Nuclear techniques in structural chemistry

Jointly published by Elsevier Science S. A., Lausanne and Akad~miai Kiad6, Budapest

Journal of Radioanalytical and Nuclear Chemistry, Articles, Vol. 203, No. 2 (1996) 399-412

NUCLEAR TECHNIQUES IN STRUCTURAL CHEMISTRY A. Vt~RTES,* K. SUVEGH,* E. KUZMANN,* K. BURGER,** L. NAGY,** K. SCHRANTZ,** N. BUZ,/~S** * Department of Nuclear Chemistry, L. E6tv6s University, H-1518 Budapest 112, P.O. Box 32 (Hungary) ** Department of lnorganic and Analytical Chemistry, A. J6zsef University, 1-1-6701 Szeged, P.O. Box 440 (Hungary)

(Received October 18, 1995) The discovery of radioactivity started the nuclear research. The nuclear techniques are very powerful tools in structural chemistry, as well. We would like to support this statement by two examples in this paper. We present a series of Mfissbauer measurements which give information about the coordination structure of some dibutyltin (IV) complexes of carbohydrate derivates. The other example will demonstrate how the positron lifetime spectra can reflect the temperature dependence of water structure. The discovery of radioactivity by Becquerel in 1896, and the Rutherford's studies on the scattering of alpha-particles by metal foils, in 1911, focused the attention on the nuclei of atoms. Consequently, a high number of studies have been dealing with properties of the nuclei since the first decades of this century. The information is continuously accumulating and we are owning more and more detailed knowledge about the structure of atomic nucleus. On the other hand, the development of the technique of optical-spectroscopy resulted in the appearance of the hyperfme structure of the spectra. It became clear th~ these hyperfine splittings are due to the interactions between the nucleus and electrons of atoms. The other direction of this interaction results in a modification of nuclear levels, as well. The energy of hyperfine interactions generally does not exceed 10-6 eV so, before M6ssbauer's discovery, it was completely impossible to observe directly the hyperfine splitting of nuclear transitions, their energy being by about 10 orders of magnitude higher. However, the appearance of a component of natural linewidth in the spectrum of nuclear resonance absorption ensures the necessary resolution. The hyperfine interaction gives the basis of the chemical applications of M6ssbauer-spectroscopy (MS). The M6ssbauer spectra are the fingerprints of the

0236-5731/96/US $15. O0 Copyright 01996 Akad~miai Kiad6 Budapest All rights reserved

A. Vt~RTESet. al: NUCLEARTECHNIQUESIN STRUCTURALCHEMISTRY nuclear levels modified by the hyperfine interactions between the nuclei and the chemical-, crystalline - and magnetic - structure of the studied samples. So, MS is an excellent tool to collect information about these parameters of materials. The investigations of atomic nucleus resulted in, also, the discovery of the subatomic particles. The theorists of nuclear physics predicted and described the particles building up the nuclei and the experimentalists of this field, thanks to the powerful accelerators, proved the existence of all of these particles, including the lately discovered top quark. On the basis of the study of the interactions of the fundamental particles with the matter, one can collect knowledges about the electronic structure of atoms and molecules and, about the geometrical and magnetic properties of materials, as well. These possibilites are used by the chemical applications of the muon-spin rotation, - resonance and - relaxation (g-SR), by the positron annihilation spectroscopy (PAS), by the Rutherford backscattering (RB), by the negative pion spectroscopy (NPS), etc. In this paper we demonstrate the applicability of the nuclear techniques in structural chemistry by an MS and by a PAS examples.

