Polymeric Structures in Aluminium and Gallium Halides

Abstract

The anionic species (Al n X 3n+1) ; with X = Cl or Br and n 1 have been recognized for a number of years to form in acidic liquid mixtures of aluminium chloride or bromide with the corresponding halides of alkali or organic cations, in relative proportions which vary with the composition of the mixture. In this work we evaluate the structure and the energetics of such polymeric series in a comparative study of Al and Ga compounds. To this end we first extend an earlier study of the ionic interactions in the Al 2 Cl 6 molecule [Z. Akdeniz and M. P. Tosi, Z. Naturforsch. 54a, 180 (1999)] to determine microscopic ionic models for Ga 2 Cl 6 , Al 2 Br 6 , and Ga 2 Br 6 . The models are then used (i) to evaluate the polymeric clusters for n 4 in the two trivalent-metal chlorides, and (ii) to explore the potential-energy hypersurface of alkali counterions in the case n = 2. We present tests of the results against available data and an evaluation of the convergence of the energy of the polymeric series towards a value of about 0.5 eV per monomer.

Full text

Page 1

Polymeric Structures in Aluminium and Gallium Halides
Z. Akdeniz, M. C ¸aliskana, Z. C ¸ic ¸ek, and M. P. Tosib
Physics Department, University of Istanbul, Istanbul, Turkey
aDepartment of Physics, Trakya University, Edirne, Turkey
bINFM and Classe di Scienze, Scuola Normale Superiore, Pisa, Italy
Reprint requests to Prof. M. P. T.; Fax: +39-50-563513; E-mail: tosim@sns.it
Z. Naturforsch. 55 a, 575–580 (2000); received February 18, 2000
Theanionic species(Al
ofyears to formin acidic liquid mixtures ofaluminium chloride or bromide with the corresponding
halides of alkali or organic cations, in relative proportions which vary with the composition of the
mixture. In this work we evaluate the structure and the energetics of such polymeric series in a
comparative study of Al and Ga compounds. To this end we first extend an earlier study of the
ionic interactions in the Al2Cl6molecule [Z. Akdeniz and M.P. Tosi, Z. Naturforsch. 54a, 180
(1999)] to determine microscopic ionic models for Ga2Cl6, Al2Br6, and Ga2Br6. The models are
then used (i) to evaluate the polymeric clusters for
(ii) to explore the potential-energy hypersurface of alkali counterions in the case
tests of the results against available data and an evaluation of the convergence of the energy of the
polymeric series towards a value of about 0.5 eV per monomer.
nX3n+1)
?withX=ClorBrand
n
? 1havebeenrecognizedforanumber
n
? 4 in the two trivalent-metal chlorides, and
n = 2. We present
Keywords:Ionic Clusters; Molecular Vapours; Molten Salts.
1. Introduction
Liquid chloro- and bromo-aluminates, represented
by the formula (AX)1?x
andAdenotesanalkalioranorganiccation,havebeen
studiedextensivelyforanumberofyears(for arecent
review see [1]). Main attention has been given to the
acidic range of composition (0?5
evidence from several types of experiments and from
molecular dynamics calculations shows that, starting
from the mixture at
dral (AlX4)
species of the type (Al
formed as the composition of the liquid mixture is
variedtowards pure AlX3. The pure compoundforms
a molecular liquid of Al2X6dimers.
The available evidence has stimulated molecular-
orbital studies by ab initio methods on the isolated
(Al2Cl7)
pirical methods on the (Al2X7)
ters [3 - 5]. It is known from these studies that the
(Al2X7)
a halogen corner [2 - 4] and that for the (Al3X10)
species a chain-like structure of corner-sharing tetra-
hedra is more stable than a ring-like structure by 10
?(AlX3)
xwhere X = Cl or Br
?
x
? 1). Various
x = 0?5 as a liquid of tetrahe-
?anions and A+counterions, polymeric
nX3n+1)
?with
n
? 2 are
?complex anion [2] as well as by semi-em-
?and (Al3X10)
?clus-
?cluster is formed by two tetrahedra sharing
?
0932–0784 / 00 / 0600–0575 $ 06.00 c
? Verlag der Zeitschrift f¨ ur Naturforschung, T¨ ubingen
? www.znaturforsch.com
-15kcal/mole[3].Apreliminaryabinitiostudyofthe
effectof analkalicounteriononthechlorinebridgein
(Al2Cl7)
an interest to study how a chain-like polymeric series
of the (Al
energetically with increasing
role of the chemical nature of the trivalent-metal ion,
e.g. about the consequences of substituting the Al
ions by Ga ions [6]. It also seems interesting to inves-
tigate the shape of the potential energy hypersurface
for counterions around the anionic species.
In the present work we address the above ques-
tions by means of a microscopic ionic model. We
start from an earlier study of the ionic interactions
in Al2Cl6-based clusters [7] and extend it in Sect. 2
to determine models of the interionic forces for Al
and Ga chlorides and bromides from properties of
the Ga2Cl6, Al2Br6, and Ga2Br6molecular dimers.
These models are then used in Sect. 3 to evaluate the
structure and the energetics of polymeric anions with
? 4 for the two trivalent-metal chlorides, and in
Sect. 4 to investigate the local potential-energy min-
ima for alkali counterions around the (Al2X7)
(Ga2X7)
with a brief summary and discussion of our results.
?has also been reported [3]. There remains
nX3n+1)
?type converges structurally and
n and to learn about the
n
?and
?clusters. We conclude the paper in Sect. 5

