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Chemical Physics Letters 406 (2005) 20–23

Structural and dynamical properties of Bi3+ in water

Serdar Durdagi, Thomas S. Hofer, Bernhard R. Randolf, Bernd M. Rode *

Department of Theoretical Chemistry, Institute of General, Inorganic and Theoretical Chemistry, University of Innsbruck,

Innrain 52a, A-6020 Innsbruck, Austria

Received 27 January 2005; in final form 22 February 2005

Available online 16 March 2005

Abstract

A molecular dynamics simulation employing three-body corrected pair potentials to describe the ion–water interaction has been

performed to investigate the structural and dynamical properties of Bi(III) in dilute aqueous solution. A first shell hydration com-

plex forming a tri-capped trigonal prism was observed. The second shell consists in average of 21 water molecules, the mean ligand

residence time of the second shell was evaluated as 8.5 ps.

� 2005 Elsevier B.V. All rights reserved.

1. Introduction

Bismuth compounds are applied orally in human and

veterinary medicine for antiacid action and for mildly

astringent action in gastrointestinal disorders including

ulcerative gastritis and colitis [1]. New bismuth contain-ing drugs are being developed. A ranitidine bismuth cit-

rate compound combines the antisecretory action of

ranitidine with the mucosal protectant and the bacterici-

dal properties of bismuth [2]. Another use of bismuth in

medicine is in radio-therapy. 212Bi, is a strong a-particleemitter, has a short half-life (1 h) [3], and can be pro-

duced in large quantities from a 224Ra generator. This

isotope can be used as a targeted radiotherapeutic agentfor cancer therapy when attached to monoclonal

antibodies via complexing ligands such as dtpa (diet-

hylenetriaminepentaacetate) and dota (1,4,7,10-tetra-

azacylododecane N,N 0, N00,N000-tetraacetate) [4].

Because of the diverse functions of bismuth ion in

chemical and biological systems, understanding of the

role and detailed structure of this ion and its compounds

in liquid media is of considerable interest for such

0009-2614/$ - see front matter � 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.cplett.2005.02.082

* Corresponding author: Fax: +43 512 507 2714.

E-mail addresses: t.hofer@uibk.ac.at (T.S. Hofer), bernd.m.

rode@uibk.ac.at (B.M. Rode).

diverse fields as chemistry, biology, and physics [5,6].

Computer simulations in general and molecular dynam-

ics (MD) simulations in particular, are of increasing

importance to reveal details of molecular motions as

well as structural and microscopic properties of the solu-

tion which are difficult to measure experimentally.Structural information on hydrated Bi3+ in aqueous

solutions has been reported from experimental studies,

producing highly variable coordination numbers

(3–10), often associated with an irregular coordination

geometry [2]. This, together with a visible �lone pair

effect� in certain complexes appears to be a characteristic

of Bi(III) as is the strong acidity of Bi(III) in aqueous

solution. The rate of ligand exchange at Bi(III) wasreported highly variable and depending on the pH of

solution [2]. Generally, the structures of Bi(III)

compounds are similar to those of As and Sb com-

pounds, albeit more complicated. The structures of the

aquocomplexes of the lanthanide ions [Ln(H2O)9]

(SO3CF3)3] and of [Bi(H2O)9]3+ [2,7] are similar. Based

on their experimental studies, Frank et al. [7] concluded

that bismuth coordinates to nine water molecules form-ing a tricapped trigonal prismatic structure without rec-

ognizable stereochemical activity of the lone pair of

electrons. Persson et al. [8] proposed that bismuth (III)

ion has coordination number eight in acidic aqueous

S. Durdagi et al. / Chemical Physics Letters 406 (2005) 20–23 21

solution. Therefore, the simulation presented here was

expected to help in resolving this experimental

uncertainty.

2. Methods

The ion–water pair potential function was con-

structed from ab initio quantum mechanical calculations

at the restricted Hartree–Fock (RHF) level using the

DZP (Dunning) [9] basis set for O and H atoms and

cc-pVDZ-PP [10] basis set for Bi3+ ion. The minimum

energy for the Bi3+–water interaction was found

�82.2 kcal/mol at the distance of 2.32 A. To constructthe Bi3+–water pair potential function, 6794 ab initio

energies were fitted with the Levenberg–Marquardt

algorithm to the analytical formula:

DEfit;2bd ¼qBi3þ � qO

riOþ AO

r5iOþ BO

r6iOþ CO

r10iOþ DO

r12iO

þX2j¼1

qBi3þ � qjrij

þ AH

raijþ BH

rbijþ CH

rcijþ DH

rdij

!;

ð1Þ

where A, B, C, and D are the optimized parameters for

O and H, q denotes the atomic net charges, and riO and

rij denote the ion-oxygen and ion-hydrogen distances.

