ab initio investigation on the ion-associated species and process in mg(no3)2 solution

Ab Initio Investigation on the Ion-Associated Species

and Process in Mg(NO3)2 Solution

HAO ZHANG,1,2 YUN-HONG ZHANG1

1The Institute for Chemical Physics, Beijing Institute of Technology, Beijing 100081,People’s Republic of China

2State Key Laboratory of Theoretical and Computational Chemistry, Institute of TheoreticalChemistry, Jilin University, Changchun 130023, People’s Republic of China

Received 2 October 2009; Revised 18 March 2010; Accepted 29 March 2010DOI 10.1002/jcc.21570

Published online 31 May 2010 in Wiley Online Library (wileyonlinelibrary.com).

Abstract: In the present article, two focal subjects, i.e., hydration of the NO�3 and associated ion species in the

Mg(NO3)2 solution are researched by using the ab initio method. Nitrate ions with the hydration number of 1–6 are

optimized at the HF/6-311G* level. Their relative energies, binding energies, and v1-NO�3 frequencies are also pre-

sented. The investigation of the binding energies shows the hydration number is 3–6 in the solvent abundant envi-

ronment. The associated species, including ion pairings, triple- and multiple-ion clusters, are also optimized at the

same level and their v1-NO�3 frequencies are calculated for comparing with the results in experiments. From the

comparison, the new associated process via aqueous free ions ? solvent-shared ion pairings ? solvent-shared triple

and multiple ion clusters ? contact multiple ion clusters ? amorphous crystal is proposed.

q 2010 Wiley Periodicals, Inc. J Comput Chem 31: 2772–2782, 2010

Key words: magnesium nitrate; hydrated nitrate; ion-associated species; associated process

Introduction

In the studies of the aqueous oxysalt solutions, the Mg(NO3)2 is

a significant one since both magnesium and nitrate ions are im-

portant in the experimental and theoretical fields. The NO�3 can

be produced from the reactions between the mineral dusts and

sea salt particles with nitrogen oxides such as NO2, NO3, N2O5,

and HNO3 at various relative humidity (RH).1–8 It is well known

that the nitrogen oxides are important species in the atmospheric

pollution. Especially the aerosol particles containing the nitrates

are significant for both direct and indirect climate forcing

depend on their properties.9–12 On the other hand, the Mg21 is

the most abundant cation after Na1 in seawater. It has very high

binding energy and thus can form the stable octahedral hexahy-

drated structure, which is suitable as a theoretical model for

calculation. Moreover, Mg21 has a strong influence on nearby

water and nitrate so as to lead to more remarkable frequency

shifts observable in the vibrational spectrum.

There are two interesting subjects in the studies of the

Mg(NO3)2 solutions. One is hydration of the nitrate ion, the

other is the existence and structure of the ion-associated species.

Hydration of the nitrate ion has been a basic subject for

investigation by chemists. Irish and coworkers reported their

research on nitrates containing alkali metal cations, especially

LiNO3 and NaNO3.13–18 They found the vibrational spectrum of

the unperturbed nitrate solutions contained a pair of closely

spaced lines in place of the single v3-mode (1384 cm21).13 Vari-

ous arguments supported that this loss of degeneracy must be

attributed to a nitrate ion-water interaction. Narcisi measured the

rocket-borne mass-spectrometer and indicated that at altitudes

below 90 km NO�3 (H2O)n (n is up to 5) is the dominant ion.19

In subsequent report by Arnold et al., they suggested NO�3 as

the core ion in various clusters has higher degrees of hydration

at the altitudes of 33–37 km.20,21 On the other hand, Caminiti

et al. investigated the hydrated structure of ions in NaNO3 solu-

tion of 5–7 mol dm23 by using the X-Ray diffraction tech-

nique.22 Their results show the number of water molecules in

the first hydrated shell of NO�3 is 3–6 in the solution while the

neutron scattering studies gives 5, accurately by Kameda et al.23

Although the hydration number of NO�3 can be obtained by the

experimental means, the structures and energies of NO�3 with

different degree of hydration in those works can hardly be meas-

ured. However, with help of calculation in theoretical chemistry

those questions can be solved easily.

The correlative calculations with nitrate hydration have been

presented for some years.24–26 Nevertheless, the number of

Contract/grant sponsor: NSFC; contract/grant numbers: 20933001,

20873006

Correspondence to: Y.-H. Zhang; e-mail: [email protected]

q 2010 Wiley Periodicals, Inc.

hydration is only 1–3 in their reports, while it is 3–6 even in

very concentrated solution.22 Thus, the calculations above can

only provide the foundational theoretical models of hydrated ni-

trate but can not explain the experimental phenomena quantifica-

tionally. In this article, we optimize the nitrate clusters with 1–6

hydrated water molecules to obtain their geometries, relative

energies, binding energies, and vibrational frequencies and com-

pare the results with those in experiments.

