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Atom-atom interaction model and internal vibrational exciton splittings in organic charge-transfer complexes: Factor group splittings of naphthalene vibrations in several crystalline complexes
Chemical Physic 34 (1975) 219-224 0 North-Holland Publishing Company
ATOM-ATOM INTERACTION MODEL AND INTERNAL VIBRATIONAL EXCITON SPLITTINGS IN ORGANIC CHARGE-TRANSFER COMPLEXES: FACTOR GROUP SPLITTINGS OF NAPHTHALENE VIBRATIONS IN SEVERAL CRYSTALLINE COMPLEXES * Freeman P. CHEN ** and Paras N. PRASAD *** Department of Che.mistry, State University of New York at Buffalo, Buffalo. New York 14214. USA Received 16 June 1978 Factor group splittings of naphthalene vibrations are experimentally investigated For naphthalcnc : 2SbCIs (CroHa : 2SbCls). naphthalene : octafluoronaphthalene (C 1oHg : CIoFa), naphthalenc : TCNB, and naphtbalene : TNB crystalline compleses by Raman spectroscopy and using the isotopically mixed crystal technique. It is Found that only 386 cni’ mode of CloHs shows factor group splittings in the first two complexesThe spiitting increases From 5 cm-I in pure CtoHa crystal to 5.5 cni’ in CroHa : 2SbCla but decreases to 1 cm-t in the CroHa : CleFs complex. Also as SbCIa is successively replaced by SbBr3 in the comples CloHg:2SbCl3, the factorgroup splitting of 386 cn? Cl,-& mode decreases and the mean of the factor group frequenciesgoes through a minimum near 0.5 moIe fraction of SbBr3. A theoretical calculation using atom-atom potential model and considering only naphthalene-naphthalcne interactions predicts that the factor group splitting on 386 cm-’ band should increase from pure CloHgcrystal to the C 1oH8 : 2SbCis crystalline comples and decrease in CtoHa : CtoFa. HOWever. the calculation also predicts a similar trend for 943 cnit band of naphthalene which shows a factor group splitting of 5 cm’ in pure CroHs but none in the CroHa : 2SbC13 complex. Furthermore, the atom-atom interaction model does not explain the effect of SbBrs substitution on the factor group splitting. The importance of cicctrostatic multipole interactions in explaining the behavior of factor group splitting is discussed.
I_ Introduction Crystalline complexes are a group of ordered bimolecular (or multimolecular) crystals whichexhibit a wide variety of crystalline arrangements and intemrolecular interactions to provide a control over the dynamics of chemical and physical processes in condensed phases [1,2]. One property of these group of crystals which continues to receive considerable attention is their electrical conductivity [2] . These crystals exhibit a continuous range of behavior from being an insulator to being highly conductive. An understanding of the nature of forces which are primarily responsible for the stabilization of the crystalline complexes is of considerable interest. In the past, most complexes containing * Supported by NSF Grant No. DMR7.502628. ** Present address: PolaroidCorporation Research Laboratory, Cambridge, Massachusetss 02139, USA. *** Alfred P. Sloan Fellow.
an aromatic nucleus were assumed to be stabilized primarily by charge-transfer interactions, hence the term charge-transfer complexes was assigned to them [l] .
During recent years this assumption has come under closer scrutiny [3] . It has been argued that even those complexes which have low lying charge-transfer transitions are, in the ground electronic state (the normal state of the crystal), stablized primarily by electrostatic and polarization interactions [33 . Kitaigorodsky [4] , on the other hand, suggests that these complexes crystallize in arrangements favored by close packing and, thus, van der Waals interactions form a major portion of their lattice energy. The dynamic manifestations of the intermolecular interaction are phonon motions and intramolecular vibrational exciton motions. In pure organic crystals the non-bonded atom-atom potential form for the van der Waals interaction has gained wide support in explaining the dynamic manifestion of the intermolecular interactions [S-7] . This fomr of the potential is
220
F.P. Chen, P.N. Prasad/Factorgroup splittings of naphthalene vibrations
comprised of an attractive force of a dispersion type (rs6 dependence) and a short range repulsive force (p-12 or exp(-cr) dependence) between two non-bonded atoms. Pairwise interactions between various non-bonded atoms of the two molecules are assumed to be additive. Calculations of both phonon and intramolecular vibrational excitons have been made for several organic crystals and compared with experimental observations [S-S] _No such study has been made for a crystalline organic complex. This type of study can provide a valuable insight into the primary forces which make up the lattice energy and, thus, stabilize the formation of a crystalline complex_ The objective of the present paper is to examine the extent of lattice stabilization provided by van der Waals interaction in crystalline complexes. In order to investigate the importance of van der Waais interaction, vibrational exciton splitting is used as a criterion and the predictions of an atom-atom interaction potential are compared with the experimentally observed values. In particular the intramolecular vibrational exciton splittings of naphthalene in the environment of several crystalline complexes are investigated. Complexes selected for the presentation are naphthalene : nctafhroronaphthalene (C,,H, : C,,F,); naphthakne : 2 antimony trichloride (CloHs : 2SbC13); naphthalene : tetracyanobenzene (CIoHs : TCNB) and naphthalene : sym-trinitrobenzene (C,9H, : TNB). In the experimental study isotopic substitution of naphthalene is used to identify the exciton (factor group) splitting_ Also, the effect of chemical substitution of the acceptor (SbBr3) is examined in the case of C,,H, : 2SbCI3. Although, atom-atom interaction shows a limited success in explaining only a portion of the experimental observation, we feel such agreement is fortuitous especially in view of the failure of the model to explain the drastic effect of the acceptor substitution (SbBr, in the C,,H, : 2SbC13 compiex). This result indicates the existence of important electrostatic and polarization forces.
