A simple effective atom-atom intermolecular potential for
halogene solids (F2, Cl-, Br2 and 12) is proposed. The centers of
inter action of the effective potential (6-exp type) are shifted from\u27
the atomic sites in order to reduce anisotropy of the intermolecular
distances.
The calculated results of the static properties for fluorine
and chlorine are in good agreement with the experimental
results. The calculated results for bromine and iodine crystals
are less satisfactory.
The limitations of the atom-atom model for description of
the dynamical properties of halogene solids are also briefly
discusse

D. Kirin

S. Dukan

English

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CROATICA CHEMICA ACTACCA-1912CCACAA 62 (4) 855-859 (1989)YU ISSN 0011-1643UDC 541Conference PaperA Simple Model For the Intermolecular Interactions in HalogeneCrystalsD. Kirin and S. DukanRuđer Bošković Institute POB 1016, 41001 Zagreb, YugoslaviaReceived February 6, 1989A simple effective atom-atom intermolecular potential forhalogene solids (F2, Cl-, Br2 and 12) is proposed. The centers ofinter action of the effective potential (6-exp type) are shifted from'the atomic sites in order to reduce anisotropy of the inter-molecular distances.The calculated results of the static properties for fluorineand chlorine are in good agreement with the experimentalresults. The calculated results for bromine and iodine crystalsare less satisfactory.The limitations of the atom-atom model for description ofthe dynamical properties of halogene solids are also brieflydiscussed.INTRODUCTIONThe physicaland iodine) havestudies.v"? Manymolecular crystal.All the halogene molecules crystallize in orthorhombic system (spacegroup Cmea) except fluorine which is a monoclinic crystal, space groupC2/e or C2/m. Bromine, chlorine and iodine molecules pack in layered struc-ture (Figure 1)13-15 with intermolecular distances in the be plane signifi-cantly shorter that the distances between molecules in adjacent planes(which are of the order of the van der Waals radii).There are a number of proposed semiempirical potential models fordescription of the static and dynamic properties of halogene crystals, withvarious degrees of success.v? The reproducibility of the solid propertiesdepends on a number of adjustable parameters describing the intermole-cular potential (usually 5 to 10 or more). Previous studies have shown thatthe simple isotropic atom-atom potential model cannot give a satisfactoryagreement between the observed and the calculated properties of halogeriesolids. These difficulties can be understood as a consequence of the electrondistribution around the halogene molecules in the crystal. The electrondistribution around atomic sites (the shape of the atom) is not sphericalbut approximately e1liptical. The departure from sphericity is almost negli-gible for the fluorine but very significant for the iodine atom." The crystalproperties of halogene solidsbeen the subject of extensiveof their physical properties(fluorine, chlorine, bromineexperimental and numericalare unusual for a typicaJl856 D. KIRIN AND S. DU KANFigure 1. The crystal structure of halogene solids (Cb, Br2 and 12)' The moleculesare in the bc plane (the shaded molecules are at ± a/2).structure of halogene solids is very anisotropic with the shortest distancesbetween atoms in the be plane. It is unlikely that the simple isotropicatom-atom potential model will describe the intermolecular interactions inhalogene crystals very accurately.There have been many attempts to develop anisotropic potential models(for review see ref. 5) in order to take into account the actual chargedistribution around the halogene atoms. Most of them are the angulardependent potentials with a number of adjustable parameters which arefitted to the observed lattice structure, cohesion energy, and phonon spectraof halogene solids. Many of the model calculations found in the literaturehave a large numberof free parameters in contrast to the few physicalproperties they describe. Besides, they cannot be easily transfered to thesimilar structures containing halogene atoms because they depend on agiven configuration, more precisely on the specific mutual orientations ofthe molecules in the