The ion-associated species such as ion pairs are another inter-

esting subject. The common techniques to detect the species in

earlier studies are conductivity and ultrasonic relaxation meas-

urements. Eigen and Tamm established the equilibrium equa-

tions from free aqueous ions to contact ion pairings in solutions

by using ultrasonic relaxation techniques.27,28 The ion associa-

tion model was represented as follow:

Mmþ ðaqÞ þ Ln�ðaqÞfree ions

!K1 ½Mmþ ðOH2ÞðOH2Þ2SIP

Ln��ðaqÞ

!K2 ½Mmþ ðOH2ÞSIP

Ln��ðaqÞ !K3 ½ML�ðm�nÞþðaqÞCIP

in which 2SIP, SIP, and CIP denote double solvent separated

(outer-outer-sphere) ion pairings, solvent-shared (outer-sphere)

ion pairings, and contact (inner-sphere) ion pairings.28

The vibrational spectroscopy is also an effective technique to

investigate the associated species in nitrate solutions and many

reports were presented.15,29–40 However, there is no consistent

opinion for the existence and structure of the associated species.

Peleg observed the Raman spectra of Mg(NO3)2–H2O system in

various concentrations and phase states.30 They divided the pro-

cess with decreased water-to-solute molar ratio (WSR) into five

regions and predicted the possible ion clusters (including the

associated species) in the different regions. Chang and Irish

investigated the same system by using the Infrared and Raman

spectroscopies.15 They proposed the mono- and bi-dentate CIPs

for the first time and thought the SIPs exist with the WSR of

42–11 while the CIPs exist with WSR \6. The CIPs will trans-

form from the mono- to bi-dentate structures with the decrease

of water.

Both Peleg and Chang considered that the CIPs would not

exist in the Mg(NO3)2 solution where the WSR is more than 6,

but James et al. doubt that viewpoint.31 They did some research

for the v1-NO�3 band in Raman spectra by using the Fourier

transformation and band component analysis. Their conclusion is

there should be an abundance of CIPs in the 4 mol dm23 (WSR

5 11) Mg(NO3)2 solution. On the other hand, Chang and Irish

thought the formation of the mono-dentate CIP would lead to a

v1-NO�3 band red-shift. However, James et al. attributed the

1052.5 cm21 component, which is on the high frequency side of

the v1-NO�3 band, to the mono-dentate CIP.

The concentrations of the Mg(NO3)2 solution investigated in

these researches were not very high for the limitation of the sat-

uration. Thus, the populations of the ion-associated species were

too low to carry out the quantitative research. Nevertheless, the

confocal Raman spectroscopy for the individual Mg(NO3)2 par-

ticles deposited on a quartz substrate is an available technique to

observe the supersaturated droplet, where the associated species

may exist largely. By studying the v1-NO�3 band, which is sensi-

tive to the formation of the associated species, the results can be

obtained as follows41: (i) The v1-NO�3 band is blue-shifted with

the decreased WSR. (ii) The curve of v1-NO�3 frequency vs.

WSR is divided into three parts by two transition points (WSR

5 18 and WSR 5 6). When the WSR is more than 18, the v1-NO�3 frequency slightly increases; it shows a substantial increase

in region where the WSR is 18–6; and when WSR is less than

6, v1-NO�3 frequency steeply ascends upon the slight decline of

WSR. (iii) When the WSR 5 6, the droplet will crystallize into

Mg(NO3)2�6H2O sometimes, or survive in the solution phase

until the formations of the amorphous states with quasi-lattice

structures, while the WSR decreases to about 5. In the report

mentioned above, the varieties in the three regions were attrib-

uted to the formations of the free ions, SIPs, and CIPs, respec-

tively. However, these conclusions are rough and not very exact

for the further studies.

In this article, the aqueous NO�3 , ion pairing (IP), triple ion

(TI), and multiple ion (MI) clusters in the Mg(NO3)2 solution

were calculated by using the ab initio method. The relationship

between the formations of the different associated species and

the variational band observed in the Raman spectra was

explained. Further more, the new associated mechanism was

presented.

Computational Methodology

All geometries were optimized at HF/6-311G* level by using

the GAUSSIAN98 program package. The similar method has

been employed in several solution systems containing magne-

sium ion22,25,42–44 and been confirmed to be reliable in this type

of system. Especially, the calculated frequencies at this level

were in good agreement with those acquired in experiments after

multiplying a scaling factor. The harmonic vibrational frequency

and zero-point energy (ZPE) corrections were carried out at the

same level. The minima optimized in our calculations possessed

all real frequencies.