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576Z. Akdeniz et al. · Polymeric Structures in Aluminium and Gallium Halides
Table 1. Interionic force parameters in Aland Gachlorides and bromides (the subscrips M and Xdenote the trivalent-metal
ion and the halogen ion; the values for Al2Cl6are from [7]).
zM
zX
RM(˚A)
?M(˚A)
RX(˚A)
?X(˚A)CX(e˚A5?2)
?X(˚A3)
?s(˚A3/e)
Al2Cl6
Al2Br6
Ga2Cl6
Ga2Br6
2.472
2.427
2.364
2.364
–0.824
–0.809
–0.788
–0.788
0.95
0.95
0.97
0.97
0.044
0.044
0.045
0.045
1.71
1.84
1.71
1.84
0.238
0.258
0.238
0.258
5.5
7.2
5.5
7.2
2.05
3.05
2.05
3.05
0.46
0.76
0.46
0.76
M-XTM-XBM-M XT-XTXB-XB
? XT-M-XT
? XB-M-XB
Al2Cl6:
Al2Br6: model 2.22
ED
QC
Ga2Cl6: model 2.13
Ga2Br6: model 2.27
ED
QC
model 2.0652.28
2.43
2.41
2.46
2.34
2.48
2.45
2.50
3.20
3.34
3.34
3.43
3.32
3.43
3.43
3.52
3.59
3.84
3.90
3.91
3.70
3.93
4.04
4.00
3.23
3.54
3.48
3.52
3.29
3.59
3.49
3.56
121
120
122.8
120.8
121
120
128.1
122.1
90
93
92.3
91.4
90
93
91.1
90.7
2.22
2.25
2.25
2.29
Table 2. Equilibrium structure of Al2Cl6,
Al2Br6,Ga2Cl6andGa2Br6(bondlengths
in˚A and bond angles in degrees; the val-
ues for Al2Cl6are from [7]).
2. Interionic Force Model
InanearlierstudyofAl2Cl6andrelatedaluminium
chloride clusters including (Al2Cl7)
constructed an expression for the potential energy
?[7] two of us
U(fr
the interionic bond vectors
dipole moments
shell model (also known as the deformation dipole
model)for thelatticedynamicsof ionicandsemicon-
ducting crystals [8]. A basic quantal justification for
this approach to molecular structure has been given
for alkali halides by means of exchange perturbation
theory [9, 10]. For the detailed expressions entering
U(fr
study, we refer to the earlier work [7].
In the determination of the model parameters for
Al2Br6we closely follow the procedure already de-
veloped in [7] for the Al2Cl6dimer. We start from an
earlier study of the (AlBr4)
with special attention to the modelling of the bridge
formed bytwo brominesin thedimer. This is doneby
introducing an effective valence
andpolarizabilities
induction by the electric field on the halogen and
its saturation by short-range overlap distortions of
its electron shells. We determine these quantities for
Al2Br6from the measured value of its topmost stret-
ching-modefrequency(?3=500cm
the Al-Al bond length (3.34˚A) and the Al-terminal
brominebondlength(2.22˚A) asmeasured inanelec-
tron diffraction experiment [13]. The other model
ij
g?
fp
i
g) of an ionic cluster as a function of
r
ij and of the electric
p
i. This involvedan extension of the
ij
g?
fp
i
g), which are also used in the present
?cluster [11] and refine it
zBrfor the bromine
?Brand
?s,whichdescribedipole
?1[12])andfrom
parameters for the bromine ion (the van der Waals
coefficient
ness parameter
brominesintheBusingform[14]oftheAl-Broverlap
repulsions)aretakenfrom[11], whiletheionicradius
CBr, the ionic radius
RBr, and the stiff-
?Brdescribing the contribution of the
RAland the stiffness parameter
taken from [7]. Overall charge neutrality determines
?Alfor the Al ion are
zAl=
?3zBr.
The extensionof these model parameters to the Ga
dimers is immediate.We use as input data for Ga2Br6
the measured Ga-Ga bond length (3.43˚A) from elec-
tron diffraction experiments [13] and the measured
value of the breathing mode of the molecular dimer
in the pure molecular liquid (?b= 290 cm
to determine the effective valence and the ionic ra-
dius of Ga, on the assumption that the other model
parameters can be transferred from the Al2Br6dimer.
For Ga2Cl6, on the other hand, transfer of all model
parameters from Ga2Br6and from Al2Cl6yields im-
mediate agreement with the rather scanty experimen-
tal evidence on the Raman frequencies of the dimer
in the liquid as measured by Boghosian et al. [16].
In particular, we calculate a frequency of 411 cm
for the breathing mode against a measured value of
410 cm
Table1showsthesetsof modelparametersthatwe
have used in the calculations reported in the sequel
fortheAlandGahalidepolymers.Itisevidentthatall
these materials are reasonably close to the ideal ionic
model, as can be judged from the values of the effec-
tive valences. The deviations from ideal ionicity are
slightly larger for bromides and for Ga compounds.
?1[15])
?1
?1[16].

