Correlation between Crystal Structure and Carbonyl-BondStretching Vibrations of Methyl Benzene Transition MetalTricarbon y 1sBY H. J. BUTTERY, G. KEELING, S. F. A. KETTLE, I. PAUL AND P. J. STAMPERDepartment of Chemistry, The University, Sheffield, S3 7HFReceived 20th February, 1969The site and factor group approaches to the interpretation of solid state infra-red and Ramanspectra of metal carbonyls are compared. A factor group analysis of seven arene chromium tri-carbonyls indicates that the effective symmetry of the vibrational repeating unit may be higher thanthat of the crystallographic point group.There has been considerable interest in the correlation between the infra-redspectra of transition metal carbonyl complexes in the 2000 cm-l region and the con-figuration of the molecule in dilute so1ution.l Owing to the general success of thismethod it seemed appropriate to extend the approach to the corresponding solidstate structure and spectra.In the present paper we report the results of a systematic study of a series of methyl-substituted benzene chromium tricarbonyls.These complexes were chosen for thefollowing reasons. (i) The local carbonyl environment in solution approximatesclosely to C3u.2 (ii) The magnitude of interaction constants is such that in solutioiithe Al and E carbonyl stretching vibrations are fairly well ~eparated.~ (iii) Allmembers of the series axe readily prepared and relatively table.^ (iv) Crystal struc-ture data is available for the benzene and hexamethylbenzene compounds.EXPERIMENTALCompounds were prepared by the method of Nicholls and Whiting 4; analytical data aregiven in table 1.Raman spectra were recorded using a Spex 1401 spectrometer with helium-neon laser excitation; finely ground samples, enclosed in capillary tubes, were used. Fre-quencies were reproducible to &l cm-l. The infra-red spectra were recorded using aTABLE 1m.p.benzene chromium tricarbonyl 160-11 ,Zdimethylbenzene chromium tricarbonyl 88lY2,3-trimethylbenzene chromium tri-carbonyl 103-4lY2,4,5-tetramethylbenzene chromium tri- 94-4.5carbonylpentamethylbenzene chromium tricarbonyl 157-8hexamethylbenzene chromium tricarbonyl 227methylbenzene chromium tricarbonyl 77-848analysislit. found calculatedC H C H162-3 ' 50.7 3.1 50.3 2-880 * 52.7 4.3 52.6 3.588-90 55.2 4.5 54.6 4.1102-4 56.5 5.0 56.3 4.798-9 57.7 5.1 57.7 5.2101-2 59.3 6.1 59.2 5.6232 a 60.3 6.0 60.5 6.BUTTERY, KEELING, KETTLE, PAUL AND STAMPER 49Unicarn SP100(Mk 11) spectrometer. Samples were ground with KBr for up to half anhour (to optimize band profiles) before pressing into discs.Frequencies were reproducibleto within IfIO.5 cm-l. Space groups were determined from the systematic absences in equi-inclination Weissenberg photographs. Data for the f h t three layers along one axis wereusually obtained.RESULTSIn table 2 we detail the observed infra-red and Raman frequencies for benzene andsix methylbenzene chromium tricarbonyl species. Also given in this table are thebenzene chronium tricarbonylmethylbenzene chromiumtricarbonyl1 ,2-dimethylbenzenechromium tricarbonyl1,2,3-trimethylbenzenechromium tricarbonyl1,2.4,S-tetramethylbenzenechromium tricarbonylpentamethylbenzenechromium tricarbonylhexamethylbenzenechromium tricarbonylTABLE 2spectra space groupinfra-red frequencies Raman frequencies (cm-1)Pzl,m Cfh 1966, 1879, 1858, 1829, (C13) 1945(~), 1887(~), 1865(~~)P212121 Dt 1961, 1875, 1865, ca.1855(sh), *1938(w). 1892(s). 1878(vw), 1867(vw)I833((=13) 1853(~~), 1835(C13)(*possibility of sh. at high energy)P ~ ~ 2 ~ 2 ~ D$ 1960, 1864, ca. 1860(sh), 1944(sh). 193%~). 1883(vs) 1872(m),1830(C13) 1861(wm), 1845(wm)P Z ~ , ~ C;, 1949, cu. 1935(sh), 1870, ca. 1944(w), 1934(w), 1884(v~), 1871(vs),P21,c C;, 1944, ca.1940(sh), ca. 1946(w), 187O(vs), ca.1854(sh), 1848, 1819(C13) 1851(m)1875(sh), 1864. 1858, ca.185O(sh), CU. 1826(~h)(C13)1867(sh), 1855(m)D i i 1945,1927, ca. 1873(sh), 1854, 1931(m). 1878(m), ca.(at least two unresolvadpeaks) 1822(C13)1854, 1849, ca. 182O(sh,C13),1865(sh). 1857(vs), 1848(s), 182O(C13)Pbca of: 1943, 1925, CU. 1868(~h). 