Molecular dynamics simulation of ferrous and ferric ions in water

Chemical Physics 144 ( 1990) 353-362 North-Holland

MOLECULAR IN WATER

DYNAMICS

SIMULATION

OF FERROUS AND FERRk

IONS

E. GUARDIA Departament de Fisica i Enginyeria Nuclear, Vniversitat PolitpC de Catalunya, Pau Gargalio 5, 08028 Barcelona. Spain

and J.A. PADRd Departament de Fisica Fonamental, Vniversitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain Received 24 October 1989; in final form 2 January 1990

Molecular dynamics simulations of single Fez+ and Fe3+ ions in aqueous solutions were carried out using a flexible SPC model for water molecules. The effects of ionic charges on the structural and dynamical properties (translational, librational, vibrational and reorientational motions) of water molecules in the first hydration shell are discussed.

1. Introduction

Molecular dynamics (MD) simulation is an efficient technique to investigate the grounds of the microscopic properties of liquids and liquid solutions. It allows one to obtain detailed information on the atomic behaviour which cannot often be directly acquired from laboratory experiments. This information is not only a beneficial complement of the experimental data but may also be very helpful for the interpretation of the results obtained from experiments. In the case of electrolyte solutions the information provided by MD simulations is particularly interesting because many of the experimental results correspond to macroscopic properties (thermodynamic and transport coefficients, dielectric constants, etc.) and because the microscopic data supplied by diffraction [l] or spectroscopic [2] experiments are the result of the superposition of several effects. Despite the usefulness of the MD simulations it must be borne in mind that MD results are based on the adoption of approximate interaction potential models. Therefore, although MD simulations can provide interesting qualitative information they cannot provide exact results. Over the past few years 0301-0104/90/$03.50 (North-Holland)

0 Elsevier Science Publishers B.V.

many works [ 3- 111 have been devoted to the improvement of potential models; however, a potential capable of reproducing all properties of water does not exist. Furthermore, in the case of ionic solutions we also have to assume an approximate model for the ion-water interactions. Nevertheless, reliable conclusions, independent of the adopted model, may be reached by comparing the results deduced from MD simulations with different reasonable interaction potentials. This work seeks to make a contribution in this sense. In this paper we report the results obtained from MD simulations of single Fe*+ and Fe3+ ions in water. We paid special attention to changes induced by the ionic charges on both the structural and dynamical properties of water molecules of the first hydration shells. Similar studies have already been performed for monovalent ions [ 12-l 8 ] and concentrated electrolyte solutions [ 19,201 but only partial studies have been devoted to the case of single polyvalent ions [ 2 1-25 1.

2. Computation details MD simulations were performed on two systems,

354

E. Guhdfa. J.A. Padrci/MD simulationofF$* and FeJ+ ions in water

each containing a single ion (Fe*+ or Fe3+ ) and 125 water molecules in a cubic box with periodic boundary conditions. The side length of the cube was 15.55 A which gives a solvent density equal to 1 g/cm3. The temperature was 298 K. For the sake of comparison, we also carried out MD simulations of pure water under identical conditions. The Toukan-Rahman model [ 8 ] was assumed for the water-water interactions. This is a flexible model that adopts the same form as the SPC model. of Berendsen et al. [ 5 ] for the intermolecular interactions. Intmmolecular forces are described by a Morse potential between the oxygen and hydrogens and by a harmonic hydrogen-hydrogen force. For the ionwater interactions we used the potentials developed by Curtiss et al. [ 23 1. These empirical potentials were derived assuming the Toukan-Rahman model for water. The values of the parameters were adjusted so as to be in good agreement with the calculated and expe~ment~ values of the vibrational frequencies of the water surrounding the ion and the Fe-O distances. The expressions and parameters of the potentials used in this work are collected in the appendix. A spherical molecule based cutoff with a radius equal to 7.5 A was used for evaluating all interactions. Although our quantitative results may be influenced by the use of this rather small cutoff, it should not significantly affect the main conclusions of this paper which are based on the qualitative changes observed when ions with different charges (or a rigid water model ) are considered. To carry out the simulations we employed the leap frog Verlet integration algorithm with coupling to a thermal bath proposed by Berendsen et al. [ 26 J. In the run with Fe2+ a time step of 0.5 fs was used while in the case of Fe3+ a time step of 0.25 fs was required to keep the temperature constant. To speed up the simulations we used the multiple time-step technique proposed by Telleman and Jiinsson [27] with n.10W=4.Each run consisted of an initial equilibration period of 15 ps and a production period of 60 ps. The average temperature in the different runs was 298 K with a deviation less than 1%. In order to analyse the influence of the internal degrees of freedom of water we also carried out auxiliary simulations of the same systems but assuming the SPC model for water-water interactions. These rigid water simulations were performed with time