unit cell.DESCRIPTION OF THE MODELIn the present paper a simple potential model for the intermolecularinteractions in halogene solids is developed. It partly takes into accountthe anisotropy of intermolecular interactions. The centers of interactionINl'ERMOLECl.JLAR INTERACTIONS IN CRYSTALS 857were shifted from the atomic positions toward the center of the molecule.The real molecule (longer and nonspherical) is replaced with the shorter»effective« molecule. In this way, we made the crystal structure moreisotropic with respect to the interatomic distances in the bc plane. Shor-tening the molecular length we made these in-plane distances long er andcomparable in size to the distances between the adjacent bc planes. On theother hand, the distances between the planes are almost unaffected. Shiftingthe interaction sites we can take into account the angular dependence ofthe interaction, of course, only on an average level. It is by no meansobvious where to put the new interaction site and, therefore, we treatedit as an additional free parameter in our model.The Buckingham (6-exp) type of interaction between the shifted site sis chosen (specified with 3 parameters A, B and al. Including the shiftingparameter SH = d' Id (d' - the distance between the intramolecular sites,d - the observed length of the molecule) there are 4 parameters for thedispersion-overlapping part of the atom-atom interaction.The electrostatic interaction in halogene solids plays a very importantrole and must be included in order to reproduce the orientation of themolecules in the unit cell. The point charge 2q is put in the center of themolecule and the charges - q at the corresponding sites along the bond inorder to represent the zero dipol and nonzero quadrupole moment of themolecule. The magnitude of the charges may be calculated from the repor-ted experimental values of the quadrupole moments but the data for halo-gene molecules are scarce and not very accurate. Because of that weincluded the quadrupole moment as an additional parameter in the model.The lattice energy in our model is given as:AUlatt = L (----6 + Be-al?u) + Uqqij Rij(1)where Uqq is the quadrupole-quadrupole interaction energy represented bythe sum of the Coulombic energies between the point charges. Rij are thedistances between the shifted interaction sites. For the crystal structure atequilibrium the lattice energy must be minimal (at zero temperature andzero pressure). We minimize (1) by small variation of the lattice parametersand the orientation of the molecule in the unit cell and compare the obtainedequi.librium structure with the observed one. Besides, all the calculatedfrequences in the phonon spectra for every point in the Brrllouine zonemu st be real (condition for the stable lattice). This is an additional test ofthe model.RESULTSA number of potential parameters were tested in order to obtain thebest agreement between the calculated and the experimental crystal struc-ture. The parameters which give a reasonably good agreement are listedin Table 1.The experimental value of the unit cell parameters and its volume,the angle which defines the orientation of the molecule in the bc plane, thecrystal energy and the length of the molecule for fluorine, chlorine, bro-858 D. KIRIN AND S. DUKANTABLE IThe values of parameters A, B, a, SR and Q in the intermolecular potential forhalo gene solidsF2* Cl2 Br2 I2A(kcal A6/mol) 260 2371 4767 11559B(kcal/mol) 39922 38329 90534 48405a (A-l) 3.95 3.00 3.00 2.50SH 0.92 0.92 0.85 0.85Q(esucm2 1O~26) 0.65 0.96 1.29 2.90* From ref. 4.TABLE IIThe experimental values of the structural parameters for halogene crystalsF2 Cl2 Br2 I2a(A) 5.500 6.145 6.567 7.136b(A) 3.180 4.395 4.468 4.686c(A) 7.280 8.154 8.639 9.784V(A) 131.33 220.24 255.08 327.176J(deg) 18.0 33.2 32.7 32.2E(kcal/mol) -2.19 -7.28 -11.99 -16.25d(A)' 1.42 1.99 2.30 2.72Ref. 13 14 14 15TABLE IIIThe calculated values of the structural parameters for halogene solidsF2 Ch Br2 I2a(A) 5.38 5.941 6.170 6.711b(A) 3.40 4.466 4.568 5.668c(A) 7.20 8.198 8.732 8.339V(A) 131.70 216.03 246.11 317.218(deg) 25.0 35.4 341. 