A M~ssbauer Study on Co-ordination Number, Symmetry of the Co-ordination Sphere of Tin (IV) in Dibutyltin (IV) Complexes of Carbohydrate Derivates The presence of carbohydrate ligands in organotin (IV) complexes modifies the biological properties of the organotin (IV) moiety and it is a reason for the increasing interest in the study of interactions between organotin (IV) compounds and carbohydrates. 1,2 We earlier reported3,4 the results of M6ssbauer studies of carbohydrate complexes of dialkyltin (IV). Experimental quadrupole splitting (QS) values were compared with those calculated on the basis of the partial quardrupole splitting (PQS) concept, and the existence of three types of compounds was demonstrated, containing the central tin (IV) atoms in (a) a trigonal-bipyramidal environment, (b) an octahedral environment, or (c) both trigonal-bipyramidal and octahedral environments. The Mfssbauer studies permitted distinction between the different co-ordination isomers of tin (IV) in the complexes, which led to information concerning factors favouring the formation of the individual isomers. 4 To study the effects of the size and steric requirements of the ligands on the stereochemistry of the co-ordination sphere and hence on the formation of given isomers, dibenzyltin (IV) complexes of

400

A. VI~RTESet. al: NUCLEARTECHNIQUESIN STRUCTURALCHEMISTRY small carbohydrates were also studied. 5 The results of latter investigations reflected the effect of the space requirement of the organic moiety on the stereochemistry of the co-ordination sphere of tin. To complement these investigations dibutyltin (IV) complexes of carbohydrate derivates with bulky substituents were prepared and studied. The results of these investigations are presented in the following. The preparation of dibutyltin (IV) carbohydrate complexes and the MOssbauer equipment and the fitting procedure of the spectra were described in previous publications. 3,4 To determine the steric arrangement of the coordination sphere in these organotin (IV) compounds QS values were calculated on the basis of the PQS concept for the possible symmetries of four-, five- and six-co-ordinated tin (IV) central atoms binding two butyl groups and two deprotonated carbohydrate hydroxyoxygen atoms, besides different numbers of non-deprotonated hydroxyl oxygens. The PQS values of the single functional groups and calculated QS values for the tin (IV) co-ordination sphere in the stereochemical arrangements are shown on Fig. 1 and in Table 1. The experimental M6ssbauer parameters determined by computer-evaluation of the spectra measured at liquid nitrogen temperature are given in Tables 2 and 3. Some representative M6ssbauer spectra are shown in Fig. 2. All spectra exhibited IS and QS values which clearly indicate the presence of tin (IV) species. In contrast to most dibuty1-4 and diethyltin (IV) 3 complexes of carbohydrates,but in agreement with the analogous dibenzyltin (IV) compounds the M6ssbauer spectra of the majority of our complexes reflected the presence of equivalent tin (IV) atoms in the samples. The evaluation of the MOssbauer measurements on the basis of the PQS concept shows that the tin (IV) central atom in the studied complexes is present in either a trigonal-bipyramidal environment, or in an octahedral environment, eventually in both. (Only one complex was found to contain tetrahedrally coordinated tin (IV).) Dialkytin (IV) complexes with a co-ordination number not higher than four must be considered monomeric. Tin (IV) species with a co-ordination number higher than four may be either oligomeric or monomeric. Five- or six-co-ordination may be due to ligand bridge formation, or the fifth and sixth coordination sites of the tin (IV) may be occupied by hydroxyl oxygens of the same carbohydrate which is bound to the tin via its two deprotonated hydroxyl groups. The present carbohydrate type ligands with their hydroxyl oxygen donor atoms are specially suitable for the formation of ligand bridges, resulting in polynuclear tin (IV) complexes. In such chain-like compounds, the species at both ends of the chain are expected to be

401

A. VI~RTES et. ah NUCLEAR TECHNIQUES IN STRUCTURAL CHEMISTRY

different from those within the chain. This difference can hardly be observed in long chain polymers and it does not exist in cyclic oligomers. The data given in Tables 2 and 3 reveal that in the trigonal-bipyramidal compounds studied the preferred configuration is Tbp4 (except for XI) in contrast to the results of previous investigations 4 which have shown the preferential formation of Tbp5 and Tbpl. The preferred configuration of octahedral complexes in both present and previous investigations proved to be Oh4. R

:x::

.O~,, ]

OH

R Td

Tbp

5

R

O"

O"

R

~

.~OH

O"/

"OH

I

O"

OH Tbpl

Oh 1

O"

R

:>

oH

,>1< ~ OH

"O" Tbp

I

9OH

O" 2

Oh2

R

R o-

OH

O" Oh3

Tbp 3 R

R oH

O" Tbp

HO~ I "0" R

R

4

R

"O . ~ O H

Oh4

Fig. I. The stereochemical arrangements of the functional groups around tin (IV) central atom. (The meanings of symbols are given in Table 1.)