Page 3

Z. Akdeniz et al. · Polymeric Structures in Aluminium and Gallium Halides 577
Table 3. Frequencies of vibrational modes for Al2Br6and
Ga2Br6(in cm
?1; values in curly brackets are estimated).
— Al2Br6—
model
— Ga2Br6—
Expt, liquid [15]Expt, gas [12]model
B1u
Au
Ag
B3g
B2g
B2u
B3u
B1u
B1g
Ag
B3u
B1g
Ag
B2u
B3u
Ag
B2g
B1u
10
34
59
59
75
80
86
104
110
159
170
199
217
355
366
419
492
500
f8g
f30g
59
9—
—
62
—
69
—
—
84
—
118
—
—
201
—
—
290
341
—
31
55
56
63
71
76
84
93
132
133
175
202
239
269
290
333
334
f67g
76
90
f110g
112
114
139
199
203
f250g
346
376
409
489
500
Table 2 completes the comparison of our results
for the equilibrium structure of the molecular dimers
with measured values from electron diffraction (ED,
from [13]) and with the results of quantum chemical
calculations(QC,from[15]).ThesymbolsXTandXB
denoteaterminalandabondinghalogen,respectively.
Values fitted to experiment are underlined.
Table 3 compares our results for the vibrational
frequencies of Al2Br6and Ga2Br6with experimental
dataongaseousAl2Br6[12] andontheGaBr3molec-
ular liquid[15], respectively. The agreement between
calculated and measured spectra in Table 3 can be
considered as very reasonable.
3. Equilibrium Structures and Energetics of the
Polymeric Series
As already discussed in earlier work (see e.g. [7]),
thepotentialenergylandscapeforthe(Al2Cl7)
is very complex.Four structures formed from corner-
sharing tetrahedra are almost degenerate in energy
and differ only for internal rotations giving differ-
ent relative orientations to the two terminal AlCl3
groups. However, of these the only mechanically sta-
ble structure at zero temperature is the C2one, which
is obtained from a C2vstructure having an eclipsed
arrangement of the terminal groups through opposite
rotations of these groups by 30
bond.Theotherstructureshaveatleastoneimaginary
?anion
?around the Al-ClB
Table 4. Calculated equilibrium structure of the (Al2Cl7)
(Al2Br7)
figuration (the ranges of values shown for bond lengths and
bond angles span those appropriate to inequivalent termi-
nal halogens; the values for (Al2Cl7)
lengths in˚A and bond angles in degrees).
?,
?, (Ga2Cl7)
?and (Ga2Br7)
?anions in the C2con-
?are from [7]. Bond
M-XT
M-XB
? XT-M-XT
? XB-M-XB
(Al2Cl7)
(Al2Br7)
(Ga2Cl7)
(Ga2Br7)
?
2.10 - 2.12
2.25 - 2.28
2.16 - 2.18
2.30 - 2.33
2.35
2.52
2.40
2.56
100 - 108
99 - 110
100 - 107
99 - 109
111
108
111
108
?
?
?
mode frequency and therefore correspond to a multi-
plicity of saddle points separating several equivalent
trueminima.Wemayexpectthatatfinitetemperature
the molecularion will be executingrapid fluctuations
between its various structures.
We have foundthat these structural properties hold
for thisanioninallothertrihalidesof presentinterest.
Table 4 reports some of our results for equilibrium
bond lengths and bond angles.
The same flexibilityunder rotations aroundthe Al-
ClBbonds in chain-like structures is displayed by the
(Al3Cl10)
four structures for these anions, which are reported in
Figure 1. All these chain-like structures are mechani-
cally stable and differ very little in binding energy, at
the level of hundredths of an eV. Again, rapid fluctu-
ations in the hot melt are indicated.
The two structures of deepest energy are shown
in Figs. 1.1 and 1.2. The trimer in Fig. 1.2 has a
“stretched” configuration corresponding to the metal
ionsandbondingchlorineslyingallinthesameplane,
while the structure in Fig. 1.1, which actually has a
slightly deeper energy, is obtained from it by rota-
tions of the terminal groups out of the plane. Relative
to the values reported for the dimeric anions in Ta-
ble 4, the bond lengths in these two structures of the
trimericanionsaresomewhatcontractedinthecentral
ionic group and somewhat expanded or (for the ter-
minalchlorines)essentiallyunchangedintheexternal
groups.
Figure 1.3 shows a “winged” structure for the
trimeric anions, in which the bonds of the terminal
metal ions to the bonding chlorines are twisted out of
the plane. Finally, Fig. 1.4 shows a “cart” structure,
in which the planar skeleton of the molecule is pre-
served but thecentral andterminalchlorines gointoa
staggered configuration. The “stretched”, “winged”,
and “cart” structures for (Al3Cl10)
?and (Ga3Cl10)
?trimeric anions. We find
?have previously

