IL NUOVO CIMENTO VOL. 10 D, N. 12 Dicembre 1988

Binding of Tetrahedral Halocomplexes of Polyvalent Metal Ions in an Ionic Model.

WANG LI

International School of Advanced Studies - Trieste, Italia

M. P . TOSI

Department of Theoretical Physics - University of Trieste - Trieste, Italia

(ricevuto il 23 Giugno 1988)

Summary. - - Long-lived tetrahedral coordination of polyvalent metal ions by halogen ions is known to be stable in a number of liquid halide mixtures. We evaluate the binding of isolated tetrahedral halocomplexes for the alkaline earth metals and for A1, with the main aim of assessing their stability and their bond length. An appropriate interionic force model is available for the halides of Mg, Ca, Sr and Ba from analyses of cohesion in their crystalline state and in dihalide molecules. The model is extended to the ha!ides of Be and A1 with the adjustment of a parameter to the measured Be-F and At-C1 bond lengths in liquid mixtures. The semi-quantitative usefulness of the model is confirmed by comparisons with bond lengths for other A1 halides and with extensive information on local vibrational frequencies from Raman scattering and infrared emission experiments on liquid halides.

PACS 61.25 - Studies of specific liquid structures.

1. - I n t r o d u c t i o n .

Local tetrahedral, coordination by halogen ions is known to be v e ry stable for A1, Be and Mg ions in molten mixtures of their halides with halogen ion donors (typically alkali halides). The best known and most important instance is that of liquid mixtures of A1C13 and alkali chlorides, which have been studied by X-ray diffraction (9 and neut ron diffraction (2) as well as by Raman scat ter ing (s,4) and

(') S. TAKAHASHI, T. MUNETA, N. KOURA and H. OHNO: J. Chem. Soc. Faraday Trans. 2, 81, 319 and 1107 (1985); S. TAKAHASHI, K. MARUOKA, N. KOURA and H. OHNO:

1497

1498 WANG LI and M. P. TOSI

infrared emission (5) techniques. Characteristic Raman spectra (3,6) and values for the Al-halogen bond length (7) have also been reported for other Al-alkali halide systems. X-ray diffraction data are again available for the Be-Li fluoride mixture at various compositions (8) and together with Raman scattering data (9) show stability of te t rahedral coordination for this polyvalent ion as well. Most of the evidence on other alkaline earth-alkali halide mixtures comes from Raman scat ter ing experiments(1~ and from thermochemical measurements(14,16). These data locate the boundary for stability of local te trahedral coordination in halide mixtures within the Ca and Sr based systems, in dependence on the alkali halide par tner species.

Two established features of these complex-forming liquids are worth stressing here in relation to the present work. First ly, the bond length within a te t rahedral ly coordinated unit is remarkably insensitive to the environment. We may refer, for example, to the X-ray data of Vaslow and Nar ten (8) on the (BeF2)c-(LiF)l_c system, showing that within an experimental uncertainty of (0.01 - 0.02)/~ the Be-F bond length is constant for concentration c in the range from 1 to 0.2 and temperature in the range (400 + 745) ~ The results of semi- empirical quantum chemistry calculations by Davis et al. (17) on the (A1C14)- and (A12Clv)- species, both in the isolated state and in the presence of a few model

J. Chem. Phys., 84, 408 (1986). (2) S. BIGGIN, S. CUMMINGS, J. E. ENDERBY and M. BLANDER: Proceedings of the Molten Salts Symposium (Las Vegas, Cal., 1985). (8) G. M. BEGUN, C. R. BOSTEN, G. TORSI and G. MAMANTOV: Inorg. Chem., 10, 886 (1971). (a) H. A. 0YE, E. RYTTER, P. KL/EBOE and S. J. CYVIN: Acta Chem. Scand., 25, 559 (1971). (5) j . HVISTENDAHL, P. KL~EBOE, E. RYTTER and H. A. 0YE: Inorg. Chem., 23, 706 (1984). (5) B. (v) A. (8) F. (9) A. (10) V.

GILBERT, G. MAMANTOV and G. M. BEGUN: J. Chem. Phys., 62, 950 (1975). MANTEGHETTI and A. POTIER: Spectrochim. Acta A, 38, 141 (1982). VASLOW and A. H. NARTEN: J. Chem. Phys., 59, 4949 (1973). S. QUIST, J. B. BATES and G. E. BOYD: J. Phys. Chem., 76, 78 (1972). A. MARONI: J. Chem. Phys., 55, 4789 (1971).