402

A. VISRTES et. al: NUCLEAR TECHNIQUES IN STRUCTURAL CHEMISTRY

Table 1 Partial quadrupole splitting (PQS) values of the functional groups, and calculated quadrupole splitting (QS) values for the tin(IV) co-ordination spheres in different stereochemical arrangements*

p Q s / m m s -1 {R] ten {R} tba {R} tbe {R} ~

= = = =

-1.37 {-O-} tetr = -0.37 -0.94 {-O-} tba = -0.21 - 1 . 1 3 { - O - } tbe = -0.09 -1.03 {-O-} ~ = -0.27

{-OH} ten {-OH} tba {-OH} the {-OH} ~

-- ~).25 --- -0.13 = +0.02 = -0.19

QS (calc.)/mms-1 Tetrahedral Td

R2Sn(O-)2

2.30

Tligonal-bipyramidal

Tbp 1 Tbp2 Tbp3 Tbp4 Tbp5

2.44 2.36 1.96 2.13 3.60

Octahedral

Oh I Oh2 Oh3

1.60 1.36 1.84 3.20

Oh4

* Deprotonated hydroxy groups represented by {O-}, while {OH} represent non-deprotonated hydroxy groups in the co-ordination sphere; tetr, tba, tbe and oct represent tetrahedral, trigonal-bipyramidal in equatorial, trigonal-bipyramidal in axial position and octahedral symmetry, respectively.

The differences between the preferred configurations of the trigonal-bipyramidal species of our present and previous investigations can be explained by the significantly higher space requirement of the carbohydrate derivates discussed in this paper. Latter bulky molecules compete with the butyl group for sterically favourable coordination sites of tin (IV). This is the reason why, in our trigonal-bipyramidal compounds the tin (IV) central atom is in surrounding with the two butyl groups in equatorial and axial positions (isomer Tbp4). A similar co-ordination sphere was earlier observed for the diethyltin (IV) complexes of lactose, maltose3 and some thiazolidine derivatives. 6 The larger the organic moiety on tin (IV), the greater the

403

A. Vt~RTES et, al: NUCLEAR TECHNIQUES IN STRUCTURAL CHEMISTRY

hindrance to the formation of such isomers. The lactose complex of dibenzyltin (IV) is therefore e.g. a Tbpl isomer, with equatorial-equatorial benzyl groups. Smaller alkyl groups allow the formation of isomers with equatorial-axial alkyl groups even for small carbohydrates, e.g. the diethyltin (IV) complex of mannitol is a Tbp4 isomer. Table 2 Experimental l l9Sn M6ssbauer parameters* of dibutyltin(IV) complexes of carbonhydrate derivatives and suggested configurations of tin(IV) Compound

Carbonhydrate derivatives

IS, rams -1.*

QS, mms -1

Configuration

I.

Saccharose

1.07

2.10

Tbp4

II.

Raffinose

1.07

2.05

Tbp4

III.

Melesitose

1'.07

2.08

Tbp4

IV.

1-Methyl-a-Dglucopyranose

1.07

2.11

Tbp4

V.

2-Nitrophenyl-13D-galactopyranose

1.08

2.11

Tbp4

VI.

1,2-Isopropylidenec~-D-glucofuranose

1.05

2.14

Tbp4

VII.

4,6-O-benzylidenmethyl-c~-D-glucopyranose

1.26

2.88

Oh4

VIII.

Dibrom-dulcitol

1.31

2.90

Oh4

IX.

