Ionic Interactions in Alkali-Aluminium Tetrafluoride Clusters

Abstract

Complex anion structures ((AlF 4) ; , (AlF 5) 2; and (AlF 6) 3;) coexist in liquid mixtures of alu-minium trifluoride and alkali fluorides in composition-dependent relative concentrations and are known to interact with the alkali counterions. We present a comparative study of the static and vibrational structures of MAlF 4 molecules (with M = any alkali), with the aim of developing and testing a refined model of the ionic interactions for applications to the M-Al fluoride mixtures. We find that, whereas an edge-bridged coordination is strongly favoured for Li in LiAlF 4 , edge-bridging and face-bridging of the alkali ion become energetically equivalent as one moves from Na to the heavier alkalis. This result is sensitive to the inclusion of alkali polarizability and may be interpreted as implying (for M = K, Rb or Cs) almost free relative rotations of the M + and (AlF 4) ; partners at temperatures of relevance to experiment. The consistency of such a viewpoint with electron diffraction data on vapours and with Raman spectra on melts is discussed.

Full text

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Ionic Interactions in Alkali – Aluminium Tetrafluoride Clusters
Z. Akdeniza?d, Z. C ¸ic ¸eka?d, A. Karamana?d, G. Pastoreb, and M. P. Tosia?c
aAbdus Salam International Centre for Theoretical Physics, I-34014 Trieste, Italy
bIstituto Nazionale di Fisica della Materia and Dipartimento di Fisica Teorica,
Universit` a di Trieste, I-34014 Trieste, Italy
cIstituto Nazionale di Fisica della Materia and Classe di Scienze, Scuola Normale Superiore,
I-56126 Pisa, Italy
dPhysics Department, University of Istanbul, Istanbul, Turkey
Reprint requests to Prof. M. P. T.; Fax: +39 050 563513, E-mail: tosim@bibsns.sns.it
Z. Naturforsch. 54 a, 570–574 (1999); received August 20, 1999
Complex anion structures ((AlF4)
minium trifluoride and alkali fluorides in composition-dependent relative concentrations and are
known to interact with the alkali counterions. We present a comparative study of the static and
vibrational structures of MAlF4molecules (with M = any alkali), with the aim of developing and
testing a refined model of the ionic interactions for applications to the M-Al fluoride mixtures.
We find that, whereas an edge-bridged coordination is strongly favoured for Li in LiAlF4, edge-
bridging and face-bridging of the alkali ion become energetically equivalent as one moves from
Na to the heavier alkalis. This result is sensitive to the inclusion of alkali polarizability and may
be interpreted as implying (for M = K, Rb or Cs) almost free relative rotations of the M+and
(AlF4)
with electron diffraction data on vapours and with Raman spectra on melts is discussed.
?, (AlF5)2?and (AlF6)3?) coexist in liquid mixtures of alu-
?partners at temperatures of relevance to experiment. The consistency of such a viewpoint
Keywords:Alkali – Aluminium Tetrafluoride; Charged Clusters; Structure of Associated Liquids.
1. Introduction
It has been known for quite some time from
Raman scattering experiments [1, 2] that in liquid
(AlF3)x
populationsoccursasthecontentofAlF3isdecreased
below the equimolar NaAlF4melt. Special interest is
offered in this range of composition by molten cry-
olite (Na3AlF6), because of its role in the industrial
electrowinning of Al metal from Al2O3[3]. The in-
terpretation of the evidence obtained from very ex-
tensive and detailed measurements of Raman spectra
and thermodynamic properties is that in liquid cry-
olite the (AlF5)2?complex anion coexists with the
(AlF4)
In recent calculations on NanAlFn+3clusters we
have drawn attention to the role of the Na counteri-
ons in stabilizing different states of coordination for
the Al ion by fluorines [7, 8]. The effect of alkali
substitutionon the Raman spectra has also been stud-
ied experimentally [5]. The characteristic bands of
the complexes become sharper in the sequence Li <
Na < K, indicating that the perturbation of the anion
?(NaF)1?xmixtures a gradual shift in cluster
?and (AlF6)3?clusters [4 - 6].
0932–0784 / 99 / 1000–0570 $ 06.00 c
? Verlag der Zeitschrift f¨ ur Naturforschung, T¨ ubingen
? www.znaturforsch.com
structures by the alkali counterions weakens in the
same order.
In the above background it seems relevant to ex-
tend our calculations to clusters with different alkali
ions.Theaimofthepresentworkistoobtainarefined
assessment of the relevant ionic interactions through
a study of the MAlF4molecules (with M = Li, Na,
K, Rb or Cs) in conjunction with the (AlF4)
The modelthatweuse wasfirst developedto evaluate
various neutral and ionized Al chloride clusters [9]
and successfully tested in that case against data
on molecular structure and vibrational frequen-
cies from experiment and from quantum-che-
mical and density-functional calculations. In the
present context it is relevant that ab initio molec-
ular orbital calculations have been carried out
both on the (AlF4)
and on gaseous LiAlF4and NaAlF4molecules
[12, 13]. Indeed, in the lack of suitable ex-
perimental data we make direct use of these
theoreticalresults on
our model parameters for the Li – F inter-
actions.
?anion.
?species in vacuo [10, 11]
LiAlF4
indetermining