steps of 2 fs (for Fe2+ ) and 1 fs (for Fe’+ ). The SHAKE procedure f 281 was used to keep the interatomic distances fixed.

3. strWtttral results Radial distribution functions corresponding to ionoxygen (gio( r) ) and ion-hydrogen (gin(r) ) are represented in figs. 1 and 2. As in the case of monovalent ions [ 18 ] we find higher g(r) peaks when the rigid model is used whereas the positions of the peaks are scarcely affected by the intramolecular motions in water. Higher g(r) maxima and shorter ion-water distances may be observed when the charge of ions increases. This is a result of the stronger attractive forces between cations and neighbouring water molecules. Moreover, the differences between g(r) for rigid and flexible models increase with the ionic charge. In table 1 the positions ofg(r) maxima (Rio, Rin) are compared with the data reported in earlier papers. The Rio distances obtained in this work are in good agreement with the experimental observations of Brunschwig et al. [ 29 ] which were used by Curtiss 15.0

-

12.5

-

Fe2+ 10.0

2

-

7.5 -

5.0 -

2.5 -

Fig. 1. Ion-oxygen and ion-hydrogen radial distribution func) flexible water, (---) rigid water. tions for Fez+ ion: (-

E. Guhrdia,J.A. Pad& /MD simulationof F@+ and Fe’+ ions in water

Fea+

. 4.b r(A)

Fig. 2. Same as fig. 1, only for Fe)+ ion.

et al. [ 231 to derive the parameters for their empirical potential. Moreover, the RIOvalue for Fe3+ is also consistent with the experimental result of Magni and Radnai [ 3 1 ] although a clear discrepancy with the experimental result reported by Kalman et al. [ 301 is observed for Fe’+. The ion-water averaged dis-

355

tances obtained in our simulations are somewhat smaller than the ones found by Kneifel et al. [25] from MD simulations with slightly different interaction models. Their ion-water potentials models were also based on the ones proposed by Curtiss et al. [ 23 ] whereas a central force model [ 28 ] was used for the water-water interactions. Unlike monovalent ions, the g(r) first minima for Fe2+ and Fe’+ are in fact intervals where g(r) =:0. Therefore, the running integration numbers resulting from the integration ofg( r) [ 191 show clear plateaus which allow an accurate determination of the corresponding coordination number (cn). As was already shown [ 231, the cn value obtained with the potential model used in this work is the same as that found experimentally, i.e. cn=6. Larger cn values were obtained with ab initio potential models for divalent ions [ 2 1,221. It should be noted that cn obtained from simulations with the rigid water are identical to the ones for flexible water despite the notorious differences between the g(r) functions obtained for both models. The data of table 1 show that water molecules in the ionic shells have larger bond lengths and smaller bond angles than the ones for the rigid SPC model. Moreover, these parameters are not affected by the presence of neighbouring ions since their values for Fe’+ and Fe3+ are the same as the ones obtained for

Table 1 Structural averaged properties in the ionic hydration shells: ion-oxygen (RIO)and ion-hydrogen (RIH) distances, coordination numbers (cn). Mean values of bond lengths (RoH), bond angles ( LHOH) and orientation of water molecules (6,). The quantities quoted in parentheses are the standard deviations

RIO(A)

RIH (A)

cn

Roti c, (A)

LHOHe) (deg)

6 (deg)

Fe’+

2.075 *’ 2.15 [25] b, 2.10 [29] =) 2.28 [30] =)

2.775 a) 2.89 [25 ] b,

6

1.018(0.013)

105.7(3.7)

163(9) 166(8) *)

Fe’+

1.975 a) 2.03 (251 b, 1.98 [29] ‘) 2.00 [31] c,

2.675 ” 2.81 [25] b,

6

1.019(0.015)

105.4(3.4)

167(7) 170(5) *’

‘1 Uncertainties are smaller than 0.025 A. b, ~ahtes from other simulations (uncertainties smaller than 0.02 A). ClExperimental data. d, Results from simulations with the rigid water model. ‘) For pure water we obtained Ron--1.018(0.014) A and LHOH= 105.7” (3.6”). The water parameters for the rigid SPC model are Ron= 1 A and LHOH= 109.5”.

