-range solvent effects The former is a solvent effect from

the water molecules that directly coordinate to the central AE2+

to form the first hydration shell and the latter is a solvent ef-

fect from the water molecules in the outer hydration shells We

could not use [AE (H2O)n]2+ (n = 1ndash5) for evaluating solvation

free energies of AE2+ since only a part of the first solvation

shell was described explicitly and the remaining part was treat-

ed via a C-PCM implicit solvation model in the smaller mod-

els To obtain more realistic solvation free energies of AE2+ we

chose a set of larger models [AE (H2O)n]2+ (n = 6ndash9) in which

the water molecules completely surround the central AE2+

Theoretically calculated hydration energies of AE2+ (AE =

Mg Ca Sr Ba and Ra) obtained by the semi-continuum clus-

ter models are given in Table 2 In Table 2 only the LC-BLYP

level results were given as HF MP2 and B3LYP gave similar

structures and binding tendencies as mentioned in the previous

section (See Tables S1-3 in supporting information) Table 2

shows that all divalent alkaline earth metal ions have negative

ΔGsolv values for the [AE (H2O)n]2+ (n = 6ndash9) semi-continuum

model This means that all the [AE (H2O)n]2+ (AE = Mg Ca

Sr Ba and Ra n = 6ndash9) species are thermodynamically stable

Table 2 also shows that the dominant components in ΔGsolv

are ΔGcluster and ΔGcont The remaining terms in Eq (1) ΔGcav

ΔGdisp-rep and nΔGvap make only minor contributions to the

solvation free energies The order of ΔGsolv values for non-

Ra2+ divalent alkaline earth metal ions were experimentally

observed to be Mg2+ gt Ca2+ gt Sr2+ gt Ba2+ [36] Although we

obtained ca 30ndash40 kcal molminus1 errors compared with the experi-

mental ones due to the use of the semi-continuum models we

could theoretically reproduce the experimental order for non-

Ra2+ divalent alkaline earth metal ions in a qualitative manner

(see Table 2) As we could obtain at least qualitative accuracy

with the semi-continuum models we are able to safely discuss

Ra2+ hydration for which there has been no experimental or

theoretical study to date As shown in Table 2 we obtained the

smallest ΔGsolv value for Ra2+ among all divalent alkaline earth

metal ions investigated in this study Thus the theoretical order

of ΔGsolv for divalent alkaline earth metal ions was predicted to

be Mg2+ gt Ca2+ gt Sr2+ gt Ba2+ gt Ra2+ As we could observe no

significant difference in ΔGsolv values among [Ra (H2O)n]2+ (n

= 6ndash9) we could not determine the most likely hydration num-

ber for Ra2+ To determine the hydration number it is necessary

to take into account the dynamical motions of the solvents us-

Figure 1 Optimized structures of [Ra (H2O)n]2+ (n = 1-9) at the HF level of theory (MP2 B3LYP and LC-BLYP levels of theory gave very similar structures and binding of H2O See Table 1) Similar structures were obtained for [AE (H2O)n]2+ (n = 1-9) (AE = Mg2+ Ca2+ Sr2+ and Ba2+)

DOI 102477jccj2013-0011 109

Table 1 AE-O distances and binding energies per water molecule for [AE (H2O)n]2+ (AE = Mg Ca Sr Ba and Ra n = 1-9)

HF MP2 B3LYP LC-BLYPAE2+ n r (AE-O)a BEb r (AE-O)a BEb r (AE-O)a BEb r (AE-O)a BEb

Mg2+ 1 198 minus255 199 minus260 196 minus300 192 minus3762 195 minus254 196 minus263 194 minus298 191 minus3593 197 minus244 197 minus256 196 minus291 193 minus3524 199 minus229 199 minus249 198 minus275 195 minus3375 204 minus217 204 minus235 203 minus255 199 minus3196 208 minus205 208 minus225 207 minus238 203 minus3047 216 minus165 219 minus190 217 minus200 212 minus2658 No structure was obtained without water (s) in the second solvation shell9

Exp Coord Num r (MgndashO) = 60 204 [4] 60 206 [5] 60 minus [6] Previous theory Coord Num r (MgndashO) = 60 203 [16] 60 212 [17] 80 213 [16]

Ca2+ 1 230 minus198 229 minus214 219 minus285 215 minus3462 234 minus187 233 minus203 224 minus257 220 minus3093 234 minus177 233 minus196 227 minus243 223 minus2964 236 minus176 234 minus195 230 minus230 226 minus2825 238 minus168 236 minus187 232 minus220 228 minus2756 241 minus159 240 minus182 235 minus208 235 minus2607 246 minus147 243 minus170 238 minus191 235 minus2518 252 minus129 247 minus159 245 minus179 241 minus2419 257 minus115 254 minus147 250 minus162 248 minus226

Exp Coord Num r (Ca-O) = 60 242 [7] 80 minus [8] 100 246 [9] Previous theory Coord Num r (Ca-O) = 79 248 [19] 83 245 [18] 92 247 [18]

Sr2+ 1 249 minus167 248 minus192 246 minus180 243 minus2342 252 minus164 251 minus170 250 minus187 246 minus2293 253 minus156 252 minus171 250 minus181 246 minus2224 254 minus152 253 minus166 251 minus177 247 minus2185 257 minus145 256 minus161 254 minus171 252 minus2146 260 minus140 257 minus157 256 minus166 255 minus2097 263 minus131 261 minus150 258 minus156 257 minus2068 265 minus122 264 minus143 267 minus148 258 minus2049 270 minus113 269 minus134 269 minus141 261 minus199

Exp Coord Num r (Sr-O) = 73 262 [13] 103 264 [11] 150 265 [10] Previous theory Coord Num r (Sr-O) = 76 260 [21] 90 269 [22] 97 264 [12] 98 263 [20]

Ba2+ 1 274 minus108 271 minus120 267 minus129 261 minus1692 273 minus108 271 minus116 268 minus129 263 minus1683 274 minus100 272 minus110 268 minus124 263 minus1654 275 minus100 273 minus111 269 minus122 265 minus1615 277 minus97 275 minus111 272 minus121 277 minus1626 280 minus94 277 minus106 276 minus118 272 minus1667 282 minus90 278 minus105 282 minus114 275 minus1628 284 minus86 286 minus105 283 minus112 279 minus1699 288 minus81 294 minus100 289 minus109 276 minus167

Exp Coord Num r (Ba-O) = 78 278 [14] 81 282 [14] 95 290 [15] Previous theory Coord Num r (Ba-O) = 78 282 [14] 93 286 [24]

Ra2+ 1 283 minus106 282 minus115 278 minus123 271 minus1602 279 minus99 278 minus108 276 minus119 270 minus1563 282 minus97 279 minus106 277 minus112 272 minus1554 282 minus91 281 minus100 278 minus111 273 minus1505 286 minus90 284 minus103 281 minus110 276 minus1516 289 minus85 286 minus100 284 minus108 280 minus1547 289 minus79 288 minus99 283 minus106 280 minus1558 291 minus79 291 minus98 293 minus106 288 minus1649 296 minus74 293 minus94 295 minus103 291 minus1608 291 minus79 291 minus98 293 minus106 288 minus1649 296 minus74 293 minus94 295 minus103 291 minus160

a AE-O distances in Aring b Binding energies in kcal molminus1 Zero-point energy (ZPE) corrected values are given