Results and Discussions

Hydrated Nitrate

Geometries and Energies

The aqueous nitrates with 1–6 inner-sphere water molecules

were optimized. We found the filled inner-sphere of NO�3 has 3–

6 water molecules, which is in good accordance to Caminiti’s

result. Our optimized geometries are all shown in Figure 1.

Their HF energies, relative energies, binding energies, and v1-NO�3 frequencies are listed in Table 1.

For the existence of delocalizing p-conjugation in NO�3 and

few electrons in it can be localized when the NO�3 H-bonding

with H2Os,45 only non-bonding lone pairs on the O-atoms can

be involved in the H-bonds. Thus, one O-atom in NO�3 can form

one or two in-plane H-bonds with H2Os. From Figure 1, when

only one water molecule is bound with a NO�3 , there are two

contact modes between them. In the first mode, they form a

2773The Calculated Ion-associated Species in Mg(NO3)2 Solution

Journal of Computational Chemistry DOI 10.1002/jcc

Figure 1. The geometries of the hydrated NO�3 with 0–6 inner-sphere water molecules.

2774 Zhang and Zhang • Vol. 31, No. 15 • Journal of Computational Chemistry


trans- structure with the Cs symmetry (as shown as 1b in Figure

1, abbreviated to ‘‘T’’ in the next sections) with one H-atom in

H2O hydrogen-bonding to one O-atom in NO�3 . The second

mode includes two hydrogen-bonds between the H2O and NO�3to form the cis- structure, where the C2v symmetry is kept (as

shown as 1a, abbreviated to ‘‘C’’).

Both in the C and T structures, the hydrogen bonds will

break the D3h symmetries in the nitrate ions and lengthen the

N��O distances. In the C structure, the N��O distances involved

in hydrogen bonds are both 1.231 A, while the free N��O dis-

tance is 1.218 A (The value is 1.227 A in the isolated NO�3 with

the D3h symmetry).

When the hydration number is 2 and 3, the added water mol-

ecules are filled in the inner-sphere of NO�3 with C or T struc-

ture mainly. In next part of discussion, we can denote the aque-

ous nitrates with different structure as mC1nT (m,n 5 0–3).

From the relative energies listed in Table 1, we can see the C

structure has lower energy than the T structure with all hydra-

tion numbers. Thus, the H2Os favor to bind with the NO�3 as C

structures until the hydration number is up to 3, which is shown

as 3a in Figure 1. In this structure, the inner-sphere of the NO�3is filled and the six lone pairs are all involved in the hydrogen

bonds. Figure 2 shows the dependence of the relative energies

on the number of T-type water molecules for the hydration num-

bers. There are linear correspondences in these three dependen-

ces. From the slopes of the three lines, we can deduce the

energy difference between C and T structure is decreasing with

the increase of the hydration number resulted by the stereo-

hindrance effect. When the hydration number is 1, 2 and 3, the

different values are 2.153 kcal/mol, 1.882 kcal/mol, and 1.701

kcal/mol, respectively.

When the hydration number is 3–6, the water molecules can

also be filled in the inner-sphere of the NO�3 . But their hydratedstructure will change. There are two water molecules between

the two O-atoms of NO�3 to form the double-hydrated structure

as shown as 4b in Figure 1. The water molecules are bound

with the NO�3 by only one hydrogen bonding. At the same time,

an additional H-bonding forms between the two water mole-

cules. One of the two water molecules is in-plane with the NO�3and another one is obviously off-plane. The dihedral angle, for

example, in the structure of 4a, is 87.478 between the off-planar

water molecule and the NO�3 plane. The two O. . .O distances in

the hydrogen bonds of H2O-NO�3 are 2.879 and 3.091 A, respec-

tively, while the one of H2O-H2O is 3.002 A. This structure of

double-hydration is denoted ‘‘D’’ in the next discussion. Thus,

the structure of 4b can be represented as D 1 2C, as well as D

1 C 1 T of 4c, and so on. In all D structures, the hydrogen

bond between the NO�3 and the off-planar water molecule is

always stronger than the in-planar one (known from the O��Odistances in the two hydrogen bonds). In addition, its O��O dis-

tances are in the middle of C and T structures. Therefore, the

order of the three kinds of hydrogen bonds affecting to the NO�3should be T[ D[ C.

When the hydration number increases to 6, the inner-sphere

water molecule reaches its maximum to form the 3D structure

(as shown as 6 in Fig. 1). More water molecules can only be

added in the second sphere of the NO�3 or be inserted in the two

water molecules in D structure (this also added in the second

sphere).

From the binding energies listed in Table 1, we can see the

binding energy is also decreasing with increasing hydration

number, which is shown in Figure 3. The curve of binding

energy vs. hydration number can be divided into two regions.