terials were extensively zone refined. The crystals used were grown from the melt in a Bridgman furnace. To prepare mixed crystals, required proportions of the components were weighed, thoroughly mixed in the growing tube followed by slow growth of the crystal in the Bridgman furnace. The samples were cooled in a stream of nitrogen vapor. The Raman spectra were obtained on a Spex double monochromator model 14018 with holographic gratings. Fig. 1 shows the observation of factor group splittings on the 386 cm-l mode of naphthalene both in pure crystal and in the complex C,,Hs : 2SbCl3. The splitting observed in pure naphthalene cystal has been established to be due to factor group splitting [8]. The present study shows that the doublet observed in CloH, : 2SbC13 crystal is also due to- factor group splitting. The spectra of the complex containing naphthalene isotopic impurity show that the magnitude of the splitting decreases as the naphthalene-ds concentration
2. Experimental study SbCl, and SbBr3 were obtained, respectively, from Fisher Chemical Company and Alfa Division of Ventrori Corporation. NaphthaleneJz* and naphthalene+ were obtained from Aldrich Chemicals. Octafluoronaphthalene was obtained from Accurate Chemicals. AU ma-
1
405
I
I
,
395
385
375
ENERGY (cm*1
Fig. 1. Raman spectra of pure CreHa crystal and the crystalline complexes(CraHs)r&CreDa)~: 2SbCla at = 125 K in the region 390 cm-r. The spectral resolution is = 0.5 cm-r.
F.P. then, P.h’. Prasd/Factorgmup
----(C,oHaI,_x CC,,Da), : PSbCl, -
&Ha : 26bCL&_~ (SbB&
SpIittings of naphtr’talene uibrations
221
tently found the splitting in the complex to be larger than that observed 2: ihe pure crystal. Furthermore, no detectable splitting is found in CIoH, : 2SbC1, crystals on other vibrations of naphthaIene which exhibit factor group splittings (of compatible magnitude to that observed for the 386 cm-l band) in pure CtOHg crystal [8]. The result of the factor group splitting study on the x 386 cm-l band of naphthalene in the C,,-,Hg : 2(SbC1,),_X(SbBr,)X complex containing SbBr, chemical impurity is graphically displayed in fig. 2. This figure also represents the variation in factor group : 2SbC1,. splitting in crystals (C,,-,H,),_-#,,D&
I
t
I
1.0
0.0
Mole Fiction (Xl Fig. 2. Graphical representation of the variation in the frequencies of the factor group components of the 386 cm-’ naphthalene mode, as a function of both the CloDg mole fraction and the SbBrs mole fraction in mixed complexes (CroHs)l-x(C~OD~)X: 2SbCI3 and CloHg : 2(SbC13)r_X(SbBr3)x.
increases. ‘This behavior is expected from exciton splitting of a band which exhibits separated band limit in the mixed crystal [8] _For further confirmation, we
We Fmd two important features in crystals containing SbBr3: (i) The factor group splitting of the 386 cm-’ naphthalene band reduces from 5.5 cm-l in the SbC13 complex to 2.9 cm-’ in the SbBr, complex, (ii) in the C,,H* : 2(SbC13)L_X(SbBr3)X, the mean of the factor group component frequencies goes through a minimum as X is increased from 0 to I. The minimum occurs at X = 0.5. In the complex with octafluoronaphthalene (CL,HB : C,,F,), the same vibration shows a small splitting (x 1 cm-‘). This splitting actually is not distinctly observable in the C10H8 : C,,F, complex, because of the presence of an overlapping band of C,,F, but can readily be identified in ClODa : C1,,F8 and in IU-C,,H~D : C,,FB complexes. No other vibrations of naphthalene show factor group splitting. On the other hand, in naphthalene : TCNB and naphthalene : TNB complexes, no factor group splitting of this vibration (or any other vibration of naphthalene) is observed_
have used the criterion that for aromatic hydrocarbons,