J Comput Chem Jpn Vol 13 No 1 (2014)110

ing ab initio molecular dynamics simulations

33 Differences in hydration character among divalent alkaline earth metal ions

As discussed in the previous section the ΔGsolv values for the

divalent alkaline metal ion series decrease monotonically with

increasing atomic number As shown in Table 2 the differ-

ence mainly originates from the difference in the ΔGcluster term

which is the formation free energy of the hydrated metal ion

cluster This means that the difference in hydration mechanism

among the divalent alkaline metal ions can be well explained

by the difference in chemical interactions between the metal

ions (AE2+) and solvent water molecules in the first hydration

shell In this section we compare the AE2+minuswater interactions

and discuss the physicochemical differences in hydration using

NPA LMO-EDA and NBO results

We found that the magnitudes of decrements in positive

charge on AE2+ are inversely proportional to the atomic num-

bers of the alkaline earth metal ions (See Table S4 in supporting

information) The tendency can be explained by the difference

in the valence electronic structure of AE2+ Figure 2 shows the

LUMO energy levels of bare AE2+ which are s-type orbitals

Figure 2 An orbital energy diagram by LC-BLYP level of the-ory for AE2+ ions (AE = Mg Ca Sr Ba and Ra) and a water molecule

Table 2 Solvation free energies (ΔGsolv in kcal molminus1) of divalent alkaline earth metal ions calculated for [AE (H2O)n]2+ (AE = Mg Ca Sr Ba and Ra) at the LC-BLYP level of theory

Components of ΔGsolva

AE2+ n ΔGsolv ΔGcluster ΔGcont ΔGcav ΔGdisp-rep nΔGvapc

Mg2+ 6 minus4957 minus3360 minus1802 230 minus148 1237 minus4912 minus3375 minus1776 250 minus155 144

Expb minus4555

Ca2+ 6 minus4003 minus2505 minus1728 260 minus152 1237 minus4060 minus2655 minus1672 283 minus158 1448 minus4138 minus2818 minus1624 313 minus174 1649 minus4202 minus2915 minus1611 326 minus186 185

Expb minus3808

Sr2+ 6 minus3469 minus1949 minus1747 255 minus150 1237 minus3572 minus2124 minus1697 275 minus170 1448 minus3705 minus2331 minus1651 297 minus184 1649 minus3792 minus2498 minus1596 321 minus203 185

Expb minus3459

Ba2+ 6 minus3184 minus1686 minus1724 256 minus153 1237 minus3249 minus1824 minus1687 293 minus175 1448 minus3365 minus2035 minus1600 303 minus197 1649 minus3457 minus2200 minus1576 334 minus201 185

Expb minus3151

Ra2+ 6 minus2960 minus1551 minus1670 289 minus151 1237 minus3111 minus1732 minus1643 294 minus173 1448 minus3064 minus1861 minus1538 353 minus182 1649 minus3143 minus1990 minus1530 383 minus190 185

No experimental result

a Obtained in C-PCM calculations See equation (1) b Ref [39] c An experimental value of 205 kcal molminus1 was used (Ref [43])

DOI 102477jccj2013-0011 111

and work as electron accepting orbitals in the hydration pro-

cess The LUMO energy level becomes higher with increases

in the atomic number of AE2+ with the exception between Ba2+

and Ra2+ due to relativistic stabilization of the 7s orbital of

Ra2+ As Mg2+ has the lowest LUMO energy level Mg2+ can be

easily hydrated to form coordination bonds with covalent char-

acter On the contrary as Ba2+ and Ra2+ have very high LUMO

energy levels these ions are expected to form ionic bonds be-

tween the metals and solvent water molecules

The differences in chemical bonding character between the

divalent alkaline earth metal ions and solvent water molecules

could be further confirmed by LMO-EDA The LMO-EDA re-

sults for gas-phase [AE (H2O)1]2+ (AE = Mg Ca Sr Ba and

Ra) are given in Figure 3 Due to the absence of solvent ef-

fects and structural change upon coordination the interaction

energies predicted by the LMO-EDA were much larger than

the binding energies and solvation free energies predicted with

the semi-continuum models (see Tables 1 and 2) Although the

interaction energies were predicted to be larger we observed

similar metal ion dependencies between the interaction ener-

gies and bindingsolvation free energies Thus we used gas-

phase calculation data to provide a detailed understanding of

the chemical bonding character between the divalent alkaline

earth metal ions and solvent water molecules

As shown in Figure 3 the total chemical interaction between

an alkaline earth metal ion and a water molecule becomes

weaker with increases in the atomic number of the alkaline

metal Figure 3 also shows that the dominant component of the

chemical interaction is the electrostatic interaction term (ΔEES)

for all the divalent alkaline earth metal ions We observed that

the ΔEES terms are also inversely proportional to the atomic

number of the alkaline earth metals This can be simply ex-

plained by the charge density on the ion surface As the diam-

eters of Mg Ca Sr Ba and Ra are 160 197 215 217 and

223 Aring respectively [35] their ratio of surface charge density

is 1 066 055 054 051 which well corresponds to the ratio

for the ΔEES terms (723 596 485 430 394 kcal molminus1 = 1

082 067 059 054)

As the electrostatic interactions (ΔEES) between the central

metal ion and water molecules in the first solvation shell are

effectively screened out by solvent water molecules in the outer

solvation shells to analyze the second largest component of the

chemical bonding interaction in the gas-phase is also impor-

tant to understand the chemical hydration character of the metal

ions The LMO-EDA results in Figure 3 show that the ΔEpol

terms which include not only polarization interaction (POL)

but also charge-transfer interaction (CT) terms are the second

largest energy component for chemical bonding between the

divalent alkaline earth metal ions and water molecules Figure

3 also shows that ΔEpol is larger for lighter alkaline earth met-

als However the CT interaction terms were not well separated

from the POL terms in the LMO-EDA scheme reported by Li

et al [44] Thus to clarify the importance of CT interaction

ie covalent interaction in the coordination process we per-

formed second-order perturbation theory analyses of the Fock

matrix in natural bond orbital (NBO) basis [45] Donor-accep-

tor (AE2+-Owater) interaction energies for [AE (H2O)n]2+ (AE =

Mg Ca Sr Ba and Ra n = 1ndash9) obtained by this analysis at

the LC-BLYP level are given in Table 3 We could find larger

donor-acceptor CT interactions in [Mg (H2O)n]2+ On the other

hand we could find no significant CT interaction in [Ba (H2O)

n]2+ and [Ra (H2O)n]2+ In these heavy alkaline earth metal ion

Figure 3 The LMO-EDA results for [AE (H2O)1]2+ (AE = Mg Ca Sr Ba and Ra) at the LC-BLYP level of theory