(1,) M. H. BROOKER: J. Chem. Phys., 63, 3054 (1975). (12) V. D. PRISYAZHNYI, S. P. BARANOV and G. P. SUNEGIN: Z. Neorg. Khim., 23, 1678 (1978) [English translation: Russian J. Inorg. Chem., 23, 923 (1978)]. (,8) K. SAKAI, T. NAKAMURA, N. UMESAKI and N. IWAMOTO: Phys. Chem. Liq., 14, 67 (1984). (14) H. H. EMONS, W. HORLBECK and D. KIESSLING: Z. anorg, aUg. Chem., 510, 152 (1984). (15) W. BUES, M. ATAPOUR and G. POPPERL: 163rd Meeting, The Electrochem Soc. (San Francisco, Cal., 1983). (18) O. J. KLEPPA and F. G. MCCARTY: J. Phys. Chem., 70, 1249 (1966); T. 0STVOLD: J. Phys. Chem., 76, 1616 (1972). (17) L. P. DAVIS, C. J. DYMEK, J. J. STEWART, H. P. CLARK and W. J. LAUDERDALE: J.

BINDING OF TETRAHEDRAL HALOCOMPLEXES ETC. 1499

external charges, agree with this view. Secondly, phenomenological ionic models are at least qualitatively adequate for liquid structure calculations on these systems. In particular computer simulation work by Saboungi et al. (18) on an A1Cl~-NaC1 mixture at various compositions has shown that a simple ionic model can account for a number of structural features, including the tetrahedral coordination of the A1 ions and the sharing of chlorines among neighbouring tetrahedra with increasing concentration of A1CI~. Furthermore the stability of tetrahedral complexes as a function of the components of the mixture has been successfully classified (,9) in an ionic viewpoint, which leads to a Mott criterion for bound-state formation relating it to a balance between the bond length in the complex and the screening length of the ionic liquid.

The above considerations have motivated the present work(2~ For theoretical work on liquid structure and complex stability one needs some assessment of phenomenological interionic forces and of complex binding energy and bond length. Calculations on an isolated complex can be expected to already provide useful information for these purposes. We carry out such calculations systematically for all the halides of A1 and of all the alkaline earth metals---including therefore also the systems in which tetrahedral coordination is not the preferred one in the liquid. For those systems that do prefer this coordination, we believe that our estimates of bond lengths should be directly comparable with the results of liquid-state diffraction experiments as these become available.

The outline of the paper is briefly as follows. In sect. 2 we present first our treatment of the potential energy for the tetrahedral configuration, which includes electronic polarization of the halogens by a deformation dipole model previously used(~1) for alkaline earth dihalide molecules. The short-range components of the interionic forces are taken to have the Busing form (~), the determination of the relevant parameters by Yuen et al. (~) being extended to include the halides of Be and A1. Results for the bond length and the binding energy of complexes are also given in this section with a discussion of the relevance of halogen polarization. The model is then used in sect. 3 to treat distorted configurations of the complex as needed for an evaluation of its normal

Am. Chem. Soc., 107, 5041 (1985). (18) M. L. SABOUNGI, A. RAHMAN and M. BLANDER: J. Chem. Phys., 80, 2141 (1984); M. BLANDER, M. L. SABOUNGI and A. RAHMAN: J. Chem. Phys., 85, 3995 (1986). (19) Z. AKDENIZ and M. P. TONI: Phys. Chem. Liq., 17, 91 (1987); Z. AKDENIZ, WANG LI and M. P. TOSI: Europhys. Lett., 5, 613 (1988). (2o) A preliminary report has been presented at the Adriatico Research Conference on Interatomic Forces in Relation to Defects and Disorder in Condensed Matter (Trieste, August 1987): see A. FERRANTE, WANG LI and M. P. TONI: Philos. Mag. A, 58, 13 (1988). (2,) G. GALLI and M. P. TONI: Nuovo Cimento D, 4, 413 (1984). (~) W. R. BUSING: Trans. Am. Crystallogr. Assoc., 6, 57 (1970). (28) p. S. YUEN, R. M. MURFITT and R. L. COLLIN: J. Chem. Phys., 61, 2383 (1974).

1500 WANG Li and M. P. TOSI

modes of vibration. The calculation of the vibrational frequencies is reformulated as an evaluation of the force constants in a Urey-Bradley valence force field method (~) from known interatomic force laws. The results for the vibrational frequencies are compared with the evidence which is available from experiments on complex-forming liquid halides, the relevance of electronic polarization in the theoretical results being again discussed: Finally sect. 4 gives a brief summary and discussion.