When the hydration number is less than 3, the binding energy of

the cluster is relatively high and it decreases slowly with linear

correspondence to the hydration number. However, when the

Table 1. The Calculated Hatree-Fock Energies (HFE), Relative Energies

(RE, the Isomer with the Lowest Energy among those which have the

same hydrated number is Set to be the Zero Point), Binding Energies

(BE, also the Isomer with the Lowest Energy is Used to Calculate the

BE), and the v1-NO�3 Frequencies (fv1) of the Hydrated NO�3 Clusters.

Species HFE RE BE fv1

0 2278.922267 0 12.502 1237.0

1a 2354.937019 0 11.121 1237.5

1b 2354.933588 2.153 1241.3

2a 2430.949571 0 10.023 1239.5

2b 2430.946551 1.895 1244.9

2c 2430.943573 3.764 1246.3

3a 2506.960373 0 7.03 1242.6

3b 2506.952207 5.124 1253.2

3c 2506.957494 1.807 1243.4

3d 2506.95481 3.491 1246.9

4a 2582.963922 1.558 1247.1

4b 2582.966405 0 6.906 1247.3

4c 2582.963665 0.161 1250.4

5a 2658.97224 0 6.643 1251.6

5b 2658.969981 1.418 1252.2

6 2734.977655 0 1258.2

In the table, the HFE is in a. u., the RE and BE are in kcal and the fv1 isin cm21. The species of ‘‘0’’ denotes the isolated NO�3

Figure 2. The dependences of relative energy on the number of C

structures of the NO�3 with hydrated number of 1–3. In the figure,

squares denote the hydrated number is 1, circles denote 2, and

triangles denote 3.



hydration number is more than 3, the inner-sphere is filled, and

the binding energy decreases rapidly to show a stage. After the

stage, the curve keeps decreasing gently with also linear corre-

spondence. The dependence indicates both hydration and dehy-

dration are easy when the hydration number is 3–6 so that these

clusters may be observed together in the spectra. Nevertheless,

when the hydration number is less than 3, the clusters are too

hard for dehydration to be observed in the abundant water envi-

ronment. These calculated results are consistent with those

reported by Caminiti.22

Vibrational Frequency

In the investigation of the hydration, the effect of the hydrated

water to the v1-NO�3 band is an important subject. Until present,

there is no consistent understanding on this effect. From the

investigation of ion pairing, some researchers predicted the bind-

ing of water can increase the effective mass of the O-atom in

NO�3 and thus induces the v1-NO�3 band red shift. The ion pair-

ing can break the hydrogen bonding structure to lead to the blue

shift as observed in the concentrating solution.29

The v1-frequencies from our calculations are also listed in

Table 1. From these data, we know the v1-frequency is blue

shifted with the increasing hydration number, which is contrary

to the prediction above.

Figure 4 shows the dependence of the v1-frequency on the

hydration number. In Figure 4, circles and triangles denote the

NO�3 with 1–3 hydrated water molecules bound as C and T

structures. The crosses denote the NO�3 containing the D struc-

tures in the structures with 4–6 hydrated water molecules (if

there are isomeric compounds, the one with the lowest energy is

selected). These three kinds of points have the linear corre-

spondences with the hydration number, respectively. Further-

more, we can deduce that when a water molecule is added in C,

T, and D structures, the v1-NO�3 frequencies increases for 2.55,

5.95, and 5.55 cm21, respectively. The order of hydrated effect

to the v1-NO�3 frequency is T [ D [ C, which is in accordance

to that of the hydrogen bonding intensity. This result indicates

the shift of the v1-NO�3 band is determined by the hydrogen

bonding intensity.

Aqueous Ion-Associated Species and the Effects

to the v1-NO�3 Band

For understanding the relation of spectral varieties with increas-

ing concentration to the formations of the associated species, we

optimized several types of aqueous clusters and calculated their

vibrational frequencies.

Ion Pairing

The foundational theoretical models of ion pairings (IP) opti-

mized are shown in Figure 5 including two SIPs (S1 and S2),

the monodentate CIP (MC), and bidentate CIP (BC). The mod-

els contain only the inner-sphere water molecules of Mg21.

There are two typical SIPs as shown as S1 and S2. The differ-

ence between them is the Mg��N is in the NO�3 plane in the S1

structure and vertical to that in the S2. Despite environmental

influence, the energy of S2 is 1.273 kcal/mol higher than the

energy of S1. However, the cross section of the NO�3 contacted

with the environment in S1 is larger than that in S2, so that the

NO�3 is easier to be disassociated from S1 via impact by the

other H2Os. Thus, both two SIPs would exist in the actual solu-

tion with almost same populations for the little energy difference

in thermodynamics, while the S2 have longer survival time in

dynamics. Therefore, the S2 might be more observed in

experiments.

We also optimized two CIPs (MC and BC as shown in Fig.