J Comput Chem Jpn Vol 13 No 1 (2014)112

hydrates CT interactions were predicted to be smaller than

10 kcal molminus1 From the NPA LMO-EDA and NBO results

we concluded that the light divalent alkaline earth metal ions

(Mg2+ Ca2+) form more covalent coordination bonds and the

heavy divalent alkaline earth metal ions (Ba2+ Ra2+) form more

ionic coordination bonds

4 Concluding Remarks

The geometries thermodynamic stabilities and electronic

structures of hydrated divalent alkaline earth metal ions (AE2+

AE = Mg Ca Sr Ba and Ra) were theoretically investigated us-

ing quantum chemical calculations at the HF MP2 B3LYP and

LC-BLYP levels of theory through the application of a relativ-

istic model core potential (MCP) method We observed reason-

able agreement between our results and previous experimental

results for hydrated non-Ra2+ metal ions The heaviest divalent

alkaline earth metal ion the Ra2+ ion the hydration number of

which has not been observed experimentally was predicted to

be in the range of 6ndash9 The solvation free energy of hydrated

Ra2+ was calculated to be ca minus310 kcal molminus1 which was the

weakest among the hydrated divalent alkaline metal ions The

chemical interaction between hydrated Ra2+ and solvent water

molecules mainly consists of electrostatic interaction to form

ionic bonds Unlike the hydration of the light divalent alkaline

earth metal ions (Mg2+ Ca2+) CT interactions ie covalent in-

teractions to form coordination bond do not play an important

role in the hydration of Ra2+

This study was supported by JSPS KAKENHI Grant Number

25810002 and Yamada Science Foundation AM is also grate-

ful to JSPS for the Research Fellowships for Young Scientists

Some of the calculations reported here were performed using

computing resources in the Research Center for Computational

Science Okazaki Japan

References

[1] M P Curie P Curie Comptes Rendus 127 175 (1898) [2] E D Glendening D Feller J Phys Chem 100 4790

(1996) [CrossRef] [3] Y-K Han H Y Jeong J Phys Chem 100 18004

(1996) [CrossRef] [4] R Caminiti G Licheri G Piccaluga G Pinna Chem

Phys Lett 47 275 (1977) [CrossRef] [5] H Ohtaki T Radnai Chem Rev 93 1157 (1993)

[CrossRef] [6] N A Matwiyoff H Taube J Am Chem Soc 90 2796

(1968) [CrossRef] [7] G Licheri G Piccaluga G Pinna J Chem Phys 64

2437 (1976) [CrossRef] [8] A K Katz J P Glusker S A Beebe C W Bock J Am

Chem Soc 118 5752 (1996) [CrossRef] [9] N A Hewish G W Neilson J E Enderby Nature 297

138 (1982) [CrossRef] [10] G W Neilson R D Broadbent Chem Phys Lett 167

429 (1990) [CrossRef] [11] P DrsquoAngelo H Nolting N V Pavel Phys Rev A 53

798 (1996) [Medline] [CrossRef] [12] T Driesner P T Cummings J Chem Phys 111 5141

(1999) [CrossRef] [13] D M Pfund J G Darab J L Fulton Y Ma J Phys

Chem 98 13102 (1994) [CrossRef] [14] P DAngelo N V Pavel D Roccatano H-F Nolting

Phys Rev B 54 12129 (1996) [CrossRef] [15] J N Albright J Chem Phys 56 3783 (1972) [CrossRef] [16] A Tongraar B M Rode Chem Phys Lett 346 485

(2001) [CrossRef]

Table 3 Donor-acceptor (AE2+-Owater) interaction energies for [AE (H2O)n]2+ (AE = Mg Ca Sr Ba and Ra n = 1-9) obtained by second-order perturbation theory analyses of Fock matrix in natural bond orbital (NBO) basis at the LC-BLYP level of theory The averaged energies per a AE2+-Owater bond are given in kcal molminus1

AE2+

n Mg2+ Ca2+ Sr2+ Ba2+ Ra2+

1 130 62 54 32 152 242 78 68 35 183 308 90 81 50 254 399 133 102 61 345 405 152 123 69 416 408 196 146 72 507 367 242 158 83 628 minus 276 159 92 619 minus 279 157 87 62

DOI 102477jccj2013-0011 109

Table 1 AE-O distances and binding energies per water molecule for [AE (H2O)n]2+ (AE = Mg Ca Sr Ba and Ra n = 1-9)

HF MP2 B3LYP LC-BLYPAE2+ n r (AE-O)a BEb r (AE-O)a BEb r (AE-O)a BEb r (AE-O)a BEb

Mg2+ 1 198 minus255 199 minus260 196 minus300 192 minus3762 195 minus254 196 minus263 194 minus298 191 minus3593 197 minus244 197 minus256 196 minus291 193 minus3524 199 minus229 199 minus249 198 minus275 195 minus3375 204 minus217 204 minus235 203 minus255 199 minus3196 208 minus205 208 minus225 207 minus238 203 minus3047 216 minus165 219 minus190 217 minus200 212 minus2658 No structure was obtained without water (s) in the second solvation shell9

Exp Coord Num r (MgndashO) = 60 204 [4] 60 206 [5] 60 minus [6] Previous theory Coord Num r (MgndashO) = 60 203 [16] 60 212 [17] 80 213 [16]

Ca2+ 1 230 minus198 229 minus214 219 minus285 215 minus3462 234 minus187 233 minus203 224 minus257 220 minus3093 234 minus177 233 minus196 227 minus243 223 minus2964 236 minus176 234 minus195 230 minus230 226 minus2825 238 minus168 236 minus187 232 minus220 228 minus2756 241 minus159 240 minus182 235 minus208 235 minus2607 246 minus147 243 minus170 238 minus191 235 minus2518 252 minus129 247 minus159 245 minus179 241 minus2419 257 minus115 254 minus147 250 minus162 248 minus226

Exp Coord Num r (Ca-O) = 60 242 [7] 80 minus [8] 100 246 [9] Previous theory Coord Num r (Ca-O) = 79 248 [19] 83 245 [18] 92 247 [18]

Sr2+ 1 249 minus167 248 minus192 246 minus180 243 minus2342 252 minus164 251 minus170 250 minus187 246 minus2293 253 minus156 252 minus171 250 minus181 246 minus2224 254 minus152 253 minus166 251 minus177 247 minus2185 257 minus145 256 minus161 254 minus171 252 minus2146 260 minus140 257 minus157 256 minus166 255 minus2097 263 minus131 261 minus150 258 minus156 257 minus2068 265 minus122 264 minus143 267 minus148 258 minus2049 270 minus113 269 minus134 269 minus141 261 minus199

Exp Coord Num r (Sr-O) = 73 262 [13] 103 264 [11] 150 265 [10] Previous theory Coord Num r (Sr-O) = 76 260 [21] 90 269 [22] 97 264 [12] 98 263 [20]

Ba2+ 1 274 minus108 271 minus120 267 minus129 261 minus1692 273 minus108 271 minus116 268 minus129 263 minus1683 274 minus100 272 minus110 268 minus124 263 minus1654 275 minus100 273 minus111 269 minus122 265 minus1615 277 minus97 275 minus111 272 minus121 277 minus1626 280 minus94 277 minus106 276 minus118 272 minus1667 282 minus90 278 minus105 282 minus114 275 minus1628 284 minus86 286 minus105 283 minus112 279 minus1699 288 minus81 294 minus100 289 minus109 276 minus167