356

E. Guckdia,J.A. Padr&/MD simulationof F8’ and Fe’+ ions in water

pure water and water close to monovalent ions [ 32,181. This result disagrees with the experimentally observed [ 33,341 increase of the O-H distance for water in ionic solutions. Therefore, the intramolecular potential model used in this work should be improved if a realistic reproduction of the deformations of water molecules due to the neighbouring ions is desired. The results of Kneifel et al. [ 251 with a central force model for water are also inconsistent with the experimental observations on the O-H bond lengths for aqueous solutions. During the simulations we also computed the angle (6) between the dipole vector of water molecules and the ion-oxygen position vector. The probability distributions of cos 6 represented in fig. 3 are narrower and the mean values of cos 8 shift towards - 1 when the ionic charge increases. This means that cations induce symmetric arrangements of water molecules around them and their influence increases with the charge. Although for monovalent ions the orientation effects rapidly diminish with the distance in the case of polyvalent ions, their influence is still important beyond the first hydration shell (fig. 4 ). The strong orientation of water molecules in the hydration shells is clearly reflected by the negative values of (cos f3(r) ) at distances close to the positions of 0.30

0.25

I I

0.20

-

1 .OO

0.75 1 0.50

-

0.25

-0.75

-1.00

1 1

!I , 0.00

,

,

I

, , 1 I 2.00

I

I ( 1 I 4.00

I

I ( I 6.00

I

a

Fig. 4. Mean value of cos 0 for the flexible water model as a function of the ion-oxygen distance for Fe’+ (-), Fe3+ (---) andNa+ (---) [ 181.

the gi,,( r) maxima. Water molecules between two hydration shells are less ordered and (cos e(r) ) for r values around the g( r) minima are closer to zero. It should be noted that in the case of Fe*+ and Fe3+ (cos 0(r) ) are discontinuous since the probability of finding water molecules at distances between the first and second hydration shell is negligible. We did not observe any significant influence of the intramolecular motions of water on the ion-water orientation.

3 I

I

6 g 0.15 0

:‘i

4. Dynamical results

I

;r’ g.10

0.05

0.00

4.1. Translational motions

I “‘.&

\ --.._ -----------.--__. ________________ \

-1.00I ”

”

I ” -0.75

”

I ’ -0.50

“‘I”“1

-0.25

0.00

cos 8 Fig. 3. Probability distribution of cos f3for the water molecules (flexible model) in the hydration shell of Fez+ (-), Fe”+ (---) and Na+ (---) [ 181.

To obtain information on the microscopic dynamics of ions we calculated the normalized velocity autocorrelation functions Cr( t )_The resulting curves for the ions in flexible and rigid water are represented in figs. 5 and 6. As in the case of monovalent ions [ 18 ] the backscattering (negative values of C, ( t) ) is more important for the flexible mode. This indicates that the oscillatory motions of ions due to the collisions

E. Guctrdia,J.A. Padrb/MD simulationofF#+ and Fe’+ ions in water

Fe2+

-o.50

.m,

0.00

0.10

0.20

0.30

0.40

0.50

t(ps> Fig. 5. Fe’+ velocity autocorrelation functions: (-) water, (---) rigid water. 1