5). In the MC, the NO�3 replaces one water molecule in the hex-

ahydrated Mg21. One O-atom in the NO�3 bonds directly with

the Mg21, the other one hydrogen-bonds with two water mole-

cules simultaneously, and the last one is unrelated to the hexa-

hydrated Mg21. In the BC, the NO�3 is chelated to Mg21 by

replacing two hydrated water molecules. Two O-atoms bond

Figure 3. The dependence of binding energy on the hydrated num-

ber of the aqueous NO�3 .

Figure 4. The dependence of calculated v1-NO�3 frequency on the

hydrated number of the aqueous NO�3 .



directly to Mg21 and the other one is not hydrogen bonding

with the hexahydrated Mg21.

From previous reports, the CIPs were predicted to form and

the obvious blue shift of the v1-NO�3 band was attributed to

them, when the WSR was less than 6. However, the calculated

v1-NO�3 frequencies in all ion pairings (as listed in Table 2) are

lower than that in the isolated NO�3 except for the S2. The fre-

quencies are 1207.6 cm21 in S1, 1245.8 cm21 in S2, 1214.8

cm21 in MC, 1181.2 cm21 in BC, and 1237.0 cm21 in isolated

NO�3 . It is opposite to the blue shifts observed in experiments

but consistent with the point of Chang and Irish.15

For confirming the contact effect of Mg21 with NO�3 to the

v1-NO�3 band, we removed all water molecules in the BC and

obtained the equilibrium geometry of UBC (unhydrated BC) as

Figure 5. The geometries of the optimized ion pairings (IP).



shown in Figure 5. The frequency of the UBC (1117.3 cm21) is

lower than both BC and isolated NO�3 , which indicates simple

contact of Mg21 and NO�3 leads the v1-NO�3 band red shift and

the polarized water by Mg21 can make it blue shift. We try to

explain the red shift via the point of Hester et al. They have an-

alyzed the effects of metal cation to the vibrational frequencies

of NO�3 in the CIPs. They considered the effects can be divided

into polarization and the M��O bonding, which lead the v1-NO�3

band red shift and blue shift, respectively.46,47 In the magnesium

nitrate system, the polarization of Mg21 is dominated and thus

makes the red shift more remarkable. On the other hand, the

blue shift introduced by hydrated water referred above can be

confirmed again. In the four ion pairings, S2 has three hydrogen

bonds between the NO�3 and the hydrated water molecules, MC

and S1 have two while BC has no one. The order of the H-

bonding numbers is in accordance with that of the v1-frequency(fS2 [ fMC [ fS1 [ fBC). The result shows that more H-bonds

can lead larger blue shift. Combining the results here and those

obtained in the section on ‘‘hydrated nitrate,’’ we can conclude

the water (or the H-bonding) can lead to the v1-NO�3 band blue

shift both in hydrated nitrates and in ion pairings. And it is

more remarkable in the ion pairings due to the polarization of

the water by the Mg21.

The v1-frequency of S2 is 8.8 cm21 higher than that of the

isolated NO�3 . The value is some higher than that observed in

experiment (In the Raman spectroscopy for the individual

Mg(NO3)2 particle, v1-NO�3 band shifts from 1048.0 to 1051.7

cm21, i.e., only 3.7 cm21).41 However, the NO�3 forms only

three hydrogen bonds in the S2, while the maximum is 6. That

is, the S2 can bind with three more water molecules in the sol-

vent abundant environment. Therefore, we optimized the S20

structure as shown in Figure 5 (S2 1 3H2O). In the structure,

the six lone pairs in the NO�3 are all involved in the hydrogen

bonds. It is reasonable to compare the blue shift in experiment

and that from NO�3 with 3–6 hydrated water molecules to S20.The v1-NO

�3 frequency of S20 is 9.4 cm21 higher than that of

trihydrated NO�3 , 4.7 cm21, of tetrahydrated NO�3 , 0.4 cm21, of

pentahydrated NO�3 , 6.2 cm21 and lower than that of hexahy-

drated NO�3 . We can predict from the values that the slight blue

shift (less than 3.7 cm21) between the WSR of 18.0–6.0 in

experiment might be attributed to the formation of the S20. We

can even deduce that the hydration number of NO�3 in extremely

diluted solution is 4–5. It is very consistent with the neutron

scattering results.23

Triple Ion (TI) and Multiple Ion (MI) Clusters

As mention above, there are nine water molecules in the S20.And there is also another NO�3 with 3–6 water molecules

because the stoichiometric ratio of Mg21: NO�3 is 1:2 in the so-

lution. Thus, the minimum of the WSR is 15–12 when the S20 isdominated in the solution. When the WSR is less than 12, the

vacant site will emerge on the inner-sphere of Mg21 or NO�3 . Ifit is between the two ions, the S20 will transfer to the CIP. In