Exp Coord Num r (Ba-O) = 78 278 [14] 81 282 [14] 95 290 [15] Previous theory Coord Num r (Ba-O) = 78 282 [14] 93 286 [24]

Ra2+ 1 283 minus106 282 minus115 278 minus123 271 minus1602 279 minus99 278 minus108 276 minus119 270 minus1563 282 minus97 279 minus106 277 minus112 272 minus1554 282 minus91 281 minus100 278 minus111 273 minus1505 286 minus90 284 minus103 281 minus110 276 minus1516 289 minus85 286 minus100 284 minus108 280 minus1547 289 minus79 288 minus99 283 minus106 280 minus1558 291 minus79 291 minus98 293 minus106 288 minus1649 296 minus74 293 minus94 295 minus103 291 minus1608 291 minus79 291 minus98 293 minus106 288 minus1649 296 minus74 293 minus94 295 minus103 291 minus160

a AE-O distances in Aring b Binding energies in kcal molminus1 Zero-point energy (ZPE) corrected values are given

J Comput Chem Jpn Vol 13 No 1 (2014)110

ing ab initio molecular dynamics simulations

33 Differences in hydration character among divalent alkaline earth metal ions

As discussed in the previous section the ΔGsolv values for the

divalent alkaline metal ion series decrease monotonically with

increasing atomic number As shown in Table 2 the differ-

ence mainly originates from the difference in the ΔGcluster term

which is the formation free energy of the hydrated metal ion

cluster This means that the difference in hydration mechanism

among the divalent alkaline metal ions can be well explained

by the difference in chemical interactions between the metal

ions (AE2+) and solvent water molecules in the first hydration

shell In this section we compare the AE2+minuswater interactions

and discuss the physicochemical differences in hydration using

NPA LMO-EDA and NBO results

We found that the magnitudes of decrements in positive

charge on AE2+ are inversely proportional to the atomic num-

bers of the alkaline earth metal ions (See Table S4 in supporting

information) The tendency can be explained by the difference

in the valence electronic structure of AE2+ Figure 2 shows the

LUMO energy levels of bare AE2+ which are s-type orbitals

Figure 2 An orbital energy diagram by LC-BLYP level of the-ory for AE2+ ions (AE = Mg Ca Sr Ba and Ra) and a water molecule

Table 2 Solvation free energies (ΔGsolv in kcal molminus1) of divalent alkaline earth metal ions calculated for [AE (H2O)n]2+ (AE = Mg Ca Sr Ba and Ra) at the LC-BLYP level of theory

Components of ΔGsolva

AE2+ n ΔGsolv ΔGcluster ΔGcont ΔGcav ΔGdisp-rep nΔGvapc

Mg2+ 6 minus4957 minus3360 minus1802 230 minus148 1237 minus4912 minus3375 minus1776 250 minus155 144

Expb minus4555

Ca2+ 6 minus4003 minus2505 minus1728 260 minus152 1237 minus4060 minus2655 minus1672 283 minus158 1448 minus4138 minus2818 minus1624 313 minus174 1649 minus4202 minus2915 minus1611 326 minus186 185

Expb minus3808

Sr2+ 6 minus3469 minus1949 minus1747 255 minus150 1237 minus3572 minus2124 minus1697 275 minus170 1448 minus3705 minus2331 minus1651 297 minus184 1649 minus3792 minus2498 minus1596 321 minus203 185

Expb minus3459

Ba2+ 6 minus3184 minus1686 minus1724 256 minus153 1237 minus3249 minus1824 minus1687 293 minus175 1448 minus3365 minus2035 minus1600 303 minus197 1649 minus3457 minus2200 minus1576 334 minus201 185

Expb minus3151

Ra2+ 6 minus2960 minus1551 minus1670 289 minus151 1237 minus3111 minus1732 minus1643 294 minus173 1448 minus3064 minus1861 minus1538 353 minus182 1649 minus3143 minus1990 minus1530 383 minus190 185

No experimental result

a Obtained in C-PCM calculations See equation (1) b Ref [39] c An experimental value of 205 kcal molminus1 was used (Ref [43])

DOI 102477jccj2013-0011 111

and work as electron accepting orbitals in the hydration pro-

cess The LUMO energy level becomes higher with increases

in the atomic number of AE2+ with the exception between Ba2+

and Ra2+ due to relativistic stabilization of the 7s orbital of

Ra2+ As Mg2+ has the lowest LUMO energy level Mg2+ can be

easily hydrated to form coordination bonds with covalent char-

acter On the contrary as Ba2+ and Ra2+ have very high LUMO

energy levels these ions are expected to form ionic bonds be-

tween the metals and solvent water molecules

The differences in chemical bonding character between the

divalent alkaline earth metal ions and solvent water molecules

could be further confirmed by LMO-EDA The LMO-EDA re-

sults for gas-phase [AE (H2O)1]2+ (AE = Mg Ca Sr Ba and

Ra) are given in Figure 3 Due to the absence of solvent ef-

fects and structural change upon coordination the interaction

energies predicted by the LMO-EDA were much larger than

the binding energies and solvation free energies predicted with

the semi-continuum models (see Tables 1 and 2) Although the

interaction energies were predicted to be larger we observed

similar metal ion dependencies between the interaction ener-

gies and bindingsolvation free energies Thus we used gas-

phase calculation data to provide a detailed understanding of

the chemical bonding character between the divalent alkaline

earth metal ions and solvent water molecules

As shown in Figure 3 the total chemical interaction between

an alkaline earth metal ion and a water molecule becomes

weaker with increases in the atomic number of the alkaline

metal Figure 3 also shows that the dominant component of the

chemical interaction is the electrostatic interaction term (ΔEES)

for all the divalent alkaline earth metal ions We observed that

the ΔEES terms are also inversely proportional to the atomic

number of the alkaline earth metals This can be simply ex-

plained by the charge density on the ion surface As the diam-

eters of Mg Ca Sr Ba and Ra are 160 197 215 217 and

223 Aring respectively [35] their ratio of surface charge density

is 1 066 055 054 051 which well corresponds to the ratio

for the ΔEES terms (723 596 485 430 394 kcal molminus1 = 1

082 067 059 054)