1928(~m), 1873(m), 1 8 6 5 ( ~ ~ ) ,1851(vs), 1846(s), l82l(Cl3)8 1 W 1 3 )probable space groups of the compounds, either as determined by us or, for benzenechromium tricarbonyl and hexamethylbenzene chromium tricarbonyl,6 from dataavailable in the literature.DISCUSSIONIt is convenient to consider fist benzene chromium tricarbonyl. The crystalstructure of this compound has been determined by Bailey and Dahl 5 ; it crystallizesin the P2,1m(C5,) space group with two molecules in the unit cell, each moleculehaving C, site symmetry.There are two approaches which have commonly been used to discuss the infra-redspectra of crystals, the site group and factor group approaches.The former isessentially an isolated molecule approach, the spectrum being considered to arise fromthe vibrations of uncoupled molecules having, however, the symmetry of their crystalsite and not that of isolated molecule. The factor group approach includes inter-molecular couplingand the fundamental vibrating unit is regarded, rather, as composedof all of the molecules in a unit cell.Benzene chromium tricarbonyl allows a ready assessment of the relative merits ofthe two approaches and indicates which method it would probably be most profitableto employ for the interpretation of the solid state spectra of metal carbonyls.Thesite group approach predicts that the reduction in molecular symmetry from CSy(isolated molecule) to C,(crystal) will lead to three coincident infra-red and Rama50 MBTHYL BENZENE TRANSITION METAL TRICARBONYLSbands. However, the factor group approach, whilst also predicting three infra-red andthree Raman bands requires that the two sets should show no coincidences (the factorgroup is isornorphous with the C,, point group and possesses the set of operations i . T,where T is the set of translation operations, which is analogous to the presence of acentre of symmetry in an isolated molecule.The genesis of these predictions areshown in table 3. Comparison with table 2 shows that there are no coincidencesbetween the infra-red and Raman spectra of benzene chromium tricarbonyl indicatingthe inadequacy of the site group approach. For all the cases we consider, the sitegroup approach leads to a prediction of too few infra-red and Raman peaks. Wetherefore confine our attention to the use of the factor group method.TABLE 3factor group ( ~ 2 ~ ) site group (C,) isolated molecule (C3")A' (i.r. and Raman Al (i.r. and Ramanactive) active)A'+A" (both i.r. and- E (i.r. and Ramanand Raman active) active)77Au (i.r. active)Ag (Raman active)Au+Bu (both i.r.Ag+Bg (both RamanThe relationship between modes of the isolated benzene chromium tricarbonyl moleculeThis diagram neglects the mixings which occuractive)active)and the site and factor group predictions.in either site or factor group approaches.We next consider the molecule hexamethylbenzene chromium tricarbonyl, thecrystal structure of which has been determined by Bailey and Dahl.6 The compoundcrystallizes in the Pbca( 042) orthorhombic space group with eight molecules in the unitcell.By arguments analogous to those used above, the factor group approach leadsto a prediction of nine infra-red and twelve Raman peaks which should show nocoincidences (the site group approach predicts three, coincident peaks in each spec-trum). Inspection of table 2 reveals that only five infra-red and five Raman peaks areobserved.It would appear that there are possibly four coincidences (within the limitsof error). However, the presence of a centre of inversion in the unit cell establishes thatthese coincidences are accidental and result from the relatively small magnitude of theintermolecular coupling constants (compared, say, with those in benzene chromiumtricarbonyl). These observations force the conclusion that in the solid state thepresence of a centre of inversion is not incompatible with such coincidences.The discrepancy between the predicted and observed number of infra-red andRaman peaks in the spectra of hexamethylbenzene chromium tricarbonyl may beaccounted For on the basis of a potentially general simplification. A study of thecrystal structure of hexamethylbenzene chromium tricarbonyl reveals that, althoughthe molecules occupy general positions, with site symmetry C1, each Cr(C0)3fragment may, within the limits of experimental error, be regarded as havirg C,symmetry with the mirror plane almost parallel to the b glide plane. Further, thesepseudo mirror planes will be essentially parallel for all of the molecules within aunit cell.Now, the factor group approach is applicable because the wavelength ofthe incident radiation is much greater than the size of a unit cell (for infra-red spectraby a factor of ca. 104), so that vibrations within well-separated unit cells are excited inphase, i.e., the excitation processes are insensitive to the existence of translation of theorder of magnitude of the unit cell.A consequence of this is that '' accidental BUTTERY, KEELING, KETTLE, PAUL AND STAMPER 51mirror planes as apparent in