isotopic substitution has only mild effect on the factor group splitting [S] . The corresponding band of C10D8 is in the region complicated by the overlapping bands of SbCl,. For this reason, we used another isotopic naphthalene, LU-C,,-&D. We observe a similar behavior for the corresponding vibration of &,,H,D; the factor group splitting increases from 4.3 cm-l in pure crystal to 4.7 cm-1 in the complex a-CIoH,D : ZSbCl,. This observation along with the isotopically mixed crystal result establishes that the splitting observed in the crystal of the complex is a factor group splitting. We find that the factor group splitting observed on the 386 cm-1 bid of naphthalene is 5.5 cm-1 in the C,,H, : 2SbC1, complex and 5 cm-l in the Cr,,H8 pure crystal. We have repeated our study and consis-
3. Theoretical
calculation using atom-atom
interaction
In this section, a theoretical calculation of factor group splittings of naphthalene vibrations is presented using the empirical atom-atom interaction potential. The detailed crystal structure data are available for both C,,H, : ZSbCl, and CloH, : C10F8 complexes. In the crystal of the C10H8 : 2SbC13 complex, the naphthalene molecule is situated at the center of inversion such that one SbCI, molecule is directly above one aromatic ring while the second SbCI, is directly below the other aromatic ring of the naphthalene molecule [V] _In this arrangement the SbC$ (acceptor) stack in planes alternating with layers of naphthalene (donor). In the crystal
222
FP. CJzen. PN. Pramd/Factorgroup
of the Cl,,Hs
: Cl,,Fs
complex,
ternate along the stack axis [lo] complexes
CIOHS and C!,,F, al. Thus, crystals of both
consist of planes in which naphthalene mo-
Iecules are nearest neighbors
splitrings of napJuhalene vibrahbns
ber of equivalent sites per unit cell. B is a unitary matrix transforming the site functiolito the factor group representation. ‘II&molecules
at sites a and b are inter-
[9,10]. In our calculation of factor group splittings of naphthalene vibration using atom-atom potential, only naphtbalene molecules are considered and the interaction involving the other component (SbCl, or CloFs) is ignored. In other words we consider only the sublattice of the naphthalene molecules. As we.were only interested in testing the predictions of the atom-atom interaction model with our experimental observations and not in the detailed dynamics of motions, the simplified approach of Rich and Dows [5,12] was used for the calculation. In this method the exciton interaction shift M,, of the factor group state Lyis given as
change equivalent and not translationally equivalent [I I] _Vpppis the interaction potential between the moleculesp andp’. The second derivative of the interaction potential with respect to the normal coordinate is related to the second derivative of the potential with respect to the atomic positions by the following approximate equation:
M, = tC
Here rii is the distance between atoms i and j of molecules p and p’_ Lkii/ari is the cosine of the angle between the position vector of atom i and the interatomic vector. &,/a$ is the amplitude of the motion of atom i in the particular normal mode of molecule p. In the calculation, the atomic Cartesian displacements for naph-
BzaBrub
(I)
P’
In this equation, v. is the unperturbed frequency (in wave numbers) of the unperturbed mode, Q represents its normal coordinate. The sum runs over lattice sites with moleculesp on site a, and p’ on site b; r is the num-
(2)
Table 1 Factorgroup splittins of naphthalenevibrations System
Unperturbed
MolecuIar
Crystal frequencies
frequencies
symmetries
(cm-‘)
Factor group splittino.?I(cm-‘) ‘j
(cm-’j
talc.
obs.
talc.
obs.
396.5 400.8 953.0 953.2
389 394 949 953
4.3
5
0.2
4
386.2 392.9 943.7 949.2
385.5 391.0 956
6.8
5.5
5.46
0
0.2
1.0 a)
0.1
0
-_naphthalene
CIOHs : 2SbCis
CIOHS: C,oFs
386
Bg
943
Big
356
Big
943
B1g
386
%
943
B1g
386.0
388
386.2
?
943.0
95.5
943.1
‘j Factorgroup splitting measured in CloDa : ClaFs complex (see text).
F.P. Chea, P.N. Prasad/Factorgroupsplittingsof naphthalenevibrations
thalene modes given by Rich [12] was used. The parameters A, B and C used for the potential function, vq = -Ari6
+ B exp(-C?$,
were those of Williams [13]. Factor group splittings on both the 386 cm-l and the 943 cm-’ vibrations of naphthalene are calculated for pure C,oH, crystal, C,oH, : 2SbCI,, and C,,Hs : C1,,Fg. The values obtained are listed in table 1, which also lists the experimentally observed values.