As the electrostatic interactions (ΔEES) between the central

metal ion and water molecules in the first solvation shell are

effectively screened out by solvent water molecules in the outer

solvation shells to analyze the second largest component of the

chemical bonding interaction in the gas-phase is also impor-

tant to understand the chemical hydration character of the metal

ions The LMO-EDA results in Figure 3 show that the ΔEpol

terms which include not only polarization interaction (POL)

but also charge-transfer interaction (CT) terms are the second

largest energy component for chemical bonding between the

divalent alkaline earth metal ions and water molecules Figure

3 also shows that ΔEpol is larger for lighter alkaline earth met-

als However the CT interaction terms were not well separated

from the POL terms in the LMO-EDA scheme reported by Li

et al [44] Thus to clarify the importance of CT interaction

ie covalent interaction in the coordination process we per-

formed second-order perturbation theory analyses of the Fock

matrix in natural bond orbital (NBO) basis [45] Donor-accep-

tor (AE2+-Owater) interaction energies for [AE (H2O)n]2+ (AE =

Mg Ca Sr Ba and Ra n = 1ndash9) obtained by this analysis at

the LC-BLYP level are given in Table 3 We could find larger

donor-acceptor CT interactions in [Mg (H2O)n]2+ On the other

hand we could find no significant CT interaction in [Ba (H2O)

n]2+ and [Ra (H2O)n]2+ In these heavy alkaline earth metal ion

Figure 3 The LMO-EDA results for [AE (H2O)1]2+ (AE = Mg Ca Sr Ba and Ra) at the LC-BLYP level of theory

J Comput Chem Jpn Vol 13 No 1 (2014)112

hydrates CT interactions were predicted to be smaller than

10 kcal molminus1 From the NPA LMO-EDA and NBO results

we concluded that the light divalent alkaline earth metal ions

(Mg2+ Ca2+) form more covalent coordination bonds and the

heavy divalent alkaline earth metal ions (Ba2+ Ra2+) form more

ionic coordination bonds

4 Concluding Remarks

The geometries thermodynamic stabilities and electronic

structures of hydrated divalent alkaline earth metal ions (AE2+

AE = Mg Ca Sr Ba and Ra) were theoretically investigated us-

ing quantum chemical calculations at the HF MP2 B3LYP and

LC-BLYP levels of theory through the application of a relativ-

istic model core potential (MCP) method We observed reason-

able agreement between our results and previous experimental

results for hydrated non-Ra2+ metal ions The heaviest divalent

alkaline earth metal ion the Ra2+ ion the hydration number of

which has not been observed experimentally was predicted to

be in the range of 6ndash9 The solvation free energy of hydrated

Ra2+ was calculated to be ca minus310 kcal molminus1 which was the

weakest among the hydrated divalent alkaline metal ions The

chemical interaction between hydrated Ra2+ and solvent water

molecules mainly consists of electrostatic interaction to form

ionic bonds Unlike the hydration of the light divalent alkaline

earth metal ions (Mg2+ Ca2+) CT interactions ie covalent in-

teractions to form coordination bond do not play an important

role in the hydration of Ra2+

This study was supported by JSPS KAKENHI Grant Number

25810002 and Yamada Science Foundation AM is also grate-

ful to JSPS for the Research Fellowships for Young Scientists

Some of the calculations reported here were performed using

computing resources in the Research Center for Computational

Science Okazaki Japan

References

[1] M P Curie P Curie Comptes Rendus 127 175 (1898) [2] E D Glendening D Feller J Phys Chem 100 4790

(1996) [CrossRef] [3] Y-K Han H Y Jeong J Phys Chem 100 18004

(1996) [CrossRef] [4] R Caminiti G Licheri G Piccaluga G Pinna Chem

Phys Lett 47 275 (1977) [CrossRef] [5] H Ohtaki T Radnai Chem Rev 93 1157 (1993)

[CrossRef] [6] N A Matwiyoff H Taube J Am Chem Soc 90 2796

(1968) [CrossRef] [7] G Licheri G Piccaluga G Pinna J Chem Phys 64

2437 (1976) [CrossRef] [8] A K Katz J P Glusker S A Beebe C W Bock J Am

Chem Soc 118 5752 (1996) [CrossRef] [9] N A Hewish G W Neilson J E Enderby Nature 297

138 (1982) [CrossRef] [10] G W Neilson R D Broadbent Chem Phys Lett 167

429 (1990) [CrossRef] [11] P DrsquoAngelo H Nolting N V Pavel Phys Rev A 53

798 (1996) [Medline] [CrossRef] [12] T Driesner P T Cummings J Chem Phys 111 5141

(1999) [CrossRef] [13] D M Pfund J G Darab J L Fulton Y Ma J Phys

Chem 98 13102 (1994) [CrossRef] [14] P DAngelo N V Pavel D Roccatano H-F Nolting

Phys Rev B 54 12129 (1996) [CrossRef] [15] J N Albright J Chem Phys 56 3783 (1972) [CrossRef] [16] A Tongraar B M Rode Chem Phys Lett 346 485

(2001) [CrossRef]

Table 3 Donor-acceptor (AE2+-Owater) interaction energies for [AE (H2O)n]2+ (AE = Mg Ca Sr Ba and Ra n = 1-9) obtained by second-order perturbation theory analyses of Fock matrix in natural bond orbital (NBO) basis at the LC-BLYP level of theory The averaged energies per a AE2+-Owater bond are given in kcal molminus1

AE2+

n Mg2+ Ca2+ Sr2+ Ba2+ Ra2+

1 130 62 54 32 152 242 78 68 35 183 308 90 81 50 254 399 133 102 61 345 405 152 123 69 416 408 196 146 72 507 367 242 158 83 628 minus 276 159 92 619 minus 279 157 87 62

J Comput Chem Jpn Vol 13 No 1 (2014)110

ing ab initio molecular dynamics simulations

33 Differences in hydration character among divalent alkaline earth metal ions

As discussed in the previous section the ΔGsolv values for the

divalent alkaline metal ion series decrease monotonically with

increasing atomic number As shown in Table 2 the differ-

ence mainly originates from the difference in the ΔGcluster term

which is the formation free energy of the hydrated metal ion

cluster This means that the difference in hydration mechanism

among the divalent alkaline metal ions can be well explained

by the difference in chemical interactions between the metal

ions (AE2+) and solvent water molecules in the first hydration

shell In this section we compare the AE2+minuswater interactions

and discuss the physicochemical differences in hydration using

NPA LMO-EDA and NBO results

We found that the magnitudes of decrements in positive

charge on AE2+ are inversely proportional to the atomic num-

bers of the alkaline earth metal ions (See Table S4 in supporting

information) The tendency can be explained by the difference

in the valence electronic structure of AE2+ Figure 2 shows the

LUMO energy levels of bare AE2+ which are s-type orbitals

Figure 2 An orbital energy diagram by LC-BLYP level of the-ory for AE2+ ions (AE = Mg Ca Sr Ba and Ra) and a water molecule

Table 2 Solvation free energies (ΔGsolv in kcal molminus1) of divalent alkaline earth metal ions calculated for [AE (H2O)n]2+ (AE = Mg Ca Sr Ba and Ra) at the LC-BLYP level of theory

Components of ΔGsolva

AE2+ n ΔGsolv ΔGcluster ΔGcont ΔGcav ΔGdisp-rep nΔGvapc

Mg2+ 6 minus4957 minus3360 minus1802 230 minus148 1237 minus4912 minus3375 minus1776 250 minus155 144

Expb minus4555

Ca2+ 6 minus4003 minus2505 minus1728 260 minus152 1237 minus4060 minus2655 minus1672 283 minus158 1448 minus4138 minus2818 minus1624 313 minus174 1649 minus4202 minus2915 minus1611 326 minus186 185