Table 1, summarizes the optimized parameters. The

net charges of oxygen and hydrogen were set to

�0.65966 and 0.32983, respectively, according to the

flexible BJH–CF2 water model [11,12]. The water geom-etry was kept constant through out the calculations at

the experimental gas-phase values of O–H = 0.9584 A

and H–O–H = 104.45� [13].A total of 14508 ab initio energy points were gener-

ated to describe the water–Bi3+–water energy surface

and to construct a three-body correction function. The

three-body correction energy is defined as:

DEcorr3bd ¼ EHF

½BiðH2OÞ2�3þ � EHF

Bi3þ� 2 � EHF

H2O

�X2w¼1

E2bd

½BiðH2OÞ�3þ � EBJH�CF2H2O�H2O

; ð2Þ

where EHF

½BiðH2OÞ2�3þ is the HF-SCF energy of [Bi(H2O)2]

3+,

EHF

Bi3þand EHF

H2Oare the HF-SCF energies of Bi(III) and

water at the experimental gas phase geometry [13],

E2bd

½BiðH2OÞ�3þ are the two-body fitted Bi–water energies

Table 1

Optimized parameters of the analytical Bi3+–water pair potential function

A (kcal mol�1 A5) B (kcal mol�1 A6)

Bi3+–O �27842.62 66581.36

A (kcal mol�1 A4) B (kcal mol�1 A7)

Bi3+–H 641.15 �3780.76

and EBJH�CF2H2O�H2O

denotes the water–water interaction

according to the BJH–CF2 water model [11,12].

The three-body correction energies were fitted to the

equation:

DEfit;3bd ¼ 0:06 � e½0:20�ðr1þr2Þ� � e�½0:50�r3� � ðrlimit � r1Þ2

� ðrlimit � r2Þ2; ð3Þ

where r1 and r2 are the Bi–O distances, r3 is the O–O dis-

tance between two water molecules and rlimit is the cut-

off limit (set to 6.0 A) after which three-body terms

become negligible.

After an equilibration of 150.000 steps, a sampling

molecular dynamics simulation based on pair potentialplus three-body corrections was performed for 500.000

time steps and configurations collected every 100th step.

The simulation protocol was similar to that of previous

investigations of various ions [17]. The cubic elementary

box of 24.6 A side length contained 1 Bi3+ ion and 499

water molecules corresponding to the density of

0.997 g/cm3. A canonical NVT ensemble at 298.16 K

was used with periodic boundary conditions, and thetemperature was kept constant by the Berendsen algo-

rithm [14]. The flexible BJH–CF2 water model [11,12]

including an intramolecular potential was used. Conse-

quently, the time step of the simulation was set to

0.2 fs, which allows for explicit movements of hydro-

gens. A cut-off of 12 A was set except for O–H and

H–H non-Coulombic interactions where it was set to

5.0 and 3.0 A. The reaction field method was used toaccount for long-range electrostatic interactions.

3. Results

Bi–O and Bi–H radial distribution functions (RDFs),

and their corresponding integration numbers obtained

from classical simulations are presented in Fig. 1. Asharp Bi–O peak was observed having its maximum at

2.57 A. The first hydration shell is rather well separated

from the second shell, leading to a coordination number

of 9. The probability, gBi–O, between first and second

shell reaches zero, thus indicating that no exchange pro-

cess occurred during the simulation time. A broad sec-

ond shell peak observed between 4.2 and 5.7 A with a

maximum at 5.05 A contains about 21 water molecules.The broad peak shows a high flexibility of water

molecules within this shell. These results are in perfect

C (kcal mol�1 A10) D (kcal mol�1 A12)

�262839.46 362058.65

C (kcal mol�1 A9) D (kcal mol�1 A12)

5637.38 2934.62

Fig. 1. Bi–O and Bi–H RDFs and their corresponding integration

numbers.

Fig. 2. Coordination number distributions (CNDs) of bismuth (III)

ion in water.