flexible

.oo

0.75

Fe3+

0.50

0.25

0.00

0.00

0.10

0.20

0.50

0.40

0.50

t(ps>

displacements. For rigid water, DI diminishes when the ionic charge increases but for Fe3+ with flexible water DIwas larger than for monovalent and divalent ions (table 2 ) . The translational motions of water molecules of the first hydration shell were analysed through the normalized velocity autocorrelation functions C,( t ) and the mean square displacements of the oxygen atoms. From the latter we obtained the self-diffusion coefficients Do.As may be observed in fig. 7 the decay time of C,(t) becomes shorter when the ionic charge increases. Moreover the water molecules close to Fe’+ and Fe3+ show deeper minima and more persistent oscillations than pure water. This is a consequence of the marked oscillatory motions induced by the ionwater Coulomb forces. With regard to the Do coefficients we see in table 2 that they diminish when water is close to the ions. The changes in Do when ions of different charge or different water models were considered are similar to those observed for DI.This behaviour may be associated with the formation of ionic complexes with less mobility than the single molecules. This assumption is supported by the long residence times (Tag) of water molecules in the first coordination shell. We applied the procedure used in earlier works [ 13,18 ] to calculate tlw for monovalent ions. Although our simulations were too short for an accurate determination of T,~ for divalent and trivalent ions we observed that q, values were greater than 10’ ps (the experimental values [ 351 are rIw= 3.1 X lo5 ps for Fe’+ and 7 = 3.3 x 10’ ps for Fe3+ ) . In general, both DIand Do’dwiminishwhen the ionic charges increase Table 2 Self-diffusion coefftcients (0, in 10e9 m* s- ’ ) of ions and water molecules of their hydration shells for the flexible (F) and rigid (R) water models. The error of D coefficients is f 0.1 x 10V9m2 S-’

Fig. 6. Same as fig. 5, only for Fe’+.

with the surrounding water molecules are enhanced when these molecules are distorted. To investigate the mobility of ions we calculated the selfdiffusion coefftcients D,.Because of the persistence of the oscillations in Ci ( t ) we cannot calculate D,by integration of these functions. Thus we obtained D,from the long time slope of the mean square

357

F

R

ions (4)

Na+ [ 181 Fez’ Fe’+

0.9 0.95 1.45

1.5 1.25 1.0

water (DO)

purewater

4.6 1.5 1.3 1.85

3.1 2.7 1.6 1.5

Na+ she11[ 181 Fe2+ shell Fe3+ shell

358

E. Guhdia, J.A. Padrb /MD simulation of Fe’+ and Fe’+ ions in water

0

500

1000

1500

w(cm-’

2000

2500

)

I

I”“I”“I”“I”“I”“I 0.00 0.10

0.20

0.30

0.40

Fig. 8. Power spectra of the oxygen velocity autocorrelation funo tions for pure water (---), Fe*+ (-) and Fe”+ (---) hydration shells (flexible water model).

0.50

t(ps> Fig. 7. Oxygen velocity autocorrelation functions of pure water and water molecules of the ion hydration shells (flexible water model ) .

but for Fe3+ with flexible water we obtained larger D values than for Na+ and Fe’+. This fact may be attributed to the formation of more compact complexes (see Rto in table 1) whose mobility is favoured by the smaller probability for the formation of hydrogen bonds with water molecules beyond the first hydration shell. We calculated the power spectra by Fourier transformations of the corresponding C(t) functions, f(w)=

TC(t)cosoxdt.

(1)

0

The results for oxygen atoms are represented in fig. 8. fo( o) for pure water shows a sharp peak at about 50 cm-‘. This peak may be ascribed to the O-O-O flexion motions [ 36 ] and it becomes broader and blue shifted for water close to cations. These results are in agreement with those obtained for Ca*+ [ 201, F- and Na+ [ 18 1. A small peak, analogous to the one found

for the F- hydration water [ 18 1, was found for Fe*+ around 1950 cm-‘. 4.2. Librational and vibrational modes

The standard way to investigate the librational and vibrational water motions from MD simulations is based on the calculation of the power spectrumfn (0) corresponding to the Cr.,( t ) functions for the hydrogen atoms [ 8,37-391. We calculated the&(o) spectra using eq. ( 1) and the resulting curves are presented in fig. 9. fn (w) shows three frequency bands corresponding to the librational motions of water molecules, the HOH bending motions and the OH stretching motions. For pure water, these bands are located around 500, 1900 and 3500 cm-‘, respectively. For water in hydrogen shells of Fe*+ and Fe’+ the librational band is blue shifted and the stretching band is red shifted. These features are consistent with the ones from other simulations [ 18,24,25,37] and ab initio calculations [ 401. With regard to the bending vibrations of water we found that the positions of the corresponding peaks for water close to the cations