Expb minus3808

Sr2+ 6 minus3469 minus1949 minus1747 255 minus150 1237 minus3572 minus2124 minus1697 275 minus170 1448 minus3705 minus2331 minus1651 297 minus184 1649 minus3792 minus2498 minus1596 321 minus203 185

Expb minus3459

Ba2+ 6 minus3184 minus1686 minus1724 256 minus153 1237 minus3249 minus1824 minus1687 293 minus175 1448 minus3365 minus2035 minus1600 303 minus197 1649 minus3457 minus2200 minus1576 334 minus201 185

Expb minus3151

Ra2+ 6 minus2960 minus1551 minus1670 289 minus151 1237 minus3111 minus1732 minus1643 294 minus173 1448 minus3064 minus1861 minus1538 353 minus182 1649 minus3143 minus1990 minus1530 383 minus190 185

No experimental result

a Obtained in C-PCM calculations See equation (1) b Ref [39] c An experimental value of 205 kcal molminus1 was used (Ref [43])

DOI 102477jccj2013-0011 111

and work as electron accepting orbitals in the hydration pro-

cess The LUMO energy level becomes higher with increases

in the atomic number of AE2+ with the exception between Ba2+

and Ra2+ due to relativistic stabilization of the 7s orbital of

Ra2+ As Mg2+ has the lowest LUMO energy level Mg2+ can be

easily hydrated to form coordination bonds with covalent char-

acter On the contrary as Ba2+ and Ra2+ have very high LUMO

energy levels these ions are expected to form ionic bonds be-

tween the metals and solvent water molecules

The differences in chemical bonding character between the

divalent alkaline earth metal ions and solvent water molecules

could be further confirmed by LMO-EDA The LMO-EDA re-

sults for gas-phase [AE (H2O)1]2+ (AE = Mg Ca Sr Ba and

Ra) are given in Figure 3 Due to the absence of solvent ef-

fects and structural change upon coordination the interaction

energies predicted by the LMO-EDA were much larger than

the binding energies and solvation free energies predicted with

the semi-continuum models (see Tables 1 and 2) Although the

interaction energies were predicted to be larger we observed

similar metal ion dependencies between the interaction ener-

gies and bindingsolvation free energies Thus we used gas-

phase calculation data to provide a detailed understanding of

the chemical bonding character between the divalent alkaline

earth metal ions and solvent water molecules

As shown in Figure 3 the total chemical interaction between

an alkaline earth metal ion and a water molecule becomes

weaker with increases in the atomic number of the alkaline

metal Figure 3 also shows that the dominant component of the

chemical interaction is the electrostatic interaction term (ΔEES)

for all the divalent alkaline earth metal ions We observed that

the ΔEES terms are also inversely proportional to the atomic

number of the alkaline earth metals This can be simply ex-

plained by the charge density on the ion surface As the diam-

eters of Mg Ca Sr Ba and Ra are 160 197 215 217 and

223 Aring respectively [35] their ratio of surface charge density

is 1 066 055 054 051 which well corresponds to the ratio

for the ΔEES terms (723 596 485 430 394 kcal molminus1 = 1

082 067 059 054)

As the electrostatic interactions (ΔEES) between the central

metal ion and water molecules in the first solvation shell are

effectively screened out by solvent water molecules in the outer

solvation shells to analyze the second largest component of the

chemical bonding interaction in the gas-phase is also impor-

tant to understand the chemical hydration character of the metal

ions The LMO-EDA results in Figure 3 show that the ΔEpol

terms which include not only polarization interaction (POL)

but also charge-transfer interaction (CT) terms are the second

largest energy component for chemical bonding between the

divalent alkaline earth metal ions and water molecules Figure

3 also shows that ΔEpol is larger for lighter alkaline earth met-

als However the CT interaction terms were not well separated

from the POL terms in the LMO-EDA scheme reported by Li

et al [44] Thus to clarify the importance of CT interaction

ie covalent interaction in the coordination process we per-

formed second-order perturbation theory analyses of the Fock

matrix in natural bond orbital (NBO) basis [45] Donor-accep-

tor (AE2+-Owater) interaction energies for [AE (H2O)n]2+ (AE =

Mg Ca Sr Ba and Ra n = 1ndash9) obtained by this analysis at

the LC-BLYP level are given in Table 3 We could find larger

donor-acceptor CT interactions in [Mg (H2O)n]2+ On the other

hand we could find no significant CT interaction in [Ba (H2O)

n]2+ and [Ra (H2O)n]2+ In these heavy alkaline earth metal ion

Figure 3 The LMO-EDA results for [AE (H2O)1]2+ (AE = Mg Ca Sr Ba and Ra) at the LC-BLYP level of theory

J Comput Chem Jpn Vol 13 No 1 (2014)112

hydrates CT interactions were predicted to be smaller than

10 kcal molminus1 From the NPA LMO-EDA and NBO results

we concluded that the light divalent alkaline earth metal ions

(Mg2+ Ca2+) form more covalent coordination bonds and the

heavy divalent alkaline earth metal ions (Ba2+ Ra2+) form more

ionic coordination bonds

4 Concluding Remarks

The geometries thermodynamic stabilities and electronic

structures of hydrated divalent alkaline earth metal ions (AE2+

AE = Mg Ca Sr Ba and Ra) were theoretically investigated us-

ing quantum chemical calculations at the HF MP2 B3LYP and

LC-BLYP levels of theory through the application of a relativ-

istic model core potential (MCP) method We observed reason-

able agreement between our results and previous experimental

results for hydrated non-Ra2+ metal ions The heaviest divalent

alkaline earth metal ion the Ra2+ ion the hydration number of

which has not been observed experimentally was predicted to

be in the range of 6ndash9 The solvation free energy of hydrated

Ra2+ was calculated to be ca minus310 kcal molminus1 which was the

weakest among the hydrated divalent alkaline metal ions The

chemical interaction between hydrated Ra2+ and solvent water

molecules mainly consists of electrostatic interaction to form

ionic bonds Unlike the hydration of the light divalent alkaline

earth metal ions (Mg2+ Ca2+) CT interactions ie covalent in-

teractions to form coordination bond do not play an important

role in the hydration of Ra2+

This study was supported by JSPS KAKENHI Grant Number

25810002 and Yamada Science Foundation AM is also grate-

ful to JSPS for the Research Fellowships for Young Scientists

Some of the calculations reported here were performed using

computing resources in the Research Center for Computational

Science Okazaki Japan

References

[1] M P Curie P Curie Comptes Rendus 127 175 (1898) [2] E D Glendening D Feller J Phys Chem 100 4790

(1996) [CrossRef] [3] Y-K Han H Y Jeong J Phys Chem 100 18004

(1996) [CrossRef] [4] R Caminiti G Licheri G Piccaluga G Pinna Chem

Phys Lett 47 275 (1977) [CrossRef] [5] H Ohtaki T Radnai Chem Rev 93 1157 (1993)