Dibrom-mannitol

1.29

2.84

Oh4

* Liquid-nitrogen temperature data ** The isomer shifts refer to CaSnO 3'

From the M6ssbauer parameters of the compounds in Table 2 the data of samples I-VI are equal within the experimental error indicating similar coordination spheres. The comparison of the structures of the ligands belonging to latter complexes suggest the co-ordination of the 2. and 3. hydroxy oxygens of the common D-glucose or D-gala,~tose moiety by tin (IV).

404

A. VI~RTES et. al: NUCLEAR TECHNIQUES IN STRUCTURAL CHEMISTRY

1.00"

j,,~, 9

5

0.98.

./"" L

1

\

0.96"

a)

0.94'

0.92'

0.90

|

I

-5

0 Velocity (mm/s)

1

0"98 1

~

_~ 0.96"

__

b)

0.94

n,'

0.92

0.90 5 Velocity (mm/s)

Fig. 2. The M6ssbauer spectra of compounds N ~ IV (a) and N ~ XI (b). The spectra were recorded at liquid nitrogen temperature (~ 80 K)

405

A. VI~RTESet. al: NUCLEAR TECHNIQUESIN STRUCTURALCHEMISTRY Table 3 Experimental l lgsn M~Jssbauerparameters after decompositionof spectra, suggested configurationsof tin(IV) and ratios (R) of the areas assigned to the different doublets

Cornpouns

Carbohydrate

IS, mms-1

QS, rams-1

Configura- IS, tion mms-1

QS, mms-1

Configuration

R

X

L-galactose

1.19

2.66

Tbp4

1.39

3.54

Tbp5

2:1

XI

Arbutine

1.08

2.46

Tbp I

1.45

2.80

Oh4

5:2

XII

Cellobiose

1.05

2.12

Tbp4

1.22

2.86

Oh4

3:2

The MOssbauer parameters of the compounds containing tin (IV) in two different surroundings are presented in Table 3 together with the suggested configurations and the ratios of the integral intensities of lines assigned to the two types of tin centres. Latter can be considered to be proportional with the concentration ratio of the different tin (IV) atoms. It is to be seen, that in the systems studied tin (IV) with Oh4 or Tbp5 is situated as chain closing unite, i.e. the oligomer chain is terminated at both ends by tin (IV) moieties with the two alkyl groups in axial positions. Previous investigations led to a similar conclusion with the difference that in complexes of ligands with smaller size tin (IV) in Tbp5 configuration is almost always the terminal unite.

A Positron Lifetime Study on the Structure of Liquid Water Water is the most common solvent used in chemistry. Consequently, its structure attracts an expressed attention continuously: large number of works is published weekly dealing with the structure of water experimentally or theoretically. This is not surprising: liquid water has two anomalous properties, i.e., its density minimum at 4 ~ and its specific heat minimum around 35 ~ Both of these properties are connected with the H-bond structure of water. A water molecule is able to form four independent hidrogen-bonds and - in consequence - ' e v e n a few molecules are able to build up considerably complicated structures. It is well founded that the water molecules are associated greatly in liquid phase forming hydrogen-bonded clusters. The energy of the H-bonds are determined by the configuration of the cluster 7 meanwhile the 'concentration' of