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Z. Akdeniz et al. · Alkali – Aluminium Tetrafluoride Clusters571
The plan of the paper is as follows. In Sect. 2 we
give a brief presentation of the essential aspects of
the model and the determination of its parameters.
Our results for the static and vibrational structures
of the MAlF4molecules are reported in Sections 3
and 4, respectively. Each static structure is obtained
as a zero-force configuration of the ionic assembly at
zero temperature, and its mechanical stability is then
assessed by the evaluation of its vibrational frequen-
cies. Finally, Sect. 5 reports a brief summary and a
discussion of the results.
2. Interionic Forces in the MAlF4Clusters
We start by recalling the essential points of the
model that was used in [9] for the potential energy of
a metal halide cluster as a function of the interionic
bond vectors and of the dipole moments carried by
the halogens.
AsinthestandardBornmodelforcohesioninionic
crystals [14], the potential energy function is built
from Coulomb, overlap repulsive and van der Waals
interactions.Inaddition,polarizationenergytermsare
included. Electron-shell deformability is described
through (i) effective valences
charge compensation (Σ
and overlap polarizabilities of the halogens, account-
ing for electrical dipole induction and for changes
in the state of overlap between near-neighbour shells
from relative ionic displacements.
InrelationtotheMAlF4clusters,however,itshould
be noticed that the electrical polarizability of the K+,
Rb+andCs+ionsis actuallylarger thanthatof theF
ion [15]. In this work we have therefore extended the
model to include the classical polarization energy of
thealkaliions.OnlyfortheLi+ionisthepolarizability
completely negligible. For the other alkalis we have
usedthepolarizabilitiesreportedintheworkofJaswal
and Sharma [16].
The other new aspect of the model concerns the
overlap repulsive interactions between the alkali ions
andthefluorineion.Asin[9]wewritetheoverlappo-
tentials in the form proposed by Busing [17], namely
z
i subject to overall
i
z
i = 0), and (ii) electrical
?
?
ij(r) =
f(?
i+
?
j)exp[(R
i+
R
j
?
r)?(?
i+
?
j)]? (1)
where
0.05 e2/˚A2, while
and hardness parameters which for metal ions can be
taken to be proportional to each other. For the alkali
f is chosen to have the standard value
f =
R
iand
?
iare characteristic radii
Table 1. Interionic force parameters (the other parameters
are as in [8]). The symbols FT and TF indicate the source
used for the ratio
RM
??M(see [18], [19]).
?zF
0.941
0.945
0.945
0.946
0.948
0.949
RAl(˚A)
0.997
1.000
0.998
1.011
1.002
1.005
?Al(˚A)
0.0536
0.0538
0.0537
0.0539
0.0539
0.0541
RM(˚A)
0.747
0.996
1.012
1.300
1.402
1.562
?M(˚A)
0.0769
0.0979
0.120
0.109
0.0998
0.0608
LiAlF4(TF)
NaAlF4(TF)
NaAlF4(FT)
KAlF4(TF)
RbAlF4(TF)
CsAlF4(TF)
ions we have taken the ratios
alkali halides and tested the sensitivity of the results
by two alternative choices. These are denoted in the
following as FT [18] and TF [19].
Further simplification is achieved by assuming
transferability of potential-energy parameters for
halogens between different compounds [9]. Adopt-
ing,therefore,theparametersforthefluorineionused
in earlier studies of fluorides [8], the potential energy
functionforeachMAlF4clusterinvolvesthreedispos-
ableparameterswhicharetheradii
twometalionsandtheeffectivevalenceofthefluorine
ion. These have been determined by fitting the mea-
sured values of (i) the Al-F bond length in (AlF4)
(1.69˚A [10]), (ii) the M-F bond length from molec-
ular-orbital calculations in LiAlF4[13] and from ex-
periment in the other MAlF4molecules [20], and (iii)
the Al-F bond stretching frequency (the topmost
vibrational mode) of the MAlF4molecules from IR
matrix data [21].
Table 1 reports the values of the effective fluorine
valence and the metal-ion repulsive parameters that
we have obtained. The effective valences are smaller
than the full nominal valences by only about 5% in
all cases, so that these molecules are seen to conform
closely to the ideal ionic model. A reduction of the
nominalvalenceby7% wasfoundfor thefluorineion
in NaF crystals from dielectric constant studies [22].
The repulsive parameters of Al are also essentially
constant throughthe family of clusters. The results of
the alternativechoicesof repulsiveparameters for the
alkali ions (FT versus TF) are illustrated in Table 1
for NaAlF4. Their consequences will be tested in the
calculations of the static structure that we report in
the next section.
RM
??Mfrom work on
RAland
RMofthe
?
B1
3. Structure of MAlF4Clusters
We comparatively discuss in this section the edge-
bridged (two-fold coordinated) and face-bridged