2. - B ind ing and bond length.

The potential energy U of the tetrahedral configuration for a (MX4) Z-4 complex formed by a metal ion M of valence Z with four halogen ions X, relative to the state of free ions, is taken to be a function of the M-X bond length r and of the magnitude p of a dipole moment, which is located on each X ion and is outwardly directed along the bond. In the deformation dipole model(~') this function is given by

6e 2 10p 2 2p 2 (2.1) U(r ,p )=- 4Ze-----~2 + - 7 - 4 p [ E ( r ) - B ( r ) ] + - ~ - + + 4r + 6r

r ot X

where

Z e 61/2 _~e (2.2) E(r) = --~ - rr2

and

(2.3) I Y I

B(r)= x g

Here, r ' = (8/3)1/2r is the X-X distance, r is the short-range part of the interaction between two ions at distance rij, E(r) is the electric field created on an X ion by the ionic charges and B(r) describes the effect of M-X overlap on halogen ion dipolar deformation. This is determined by the overlap repulsive

rep force between the two ions, which contributes to CMx(r) by the amount CMx(r). The further constants entering the above equations are the halogen polarizability ~x, the halogen effective shell charge Y and the halogen shell-core force constant K.

The equilibrium value po(r) of the dipole moment is immediately obtained by

(~) See, for instance, J. R. FERRARO and J. S. ZIOMEK: Introductory Group Theory (Plenum Press, New York, N.Y., 1975).

B I N D I N G O F T E T R A H E D R A L H A L O C O M P L E X E S E T C . 1501

minimization of eq. (2.1) as

(2.4) po(r) = ~x[E(r) - B(r)]/(1 + 5~x/r '~)

whereupon the potential energy as a function of the bond length becomes

(2.5) U(r, po(r)) = 4Ze2 + 6e2 - 2po(r)[E(r) - B(r)] + 4r + 6r - - 7 - 7

Numerical minimization of this function yields the equilibrium value ro of the bond length and the molecular well depth Uo = - U(ro, po(ro)).

The short-range interionic potentials r that were adopted in the calculations reported below consist of an attractive van der Waals term and an overlap repulsive term in the form proposed by Busing(22),

c~cj _ _ - - r e p .. (2.6) r = r~j + r (r~3)

with

(2.7) rep �9 r (rij) = f (Pi + ~j) exp [(Ri + R j - rij)/(pi + pj)]

These potentials have the obvious advantage that a family of compounds can be described by a limited number of independent parameters.

2"1. R e s u l t s f o r the hal ides of Mg, Ca, Sr and Ba. - The parameters entering eqs. (2.3), (2.6) and (2.7) were taken for Mg, Ca, Sr and Ba halides from the work of Yuen et al. (~) and of Galli and Tosi (~1), except for slight changes in the halogen polarizability according to the work of Jaswal and Sharma(25). The model is therefore already known to provide a good description of these systems in the crystalline state and in the dihalide molecular state. Our calculated values for the equilibrium bond length and potential energy well in a complex are given in table I.

TABLE I. - Equil ibrium bond length ro (1~) and well depth Uo (kcal/mol) for alkaline earth halide complexes.

F C1 Br I

ro Uo ro Uo ro Yo ro Uo

Mg 1.88 668 2.35 576 2.50 548 2.70 511 Ca 2.18 592 2.63 509 2.80 487 3.00 459 Sr 2.33 557 2.81 483 2.94 463 3.14 437 Ba 2.49 522 2.96 455 3.10 437 3.30 414

(2~) S. S. JASWAL and T. P. SHARMA: J. Phys. Chem. Solids, 34, 509 (1973).

1502 WANG LI a n d M. P. TOSI

The reliability of the model in relation to complexes in these systems can only be gauged through a calculation of vibrational frequencies, that we shall give in sect. 3 below. For the present we merely note the following points.

i) Our calculated values for the bond length in alkaline earth halide complexes are only slightly larger than the measured bond lengths (26) in the corresponding dihalide molecules, the difference being of order ( 0 . 1 - 0.2)/~. This property, and values of U0 having the magnitude indicated in table I, were anticipated in earlier work (29) on molten alkaline earth-alkali halide mixtures. Comparison of U0 with the theoretical results of Galli and Tosi (22) for the binding energy of dihalide molecules shows that, given a free supply of halogen ions, a complex is energetically stable against dissociation into MX2 + 2X-.

ii) Our results for the bond length are insensitive to the inclusion of halogen polarizability, which was examined by simply setting ax = 0 in the model. This leads to changes of r0 at the level of a few to several hundredths of an angstrSm. On the contrary the values of U0 are quite sensitive to halogen polarization. Relative to a model with ax = 0, the well is deepened by up to several tens of kcal/mol. These figures may be taken as indicative of the uncertainty of the results in table I.