the crystal structure of hexamethylbenzene chromiumtricarbonyl will be indistinguishable from real ones, i.e., spectrally, the molecules willbehave as if they are located at special (C,) rather than general positions. From agroup-theoretical viewpoint this means that the crystallographic unit cell of hexa-methylbenzene chromium tricarbonyl is twice the size of the primitive (inf'ra-red andRaman) unit cell.The effective coincidence between the molecular and glide planes requires a similarrelationship between a twofold axis and the original screw axis along the principalaxis. Consequently, the effective space group is not P b , , ( D ~ ~ ) but Pbcm(Dirf).The newfactor group leads to a prediction of six non-coincident infra-red and Raman peaks.PENTAMETHYLBENZENE CHROMIUM TRICARBONYLThis compound has infra-red and Raman spectra similar to those of the hexa-methyl compound discussed above, suggesting that they may be isomorphous. Thissupposition was confirmed by X-ray single measurements which showed that theyhave both the same space group and unit cells which are almost identical in size. Asthe two compounds are isostructural the pentamethyl derivative presumably has thesame pseudo mirror plane as the hexamethyl compound.METHYLBENZENE CHROMIUM TRICARBONYLThis complex crystallizes in the P212121 space group ( D i ) , the four molecules in eachunit cell occupying general positions.The normal factor group analysis leads to aprediction of twelve peaks in the Raman spectrum, nine of which should also be seenin the infra-red spectrum. However, experimentally, we observe four infra-red andfive (possibly six) Raman bands. If we assume an effective site group symmetry of C,for the methylbenzene chromium tricarbonyl molecules, the appropriate supergroup isDz x C, = D&. Within this group the molecules occupy pseudo special positions.The new factor group leads to the prediction of six infra-red and six Raman bands.This is in accord with the observed spectra (table 2).1,2-DIMETHYL CHROMIUM TRICARBONYLThis compound is isomorphous with methyl benzene chromium tricarbonyl,crystallizing in the P212121 (Dl) space group, each of the four molecules in the unit celloccupying general positions.Moreover, the infra-red and Raman spectra of the twocompounds are similar. Consequently, a D;, supergroup is again indicated.1,2,3-TRIMETHYLBENZENE CHROMIUM TRICARBONYL AND 1 , 2 , 4 , 5 - T E T R A -METHYLBENZENE CHROMIUM TRICARBONYLAs the discussion of these two complexes is similar we consider them together.Both crystallize in the P21,c space group (C;,) with four molecules in the unit cell.Because, compared with the factor group (Cq,) predictions of six Raman and six infra-red bands, they show five and six infra-red absorptions respectively and both mayshow five Raman bands, there is no necessity to invoke a vibrational space group ofhigher symmetry.CONCLUSIONThese analyses suggest the following generalization.When the infra-red and Ramanspectra are both simpler than those predicted by the factor group approach this ma52 METHYL BENZENE TRANSITION METAL TRICARBONYLSimply the existence of eflectiue symmetry operations ia the unit cell, and thus a vibrationalspace group of higher symmetry.However, the above generalization is a necessary, but not sufficient, condition forthe existence of effective symmetry operations, since there could be other reasons whyfewer than the predicted number of peaks may be observed, such as accidental degen-eracy or low intensity. Nevertheless, it should be of value in the interpretation ofsolid-state vibrational spectra. Ultimately, in a solid state vibrational analysis onemust use a vibrational space group, which may, or may not, be identical to thecrystallographic space group (just as for magnetic problems one recognizes theexistence of magnetic space groups).We are indebted to the Science Research Council for maintenance grants (H.J. B.and G. K.) and a post-doctoral fellowship (I. P.). One of us (P. J. S.) is indebted toStaffordshire County Council for a postgraduate award. We are grateful to Prof.D. A. Long and Dr. A. R. Gee for the provision of Raman facilities.see, e.g., J. Dalton, I. Paul, J. G. Smith and F. G. A. Stone, J. Chern. SOC. A, 1968,1195, andreferences cited therein.L. E. Orgel, Inorg. Chern., 1962, 1,25.F. A. Cotton and C. S. Kraihanzel, J. h e r . Chem. SOC., 1962, 84,4432.B. Nicholls and M. C. Whiting, J. Chem. SOC., 1959, 551.M. F. Bailey and L. F. Dahl, Znorg. Chern., 1965,4, 1314.M. F. 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