contrast, if it is on the end of the S20, the third aqueous ion will

occupy the vacant site to form the TI, even the further MI. The

two trends are competitive in the further dehydrating process of

S20. In the previous reports, the large blue shift was attributed to

the formations of CIPs at WSR \ 6. However, our calculations

indicated the v1-NO�3 band would red-shift when whichever CIP

formed. Although the calculations on the HF/6-311G* level is

not enough to explain the experimental results quantificationally,

they are still available in qualitative studies, such as the shifted

trend of the vibrational bands. Thus, we consider the blue shift

in experiment should not attribute to the formations of the CIPs

but the TIs or MIs. The TIs and MIs optimized by us are shown

in Figure 6, and their calculated v1-frequencies are listed in

Table 3.

The TIs are divided into two categories, the first one contains

one aqueous Mg21 and two NO�3 (as shown as 1–10 in Fig. 6),

and the second one contains one NO�3 and two Mg21 (as shown

as 11–16). The former can be further divided into SIP-SIP (1–

2), MC-MC (3–6), MC-BC (7–8), and BC-BC (9–10) based on

the different contact modes. From Table 3, it can be noticed that

all v1-frequencies of TIs containing two NO�3 except for struc-

ture 2 are 10–20 cm21 higher than those of IPs, but still lower

than that of the isolated NO�3 , which is 22–56 cm21 higher than

those of IPs. This result indicates the formation of these TIs is

not the cause of blue shift. Nitrates in structure 2 are bonding

with Mg21 by S2-S2 mode, which is mentioned specially in pre-

vious section. The frequency of structure 2 has no obvious

change comparing with that of S2 (1245.8 vs. 1245.5 cm21),

i.e., if the S2 (or S20) exist in the actual solution, the TI with 2

structure may also exist although the spectral variety can not be

observed when the transformation takes place from S2 to 2. In

the experimental spectra, there is surely not transition point at

the WSR 5 12.41

For the TIs containing two Mg21, five equilibrium geome-

tries were optimized as shown as 11 (S1-S1 structure), 12 (S2-

S2), 13 (S1-MC), 14 (MC-MC), and 15 (MC-BC) in Figure 6.

Their calculated frequencies are also listed in Table 3. Compar-

ing Table 3 with Table 2, we can know the frequencies of all

TIs are larger remarkably than those of IPs which have analo-

gous associated structures except for 12 with special S2-S2

structure. For 13–15 with the CIP-CIP structures, their frequen-

cies are even higher than that of the hexahydrated NO�3 , that is,the v1-frequency will increase quickly when the species form.

For the TIs of 11 and 12 with different SIP-SIP structure, we

compared their v1-frequency with S20 for corresponding to the

experimental spectra (in the 11 and 12, all lone pairs involved in

the hydrogen bonding and thus they ought to compare with the

inner-sphere filled of S20). The v1-frequency of 11 is 2.8 cm21

higher than that of S20, whereas the formation of 12 can lead it

Table 2. The Calculated v1-NO�3 Frequencies (fv1) which is in cm21 of

the Optimized Ion Pairings (IP).

Species fv1

S1 1207.6

S2 1245.8

S20 1252.0

MC 1214.8

BC 1181.2

UBC 1117.3



Figure 6. The geometries of the optimized triple (TI) and multiple ion (MI) clusters.

red shift of 9.2 cm21. Therefore, the TI with more 11 than 12

structure is predicted to form when the S20 binds the second

hydrated Mg21 at lower WSR for the continuing blue shift in

experiment.

For studying the effects from the contacts of more polarized

water molecules and the second Mg21, we performed the same

operation to the ‘‘Ion pairings’’ section, in which the water mol-

ecules in TI were deleted and only the nitrate and two magne-

sium ions were optimized. We obtained the equilibrium geome-

try as 16 as shown in Figure 6. It is analogous with 14, which is

also the MC-MC structure. The calculated v1-frequency of

unhydrated 16 (1240.5 cm21) is higher than that of the isolated

NO�3 (1237.0 cm21), and of course higher than the unhydrated

ion pairing of UBC (1117.3 cm21). The result indicates the sec-

ond Mg21 can lead the v1-NO�3 frequency increase largely from

that with one Mg21 due to average population of the electric

field produced by the two Mg21 on the both sides of NO�3 , i.e.,the two magnesium ions weaken the polarization effects each

other. As mentioned above, the weakness of the polarization

will lead the red shift decrease and make the Mg��O bonding

effect (lead to blue shift) dominating. On the other hand, the dif-

ference of frequency between the hydrated 14 (1273.0 cm21)

and unhydrated 16 (1240.5 cm21) shows the blue shift resulted

by the polarized water molecules is only 32.5 cm21, about a

half of the 63.9 cm21 in the BC, which indicates the effect from

the water molecules is much weaker in TIs than in IPs though it

still lead the blue shift. In our work, we tried to investigate the

effects of water molecules to the v1-NO�3 frequencies detailed in

the IP, TI, and MI clusters in detail as we have done in the

hydrated NO�3 section. However, we can know the hydrated

structure between H2O molecules and NO�3 or Mg21 ions can

affect the v1-NO�3 frequencies obviously from Figures 4 and 5.