2"2. Interionic force model and results for Be and A1 halides. - The estimation of short-range interionic forces in Be and A1 halides can be reduced to the determination of a single metal-dependent parameter through the following assumptions: a) the van der Waals constants cA, and cBe are negligibly small, in view of the very small polarizability of these ions; b) the overlap repulsive parameters for the halogens can be taken over from the other alkaline earth halides, and c) the overlap parameters RM and p~ for the metal ion are not independent--in fact, from the results of Yuen et al. (~) we find the linear relationship

(2.8) RM ---- 18.6t~M,

as illustrated in fig. 1. An estimation of overlap polarization parameters is instead very uncertain.

As will also become clear from the results in sect. 3 below, it is probably unwarranted at the present stage to go beyond a nonpolarizable-halogen model for these systems. In addition to examining such a model, however, we have also made for illustrative purposes some crude guesses at values of halogen polarization parameters by extrapolation from those available for the other alkaline earth halides, in spite of the different electronic structure of the Be 2+ ion (no p states in the ionic core) and of the different charge state of the A1 e§ ion.

(26) p. AKISHIN and V. P. SPIRIDONOV: Kristallografiya, 2, 475 (1957).

BINDING OF TETRAHEDRAL HALOCOMPLEXES ETC. 1503

Q:

1.80

1.62 B ~ / /

1./-J+ C So , /

1.26 M /

1.08

0.90 ~ = = i = i , , , 0.040 0.052 0.064 0.076 0.088 0.100

o(,~) Fig . 1. - L i n e a r r e l a t ion b e t w e e n t h e m e t a l r ad ius RM and t he m e t a l r epu l s ive p a r a m e t e r PM in t h e ha l ides of Mg, Ca, S r and Ba.

TABLE II . - I n t e r i o n i c force parameters and binding properties of complexes in Be and Al halides (*).

RM PM Rx ~x Cx ax IYI/K ro Uo (/~) (/~) (/~) (/~) (eA 5/2) (A ~) (~3/e) (/~) (kcal/mol)

B e - F N P X 0.782 0.0420 1.32 0.215 2.08 - - - - (1.58) 760 P X 0.733 0.0394 1.32 0.215 2.08 0.88 0.67 (1.58) 800

Be-C1 N P X 0.782 0.0420 1.71 0.238 5.50 - - - - 2.10 600 P X 0.733 0.0394 1.71 0.238 5.50 3.00 0.83 2.05 670

B e - B r N P X 0.782 0.0420 1.84 0.258 7.17 - - - - 2.24 560 P X 0.733 0.0394 1.84 0.258 7.17 4.17 1.2 2.19 630

B e - I N P X 0.782 0.0420 2.02 0.289 10.1 - - - - 2.45 510 P X 0.733 0.0394 2.02 0.289 10.1 6.29 1.7 2.40 580

A1-F N P X 1.06 0.0571 1.32 0.215 2.08 - - - - 1.66 1400 P X 1.05 0.0565 1.32 0.215 2.08 0.88 0.48 1.71 1480

A1-C1 N P X 1.06 0.0571 1.71 0.238 5.50 - - - - (2.15) 1110 P X 1.05 0.0565 1.71 0.238 5.50 3.00 0.83 (2.15) 1290

A1-Br N P X 1.06 0.0571 1.84 0.258 7.17 - - - - 2.27 1050 P X 1.05 0.0565 1.84 0.258 7.17 4.17 1.2 2.28 1240

Al- I N P X 1.06 0.0571 2.02 0.289 10.1 - - - - 2.45 980 P X 1.05 0.0565 2.02 0.289 10.1 6.29 1.7 2.45 1180

(*) f= 0.05 e2/~?. Values of ro in parentheses have been fitted to experimental data. The halogen polarizability ~x is from the work of Jaswal and Sharma (25) and the halogen shell deformation parameter Y/K is taken from other alkaline earth halides (Galli and Tosi (21)), extrapolation being involved in the case of the fluorides. As discussed in sect. 3 of the main text, this choice of polarization parameters very likely overestimates the effects of halogen polarization for the systems in this table, especially for the chloride, bromide and iodide of Be.