[CrossRef] [6] N A Matwiyoff H Taube J Am Chem Soc 90 2796

(1968) [CrossRef] [7] G Licheri G Piccaluga G Pinna J Chem Phys 64

2437 (1976) [CrossRef] [8] A K Katz J P Glusker S A Beebe C W Bock J Am

Chem Soc 118 5752 (1996) [CrossRef] [9] N A Hewish G W Neilson J E Enderby Nature 297

138 (1982) [CrossRef] [10] G W Neilson R D Broadbent Chem Phys Lett 167

429 (1990) [CrossRef] [11] P DrsquoAngelo H Nolting N V Pavel Phys Rev A 53

798 (1996) [Medline] [CrossRef] [12] T Driesner P T Cummings J Chem Phys 111 5141

(1999) [CrossRef] [13] D M Pfund J G Darab J L Fulton Y Ma J Phys

Chem 98 13102 (1994) [CrossRef] [14] P DAngelo N V Pavel D Roccatano H-F Nolting

Phys Rev B 54 12129 (1996) [CrossRef] [15] J N Albright J Chem Phys 56 3783 (1972) [CrossRef] [16] A Tongraar B M Rode Chem Phys Lett 346 485

(2001) [CrossRef]

Table 3 Donor-acceptor (AE2+-Owater) interaction energies for [AE (H2O)n]2+ (AE = Mg Ca Sr Ba and Ra n = 1-9) obtained by second-order perturbation theory analyses of Fock matrix in natural bond orbital (NBO) basis at the LC-BLYP level of theory The averaged energies per a AE2+-Owater bond are given in kcal molminus1

AE2+

n Mg2+ Ca2+ Sr2+ Ba2+ Ra2+

1 130 62 54 32 152 242 78 68 35 183 308 90 81 50 254 399 133 102 61 345 405 152 123 69 416 408 196 146 72 507 367 242 158 83 628 minus 276 159 92 619 minus 279 157 87 62

DOI 102477jccj2013-0011 111

and work as electron accepting orbitals in the hydration pro-

cess The LUMO energy level becomes higher with increases

in the atomic number of AE2+ with the exception between Ba2+

and Ra2+ due to relativistic stabilization of the 7s orbital of

Ra2+ As Mg2+ has the lowest LUMO energy level Mg2+ can be

easily hydrated to form coordination bonds with covalent char-

acter On the contrary as Ba2+ and Ra2+ have very high LUMO

energy levels these ions are expected to form ionic bonds be-

tween the metals and solvent water molecules

The differences in chemical bonding character between the

divalent alkaline earth metal ions and solvent water molecules

could be further confirmed by LMO-EDA The LMO-EDA re-

sults for gas-phase [AE (H2O)1]2+ (AE = Mg Ca Sr Ba and

Ra) are given in Figure 3 Due to the absence of solvent ef-

fects and structural change upon coordination the interaction

energies predicted by the LMO-EDA were much larger than

the binding energies and solvation free energies predicted with

the semi-continuum models (see Tables 1 and 2) Although the

interaction energies were predicted to be larger we observed

similar metal ion dependencies between the interaction ener-

gies and bindingsolvation free energies Thus we used gas-

phase calculation data to provide a detailed understanding of

the chemical bonding character between the divalent alkaline

earth metal ions and solvent water molecules

As shown in Figure 3 the total chemical interaction between

an alkaline earth metal ion and a water molecule becomes

weaker with increases in the atomic number of the alkaline

metal Figure 3 also shows that the dominant component of the

chemical interaction is the electrostatic interaction term (ΔEES)

for all the divalent alkaline earth metal ions We observed that

the ΔEES terms are also inversely proportional to the atomic

number of the alkaline earth metals This can be simply ex-

plained by the charge density on the ion surface As the diam-

eters of Mg Ca Sr Ba and Ra are 160 197 215 217 and

223 Aring respectively [35] their ratio of surface charge density

is 1 066 055 054 051 which well corresponds to the ratio

for the ΔEES terms (723 596 485 430 394 kcal molminus1 = 1

082 067 059 054)

As the electrostatic interactions (ΔEES) between the central

metal ion and water molecules in the first solvation shell are

effectively screened out by solvent water molecules in the outer

solvation shells to analyze the second largest component of the

chemical bonding interaction in the gas-phase is also impor-

tant to understand the chemical hydration character of the metal

ions The LMO-EDA results in Figure 3 show that the ΔEpol

terms which include not only polarization interaction (POL)

but also charge-transfer interaction (CT) terms are the second

largest energy component for chemical bonding between the

divalent alkaline earth metal ions and water molecules Figure

3 also shows that ΔEpol is larger for lighter alkaline earth met-

als However the CT interaction terms were not well separated

from the POL terms in the LMO-EDA scheme reported by Li

et al [44] Thus to clarify the importance of CT interaction

ie covalent interaction in the coordination process we per-

formed second-order perturbation theory analyses of the Fock

matrix in natural bond orbital (NBO) basis [45] Donor-accep-

tor (AE2+-Owater) interaction energies for [AE (H2O)n]2+ (AE =

Mg Ca Sr Ba and Ra n = 1ndash9) obtained by this analysis at

the LC-BLYP level are given in Table 3 We could find larger

donor-acceptor CT interactions in [Mg (H2O)n]2+ On the other

hand we could find no significant CT interaction in [Ba (H2O)

n]2+ and [Ra (H2O)n]2+ In these heavy alkaline earth metal ion

Figure 3 The LMO-EDA results for [AE (H2O)1]2+ (AE = Mg Ca Sr Ba and Ra) at the LC-BLYP level of theory

J Comput Chem Jpn Vol 13 No 1 (2014)112

hydrates CT interactions were predicted to be smaller than

10 kcal molminus1 From the NPA LMO-EDA and NBO results

we concluded that the light divalent alkaline earth metal ions

(Mg2+ Ca2+) form more covalent coordination bonds and the

heavy divalent alkaline earth metal ions (Ba2+ Ra2+) form more

ionic coordination bonds

4 Concluding Remarks

The geometries thermodynamic stabilities and electronic

structures of hydrated divalent alkaline earth metal ions (AE2+

AE = Mg Ca Sr Ba and Ra) were theoretically investigated us-

ing quantum chemical calculations at the HF MP2 B3LYP and

LC-BLYP levels of theory through the application of a relativ-

istic model core potential (MCP) method We observed reason-

able agreement between our results and previous experimental

results for hydrated non-Ra2+ metal ions The heaviest divalent

alkaline earth metal ion the Ra2+ ion the hydration number of

which has not been observed experimentally was predicted to

be in the range of 6ndash9 The solvation free energy of hydrated

Ra2+ was calculated to be ca minus310 kcal molminus1 which was the

weakest among the hydrated divalent alkaline metal ions The

chemical interaction between hydrated Ra2+ and solvent water

molecules mainly consists of electrostatic interaction to form

ionic bonds Unlike the hydration of the light divalent alkaline

earth metal ions (Mg2+ Ca2+) CT interactions ie covalent in-

teractions to form coordination bond do not play an important

role in the hydration of Ra2+

This study was supported by JSPS KAKENHI Grant Number

25810002 and Yamada Science Foundation AM is also grate-

ful to JSPS for the Research Fellowships for Young Scientists

Some of the calculations reported here were performed using

computing resources in the Research Center for Computational

Science Okazaki Japan

References

[1] M P Curie P Curie Comptes Rendus 127 175 (1898) [2] E D Glendening D Feller J Phys Chem 100 4790