However, the hydrated structures are all different in the different

and even same ion associated clusters so that the detailed influ-

ences of varied H2O molecules to the v1-NO�3 frequencies of the

clusters shown in Figures 5 and 6 are all different and can be

classified hardly, while we can only know all kinds of water

molecules (including binding and non-binding water molecules

with NO�3 ion in the inner- and outer- spheres of aqueous Mg21

ion) can lead to the blue-shift of the v1-NO�3 band.

From the discussions above, we can predict the large blue

shift in very concentrated solution might attribute to the forma-

tions of the TI containing one nitrate and two aqueous magne-

sium ions, especially to those with the CIP-CIP structures.

For the MIs, we optimized two clusters both with one mag-

nesium and three nitrate ions as 17 and 18 as shown in Figure

6. The two clusters contain three MC and BC structures, respec-

tively. From Table 3, their v1-frequencies are 10–15 cm21

higher than those containing two nitrate ions with analogous

associated structures. The increased frequency might be due to

the weakness of the polarization by the counteraction of the pos-

itive charges on the Mg21 by the added electronegative NO�3 .However, the frequencies of this kind of MIs are also lower

than the NO�3 with 4–5 hydrated water molecules so that it

would not be the reason for the blue shift of the v1-NO�3 band at

lower WSR.

We did not obtain the optimized MI clusters with three or

more than three aqueous Mg21 which possessed the quasi-lattice

structures (For example, one nitrate is bound by six water mole-

cules in the Mg(NO3)2�6H2O crystal48). In the Raman spectrum

at the WSR 5 1.8, the v1-NO�3 frequency is up to 1057.6 cm21,

which is very close to those in the Mg(NO3)2�6H2O (1059

cm21) and amorphous (1061 cm21) crystals, can confirm the

quasi-lattice structure. Although the v1-NO�3 frequencies of this

kind of MI can not be calculated directly, we can still predict

from previous discussions that the existence of more magnesium

ions will average the electric field further so that the polarization

of the magnesium ions is more unremarkable than that in TIs

and the blue shift resulted by the Mg��O bonding dominates to

the v1-NO�3 frequency until close to that in the amorphous

crystal.

Predicting the Evolvement of v1-NO�3 Band with the

Increasing Concentration

Concluding the previous discussions, we can predict the evolve-

ment process of v1-NO�3 band in the Mg(NO3)2 solution with

the decrease of WSR.

When WSR[18, magnesium and nitrate ions exist mainly as

free aqueous ions or 2SIPs.

When the WSR 5 18, the SIP with the S20 structure begins

to form, which will lead to the small blue shift of the v1-NO�3

band. In the region where the WSR is 18–12, there is no further

association but the population of S20 increases.When the WSR 5 12, the TI with 2 or 11 structures begin to

form (the 2 would be dominating because it is neutral). The v1-frequencies of 2 are very close to that of S20 so that there is not

obvious transition point at this WSR. With the continued

decrease of the WSR, the chain of the clusters grows and the

associated structures will transform from the S2 (such as 2 or 12

in Fig. 6) to the S1 (such as 11) mode. The reason for the trans-

Table 3. The Calculated v1-NO�3 Frequencies (fv1) which is in cm21 of

the Optimized Triple and Multiple Ion (TI and MI) Clusters.

Species Name fv1(1) fv1(2) fv1(3)

TI with 2 nitrates 1 1219.3 1220.6

2 1245.5 1245.5

3 1227.6 1229.2

4 1227.9 1229.4

5 1225.1 1229.5

6 1225.1 1229.1

7 1202.8 1225.8

8 1200.7 1222.4

9 1199.6 1202.0

10 1198.1 1201.1

TI with 2 magnesium ions 11 1254.8

12 1242.8

13 1268.9

14 1273.0

15 1265.3

16 1240.5

MI with 3 nitrates 17 1215.5 1215.7 1219.3

18 1235.8 1238.6 1245.5

The number of the fv1 is equal to that of the NO�3 in the cluster.