4. Discussion A comparison of the values calculated from atomatom interaction model with those experimentally observed for the 386 cm-’ band shows a qualitative agreement in the trend. Experimentally, we observe that factor group splitting on the 386 cm-’ band increases in going from pure C H crystal to the complex C,,H, : 2SbC13 and :t”de8creasesin going to the complex C,oH, : C,oFa_ The theoretical calculation also predicts this trend. However, we feel that this agreement is fortuitous and should not be taken as an evidence for the validity of the atom-atom interaction for crystalline complexes in general. The atom-atom interaction does not provide a quantitative agreement with observed factor group splittings even for pure naphthalene crystal [8] _For example, it predicts a splitting of 0.2 cm-l for 943 cm-l vibration in pure naphthalene, whereas a splitting of 4 cm-l is experimentally observed_ In the case of the C,oH* : 2SbC13 complex, there are many observed features which cannot be explained by the atom-atom interaction model. First, the calculation predicts au increase in the factor group splitting of the 943 cm-1 band of naphtbalene in going from pure C,,Hs to C,,-,H,, : 2SbC1,. On the other hand, experimentally we observe the opposite: the factor group reduces from 4 cm-l in pure C,oH, to within the linewidth (< 1 cm-l) of the transition in the C,oH, : 2SbC1, crystal. Second, the factor group splitting decreases as SbC13 is successively replaced by SbBr3. One may argue that the lattice parameters (unit cell dimensions) of the two complexes C,oHa : 2SbC1, and C,,Ha : 2SbBr3 are not the same and this leads to a difference in the naphthalene-naphthalene interaction for the two complexes. The crystal structure of the C,,H, : 2SbBr, complex
213
has not been reported. However, on the basis of our study of phonons [14] in these complexes we fiid that the two complexes have the same crystal structure. The phonons of the naphthalene sublattice do not change in frequency as SbCl, is replaced by SbBr, suggesting that the unit cell dimensions for C,,H, : 2SbC1, and C,,H, : 2SbBr, complexes are very similar. These results are consistent with the fact that pure crystals of SbCl, and SbBrj are known to have almost identical unit cells 1151. For this reasons, we feel that the difference in the factor group splittings observed for CIOHs : 2SbC13 and C1uHg : 2SbBr3 is not due to a difference in their crystal structure (or unit cell dimensions)_ The acceptor molecule (SbCl, or SbBr,) participates in the interaction. There is no close lying motion of either SbCl, or SbBr, near the 386 cm-l naphtbalene vibration that a near resonance interaction of Fermi-resonance type could give rise to such differences. The mean of the factor group components does not show a monotonic shift as the SbCl, is replaced by SbBr,, but exhibits a minimum near 0.5 mole fraction of SbBr3 (fig. 2). In the C,,Hs : 2SbC1, complex, the naphtbalene molecule is considerably distorted from D,, symmetry [9] . This symmetry reduction along with the rr-electron interaction with SbCl, changes the distribution of electron densities in naphthalene molecules. On this basis, one may question the use of William’s parameters A, B and C, which have been derived for pure hydrocarbons [ 131. It has been shown that in cases of hydrogen bond formation [ 161, these parameters are different due to a change in the occupation number of electrons in the valence shell. The change in the values of these parameters A, B and Cwill be dependent on the nature of the acceptor. This might explain the reduction in factor group splitting in going from the C,,H, : ZSbCl, complex to the C,,H, : 2SbBr3 complex. However, it does not explain the cause of the selective enhancement of the factor group splitting of 386 cm-’ of naphthalene in the complex C,,H, : 2SbC1, _On the basis of an atom-atom potential, both 386 cm-* and 943 cm-’ modes of naphthalene should show larger splittings In the C1,,Hg : 2SbC13 complex compared to that in the pure naphtbalene. Other possible interactions are electrostatic multipole and polarization interactions. Both these interactions would be dependent on the nature of the acceptor_ These interactions are anisotropic and can give rise to mode selective dynamic intermolecular interactions_
224
F_P. then, PN. PrasadfFactorgroup
This property can expkirk a selective enhancement of the factor group splitting. One type of multipole interaction involves dipoles created by a transfer of r-electrons from the aromatic ring of naphthalene to SbClj . The multipole and polarization interaction can also explain the reduction in factor group splitting in going from the C,,H, : ZSbCI, crystal to C,,H, : ZSbBr,. The minimum observed in the curve of the mean of the factor group splitting versus concentration of the SbBr, is attributed to the formation of the mixed complex C,oH8 : 2(SbCl& (SbBr3)o 5_ In the mixed complex the naphthalene molecule-undergoes different distortion as the SbCI,-C,,H, dipole and the C,,H,SbBr, dipole do not cancel each other. The vibrational frequency can have a different value. The concentration of the mixed complex C,,H, : 2(SbCI,)o, (SbBr$,, 5 will be maximum when the composition of the m$ed crystal approaches 0.5 mole fraction of SbCI, (or SbBr& This is the concentration at which the mean of the factor group splitting exhibits a minimum. We would like to add that our phonon study of this complex [ 141 does reveal an impurity induced band in C,oH, : 2(SbCI,), (SbBr3)1_X and the intensity of this band is maximum when X = OS. We attributed the appearance of this band to the formation of the mixed complex C,oH8 : Z(SbCI,), ,(SbBr,)o 5_ In conclusion we observe that the ato&atom interaction model is not satisfactory for the C,oH8 : 2SbC13 complex. We note that other workers [ 171 have also found atom-atom interaction unsatisfactory for crystals containing molecules with polar groups. Our experimental result is consistent with what can be expected if important multipole-interactions existed_ The validity of such interaction can only be established by an actual calculation using such potentials and a quantitative verification of the theoretical prediction.
splittings of naphthalene vibrations
Acknowledgement
We wish to thank Professor R. Kopehnan of the University of Michigan for providing us with the sample of c&,,,H,D.
References
[I] F.H. Herbstein, in: Perspectivesin structural chemistry. Vol.4, eds:J.D. Dunitz and J.A. Ibers (Wiley, New York. 1971) p. 166.
[2J J.J. Andri, A. Bieber and F. Gautier, Ann. Phys. 1 (1976) 145. [3] M.W. Iianna and J.L. Lippert, in: Molecular complexes, Vol. 1. ed. R. Foster &lek, London 1973) p_ 1. [4] A.I. Kitaigorodsky, MoIecular cyrstals and moIecuIes (Academic Press, New York, 1973) p_ 125. IS] N. Rich and D.A. Dews, Mol. Cryst. 5 (1968) 111.
[6] G.S. Pawley and SJ. Cyvin, J. Chem. Phys. 52 (1970) 4073. [7] G. Taddei, H. Bonadeo. M.P. Marzocchi and S. CaIifano.