1504 WANG LI and M. P. TOSI

On the above assumptions the only independent parameters for all the Be and A1 halides are the radii RBe and RA1 for the Be 2+ and A1 *+ ion. These were determined by fitting the measured Be-F and A1-C1 bond lengths in liquid halide mixtures, from the data of Vaslow and Narten (8) (rBe-F = 1.58/~) and of Biggin e t

a l . ( 2 ) (rAl.c~=2.15/~). The resulting values of the parameters and the corresponding values of r0 and U0 are given in table II, the two alternative treatments of halogen polarizability being indicated by the symbols NPX (nonpolarizable halogens) and PX (polarizable halogens).

We note again from the last two columns of table II the relative insensitivity of the bond length and the huge sensitivity of the well depth to the details of the model. The main test of the model will again be deferred to the calculation of the vibrational frequencies in sect. 3 below. However, values for the Al-halogen bond lengths have been proposed previously by Manteghetti and Potier (7) on the basis of X-ray structural data and Raman scattering data. Their values are rAl-C1 = 2.10A (in fair agreement with the values r A l - C 1 = (2.13 + 2.15)/~ from recent X-ray data(') and rAl.cl=2.15A from neutron diffraction(2)), rAl_Br =

= (2.27 -- 2.28)/~ and rAl-i = 2.42/~. The latter values are in close agreement with our results in table II.

3. - V i b r a t i o n a l f r e q u e n c i e s .

As is well known(24), a tetrahedral MX4 molecule has four independent vibrational frequencies, corresponding to normal modes which are reproduced in fig. 2 for reader's convenience. The mode vl is associated with pure bond

Fig. 2. - Normal modes of vibration of tetrahedral MX4 molecules.

stretching in the tetrahedral configuration and is the most commonly observed in Raman scattering experiments on molten salt mixtures. The other modes describe distortions of the equilibrium tetrahedral shape and thus involve bond bending as well. It is also clear from the figure that for a (MX4) 2- complex, with M a divalent ion, the v4 mode is the precursor for break-up into a neutral dihalide molecule plus two isolated halogen ions. A similar comment applies to the v3 mode in the case of a (MX4)- complex made by a trivalent ion.

The potential energy of the complex in an arbitrarily distorted configuration is easily written, within the ionic model described in sect. 2, as a function of

BINDING OF TETRAHEDRAL HALOCOMPLEXES ETC. 1505

geo~:z~rical parameters which may be taken as the changes hri in the four M-X

bonds and the changes h~j in the X~-M-Xj angles for pairs of halogens. Therefore, for small values of these deviations from equilibrium our model is equivalent to a realization of the Urey-Bradley valence force field method (u), which writes the change of potential energy in a molecular vibration as

(3.1)

21/2 2 + l (2F- F') ~ AriArj +-~-ro(r + F') ~ Ar~5a~j- ~F' ~ AaijA~j~,

i~j i~j i~j~k

the sums running over the halogens. The four force constants K, F, F' and H can clearly be evaluated in our model by evaluating the change in potential energy in four suitably distorted configurations and by comparison with eq. (3.1).

Specifically, we have considered the following distorted configurations:

i) hri = hr (all i) and h~ij= 0 (all i,j), determining the force constant K § 4F which is associated with the vl mode;

ii) Ar~ = 0 (all i) and A~12 = ~34 = -- 2 A~13 = -- 2 ~14 = -- 2 A~23 = = - - 2 A a u = A a , determining the force constant (3H+F-F') /4 which is associated with the v2 mode;

i i i ) A r i = A r 2 ----- A r 3 ---- - - A t 4 / 3 --- Ar and Aa~j = 0 (all i,j), which determines the force constant 3K + 4F + 4F' (modes v3 and v4);

iv) Ar~ = 0 (all i) and A~14 = A ~ = A~4 = -- A~12 = -- A~I~ = -- Aa23 = A~, yielding the force constant (3H + F - 9F')/2 (modes v8 and v,). The corresponding results for the vibrational frequencies are reported in table III, comparison with Raman scattering experiments on complexes in molten halides being shown wherever possible.

The first general observation that can be made on all the theoretical results in table III is that they show definite trends for the relative magnitudes of the four vibrational frequencies in each system and for the variation of each vibrational frequency with changing a) the metal ion and b) the halogen ion. The same trends are evident also in the available experimental data. Clearly, complexes are considerably stiffer against bond stretching than against bond bending and stiffness generally decreases in going from A1 and Be to Ba and from F to I. The frequency of the v4 mode governing dissociation of a free, doubly charged complex is becoming quite low at the bottom of the alkaline earth metal series.

