J. CHEM. SOC. FARADAY TRANS., 1994, 90(9), 1265-1269 Vibrational Spectroscopic Analysis of Group 6 Metal Hexacarbonyls in the Solid State Upali A. Jayasooriya School of Chemical Sciences, University of East Anglia, Norwich, UK NR4 7TJ Vibrational spectra of group 6 metal hexacarbonyls in the solid state are analysed using the ‘oriented gas’ and ‘ latent symmetry’ approaches. An explanation of lifting of degeneracies and relative intensities is provided, including the intensity predictions for the factor group components of distortion-induced intensities of molecu- larly forbidden modes. Vibrational spectroscopy is a tecnique which is used rou-tinely to obtain structural information on molecules in phases where the intermolecular interactions present are neg- ligible.However, the same cannot be said about the solid state when there is appreciable intermolecular coupling. One reason for this is a dearth of simple crystal structure-spectra correlations, with regard to solid-state effects. When a highly symmetric molecule crystallises it com-monly adopts a site which has significantly lower symmetry than that of the molecule itself. In such cases it is always a matter of interest to investigate the extent to which the packing arrangement perturbs the molecular properties. This problem is of particular interest for species of 0,symmetry because there are Wigner-Seitz unit cells of 0,symmetry, the octahedron itself is not one of these. Octahedral molecules, then, are likely to be forced to adopt sites of rather low sym- metry.An excellent example is provided by the octahedral metal carbonyls M(CO),, M = Cr, Mo, W, all of which crys- tallise in Pnmu (D::) with four molecules per unit cell, each molecule occupying a site of C,symmetry.’ The first vibrational spectroscopic data on these were published in 1955 by Hawkins et a2.’ and this was followed by a series of studies mainly aimed at recognising and assign- ing the molecular vibrational modes.3 In 1973 single-crystal Raman experiments were used4 to obtain symmetry species of the vibrational modes in the solid state. Then in 1978, Kariuki and Kettle’ used Raman spectra of mixed crystals to show the presence of strong intermolecular vibrational coup- ling in the v3(CO), e, mode and the absence of such coupling effects in the case of the v,(CO),a, mode.Further, the weak bands at 1964 (Cr), 1966 (Mo) and 1957 (W) cm-l were iden- tified as Raman activity shown by the only infrared-active v6(CO), t,, mode of the isolated molecule. In the same year Scheuermann and Nakamoto, reported Raman spectra of chromium hexacarbonyl isolated in an argon matrix at 13 K and in the solid state at 292 and 13 K. These workers have observed many more bands in the solid-state spectrum at low temperature and have assigned frequencies to six inactive fundamentals of t,, ,t,, and t,, symmetries, which were pre- viously only inferred from overtone and combination modes. However, surprisingly, their assignments are based on an earlier crystal structure determination7 which has since been shown to be in error.’ All extant single-crystal vibrational spectroscopic data, consisting of Raman and reflection IR spectra, are due to Adams and co-worker~.~.~ The following is an attempt to understand some of the solid-state effects shown by these compounds. The ‘oriented gas model’g is first used to explain the intensity distribution in the carbonyl stretching frequency region of the Raman spectrum.Its applicability is illustrated using the v(CO), e, mode, which has been shown previously to be the more vibrationally coupled of the two Raman-ative v(C0) molecu- lar modes. Secondly the ‘latent symmetry approach’” is used to obtain qualitative intensity predictions on the whole of the IR and Raman spectra. In this technique, purely symmetry- based arguments are used to investigate the evolution of the real crystal structure from the isolated molecule via the latent or near-symmetries present in the solid state.During this process of evolution, any vibration allowed in the final factor- group analysis but forbidden under the molecular and/or latent symmetry (i.e. the corresponding matrix element =0, under these symmetries) is predicted to have a value for its matrix element which is proportional to the extent of devi- ation of the real structure from the latter symmetries. There- fore the useful latent symmetries are those involving the minimum of distortion from the real crystal structure. The utility of the latter approach is illustrated by providing expla- nations of the following experimental observations.The close similarity between the single-crystal Raman spectra of b,, and b,, factor-group symmetries.* Also similar to each other are the IR spectra of b,, and b,, factor-group symmetries. These observations are highlighted in the splitting pattern of the four factor-group components arising from the molecular e, carbonyl stretching mode. Here the b,, and b2g com- ponents are almost degenerate while a, and b3, ar.: substan-tially split.’ Further, molecular IR and Raman activities are almost strictly maintained through to the solid state so that only about half the factor-group predictions are realised in practice. The only exception to this is the molecularly Raman-inactive t ,, mode found in the carbonyl stretching region of the Raman spectrum.This shows up in the single- crystal Raman spectra with intensity only in the a, and b3, symmetries even though six Raman-active factor-group modes are predicted theoretically (Table 1). Discussion X-Ray Crystal Structure The complete crystal and molecular structure has been reported for chromium hexacarbonyl and therefore this compound is used mainly for the following discussion. However, the conclusions are of general validity for this whole class of isomorphous compounds. A careful examination of the crystal structure shows that these molecules crystallise with molecular three-fold axes approximately parallel to each other and to the crystallo- graphic ‘a’ axis [Fig. l(b)].This near-symmetry would not show up in the space group and thus will have no effect on the factor-group predictions, conventionally used to explain vibrational spectra in the solid state. Note that in this case, even if the molecular three-fold axes are exactly parallel, it would still not change the space group and hence the factor group. However, it is possible to use this near-symmetry or J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 1 Correlation between the factor group, site group, the most significant latent factor group, latent site group and the molecular point group symmetry of Cr(CO), latent latent factor molecular site factor group group molecular Oh D,, '2h D4h 0:: Oh / The effect of the tetragonal latent space group which is of only intermolecular origin, is indicated by dotted lines. This shows that when the degenerate sets of functions (xz, yz); elg and (x2 -y2, xy):,eZg under D6h are correlated with those in D,, , only the former degeneracy is maintained.'latent symmetry'" in order to simplify the application of the 'oriented gas approximation '' for the estimation of intensities of vibrational transitions in these solids. The Raman itensities of the factor goup components derived from the e, carbonyl stretching mode are chosen as an example. Oriented Gas Model The two tensors for the components of e, modes in the point group 0,are given by Poulet and Mathieu,' and are: -u 0 (1)[ : -; 2\] rrand -+a -These are to be expressed in terms of crystallographic axes using a similarity transformation relating the two axial systems, molecular and crystal.The relationship between these two axial systems is shown in Fig. 2, which gives the transformation matrix : The two tensor components of the molecular e, mode in terms of the crystal axes are therefore; Now the use of the projection operator technique in the factor group Diz gives the derived polarisability tensors cor- responding to the respective factor-group components as : 0 -J2a 0 O J2u:] 000 ab2g = ; ab3p = [o 0 a] (4)[ ;J2u 0 OUO These tensors when squared are proportional to the Raman intensities of the corresponding factor-group modes due to a single unit cell, or an aligned single crystal.If one were to compare the experimental single-crystal Raman spectroscopic data with these predictions, it is essential to take great care to compare spectra run under exactly similar conditions. Such data are not available at present. However, one may use the spectra from polycrystalline samples where all symmetries appear in the same spectrum. To do this, it is necessary to obtain expressions assuming all orientations of these unit cells with respect to the observer's axes with equal probabil- ity. Following the method given for this by Wilson et ~1.'~ one arrives at the following intensity ratio for these factor- group modes observable from a randomly oriented poly- crystalline sample. la, : Ibl, Ibzs Ib3, 1 2 2 : 1 (The v4 dependence of the intensities is assumed to be the same for all four modes because of the closeness of their 0 J2u 0 -J2u 0 absolute frequencies.) The polycrystalline Raman spectra of these hexacarbonyls [j2-; ;] and [-d: ;] (3) show that it is not possible to resolve all these factor-group J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 e Fig. 1 Crystal structure’ of Cr(CO), projected down the X-axis. (a) The two hexagonal sub-lattices, obtained by the molecular pairing (k, r) and (m,n), which combine to give the real structure. The molecules within a unit cell are named k, I, m,n as shown in Fig. 3. (b) The full structure showing the molecular three-fold axes parallel to each other and to the crystallographic X-axis.(c) The two approximately tetragonal sub-lattices, obtained by the molecular pairing (k, n) and (I, m),which combine to give the real structure. This tetragonal sym- metry is purely intermolecular in origin with no intramolecular counterpart. components in order to measure their intensities separately.’ However the b,, component which is assigned to ca. 2024 cm-’ (vide infra) stands well clear of the other three. There- fore the intensity ratios between this and the sum of the intensities of the a,, bl, and b,, modes are measurable and are ca. 1 : 6.2 and CQ. 1 :5.2 for Cr(CO), and Mo(CO),, Y I, 1 -1 -1X J3 J3 J3 1 -1 Y -1 -1 -Z J2 J* J2 0 I[: Y J6 J6 J3 Fig. 2 Relationship between the molecular (X, Y, 2)and crystallo- graphic (x, y, z) axes respectively.These results are in reasonable agreement with the predictions from the above calculation especially when one takes into account the approximate nature of the model used here. Much effort had been spent in the past in attempt- ing to improve the oriented gas model in general, particularly with reference to lattice modes.’ Latent Symmetry Approach There are many subtleties of the vibrational spectra of these systems not explained by the latter technique. Here we resort to the so-called ‘latent symmetry approach’,’’ where near- symmetries present in the solid state or those symmetries which are hidden from the space and factor-group decriptions, like the parallel three-fold axes in the present case, are made use of in the spectral interpretation.This is a qualitative approach providing valuable insight into the sym- metries of the significant perturbing potentials of the molecu- lar environment in the crystalline state. In order to make use formally of the fact that the molecu- lar three-fold symmetry axes are parallel in the solid state, one has to relate this latent symmetry element to the space- group symmetry of this material. The method of searching for the latent symmetries adopted here is to take one of the mol- ecules from the four symmetry-related molecules in the unit cell, and divide the total potential of its environment into the individual contributions made by each of the other molecules in the unit cell, together with all molecules translationally related to the latter.Fig. l(b) shows the crystal structure projected down the x axis and Fig. 1(a) shows the two hexagonal substructures combined to give the real structure [i.e. Fig. l(b)]. The mol- ecules within a unit cell are named k, l, m and n (Fig. 3) and the intermolecular potentials shown in Fig. l(a) are for the molecular pairs (k,I) and (m,n). These two substructures have clear hexagonal symmetry, and the three-fold axes in these hexagonal substructures are displaced with respect to each other along the z direction. If one were to bring these two structures to register by translations along z and x directions (necessary translations indicated in Fig. 3), the resulting structure will have the space group P6,lmcm; D&, with only two molecules per primitive unit cell in sites of symmetry D3d.The ‘distortions’ relating this structure and the real structure are purely non-primitive translations, and therefore to a first good approximation are not expected to affect the intensities of the internal mode vibrations. lo Fig. l(c) shows another possible pairing of these molecules, into (k,n) and (I, m)interactions. These are two substructures of approximately tetragonal symmetry. Here note that this tetragonal distribution is purely intermolecular in origin with no intramolecular counterpart. If one ignores the molecular symmetry in this case and consider only the intermolecular distribution, it approximates to the space group P4/mmm; Dih, with only one molecule per primitive unit cell in a site of D& symmetry.The only other possible pairing of molecules of (k,m) and (I, n) does not show any extra symmetry with each pair con- fined to a mirror plane already recognised in the real space group. In summary, only two latent-symmetry structures are therefore recognised with space groups P6,lmcrn; D&, and P4/mmm; Dih, with the former being the most significant with full intra- and inter-molecular symmetries. The symmetry correlations between the molecular point group 0,and the site and factor groups of latent and real space groups are given in Table 1. The four factor-group symmetries, active in the Raman under the Dii structure, pair up into two doubly degenerate modes under the latent space group D&.Therefore one would predict the b,, and b,, spectra, which correlate with the e irreducible representa- t Fig. 3 Crystal structure' of Cr(CO), projected down the Y-axis. The non-primitive translations parallel to Z and X axes necessary to bring the two hexagonal sub-structures to register are indicated for one molecule. Translations needed for the other molecules are obtained simply by transforming these translational vectors using the 0:: symmetry elements. tion of D&,, to be the same to a first approximation, and similarly, for the a, and b,, pair, which correlates with the e2, irreducible representation of @h. However, the molecular environment in the real structure has a contribution to its potential from a tetragonal distribution of molecules as indi- cated in Fig.l(c). The effect of this D,&hlatent-symmetry