406

A. VI~RTESet. al: NUCLEARTECHNIQUESIN STRUCTURALCHEMISTRY different clusters depends on the temperature 8,9 and the concentration of solute molecules.l~ However, the information available about the structure of clusters is limited: it is provided by calculations and the experimental check is almost impossible. Several strict ab initio calculations were performed for small (3-8 molecules) water clusters. 7 Even the effects of different solute molecules were calculated. 1~ The most interesting result of the calculations is the high stability of cyclic clusters in contrast to linear structures. The trimer (three-molecule cluster) is the only species where the energy per H-bond value is larger for the chain-like structure. For larger clusters the cyclic cofiguration is always preferable. Beside the number of water molecules constructing the cluster the different configurations of the same cluster might result in different binding energies. 7 The relative arrangement of H-bonds and 'free' electron pairs or the overall symmetry of the cluster all affect the stability of a certain structure. Calculations showed that even the size of solute ions change the configuration of clusters, e.g., in the case of hexamer C1- and Br- ions stabilize a V-shaped cage while I- prefers a distorted octahedral cluster. 1~ For methanol clusters the calculations predict structural transitions at well defined temperatures: for trimers three sharp structural changes are suggested in the 190-250 K temperature range indicating transitions from cyclic configuration to different chain-like structures. 11 In a thin vapour the clusters predicted by calculations were observed experimentally9,11 for water and several other molecules forming H-bonds (methanol, ammoniac). The 'concentration' of the clusters of different size varied with the temperature showing quite different number distributions in a 20 K temperature range. The most serious problem the calculations leave unsolved is raised by the liquid phase. Ab initio calculations can be applied only for a separated cluster in a vacuum. If the cluster is placed in a liquid phase the effects of the surroundings become too complicated to handle mathematically. The commonly applied method to avoid these complications is the application of approximate potential functions and the subsequent comparison of the results with experimental data, i.e., with X-ray and neutron scattering structure functions. 12 Although this method provides surprisingly good correlations with experimental data, it has a remarkable disadvantage: both the experimental data and the theoretical results give 'integrated' information on the structure of the liquid. It seems - on the basis of calculations - that the structural change of liquid water under the influence of increasing temperature is not monotonous. Studying the coordination number of oxigen atoms vs. temperature function 12 an interesting fact can be found: this curve changes flatly only for O-H neighbours. It decreases 407

A. Vt~RTES et. al: NUCLEAR TECHNIQUES IN STRUCTURAL CHEMISTRY

almost linearly from 5.1 (at the melting point) to about 4.1 (at the boiling point). On the other hand, the co-ordination number for O-O pairs remains constant up to about 35 ~ (about 4.1) and somewhere above this temperature it begins to increase rapidly reaching almost 5.4 at the boiling point. Unfortunately these results do not characterize the 'concentration' of hydrogen bonds. To obtain some information on this parameter several Raman spectroscopic data can be used. In Raman spectra the H-bond provides separate lines at certain wave numbers. However, due to the numerous slightly different bonds, the lines are broad and poorly resolved and their exact determination is complicated. On the other hand, using the integral of the lines instead of the wave numbers gives a possibility to determine the 'H-bond concentration'. Studying these integrals at different temperatures a sharp decrease of the 'H-bond concentration' can be observed at around 40 ~ 13 A further indication for the existance of an abrupt structural change was given by micro-wave absorption measurements. 14 The micro-wave absorption ability of pure water increases when the temperature is increased from 20, ~ to 40 ~ At 40 ~ it drops sharply followed by a slower decrease up to about 70 ~ where it begins to increase again. These data suggest the structural changes of clusters at well defined, narrow temperature intervals. To study structural changes in liquid phase positron lifetime spectroscopy gives a unique possibility. 15 Positrons are the antiparticles of electrons having the same physical parameters (spin, electric charge, mass) as electrons. They are stable in a vacuum but annihilate in a short time meeting with electrons. Their lifetime is influenced by the electron density around them very much. Consequently, very small changes of the electron density result in well-detectable changes in positron lifetime parameters. Another possibility provided by positrons to investigate the electron density is the formation of positronium (Ps) atoms. The positronium is the bond state of a positron and an electron. It is very similar to a hydrogen atom. It has two groundstates distinguished by the spin: the singlet (S=0, para-Ps) state annihilates with a lifetime of 125 ps while the triplet (S= 1, ortho-Ps) state lives much longer (140 ns) in a vacuum. However, in the matter ortho-Ps atoms do not live so long: the positrons do not annihilate with their 'own' electron but with an electron of opposite spin from the surroundings. This so-called pick-off annihilation decreases the lifetime of o-Ps to 1-4 ns depending on the electron density of the material. The largest advantage of positron lifetime spectroscopy in the study of structural changes is that positrons are able to detect local alterations in electron density. Although every positron annihilate at separated places of the material, not all of 408