J. Chem. Phys. 58 (1973) 966. [8] P.N. Prasad and R. Kopehnan, J. Chem. Phys. 57 (1972) 856. [9] R. Hulme and J.T. Szymanski, Acta Cryst. B25 (1969) 753. [IO] J. Potenza and D. Mastropaolo, Acta Cryst. B31 (1975) 2.527. [ 1I] R. Kopehmm, J. Chem. Phys. 47 (1967) 263:. [ 121 N. Rich, Ph.D. Dissertation, University of South California, USA (1968). [ 131 DE. WiUiams,J- Chem. Phys. 45 (1966) 3770. [14] F.P. Chen and P.N- Pmsad, Solid State Commun. 21 (1977) 871. [ 1.51I. Lindquist, and A. N&i, J. Inorg. Nucl. Chem. 2 (1956) 345; D.W. Cushen and R. Huhne. J. Chem. Sot. (1962) 2218. [ 16] J. Caillet and P. Claverie, Acta Cryst. A31 (1975) 448. 1171 M.G. Munowitz, G-L. Wheeler and S.D. Colson, Mol. Phys. 34 (1377) 1727, and references
therein.
ATOM-ATOM INTERACTION MODEL AND INTERNAL VIBRATIONAL EXCITON SPLITTINGS IN ORGANIC CHARGE-TRANSFER COMPLEXES: FACTOR GROUP SPLITTINGS OF NAPHTHALENE VIBRATIONS IN SEVERAL CRYSTALLINE COMPLEXES * Freeman P. CHEN ** and Paras N. PRASAD *** Department of Che.mistry, State University of New York at Buffalo, Buffalo. New York 14214. USA Received 16 June 1978 Factor group splittings of naphthalene vibrations are experimentally investigated For naphthalcnc : 2SbCIs (CroHa : 2SbCls). naphthalene : octafluoronaphthalene (C 1oHg : CIoFa), naphthalenc : TCNB, and naphtbalene : TNB crystalline compleses by Raman spectroscopy and using the isotopically mixed crystal technique. It is Found that only 386 cni’ mode of CloHs shows factor group splittings in the first two complexesThe spiitting increases From 5 cm-I in pure CtoHa crystal to 5.5 cni’ in CroHa : 2SbCla but decreases to 1 cm-t in the CroHa : CleFs complex. Also as SbCIa is successively replaced by SbBr3 in the comples CloHg:2SbCl3, the factorgroup splitting of 386 cn? Cl,-& mode decreases and the mean of the factor group frequenciesgoes through a minimum near 0.5 moIe fraction of SbBr3. A theoretical calculation using atom-atom potential model and considering only naphthalene-naphthalcne interactions predicts that the factor group splitting on 386 cm-’ band should increase from pure CloHgcrystal to the C 1oH8 : 2SbCis crystalline comples and decrease in CtoHa : CtoFa. HOWever. the calculation also predicts a similar trend for 943 cnit band of naphthalene which shows a factor group splitting of 5 cm’ in pure CroHs but none in the CroHa : 2SbC13 complex. Furthermore, the atom-atom interaction model does not explain the effect of SbBrs substitution on the factor group splitting. The importance of cicctrostatic multipole interactions in explaining the behavior of factor group splitting is discussed.
I_ Introduction Crystalline complexes are a group of ordered bimolecular (or multimolecular) crystals whichexhibit a wide variety of crystalline arrangements and intemrolecular interactions to provide a control over the dynamics of chemical and physical processes in condensed phases [1,2]. One property of these group of crystals which continues to receive considerable attention is their electrical conductivity [2] . These crystals exhibit a continuous range of behavior from being an insulator to being highly conductive. An understanding of the nature of forces which are primarily responsible for the stabilization of the crystalline complexes is of considerable interest. In the past, most complexes containing * Supported by NSF Grant No. DMR7.502628. ** Present address: PolaroidCorporation Research Laboratory, Cambridge, Massachusetss 02139, USA. *** Alfred P. Sloan Fellow.
an aromatic nucleus were assumed to be stabilized primarily by charge-transfer interactions, hence the term charge-transfer complexes was assigned to them [l] .