(1996) [CrossRef] [3] Y-K Han H Y Jeong J Phys Chem 100 18004

(1996) [CrossRef] [4] R Caminiti G Licheri G Piccaluga G Pinna Chem

Phys Lett 47 275 (1977) [CrossRef] [5] H Ohtaki T Radnai Chem Rev 93 1157 (1993)

[CrossRef] [6] N A Matwiyoff H Taube J Am Chem Soc 90 2796

(1968) [CrossRef] [7] G Licheri G Piccaluga G Pinna J Chem Phys 64

2437 (1976) [CrossRef] [8] A K Katz J P Glusker S A Beebe C W Bock J Am

Chem Soc 118 5752 (1996) [CrossRef] [9] N A Hewish G W Neilson J E Enderby Nature 297

138 (1982) [CrossRef] [10] G W Neilson R D Broadbent Chem Phys Lett 167

429 (1990) [CrossRef] [11] P DrsquoAngelo H Nolting N V Pavel Phys Rev A 53

798 (1996) [Medline] [CrossRef] [12] T Driesner P T Cummings J Chem Phys 111 5141

(1999) [CrossRef] [13] D M Pfund J G Darab J L Fulton Y Ma J Phys

Chem 98 13102 (1994) [CrossRef] [14] P DAngelo N V Pavel D Roccatano H-F Nolting

Phys Rev B 54 12129 (1996) [CrossRef] [15] J N Albright J Chem Phys 56 3783 (1972) [CrossRef] [16] A Tongraar B M Rode Chem Phys Lett 346 485

(2001) [CrossRef]

Table 3 Donor-acceptor (AE2+-Owater) interaction energies for [AE (H2O)n]2+ (AE = Mg Ca Sr Ba and Ra n = 1-9) obtained by second-order perturbation theory analyses of Fock matrix in natural bond orbital (NBO) basis at the LC-BLYP level of theory The averaged energies per a AE2+-Owater bond are given in kcal molminus1

AE2+

n Mg2+ Ca2+ Sr2+ Ba2+ Ra2+

1 130 62 54 32 152 242 78 68 35 183 308 90 81 50 254 399 133 102 61 345 405 152 123 69 416 408 196 146 72 507 367 242 158 83 628 minus 276 159 92 619 minus 279 157 87 62

J Comput Chem Jpn Vol 13 No 1 (2014)112

hydrates CT interactions were predicted to be smaller than

10 kcal molminus1 From the NPA LMO-EDA and NBO results

we concluded that the light divalent alkaline earth metal ions

(Mg2+ Ca2+) form more covalent coordination bonds and the

heavy divalent alkaline earth metal ions (Ba2+ Ra2+) form more

ionic coordination bonds

4 Concluding Remarks

The geometries thermodynamic stabilities and electronic

structures of hydrated divalent alkaline earth metal ions (AE2+

AE = Mg Ca Sr Ba and Ra) were theoretically investigated us-

ing quantum chemical calculations at the HF MP2 B3LYP and

LC-BLYP levels of theory through the application of a relativ-

istic model core potential (MCP) method We observed reason-

able agreement between our results and previous experimental

results for hydrated non-Ra2+ metal ions The heaviest divalent

alkaline earth metal ion the Ra2+ ion the hydration number of

which has not been observed experimentally was predicted to

be in the range of 6ndash9 The solvation free energy of hydrated

Ra2+ was calculated to be ca minus310 kcal molminus1 which was the

weakest among the hydrated divalent alkaline metal ions The

chemical interaction between hydrated Ra2+ and solvent water

molecules mainly consists of electrostatic interaction to form

ionic bonds Unlike the hydration of the light divalent alkaline

earth metal ions (Mg2+ Ca2+) CT interactions ie covalent in-

teractions to form coordination bond do not play an important

role in the hydration of Ra2+

This study was supported by JSPS KAKENHI Grant Number

25810002 and Yamada Science Foundation AM is also grate-

ful to JSPS for the Research Fellowships for Young Scientists

Some of the calculations reported here were performed using

computing resources in the Research Center for Computational

Science Okazaki Japan

References

[1] M P Curie P Curie Comptes Rendus 127 175 (1898) [2] E D Glendening D Feller J Phys Chem 100 4790

(1996) [CrossRef] [3] Y-K Han H Y Jeong J Phys Chem 100 18004

(1996) [CrossRef] [4] R Caminiti G Licheri G Piccaluga G Pinna Chem

Phys Lett 47 275 (1977) [CrossRef] [5] H Ohtaki T Radnai Chem Rev 93 1157 (1993)

[CrossRef] [6] N A Matwiyoff H Taube J Am Chem Soc 90 2796

(1968) [CrossRef] [7] G Licheri G Piccaluga G Pinna J Chem Phys 64

2437 (1976) [CrossRef] [8] A K Katz J P Glusker S A Beebe C W Bock J Am

Chem Soc 118 5752 (1996) [CrossRef] [9] N A Hewish G W Neilson J E Enderby Nature 297

138 (1982) [CrossRef] [10] G W Neilson R D Broadbent Chem Phys Lett 167

429 (1990) [CrossRef] [11] P DrsquoAngelo H Nolting N V Pavel Phys Rev A 53

798 (1996) [Medline] [CrossRef] [12] T Driesner P T Cummings J Chem Phys 111 5141

(1999) [CrossRef] [13] D M Pfund J G Darab J L Fulton Y Ma J Phys

Chem 98 13102 (1994) [CrossRef] [14] P DAngelo N V Pavel D Roccatano H-F Nolting

Phys Rev B 54 12129 (1996) [CrossRef] [15] J N Albright J Chem Phys 56 3783 (1972) [CrossRef] [16] A Tongraar B M Rode Chem Phys Lett 346 485

(2001) [CrossRef]

Table 3 Donor-acceptor (AE2+-Owater) interaction energies for [AE (H2O)n]2+ (AE = Mg Ca Sr Ba and Ra n = 1-9) obtained by second-order perturbation theory analyses of Fock matrix in natural bond orbital (NBO) basis at the LC-BLYP level of theory The averaged energies per a AE2+-Owater bond are given in kcal molminus1

AE2+

n Mg2+ Ca2+ Sr2+ Ba2+ Ra2+

1 130 62 54 32 152 242 78 68 35 183 308 90 81 50 254 399 133 102 61 345 405 152 123 69 416 408 196 146 72 507 367 242 158 83 628 minus 276 159 92 619 minus 279 157 87 62

DOI 102477jccj2013-0011 113

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[18] A Tongraar K R Liedl B M Rode J Phys Chem A 101 6299 (1997) [CrossRef]

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[24] T S Hofer B M Rode B R Randolf Chem Phys 312 81 (2005) [CrossRef]

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200910 software available from Chemical Comput-ing Group Inc 1010 Sherbrooke Street West Suite 910 Montreal Canada H3A 2R7 httpwwwchemcompcom

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