A. Vt~RTESet. al: NUCLEARTECHNIQUESIN STRUCTURALCHEMISTRY them gives different lifetime signals. There are places, chemical groups and impurities in materials which are likelier to 'react' with positrons than others. For example, in metals usually only two lifetime components are observed: one for the perfect bulk material and one for vacancies. Due to their large sensitivity to the electron density, positrons distinguish, e.g., vacancies from di-vacancies relatively easily. In molecular materials the case is more complicated but - in normal cases there are only three well-resolved lifetime components observed. It is impossible to gain detailed information on the structure of matter from these three lifetime components, alone. However, structural changes always change the distribution of the electron density and - consequently - positron lifetime parameters. By positron lifetime spectroscopy both first and second order phase transformations can be detected with a great sensitivity. Sometimes the sensitivity is even better than that of the X-ray diffraction.16,17 To study the liquid structure of water we used double-destilled, ion-exchanged water having a specific conductivity below l~tS. The positron source was 22Na of 105 Bq activity. This nuclide has a useful property: it emits a ),-photon shortly after the positron emission marking the 'date of birth' of the positron. The energy of this promt photon (1.275 MeV) allows the separation of the signals of positron emission from those of the annihilation (0.511 MeV). The active Na was diffused into a thin (2 mg cm -2) glass foil at elavated temperatures and fixed in the middle of a sample holder made of glass. The sample holder was filled with water and dip into a thermo-regulated bath. The precision of the temperature control was +0.2 ~ The positron lifetime spectra were recorded by a fast-fast coincidence system. The time resolution (i.e. the FWHM of the resolution curve) was around 200 ps. For the spectrum evaluation we used standard computer programs based on the GaussNewton-Marquard method. 18 Three lifetime components could be evaluated from spectra. The shortest component (Zl~150ps , II~30% ) was associated with a mixture of para-Ps annihilation and positron-molecule complexes, the medium one with positrons annihilating without Ps-formation, and the longest lifetime with the pick-off annihilation of o-Ps. The lifetime vs. temperature plots are given in Fig. 3 for positrons and o-Ps atoms. The most striking feature of both curves is the local minimum at 41 ~ Note that the temperature value where this abrupt change occures coincides with that predicted by calculations 12 and observed by Ramanspectroscopy 13 and micro-wave absorption measurements. 14 At the first glance, the o-Ps lifetime curve shows another strange feature: the lifetime values decrease (in general) with the increasing temperature. The density of water decreases in the studied temperature range monotonously meaning a

409

A. VI~RTESet. al: NUCLEARTECHNIQUESIN STRUCTURALCHEMISTRY decreasing average electron density in the liquid. The smaller electron density should result in a smaller pick-off probability and longer lifetime. On the other hand, it is well-known that the H-bond 'concentration' decreases in water with the increasing temperature. 13 Thus, lots of non-bonding electron pairs - formerly localized in H-bonds - become 'free'. Ps-atoms, which are very similar to hydrogen, tend to form 'bonds' with these electron pairs and this 'bond' increases the overlap between the positron of the ortho-Ps and 'foreign' electrons hax~ing opposite spin. Thus the probability of the pick-off annihilation is increased resulting in a decreasing lifetime value. The lifetime of positrons does not show a well-expressed general trend beside the extrema. The trend is slightly increasing indicating that positrons react to the changes of the average electron density. The minima of the lifetime curves suggest a structural change in liquid water at 41 ~ Both lifetimes drops sharply indicating the abrupt change of annihilation conditions. On the basis of the lifetime curves we can not identify this structural change exactly but some suggestions can be done. However, the following explanation needs further studies to confirm. The first step indicated by positron lifetimes is a slight decrease of the electron density above 36 ~ As none of the physical parameters of water changes at this temperature, this decrease suggests small changes of the electron structure of certain clusters. Above 40 ~ the changes of the electron structure initiate an abrupt change of the geometrical structure of clusters. The new structure changes the annihilation conditions resulting in a decrease of the lifetime values. According to former calculations for methanol clusters,ll we think that not all kinds of clusters change their geometrical structure at the same temperature. On the contrary, the lifetime curves show that the structural changes of the clusters cause a continuous change in the structure of the liquid between 40 and 60 ~ These structural changes might not be too dramatic otherweise even some physical parameters of water should change. We think that in this temperature range certain configurations of the clusters are transformed to other, more stable structures. This procedure does not necessarily mean significant changes of O-H, O-O, and O-H - O distances.