Page 4

578Z. Akdeniz et al. · Polymeric Structures in Aluminium and Gallium Halides
1.1
1.2
1.3
1.4
Fig. 1. Ball-and-stick models of fourstable structures of the
(M3Cl10)
in the text).
?anion forM =Alor Ga(seethe discussion given
been reported from semi-empirical molecular orbital
calculations by Dymek et al. [5].
Figure 2 shows a “stretched” chain-like config-
uration that we have found for the (Al4Cl13)
(Ga4Cl13)
rines forming the backbone of the tetramer lie in a
single plane. The bond lengths to the central bond-
ing chlorine are 2.34˚A in (Al4Cl13)
(Ga4Cl13)
inTable4 for (Al2Cl7)
?and
?anion. All metal ions and bonding chlo-
?and 2.40˚A in
?,i.e.practicallythesameasthosereported
?and(Ga2Cl7)
?. Fortheother
Table 5. Incremental binding energy
(Al
(in eV).
?E(n)
of the
nCl3n+1)
?and (Ga
nCl3n+1)
?series as a function of
n
n = 1
n = 2
n = 3
n = 4
(Al
(Ga
nCl3n+1)
?
2.29
2.18
0.76
0.78
0.61
0.61
0.49
0.53
nCl3n+1)
?
Fig. 2. A ball-and-stick model of the “stretched” structure
of the (M4Cl13)
?anion for M = Al or Ga.
bond lengths similar comments apply as those given
above for (Al3Cl10)
We conclude this section by reporting in Ta-
ble 5 the increments
(Al
creasing
defined
b
the binding energy of the
polymericseries and
MCl3. It is evidentthat theincrease inbindingenergy
of thetwopolymericseries onadditionofanAlCl3or
GaCl3group is converging quite rapidly to a constant
amount of about 0.5 eV.
?and (Ga3Cl10)
?.
?E(n)in binding energy of the
nCl3n+1)
?and (Ga
n by unity in the range 1
nCl3n+1)
?poly-anions on in-
? 4. We have
?
n
?E(n)
?
E(n)
?
E(n?1)
b
?
Eb(MCl3), with
n-th member of the
E(n)
b
Eb(MCl3) the bindingenergy of
4. Energy Minima for Alkali Counterions
Wereportinthissectionourresultsonthepotential
energy minima of alkali counterions near dimeric an-
ions, with main attention to the cases A = Li, Na or K
around an (Al2Cl7)
results have been obtained for a Na counterion near
(Ga2Cl7)
scribingtheoverlaprepulsionandthepolarizabilityof
alkali cations are as in earlier work on fluorides [17].
We find no qualitative dependence on the halogen,
but a somewhat different structural behaviour for Li
as opposed to Na and K. Figure 3 shows the deepest-
energy configurationfor Naor Karoundan (Al2X7)
anion. The alkali cation is coordinated by four of the
terminalhalogens,thebondlengthbeing3.60˚Ainthe
caseofKAl2Cl7.ThecorrespondingK-ClBdistanceis
4.99˚AandtheAl-ClB-Albondangleis115
empirical molecular orbital calculations on AAl2Cl7
?or an (Al2Br7)
?anion. Similar
?or (Ga2Br7)
?. The model parameters de-
?
?.Insemi-