During recent years this assumption has come under closer scrutiny [3] . It has been argued that even those complexes which have low lying charge-transfer transitions are, in the ground electronic state (the normal state of the crystal), stablized primarily by electrostatic and polarization interactions [33 . Kitaigorodsky [4] , on the other hand, suggests that these complexes crystallize in arrangements favored by close packing and, thus, van der Waals interactions form a major portion of their lattice energy. The dynamic manifestations of the intermolecular interaction are phonon motions and intramolecular vibrational exciton motions. In pure organic crystals the non-bonded atom-atom potential form for the van der Waals interaction has gained wide support in explaining the dynamic manifestion of the intermolecular interactions [S-7] . This fomr of the potential is
220
F.P. Chen, P.N. Prasad/Factorgroup splittings of naphthalene vibrations
comprised of an attractive force of a dispersion type (rs6 dependence) and a short range repulsive force (p-12 or exp(-cr) dependence) between two non-bonded atoms. Pairwise interactions between various non-bonded atoms of the two molecules are assumed to be additive. Calculations of both phonon and intramolecular vibrational excitons have been made for several organic crystals and compared with experimental observations [S-S] _No such study has been made for a crystalline organic complex. This type of study can provide a valuable insight into the primary forces which make up the lattice energy and, thus, stabilize the formation of a crystalline complex_ The objective of the present paper is to examine the extent of lattice stabilization provided by van der Waals interaction in crystalline complexes. In order to investigate the importance of van der Waais interaction, vibrational exciton splitting is used as a criterion and the predictions of an atom-atom interaction potential are compared with the experimentally observed values. In particular the intramolecular vibrational exciton splittings of naphthalene in the environment of several crystalline complexes are investigated. Complexes selected for the presentation are naphthalene : nctafhroronaphthalene (C,,H, : C,,F,); naphthakne : 2 antimony trichloride (CloHs : 2SbC13); naphthalene : tetracyanobenzene (CIoHs : TCNB) and naphthalene : sym-trinitrobenzene (C,9H, : TNB). In the experimental study isotopic substitution of naphthalene is used to identify the exciton (factor group) splitting_ Also, the effect of chemical substitution of the acceptor (SbBr3) is examined in the case of C,,H, : 2SbCI3. Although, atom-atom interaction shows a limited success in explaining only a portion of the experimental observation, we feel such agreement is fortuitous especially in view of the failure of the model to explain the drastic effect of the acceptor substitution (SbBr, in the C,,H, : 2SbC13 compiex). This result indicates the existence of important electrostatic and polarization forces.
terials were extensively zone refined. The crystals used were grown from the melt in a Bridgman furnace. To prepare mixed crystals, required proportions of the components were weighed, thoroughly mixed in the growing tube followed by slow growth of the crystal in the Bridgman furnace. The samples were cooled in a stream of nitrogen vapor. The Raman spectra were obtained on a Spex double monochromator model 14018 with holographic gratings. Fig. 1 shows the observation of factor group splittings on the 386 cm-l mode of naphthalene both in pure crystal and in the complex C,,Hs : 2SbCl3. The splitting observed in pure naphthalene cystal has been established to be due to factor group splitting [8]. The present study shows that the doublet observed in CloH, : 2SbC13 crystal is also due to- factor group splitting. The spectra of the complex containing naphthalene isotopic impurity show that the magnitude of the splitting decreases as the naphthalene-ds concentration
2. Experimental study SbCl, and SbBr3 were obtained, respectively, from Fisher Chemical Company and Alfa Division of Ventrori Corporation. NaphthaleneJz* and naphthalene+ were obtained from Aldrich Chemicals. Octafluoronaphthalene was obtained from Accurate Chemicals. AU ma-
1
405
I
I
,
395
385
375
ENERGY (cm*1
Fig. 1. Raman spectra of pure CreHa crystal and the crystalline complexes(CraHs)r&CreDa)~: 2SbCla at = 125 K in the region 390 cm-r. The spectral resolution is = 0.5 cm-r.
F.P. then, P.h’. Prasd/Factorgmup
----(C,oHaI,_x CC,,Da), : PSbCl, -
&Ha : 26bCL&_~ (SbB&
SpIittings of naphtr’talene uibrations
221
tently found the splitting in the complex to be larger than that observed 2: ihe pure crystal. Furthermore, no detectable splitting is found in CIoH, : 2SbC1, crystals on other vibrations of naphthaIene which exhibit factor group splittings (of compatible magnitude to that observed for the 386 cm-l band) in pure CtOHg crystal [8]. The result of the factor group splitting study on the x 386 cm-l band of naphthalene in the C,,-,Hg : 2(SbC1,),_X(SbBr,)X complex containing SbBr, chemical impurity is graphically displayed in fig. 2. This figure also represents the variation in factor group : 2SbC1,. splitting in crystals (C,,-,H,),_-#,,D&
I
t
I
1.0
0.0
Mole Fiction (Xl Fig. 2. Graphical representation of the variation in the frequencies of the factor group components of the 386 cm-’ naphthalene mode, as a function of both the CloDg mole fraction and the SbBrs mole fraction in mixed complexes (CroHs)l-x(C~OD~)X: 2SbCI3 and CloHg : 2(SbC13)r_X(SbBr3)x.