359

w(cm-’

)

Fig. 9. Same as fig. 8, only for hydrogen velocity autocorrelation functions.

are slightly shifted towards higher frequencies while quite small [ 371 or negligible [25] shifts were observed in simulations using the central force model for water. In principle, it is possible to characterize the changes induced by ions in the power spectra by infrared and Raman spectroscopy [ 2 1. However, the information on the effects of single ions is not directly accessible since at least two kinds of ions, cations and anions, arc present in the electrolyte solutions. Furthermore, the frequency shifts are concentration dependent. We observed that the shifts for the librational and vibrational modes in our simulations are clearly larger than the ones resulting from the spectroscopic experiments on electrolyte solutions [ 2 1. Nevertheless, remarkable shifts of the vibrational frequencies of hydration water but only slight shifts in the spectra corresponding to the total water were found by Probst et al. [ 37 ] from MD simulations of moderately concentrated solutions. Therefore, it is difficult to reach definitive conclusions on the reliability of the assumed microscopic model based on the comparison of the data obtained from our simulations of single ions and experiments on electrolyte solutions.

4.3. Reorientational motions To complete the description of the dynamical properties of water, we investigated the reorientational motions. We considered three different unit vectors in the water molecules, i.e. uI in the direction of the dipole vector, u2 in the intramolecular protonproton direction and u3=al XI~~ orthogonal to the plane of the water molecule. We also considered the unit vector u4 along the ion-oxygen direction. During the simulations we calculated the time correlation functions defined as [ 40-42 ] c/(t)=

(P,(~i(t)*~i(0))

>

9

(2)

where PI is the lth Legendre polynomial and Uiis one of the previously defined unit vectors. We computed C, for I= 1 and 2. After an initial decay (t-co.5 ps) that corresponds to the librational motion of water molecules, the Cr( t) functions show an exponential regime (figs. 10, 11). We determined the reorientational times (T,) by fitting C,(t) for large t to the function C,(t)=exp(

-t/q)

.

(3)

The reorientational

Debye model for the rota-

E. Guhdia, J.A. Padrb/MD simulationofF$+ and Fe’+ ions in water

360

0.80

0.60 -

s t 0.40

1

Fe3'

shell

t(ps> Fig. 10. Reorientational time correlation functions of water (flexible model) molecules in the Fe3+ hydration shell for I= 1.

Only for the higher g values, which corresponds to u1 and u4 in the Fe*+ and Fe3+ hydration shells, T]/r2 is close to 3 whereas in the remainding cases ?,/r2 is markedly lower. The q values (table 3 ) clearly increase due to the presence of the cations. Although we did not find important differences among the g values for Fe*+ and Fe3+ hydration shells, the values for these cations are larger than the ones found for Na+ [ 18 1. As a result of the geometrical arrangement of molecules (see fig. 3), the effect of cations is more important in the ul direction. Because of this unequal enlargement the reorientation of hydration water shows a remarkable anisotropy. So, unlike pure water, the g values in the u, direction (and also in the u4 direction which for cations is almost parallel to uI ) are clearly larger than for 11*and u3. Both the increase in rl and the anisotropic reorientation in the ionic hydration shells were also observed when the NMR experimental results for pure water and electrolyte solutions [44,45] were compared.

5. Conclusions

0.6 A

0.0

(,,,~,,,,,,,,,,,,,,,,,,,,, 0.0

0.5

1.o t(ps)

1.5

2.0

2.5

Fig. 11. Same as fig. 10, only for 1=2.

tional diffusion predicts that r, /Q= 3 [ 4 11. As may be observed in figs. 10 and 11 and in table 3, r, is always greater than rz but our results show important deviations from the prediction of the Debye model.