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572 Z. Akdeniz et al. · Alkali – Aluminium Tetrafluoride Clusters
Table 2. Equilibrium structure of MAlF4(II) (bond lengths
in˚A, bond angles in degrees; F* denotes a fluorine bonding
the M ion).
M-F* Al-F* Al-F
? F*-Al-F*
? F-Al-F
LiAlF4(II): TF:1.77 1.75
1.737 1.639
1.74
1.74
1.721 1.646
1.73
1.73
1.725 1.67
1.6588.3
88.4
92.8
92.8
93.6
96.5
97.3
98.3
117.7
118.2
116.8
116.7
116.4
116.0
115.8
115.6
QC [13] 1.77
NaAlF4(II): TF: 2.11
2.11
1.65
1.65
FT:
QC [13] 2.12
TF:
KAlF4(II):
RbAlF4(II): TF:
CsAlF4(II): TF:
2.51
2.64
2.84
1.66
1.66
Table 3. Equilibrium structure of MAlF4(III) (bond lengths
in˚A, bond angles in degrees; F* denotes a fluorine bonding
the Na ion).
M-F* Al-F*Al-F
? F-Al-F*
LiAlF4(III): TF:
NaAlF4(III): TF:
2.02
2.35
2.37
2.282
2.74
2.85
3.02
1.72
1.71
1.71
1.698
1.71
1.71
1.71
1.64
1.64
1.64
1.634
1.65
1.65
1.66
122.4
119.4
119.3
119.7
117.2
116.8
116.2
FT:
QC
KAlF4(III): TF:
RbAlF4(III): TF:
CsAlF4(III): TF:
(three-fold coordinated) configurations for the alkali
ion in MAlF4: these are indicated as MAlF4(II) and
MAlF4(III), respectively. We exclude a corner-brid-
ged zero-force configuration, which has a very high
energy relative to the ground state [13, 8]. We also
remark that LiAlF4(III) is obtained in our calcula-
tions as a zero-force configurationwhich is, however,
mechanically unstable.
Our results for these two structures are shown in
Tables 2 and 3, together with those of the quantum-
chemical (QC) calculations reported by Scholz and
Curtiss for LiAlF4and NaAlF4[13]. Here and in the
following Tables we underline the values that have
been adjusted in the fitting of the model parameters.
Two main remarks are in order: (i) there is little sen-
sitivity to the input on the alkali ion repulsive pa-
rameters (FT versus TF) and very good agreement
withtheavailableQC results in boththe bondlengths
and the bond angles; and (ii) the alkali ion imparts a
small distortion to the basic (AlF4)
amounts which show little dependence on the nature
of the alkali ion and on its bridging configuration.
If we exclude LiAlF4, for which the edge-bridged
structure is very definitely the ground state and the
?tetrahedron, by
Table 4. Relative energies of MAlF4(II) and MAlF4(III)
(in eV). The ground state is taken at zero energy.
II III
LiAlF4: TF:
QC
TF:
FT:
QC
TF:
TF:
TF:
0
0
0
0
0.05
0
0.01
0.05
0.30
0.21
0.12
0.14
0
0.02
0
0
NaAlF4:
KAlF4:
RbAlF4:
CsAlF4:
face-bridged one is mechanically unstable in our cal-
culations, the two structures for MAlF4have very
similar energies. This fact was already demonstrated
for NaAlF4by Scholz and Curtiss [13], who found
that the ground state is edge-bridged in Hartree-Fock
butbecomesface-bridgedafterapproximateinclusion
of correlations, with energy differences at the level of
? 0.05 eV betweenthe two structures. Our results for
the relative energy of the two structures are shown in
Table 4. We find that the edge-bridged configuration
is the ground state for NaAlF4by about 0.1 eV, but
in the case of KAlF4, RbAlF4and CsAlF4the energy
difference between the two structures is practically
completely negligible. It should be remarked that the
inclusion of electrical polarization of the alkali stabi-
lizes the edge-bridged structure relative to the face-
bridgedonebyaveryconsiderableamount–byabout
0.3 eV in KAlF4up to about 0.9 eV in CsAlF4. More
precisely, increasing size of the alkali ion favours its
three-fold coordination, but this effect is balanced by
the accompanying increase in polarizability.
We believe, therefore, that the energy differences
reported in the last three rows of Table 4 are within
noise. The conclusion from the above results for the
two static structures and for their relative energies is
that (excluding again the case of LiAlF4) they are
essentially equivalent at the temperatures of interest
for experiment. This result seems to be not incon-
sistent with the experimental evidence from electron
diffraction on high-temperature vapours [20]. These
experimentshavebeeninterpretedintermsofthetwo-
fold structure, but no distortion in the basic (AlF4)
tetrahedron has been reported – as if the alkali ion
were rapidly moving around it and averaging out the
difference between bonding and terminal fluorines.
The average Al-F bond length is reported to be in
the range 1.69 - 1.696˚A, in excellent agreement with
the averages of the calculated bond lengths given in
?