increases. ‘This behavior is expected from exciton splitting of a band which exhibits separated band limit in the mixed crystal [8] _For further confirmation, we
We Fmd two important features in crystals containing SbBr3: (i) The factor group splitting of the 386 cm-’ naphthalene band reduces from 5.5 cm-l in the SbC13 complex to 2.9 cm-’ in the SbBr, complex, (ii) in the C,,H* : 2(SbC13)L_X(SbBr3)X, the mean of the factor group component frequencies goes through a minimum as X is increased from 0 to I. The minimum occurs at X = 0.5. In the complex with octafluoronaphthalene (CL,HB : C,,F,), the same vibration shows a small splitting (x 1 cm-‘). This splitting actually is not distinctly observable in the C10H8 : C,,F, complex, because of the presence of an overlapping band of C,,F, but can readily be identified in ClODa : C1,,F8 and in IU-C,,H~D : C,,FB complexes. No other vibrations of naphthalene show factor group splitting. On the other hand, in naphthalene : TCNB and naphthalene : TNB complexes, no factor group splitting of this vibration (or any other vibration of naphthalene) is observed_
have used the criterion that for aromatic hydrocarbons,
isotopic substitution has only mild effect on the factor group splitting [S] . The corresponding band of C10D8 is in the region complicated by the overlapping bands of SbCl,. For this reason, we used another isotopic naphthalene, LU-C,,-&D. We observe a similar behavior for the corresponding vibration of &,,H,D; the factor group splitting increases from 4.3 cm-l in pure crystal to 4.7 cm-1 in the complex a-CIoH,D : ZSbCl,. This observation along with the isotopically mixed crystal result establishes that the splitting observed in the crystal of the complex is a factor group splitting. We find that the factor group splitting observed on the 386 cm-1 bid of naphthalene is 5.5 cm-1 in the C,,H, : 2SbC1, complex and 5 cm-l in the Cr,,H8 pure crystal. We have repeated our study and consis-
3. Theoretical
calculation using atom-atom
interaction
In this section, a theoretical calculation of factor group splittings of naphthalene vibrations is presented using the empirical atom-atom interaction potential. The detailed crystal structure data are available for both C,,H, : ZSbCl, and CloH, : C10F8 complexes. In the crystal of the C10H8 : 2SbC13 complex, the naphthalene molecule is situated at the center of inversion such that one SbCI, molecule is directly above one aromatic ring while the second SbCI, is directly below the other aromatic ring of the naphthalene molecule [V] _In this arrangement the SbC$ (acceptor) stack in planes alternating with layers of naphthalene (donor). In the crystal
222
FP. CJzen. PN. Pramd/Factorgroup
of the Cl,,Hs
: Cl,,Fs
complex,
ternate along the stack axis [lo] complexes
CIOHS and C!,,F, al. Thus, crystals of both
consist of planes in which naphthalene mo-
Iecules are nearest neighbors
splitrings of napJuhalene vibrahbns
ber of equivalent sites per unit cell. B is a unitary matrix transforming the site functiolito the factor group representation. ‘II&molecules
at sites a and b are inter-
[9,10]. In our calculation of factor group splittings of naphthalene vibration using atom-atom potential, only naphtbalene molecules are considered and the interaction involving the other component (SbCl, or CloFs) is ignored. In other words we consider only the sublattice of the naphthalene molecules. As we.were only interested in testing the predictions of the atom-atom interaction model with our experimental observations and not in the detailed dynamics of motions, the simplified approach of Rich and Dows [5,12] was used for the calculation. In this method the exciton interaction shift M,, of the factor group state Lyis given as
change equivalent and not translationally equivalent [I I] _Vpppis the interaction potential between the moleculesp andp’. The second derivative of the interaction potential with respect to the normal coordinate is related to the second derivative of the potential with respect to the atomic positions by the following approximate equation:
M, = tC
Here rii is the distance between atoms i and j of molecules p and p’_ Lkii/ari is the cosine of the angle between the position vector of atom i and the interatomic vector. &,/a$ is the amplitude of the motion of atom i in the particular normal mode of molecule p. In the calculation, the atomic Cartesian displacements for naph-
BzaBrub
(I)
P’
In this equation, v. is the unperturbed frequency (in wave numbers) of the unperturbed mode, Q represents its normal coordinate. The sum runs over lattice sites with moleculesp on site a, and p’ on site b; r is the num-
(2)
Table 1 Factorgroup splittins of naphthalenevibrations System
Unperturbed
MolecuIar
Crystal frequencies
frequencies
symmetries
(cm-‘)
Factor group splittino.?I(cm-‘) ‘j
(cm-’j
talc.
obs.
talc.
obs.
396.5 400.8 953.0 953.2
389 394 949 953
4.3
5
0.2
4
386.2 392.9 943.7 949.2
385.5 391.0 956
6.8
5.5
5.46
0
0.2
1.0 a)
0.1
0
-_naphthalene
CIOHs : 2SbCis
CIOHS: C,oFs
386
Bg
943
Big
356
Big
943
B1g
386
%
943
B1g
386.0
388
386.2
?
943.0
95.5
943.1
‘j Factorgroup splitting measured in CloDa : ClaFs complex (see text).
F.P. Chea, P.N. Prasad/Factorgroupsplittingsof naphthalenevibrations
thalene modes given by Rich [12] was used. The parameters A, B and C used for the potential function, vq = -Ari6
+ B exp(-C?$,
were those of Williams [13]. Factor group splittings on both the 386 cm-l and the 943 cm-’ vibrations of naphthalene are calculated for pure C,oH, crystal, C,oH, : 2SbCI,, and C,,Hs : C1,,Fg. The values obtained are listed in table 1, which also lists the experimentally observed values.