Page 5

Z. Akdeniz et al. · Polymeric Structures in Aluminium and Gallium Halides579
Fig. 3. A ball-and-stick model of the deepest-energy struc-
ture of the KAl2X7cluster for X = Cl or Br. The K ion is
shown as a dark sphere.
Blanderetal.[3]reportedasignificantdecreaseofthis
bond angle on the approach of an alkali counterion,
to a value of about 100
of 5˚A. There is, therefore, disagreement in detail
between our model and their results. However, from
an X-ray diffraction experiment on KAl2Br7crystals
Rytteretal.[18]reportedanAl-BrB-Albondangleof
109.3
to 4.0˚A. Our corresponding results for the isolated
KAl2Br7cluster are 112.6
Still considering the case of AAl2X7with A = Na
or K, we find two further distinct energy minima for
the alkali counterion at a slightly higher energy than
for the minimum shown in Figure 3. These minima
correspond to (i) bonding of the counterion to the
three terminal halogens in one of the AlX3groups,
and (ii) bonding on top of the halogen bridge to the
bridging halogen and to three further terminal halo-
gens. It is evident from our calculations, therefore,
that within our model the counterions are essentially
free to move around the isolated poly-anion. This is
consistent with essentially free migration of counter-
ions in liquid mixtures.
?for K at a K-ClBdistance
?and K-Br bond lengths in the range from 3.3
?and 3.74˚A.
[1] Z. Akdeniz, D. L. Price, M.-L. Saboungi, and M. P.
Tosi, Plasmas and Ions 1, 3 (1998).
[2] L. A. Curtiss, Proc. Joint Int. Symp. Molten Salts, ed.
G. Mamantov; The Electrochemical Society, Penning-
ton 1987, p. 185.
[3] M.Blander,E.Bierwagen,K.G.Calkins,L.A.Curtiss,
D. L. Price, and M.-L. Saboungi, J. Chem. Phys. 97,
2733 (1992).
[4] L. P. Davis, C. J. Dymek, J. J. P. Stewart, H. P. Clark,
and W.J. Lauderdale, J. Amer. Chem. Soc. 1985,
5041.
[5] C.J. Dymek, J.S. Wilkes, M.-A. Einarsrud, and H.A.
Øye, Polyhedron 7, 1139 (1988).
[6] K. R. Seddon, Proc. Int. George Papatheodorou
Symp., ed. S.Boghosian et al.; ICE/HT, Patras 1999,
p. 131.
[7] Z. Akdeniz and M. P. Tosi, Z. Naturforsch. 54a, 180
(1999).
[8] Seee.g. R.A.Cochran, Crit. Rev. Solid State Sci.2, 1
(1971); J. R. Hardy and A. M. Karo, The Lattice Dy-
namics and Statics of Alkali Halide Crystals; Plenum
Press, New York 1979.
As already noted, some details of the potential en-
ergy hypersurface for a Li counterion are somewhat
different from the situation pertaining to Na and K.
The smaller ionic size of Li tends to favour three-
fold over fourfold coordination to the halogens, and
in particular we find that the deeper energy minimum
corresponds tobindingtoonlythree ofthe four bond-
inghalogensshowninFigure3.Again,freemigration
of the Li counterions is indicated.
5. Concluding Remarks
We have in this work determined a microscopic
model of ionic interactions in aluminiumand gallium
trihalides and applied it to study the polymeric anion
series which are formed in liquid Al-alkali and Ga-
alkalihalidemixtures. Wehaveespeciallyfocused on
the multiplicity of structures which are allowed for
these chain-like anions by the considerable freedom
of rotationofmoleculargroupsaroundinternalbonds
and on the convergence of the value of the binding
energy per monomer with increasing chain length.
We have also examined the main features of the po-
tentialenergylandscapeforalkalicounterionsaround
dimeric anions.
The reasonable description afforded by our model
forthesecomplexionicclusterssuggeststhatitshould
find useful applications in further studies of these
materials in the liquid state.
Acknowledgements
Three of us (Z.A., M.C ¸., and Z.C ¸.) acknowl-
edge support received from the Turkish Scientific
and Technological Research Council (Tubitak). Z.A.
also acknowledges support from the Research Fund
of the University of Istanbul under Project Number
¨O-681/121099 and wishes to thank the Scuola Nor-
male Superiore di Pisa for their hospitalityduring the
final stages of this work.

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580Z. Akdeniz et al. · Polymeric Structures in Aluminium and Gallium Halides
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