Of course, a fully quantitative comparison between our calculated vibrational frequencies for isolated complexes and the available data on complexes in liquids is not appropriate, since the data reflect to some extent the effects of the liquid

1506 WANG LI a n d M. P. TOSI

I

~2

%)

iz I

s

" ~ Lr 5',,,]

,,..-4 oO ~.~

c

v

r r tt'~

' ~ t',.- r ~ t'*- O0

C r " ~ r

C

g-.

g-,

g-,

0 0 O0 5x]

5%]

t"*- 5"q

0 0 t'-.* ~ . - o 0

r

oO

4-, O0 ~ 5x,l

g-,

r 1 6 2

1/'5 ~-..* ~

r r r

r

r

oO

�9 r t"--

5'q

t ' .-

g-,

�9

g-, v 5"4

C"

g-,

~x] 5x]

r

r

O0

5",] 5x,]

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r 1 6 2

" ~ r

t""

t""

r

r

5X]

r

t"--

r 1 6 2

r162

r

09

BINDING OF TETRAHEDRAL HALOCOMPLEXES ETC. 1507

matrix and of temperature. Nevertheless, the following points can be made upon detailed comparison between theory and experiment. Our results are surprisingly good for the Mg halides and of acceptable quality for (BeF4) 2-. In the other Be halides, the vt mode was found to be unstable when halogen polarizability was included with the shell parameters shown in table II. One might argue that break-up of a doubly charged complex might occur in vacuo even if the complex is stable in a molten state, where charge compensation is ensured by the environment. However, we rather believe that in the present instance instability is merely an indicator of a poor choice for the polarizability parameters in table II. Therefore, for the Be halides the NPX values for v4 should be regarded as our theoretical estimates for an upper limit on the value of this frequency. Similarly, the NPX and PX values for Vl, v2 and v3 should be regarded as theoretical estimates of the ranges in which these frequencies would be expected to lie. We stress again that at the present stage only an NPX model is warranted for the halides of Be and A1. With regard to complexes of the latter metal ion, we note from table III that our NPX model is in surprisingly close agreement with experiment and that some role of halogen polarization is suggested by the behaviour of the vt mode as one goes from the fluoride to the iodide.

4. - C o n c l u d i n g r e m a r k s .

The main qualitative result of this work has been to demonstrate the usefulness of a simple ionic model in describing selected properties for a broad class of systems, where one might feel a priori that heavy quantum chemistry approaches should necessarily be taken. In particular, structural properties such as the bond lengths in tables I and II appear to be reliably predicted with an accuracy of the order of _+ 0.05/~. Semi-quantitative predictions appear to be easily achieved also for the vibrational dynamics of these systems. In this connection it may be useful to take advantage of the experimental data on vibrational frequencies of the A1 halides and of Be fluoride for the purpose of refining the primitive estimates of interionic forces that we have proposed for these systems.

On the other hand, reliable predictions of thermodynamic properties are clearly going to be much more difficult. This is demonstrated by the large sensitivity of the well depth in tables I and II to details of the model. Similarly, one would expect such simple models to be inadequate to describe diffusional dynamics and transport properties in the liquid state, where they will inevitably underestimate the lifetime of the bond.

101 - I I N u o v o C i m e n t o D

1508 WANG L1 and M. P. TOSI

�9 R I A S S U N T O

l~ noto che ioni di metal l i polivalenti in numerose miscele di a logenuri fusi sono coordinati t e t r a e d r i c a m e n t e da ioni alogeno. Ne l lavoro si calcolano le propr ie t~ di legame di complessi t e t raedr ic i isolati format i con gli alogeni dai metal l i alcal ino-terrosi e dall'A1, con par t icolare a t tenz ione alla loro stabilit/t e lunghezze di legame. Si usa a questo scopo un modello ionico der iva to per gli a logenuri di Mg, Ca, Sr e Ba da proprietf i coesive delle fasi solida e gassosa, es tendendolo poi agli a logenuri di Be e di A1. L'ut i l i t~ semi- quan t i t a t iva del modello ~ confermata dal confronto con dati sper imenta l i pe r a logenuri liquidi, r iguardant i pr inc ipa lmente le f requenze vibrazionali locali da esper iment i di diffusione Raman.

CBE[3b TeTpa3~plPleCKI4X Fa.YlOKOMHJIeKCOB IIO~llBa.YleHTHblX MeTa.~IJiIIqeCKiIX I4OHOB B

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