410

A. VI~RTES et. ah NUCLEAR TECHNIQUES IN STRUCTURAL CHEMISTRY

1800-

~

1760-

E ~ 1720o

---o

1680-

480

error

bar "~

._~ 480 i-

2

440.

o a.

420

i

i

20

40

8b

8'0

Temperature(~ Fig. 3. The temperature dependence of positron and ortho-positronium lifetimes in liquid water. The given error bars characterize all of the data points. The curves are given only to gide the eye. The intensities of the two longer lifetime components were I2~ 50% and I3-~ 20%. They were, practically, not affected by the temperature

The M5ssbauer invest~ations were supported by the National Science Foundation of Hungary OTKA T 014867) and the positron annihilation measurements by OTKA T-14845 and F-014442.

411

A. VI~RTES et. al: NUCLEAR TECHNIQUES IN STRUCTURAL CHEMISTRY

References 1. J.D. DONALDSON, S. M. GRIMES, L. PELLERITO, M. A. GIROSOLO, P. J. SMITH, A. CAMBRIA, M. FAM,/~, Polyhedron, 1987, 6, 383. 2. A. PATEL, C. POLLER, Rev. Silicon, Germanium, Tin, Lead Compounds, 1985, 8, 263. 3. L. NAGY, L. KORECZ, I. KIRICSI, L. ZSIKLA, K. BURGER, Struct. Chem., 1991, 2, 231. 4. K. BURGER, L. NAGY, N. BUZZ, S, A. VI~RTES, H. MEHNER, J. Chem. Soc. Dalton Trans.. 1993, 2499. 5. N. BUZ,/~S, M. A. PUJAR, L. NAGY, A. VI~RTES, E. KUZMANN, H. MEHNER, J. Radional. Nucl. Chem., 1995, 189, 237. 6. N. BUZAS, B. GYURCSIK, L. NAGY, Y-X ZHANG, L. KORECZ, K. BURGER, Inorg. Chim Acta, 1994, 218, 65. 7. T. P.RADHARKRISHNAN, W.C. HERNDON, J. Phys. Chem., 1991, 95, 10609. 8. K. HIRAOKA, S. MIZUSE, S. YAMABE, J. Phys. Chem., 1988, 92, 3943. 9. M. T. COOLBAUGH, J. F. GARVEY, Chem. Soc. Rev., 1992, 21, 163. 10. J. E. COMBARIZA, N, R. KESTNER, J. Chem. Phys., 1994, 100, 2851. 11. U.BUCK, J. Phys. Chem., 1994, 98, 5190. 12. G. CORONGIU, E. CLEMENTI, J. Chem. Phys., 1992, 97, 2030. 13. G. E. WALFAREN, M. R. FISHER, M. S. HOKMABADI, W.-H. YANG, J. Chem. Phys., 1986, 85, 6970. 14. GY. Z,/~RAY, Private communication. 15. e . g . S . C . SHARMA (Ed.), Positron Annihilation Studies of Fluids, World Scientific, Singapore, 1988. 16. K. SOVEGH, T. S. HORANYI, A. VI~RTES, Electrochim. Acta, 1988, 33, 1061. 17. A. Vt~RTES, K. SUVEGH, R. HINEK, P. GOTLICH, J. Phys. Chem. Solids, 1994, 55, 1269. 18. P. KIRKEAGAARD, M. ELDRUP, O.E. MOGENSEN, N.J. PEDERSEN, Comput. Phys Commun., 1981, 23,307.

412