Page 4

Z. Akdeniz et al. · Alkali – Aluminium Tetrafluoride Clusters 573
Tables 2 and 3. In the case of KAlF4a puckering of
the K-F*-Al-F* ring has been reported [23], yielding
a position of the K ion which is intermediatebetween
two-fold and three-fold bonding.
ThevibrationalspectraofthegaseousMAlF4clus-
ters have not been measured directly, but have been
estimated from IR matrix isolation data [21]. The re-
sults have been interpreted as indicating a C2vsym-
metry, which is consistent with the double-bridged
structure [21, 24]. Of course, for the heavier alkalis
the matrix may be expected to block their motions
around the (AlF4)
In summary, our results are in accord with the ab
initio molecular orbital calculations on the gaseous
LiAlF4cluster and with the experimental evidence
on the gaseous and matrix-isolated NaAlF4cluster in
predictingthetwo-fold, edge-bridgedcoordinationof
the alkali ion as being the favoured one. The trend
from LiAlF4to NaAlF4is to reduce the energy dif-
ference between edge-bridged and face-bridged con-
figurations, again in agreement with the ab initio cal-
culations. For the other alkali tetrafluoride clusters
we then find that these two configurations have es-
sentially the same cohesive energy and suggest that
the (AlF4)
ier alkalis as an almost spherical unit. These results
agreewiththefactthatfromRamanscatteringstudies
of melts [5] the perturbations of the (AlF4)
themeltareobservedtodecreaseinthesequenceLi>
Na > K.
?tetrahedron.
?tetrahedron may be seen by the heav-
?anion in
4. Vibrational Spectrum of MAlF4in the Edge-
Bridged Structure
As mentioned just above, the vibrational spectra
of the MAlF4clusters have been interpreted from IR
matrix isolation data as indicating a C2vmolecular
symmetry [21, 24]. Table 5 collects our results for
the vibrational frequencies of the gaseous MAlF4(II)
clusters, in comparison with the data of Huglen et
al. [21] from the matrix isolation experiments. The
values of the highest
fittedtodeterminetheeffectiveionicvalenceandhave
yieldedclosely similar values of this parameter in the
various clusters (see Table 1).
Theoverallqualityof thesecomparisonsis reason-
ably satisfactory. The bond-stretching modes in Ta-
ble 5 are reproduced rather accurately by the model,
B1mode frequency have been
Table 5. Frequencies of vibrational modes (in cm
MAlF4(II). For each cluster the second coulumn reports
the values estimated from IR matrix isolation experiments
(from [21]; frequencies in parentheses are calculated from
a normal-mode analysis).
?1) for
LiAlF4
NaAlF4
KAlF4
RbAlF4
CsAlF4
A1 823 817
608
560
812
621
350
808
613
378
803
627
331
805
618
351
803