47.8E(kcaljmol) -2.18 -7.33 -12.30 -16.38d'(A) 1.30 1.83 1.96 2.31mine and iodine crystals are given in Table II. The calculated values arerepresented in Table III.DISCUSSIONThe results of our calculations for the static properties of halo genesolids are presented in Table III. In spite of the very simple model we used,the calculated results are in reasonable agreement with the observed ones.The results for static properties of fluorine crystal (taken from ourprevious calculations-) showavery good agreement with the observeddata. In that respect, fluorine is similar to other diatomic molecular solids(nitrogen and oxygen) with the quadrupole moment between those ofoxygen and nitrogen." In oxygen the small quadrupole moment has verylittle effect on the molecular orientation while in nitrogen the large quadru-pole moment determines the orientation and structure (Pa3).rINTER:liIOLECULAR INTERACTIONS IN CRYSTALS 859On the other hand, the remaining halogene solids show a gradualdeparture from the typical molecular solids. It can be seen from Table IIIthat our simple model is able to reproduce the static properties of chlorinecrystal reasonably well. For bromine crystal and especially for iodine(Table III) the agreement is less satisfactory. This can be explained by thelarge departure from sphericity of halogene atoms in those crystals" andour simple model-? is not able to reproduce the observed properties. It isquestionable if it is possible to tailor the effective atom-atom potential'for a system like iodine because of the large nonspherical electronic chargedistribution. It is particularly questionable if the dynamic properties ofthese systems (vibrational spectra and phonon dispersion curves) can bereasonably well explained on the basis of the unpolarized rigid molecule.Our preliminary calculations of the lattice vibrations are not in very goodagreement with the observed Raman and IR frequencies. This means thatour simple model is not able to describe the actual anisotropy of the inter-molecular interaction. Even more complex models with a larger numberof potential parameters do not give a very good agreement for vibrationalfrequencies of halogene solids. It seems that a complete description of thephysical properties of halogene solids requires amore realistic model whichtakes into account the electronic degrees of freedom, like the shell modeli!or the Car-Parinello unified approach for treating electronic and nucleardegrees of freedom simultaneously.PREFERENCES1. S. L. P ric e and A. J. S t o n e, J. MoL. Phys. 47 (1982)1457.2. Z. Ga m b a, E. HaI a c, and H. B o nad e o, J. Chem. Phys. 80 (1984)2782;ibid 85 (1986)1202.3. K. K o b ash y and R. D. Et ter s, J. Chem. Phys .• 9 (1983)3018.4. D. Kir i n and R. D. Et ter s, J. Chem. Phys. 84 (1986)3439.5. A. J. S t o n e and S. L. P ric e, J. Phys. Chem. 92 (1982)3325.6. S. C. N y b u r g and W. Wo n g - N s. Proe. Raay. Soc. Lond. A367 (1979)29.7. E. B u r g o s, C. S. Mu r t h s. and R. R i g h i n i, MoL. Phys. 47 (1982)1391.8. S. C. N y b u r g and G. H. F a er man, Acta Cryst. BU (1985)274.9. D. E. S tog r y n and A. P. S tog r y n, MoL. Phys. 11 (1966)371.10. D. Kir i n, Acta Crust, B42 (1987)405.11. W. Co c h r a n, C. R. C. C1'iticaL Reviews in Solid State Sciences 2 (1971)1.12. R. Car and M. Par r i n e l l o, Phys. Rev. Lett. 55 (1985)2471.13. L. Me y e r, C. Bar r e t t, and S. G r e e r, J. Chem. 19 (1968)1902.14. B. M. P o well, K. M. He a 1, and B. H. Tor rie, MoL. Phys. 53 (1984)929.15. F. van Bo1h u i s, P. B. K o ste r, and T. Mig g h e 1s o n, Acta Cryst. 23(1967)90.SAŽETAKJednostavan model za opis međumolekulskih interakcija u kristalima halogenaD. Kirin i S. DukanPrikazan je jednostavan model za opis međumolekulskih interakcija u krista-lima halogena (F2, ch, Br2 i 12).Model se zasniva na efektivnom potencijalu (tipa 6-exp) s centrima interakcijepomaknutim s atoma prema središtu molekule. Na taj je način reducirana anizo-tropija u međumolekulskim udaljenostima.Izračunana statička svojstva za fluor i klor dobro se slažu s eksperimental-nim podacima, dok je slaganje za kristale broma i joda slabije.Ukratko se raspravlja o ograničenjima ovako jednostavnog modela, posebnoza opis dinamičkih svojstava (fononske frekvencije).

A Simple Model For the Intermolecular Interactions in Halogene Crystals

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