4. Discussion A comparison of the values calculated from atomatom interaction model with those experimentally observed for the 386 cm-’ band shows a qualitative agreement in the trend. Experimentally, we observe that factor group splitting on the 386 cm-’ band increases in going from pure C H crystal to the complex C,,H, : 2SbC13 and :t”de8creasesin going to the complex C,oH, : C,oFa_ The theoretical calculation also predicts this trend. However, we feel that this agreement is fortuitous and should not be taken as an evidence for the validity of the atom-atom interaction for crystalline complexes in general. The atom-atom interaction does not provide a quantitative agreement with observed factor group splittings even for pure naphthalene crystal [8] _For example, it predicts a splitting of 0.2 cm-l for 943 cm-l vibration in pure naphthalene, whereas a splitting of 4 cm-l is experimentally observed_ In the case of the C,oH* : 2SbC13 complex, there are many observed features which cannot be explained by the atom-atom interaction model. First, the calculation predicts au increase in the factor group splitting of the 943 cm-1 band of naphtbalene in going from pure C,,Hs to C,,-,H,, : 2SbC1,. On the other hand, experimentally we observe the opposite: the factor group reduces from 4 cm-l in pure C,oH, to within the linewidth (< 1 cm-l) of the transition in the C,oH, : 2SbC1, crystal. Second, the factor group splitting decreases as SbC13 is successively replaced by SbBr3. One may argue that the lattice parameters (unit cell dimensions) of the two complexes C,oHa : 2SbC1, and C,,Ha : 2SbBr3 are not the same and this leads to a difference in the naphthalene-naphthalene interaction for the two complexes. The crystal structure of the C,,H, : 2SbBr, complex
213
has not been reported. However, on the basis of our study of phonons [14] in these complexes we fiid that the two complexes have the same crystal structure. The phonons of the naphthalene sublattice do not change in frequency as SbCl, is replaced by SbBr, suggesting that the unit cell dimensions for C,,H, : 2SbC1, and C,,H, : 2SbBr, complexes are very similar. These results are consistent with the fact that pure crystals of SbCl, and SbBrj are known to have almost identical unit cells 1151. For this reasons, we feel that the difference in the factor group splittings observed for CIOHs : 2SbC13 and C1uHg : 2SbBr3 is not due to a difference in their crystal structure (or unit cell dimensions)_ The acceptor molecule (SbCl, or SbBr,) participates in the interaction. There is no close lying motion of either SbCl, or SbBr, near the 386 cm-l naphtbalene vibration that a near resonance interaction of Fermi-resonance type could give rise to such differences. The mean of the factor group components does not show a monotonic shift as the SbCl, is replaced by SbBr,, but exhibits a minimum near 0.5 mole fraction of SbBr3 (fig. 2). In the C,,Hs : 2SbC1, complex, the naphtbalene molecule is considerably distorted from D,, symmetry [9] . This symmetry reduction along with the rr-electron interaction with SbCl, changes the distribution of electron densities in naphthalene molecules. On this basis, one may question the use of William’s parameters A, B and C, which have been derived for pure hydrocarbons [ 131. It has been shown that in cases of hydrogen bond formation [ 161, these parameters are different due to a change in the occupation number of electrons in the valence shell. The change in the values of these parameters A, B and Cwill be dependent on the nature of the acceptor. This might explain the reduction in factor group splitting in going from the C,,H, : ZSbCl, complex to the C,,H, : 2SbBr3 complex. However, it does not explain the cause of the selective enhancement of the factor group splitting of 386 cm-’ of naphthalene in the complex C,,H, : 2SbC1, _On the basis of an atom-atom potential, both 386 cm-* and 943 cm-’ modes of naphthalene should show larger splittings In the C1,,Hg : 2SbC13 complex compared to that in the pure naphtbalene. Other possible interactions are electrostatic multipole and polarization interactions. Both these interactions would be dependent on the nature of the acceptor_ These interactions are anisotropic and can give rise to mode selective dynamic intermolecular interactions_
224
F_P. then, PN. PrasadfFactorgroup
This property can expkirk a selective enhancement of the factor group splitting. One type of multipole interaction involves dipoles created by a transfer of r-electrons from the aromatic ring of naphthalene to SbClj . The multipole and polarization interaction can also explain the reduction in factor group splitting in going from the C,,H, : ZSbCI, crystal to C,,H, : ZSbBr,. The minimum observed in the curve of the mean of the factor group splitting versus concentration of the SbBr, is attributed to the formation of the mixed complex C,oH8 : 2(SbCl& (SbBr3)o 5_ In the mixed complex the naphthalene molecule-undergoes different distortion as the SbCI,-C,,H, dipole and the C,,H,SbBr, dipole do not cancel each other. The vibrational frequency can have a different value. The concentration of the mixed complex C,,H, : 2(SbCI,)o, (SbBr$,, 5 will be maximum when the composition of the m$ed crystal approaches 0.5 mole fraction of SbCI, (or SbBr& This is the concentration at which the mean of the factor group splitting exhibits a minimum. We would like to add that our phonon study of this complex [ 141 does reveal an impurity induced band in C,oH, : 2(SbCI,), (SbBr3)1_X and the intensity of this band is maximum when X = OS. We attributed the appearance of this band to the formation of the mixed complex C,oH8 : Z(SbCI,), ,(SbBr,)o 5_ In conclusion we observe that the ato&atom interaction model is not satisfactory for the C,oH8 : 2SbC13 complex. We note that other workers [ 171 have also found atom-atom interaction unsatisfactory for crystals containing molecules with polar groups. Our experimental result is consistent with what can be expected if important multipole-interactions existed_ The validity of such interaction can only be established by an actual calculation using such potentials and a quantitative verification of the theoretical prediction.
splittings of naphthalene vibrations
Acknowledgement
We wish to thank Professor R. Kopehnan of the University of Michigan for providing us with the sample of c&,,,H,D.
References
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