formation is the S2 structure has longer survival time, which

makes it dominating on the end of the chain (The NO�3 has

more chance to impact with the free water molecules here),

while the S1 structure has lower energy with dominating in the

middle of the chain (less impact since the NO�3 is surrounded by

the two aqueous Mg21 ions). When the chain grows, the NO�3in the middle increase and thus the population of S2 also

increases. The v1-frequency of 11 is higher than those of 2 or

12, which might be the reason for the continuing blue shift of

the v1-NO�3 band in the WSR region of 12–6. With the growth

of the clusters, the chain structures will be associated in reticular

structure where one ion contacts with several complementary

ions just as the quasi-lattice structure. However, the cluster has

still the SIP associated mode mainly which is similar to the

Mg(NO3)2�6H2O crystal when the WSR 5 6. If there are host

crystal, the solution will crystallize into the Mg(NO3)2�6H2O,

while it would rather become extremely supersaturated if there

is not much heterogeneous nucleation. On the condition, the

water molecules in the middle of the clusters will be lost and

the MI with the CIP associated modes will form, to which the

sharp blue shift is attributed at the WSR\ 6. Figure 7 compares

the dependencies of the v1-NO�3 frequencies on WSR of the sol-

utions from the experiment and our calculation, respectively,

where the two results are in well agreement with each other in

shape.

The block plan of the associated process mentioned above is

shown in Figure 8. In the figure, the third block of ‘‘TI’’ con-

tains not only the triple ions clusters with one NO�3 surrounded

by a few Mg21 ions, but also those with one Mg21 surrounded

by a few NO�3 ions. The latter has the structure as shown as 2

in Figure 6. However, the further formation beginning from the

kind of clusters is not the clusters with SIP-CIP or CIP-CIP

structures but the MIs via binding more hydrated Mg21 ions

while the SIP structures between each two adjective ions are still

kept in the MI clusters. And then, the MIs with S1 structures

(the fourth block in Fig. 8) form. In one word, the TI clusters

with one Mg21 and two NO�3 ions can exist only with the SIP-

SIP structure. And when the CIP structures form, the associated

species have not been the TI clusters but the MI clusters (the

associated process beginning from the cluster with one Mg21

and two NO�3 ions can be expressed as solvent shared TI ? sol-

vent shared MI ? contact MI, which is same to the process

from the cluster with one NO�3 and two Mg21 ions so that the

two processes merge into one in the Fig. 8).

Conclusions

In this article, two important subjects in the Mg(NO3)2 solution,

the hydration of nitrate ion and the characteristic of ion-associ-

ated species, were investigated by using the ab initio method.

In the hydration of NO�3 , we optimized the theoretical modes

with 1–6 inner-sphere water molecules and proposed three bind-

ing modes (C, T, and D). Furthermore, the relative energies,

binding energies, and v1-NO�3 frequencies of the hydrated nitrate

clusters were calculated, from which that the hydration number

is 3–6 in the solvent abundant environment could be deduced. It

was in good agreement with Caminiti’s result.

In the associated species, some aqueous IP, TI, and MI clus-

ters were optimized, with their relative energies and v1-NO�3 fre-

quencies calculated. From comparison of frequencies with those

in experiment, the relations of the varieties of the v1-NO�3 band

to the formations of different associated species were obtained.

Our results support the points of Peleg,30 Chang and Irish15

more than those of James et al.,32 such as the little existence of

the associated species with the CIP structures at the WSR [ 6,

Figure 8. The predicted evolvement process of the associated species at the different WSR based on

our calculated results.

Figure 7. Comparing the calculated with experimental dependences

of the v1-NO�3 frequency on the WSR. In the figure, the squares

come from the confocal Raman spectroscopy for the individual

Mg(NO3)2 particles, and the circles come from our calculation. The

frequencies of the circles are corresponding with the f14, f13, f11,

fS20, the cross point of line f11–fS20 with that of WSR 5 18 and

(2f4b 1 f5a)/3 from right to left.



or the formation of the CIP will lead the v1-NO�3 band red shift.

However, there is also disagreement with the points of Peleg

and Chang. They considered the CIPs could form at the WSR \6, while we thought the CIP could hardly form and the associ-

ated species were the MI clusters with the contact structures in

the region via a intermediate process of the MIs with solvent-

shared structures in the WSR region of 12–6. The very recent

work reported by Xu et al. has also confirmed the CIPs exist

barely in the Mg(NO3)2 solution by using the molecular dynam-

ics (MD) simulation.49

At last, the ion-associated process is not as simple as that

suggested by Eigen and Tamm, which contains the dehydration

between only two aqueous ions. From Figure 8, it can be known

that the TI and MI clusters possess important status in the asso-

ciated process. The clusters exist even not only in the Mg(NO3)2solution. Our previous investigation about the MgSO4 also

reveals their important status in the associated process though

they are competitive with the CIPs in the system.44 Our recent

Raman difference spectra can also confirm this process

experimentally.

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ab initio investigation on the ion-associated species and process in mg(no3)2 solution

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