630
330
801
619
341
800
632
326
798
620
330
612
476
310 (361) 293 (291) 243 (284) 231 (281) 231 (280)
220220 171 (180) 128 (149) 120 (106) 121
269195 269178 (269) 180 (269) 182 (269)
911893893 877
330 316 302 304 302
115 15753 (102)30
B2 620644635669658
374 450 314339311
220 270172 200163 (175) 130 (148) 125 (136)
(90)
A2 231
B1 911877
303
(90)
695
317
874
304
24
668
312
874
303
(79)
696
312
868
304
17
677
313
868
303
(76)
699
308
whereasbond-bendingmodesaregenerallymoresen-
sitive to the details of the ionic interactions. Never-
theless, we have found only moderate sensitivity of
these results to the inclusion of alkali polarizability
and to the input on overlap repulsive interactions.
5. Summary and Concluding Remarks
The fundamental and industrial interest presented
by the Al-alkali fluorides would justify a special ef-
fort to use specific methods in the study of the stable
local structures in their liquid phase, i.e. diffraction
and EXAFS experiments and computer simulations.
Inthisworkwehavedevelopedarefinedphenomeno-
logical model of the ionic interactions from the study
of the MAlF4clusters in comparison with data from
experiment and from ab initio molecular orbital cal-
culations.
We have also proposed an explanation for the ob-
servation from liquid-state Raman scattering studies
that the interaction of the complex anions in the melt
with the alkali counterions is strongest in the case
of Li and progressively weakens on substitution with
Na and then with K. In the free clusters we have
found that the Li ion is fairly strongly bound to two
fluorines in the basic (AlF4)
it will act as a strong perturbation on the internal
modes of the complex anion. As we move to Na and
then to the heavier alkalis, the two-fold and three-
fold bound states of the alkali effectively become en-
ergetically equivalent. This equivalence implies that
?tetrahedron, so that

Page 5

574Z. Akdeniz et al. · Alkali – Aluminium Tetrafluoride Clusters
for the heavier alkalis the MAlF4cluster may al-
most be viewed as a diatomic molecule composed
of M+and (AlF4)
tions of the latter unit become almost independent
of the alkali partner. Confirmation for this viewpoint
can be found through a careful comparison of the fre-
quencies of the various clusters across each row of
Table 5.
?units and that the internal vibra-
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Acknowledgements
We acknowledge the award of the NATO Grant
CRG.CRG.974429. One of us (ZA) acknowledges
support from the Turkish Scientific and Technologi-
calResearchCouncil(Tubitak)andfromtheResearch
FundoftheUniversityofIstanbulunderProjectNum-
ber BA-20/040599.