The simulations presented in this paper show that the influence of cations on the orientation of the neighbouring water molecules increases with the ionic charge and for polyvalent ions this influence still remains important beyond the first hydration shell. With regard to the dynamical properties, our results confirm that the presence of ions slows down both the translational and reorientational motions of water molecules. Moreover, remarkable shifts in the spcctral densities and anisotropic reorientational times were observed for water molecules close to the ions. In general, our results are in qualitative agreement with the experimental data. Ion-water averaged distances obtained from simulations are close to the ones experimentally measured but, in contrast to the experimental observations, we did not find any significant change in the bond length and bond angles of the water molecules of the hydration shells. This unrealistic result may be attributed to the defects of the assumed potential model. The available data from spectroscopic experiments were obtained from concentrated electrolyte solutions and their comparison with our results for single ions cannot easily be used

E. Gu&dia, J.A. Padrci/MD simulationofFe” and Fe’+ ions in water

361

Table 3 Reorientation correlation times (r,,

~~2) in ps for pure water and water moreeules of ionic hydration shells for the flexible (F) and rigid (R) water models (errors in 7 are smaller than 10%)

Unit vector

I

R

F

R

2.2 1.1

3.2 1.3

12.1 3.0

8.9 2.4

31.8 9.8

27.2 8.8

30.2 9.6

22.1 8.2

2

1.8 1.2

3.0 1.6

2.6 2.1

3.4 2.2

3.9 2.2

4.7 2.5

3.4 2.0

4.3 2.2

1 2

1.2 0.7

2.2 1.0

2.1 1.5

2.8 1.6

3.8 1.9

4.8 2.1

3.5 2.0

4.4 2.4

19.3 7.2

15.1 5.2

31.6 9.5

21.8 8.5

27.9 8.5

25.0 8.0

1

14.4

F

2

to obtain definitive conclusions the interaction model.

R

Fe3+ shell

F

1

u3

Fe*+ shell

R

2 u2

Na+ shell [ 181

F 1

MI

Pure water

on the reliability

of

Acknowledgement

We acknowledge the financial CYT, Project PS 87-0026CO2.

support

tion from equilibrium H-H separation, r, the interatomic separation between atoms i and j, roe the oxygen-oxygen separation and qi the charge on atom i. The constants and the equilibrium molecular gcometry adopted in this model are given in table 4.

of DGITable 4 Flexible SPC water Potential parameters

Appendix. Interaction potentials (i) Water-water. The interaction potential proposed by Toukan and Rahman [ 8 ] is a modified version of the SPC model for water [ 5 ] which is a rigid three-site model. This new version adopts the same form for the intermolecular interactions but allows for flexible molecules. This flexible SPC model is of the form

Intermolecular potential [ 5 ]

Intramolecular potential [ 8 ]

A,=629400 lcealmol-’ Al2 C,,=625.46 keal mol-’ A6

ke=2.283 mdyn A-’ k@= - 1.469 mdyn A-’ k,=O.776 mdyn A-’ D=O.708 mdyn A a=2.561 A-’

go=-0.82 e q,=O.41 e equilibrium geometry:

~,-,n=t.oA LHOH= 109.47”

(A.1) Table 5 Pair potential parameters for Fe?+ and Fe3+ in water

K,,=D{[l-exp(-ari)]’ +[1-exp(-ar2)]2} +(kJ2)r:+kr,(r,

Knter=

1 ij

~&lr~+&lr~

+r2)+brlr2,

-

G/r&

(A.21

,

(A.3)

where r,, r2 are the O-H bond stretches, r3 the devia-

A (kcal mol- ’ ) B (A-‘) D (kcal mol-’ A6) E (keal mol-’ A*) F (kcal mol-’ A’*) 4Fe

Fe*+

Fe3+

15267.3 3.279 299.424 166.884 -265.703 2

36414.4 3.728 166.316 100.130 -99.641 3

362

E. Guhdia, J.A. Padrb /MD simulation of Fez+ and Fe’+ ions in water

(ii) Zen-water. The semi-empirical pair potentials developed by Curtiss et al. [ 231 have the analytical expression: V=A exp ( - BrFeO)-D/r&

-E/r&-, -F/r;&

+&$h/rFeO +qHqFe/rFdi +&qFe/rFeH’

,

(A-4)

where rF&, rF&, and rF&,’ are the Fe0 and the two FeH distances reSpeCtiVely.The qo, qFe and qH are the charges on 0, Fe and H respectively. The potential parameters are given in table 5. References

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