Table 2

Mean residence times (s) in ps and number of accounted exchange

events (Nex) for �direct� method as a function of t*

t* = 0 ps t* = 0.5 ps

N0ex=10 ps s N0:5

ex =10 ps s

2nd shell 367 0.56 24.2 8.49

22 S. Durdagi et al. / Chemical Physics Letters 406 (2005) 20–23

agreement with the Bi–O distance of 2.58 A evaluated

by Frank et al. [7] by X-ray diffraction. Large-angle-

X-ray scattering (LAXS) and extended-X-ray-absorp-

tion-fine structure (EXAFS) data of an 2–3 mol dm�3

[Bi(H2O)9](CF3SO3)3 solution produced a mean Bi–O

bond distance of 2.49 A for a nine-coordinated ion,

but concentration and counter ions certainly influence

this value [8].

Fig. 3. (a) O–Bi–O angular distribution functions (ADFs) within the first

(Showing the tri-capped trigonal prism, capped oxygens are presented in pa

The coordination number distributions of hydrated

Bi3+ obtained from our simulation are displayed in

Fig. 2. The exclusively nine-coordinated complex in

the first hydration shell (100% occurrence) is in agree-

ment with the experimental data of Frank et al. [7]

and contradicts the lower coordination numbersreported [8], at least for dilute solution. The second

hydration shell displays a broad coordination number

distribution (16–26; average: 21).

The angular distribution function (ADF) of O–Bi3+–

O angles is shown in Fig. 3a. The first peak is located at

69�, the highest point of the second peak at 136�, with a

minimum occurring at about 105�. This points towardsa tricapped cubic prism which is depicted in Fig. 3b, andwhich fits perfectly with crystallographic results [7].

As detailed information on water exchange between

hydration shell of ions and bulk is important for the

reactivities of the ions, the rates of water exchange pro-

cesses were evaluated by mean residence times (MRT)

analysis of the water molecules in the second coordina-

tion shell. The MRT values were evaluated using a

�direct� method [15], being the product of the averagenumber of water molecules in the hydration shell during

the duration of the simulation, divided by the number of

exchange events. Based on direct accounting and setting

the time parameter t* to 0 (all movements out of shell

are accounted) and 0.5 (only exchange processes leading

to a longer-lasting removal of a ligand) [13,14] the MRT

values listed in Table 2 were obtained. Besides mean

residence times, the simulation can supply properties

shell. (b) Nine-coordinated bismuth ion in the first hydration shell.

le gray, others in dark gray.)

S. Durdagi et al. / Chemical Physics Letters 406 (2005) 20–23 23

of ions in terms of lability of the hydration shell and sus-

tainability of exchange processes. Sustainability mea-

sures the rates of success of exchange events in leading

to longer lasting changes in the hydration structure. A

sustainability coefficient can be defined as [13,14]:

Sex ¼N 0:5

ex

N 0ex

; ð4Þ

where N 0:5ex and N 0

ex are the number of accounted

exchange events with t* = 0.5 ps and t* = 0 ps, respec-

tively. The inverse of the sustainability coefficient shows

how many border-crossing attempts are needed to pro-

duce one longer lasting change in the hydration struc-

ture of an individual ion. The Sex and 1/Sex values for

Bi3+ are 0.066 and 15.2, respectively.

As no first shell exchange was observed within thesimulation time of 100 ps, a lower limit for the MRT

in the first shell may be given as 900 ps, thus suggesting

the time scale for first-shell exchange processes to be in

the nanosecond range.

4. Conclusion

A comparison of the results of classical three-body

corrected MD simulations with ab initio QM/MM

MD simulations of Pb(II) [18] and Tl(III) [18] ions in

water shows that the classical simulations supply correct

data for structure and coordination numbers, while

dynamical data are less reliable [17]. In particular classi-

cally evaluated mean residence times are too short by

20–35%. One can assume, therefore, that the structureof hydrated Bi(III) presented here is a realistic picture of

the situation in dilute aqueous solution. For the second

shell mean residence time, however, a higher value of

�11 ps seems to be a better estimate. A QM/MM MD

simulation of Bi(III) in water will be carried out to con-

firm this.

Acknowledgement

Financial support for this work from the Austrian

Science Foundation (FWF) is gratefully acknowledged

(Project: P16221-N08).

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