factor group is only to split the e,, irreducible representation of D6h but to maintain the degeneracy of el, (Table 1).There-fore b,, and b,, spectra are predicted to be much more similar to each other than the a, and b,, pair. This is exactly what is observed experimentally as reported by Adams and Taylor in ref. 8, Fig. 4 and 8. However their assignments of a band at 2009 cm- to the b,, factor group component of the v, ,molecular e, ,mode and that at 2024 cm- ',the strongest b,, symmetry band in this spectral region, to a combination (v6 + v,) disagree with the present analysis.Adams and Taylor' have expressed their surprise at this apparent inten- sity anomaly but appear to have stuck to their assignment on the assumption that v, should show only very little factor- group splitting. Therefore we prefer the earlier assignment of Kariuki and Kettle' of the most intense b3e band (ca. 2024 cm-') to v, . With this assignment, the factor-group com- ponents of v, in the Raman fall into two pairs, b,, and b2g very close in frequency (at 2009 and 2007 cm-', respectively) approximately maintaining the el, degeneracy of the latent space group while the symmetries a, and b,, are well separat- ed (at 2003 and 2024 cm-', respectively) showing the predict- ed destruction of the corresponding e2g degeneracy due to the distortions relating the real and latent symmetry structures.Use of Table 1 provides similar predictions for the IR spectra. The IR activity under & is confined to a2, and el, irreducible representations and the latter remains degenerate under the tetragonal symmetry and correlates with b,, and J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 b,, under the real factor group, Diz. Therefore b,, and b,, spectra are predicted to be similar to each other, but different to the b,, spectrum, in agreement with the reported IR spectra of Adams and Taylor in Fig. 2 of ref. 8. Distortion-induced IR and Raman intensities due to for- bidden modes of molecular units at polar site symmetries in crystals have been discussed by Jain and Bhattacharjee.' They have used perturbation theory and group theory to make predictions within the site group approximation.The assignment of a band at 1964 cm- ' in Cr(CO), (band h in ref. 5) to a genuine factor-group component derived from the molecular t,, mode (vg) by Kariuki and Kettle,' in accord with some earlier isotopic substitution work,,' is in agree- ment with Jain and Bhattacharjee's' , distortion-induced activity predictions. However, the molecular t,, mode is expected to give rise to six factor-group modes in the Raman, 2a, + b,, + 2b2, + b,, (Table 1). Jain and Bhattacharjee's', treatment does not provide an explanation as to which of these factor-group components would show the most inten- sity. The latent symmetry approach presented in this paper provides a criterion for such a distinction between the factor- group components.The correlation given in Table 1 shows the clear preservation of geradelungerade separation from the molecule to the hexagonal latent space group, and if this is strictly valid the molecularly IR-active modes would have no predicted Raman factor-group components and vice uersa. This is mainly what is observed experimentally, except for a very few exceptions. These exceptions however find an expla- nation in the intermolecular tetragonal latent symmetry space group. As already discussed, the irreducible representa- tions a, and b,, which correlate with e,, under D6h are the more sensitive modes to the intermolecular tetragonal poten- tial contribution, and are therefore predicted to be the most intense factor-group components of the molecularly for-bidden modes in the Raman.These predictions are in agree- ment with all experimental observations for this whole class of compounds.'*' Similar considerations would predict the distortion-induced IR activity of the molecularly only Raman-active modes to show intensity mainly in b,, sym-metry. Conclusion Here we provide an example of the latent symmetry approach to vibrational spectroscopy in the solid state which provides a physical realisation of the vibrational spectral con- sequences of intermolecular interactions present in the solid state, and thus an understanding of some relatively compli- cated spectral patterns of an important set of complexes, the hexacarbonyls of the Group 6 metals.This technique, which uses mainly symmetry-based arguments, provides an under- standing of these systems which is ostensibly independent of a particular mathematical model. This method clearly extends one's understanding beyond the oriented gas approximation' and is also shown to extend to the factor- group components of the distortion-induced IR and Raman intensity predictions due to forbidden modes of molecular units.', Further, explanation of the subtleties of the solid- state spectra in this way provides a clear picture of the important perturbations present, which would be of value in the determination of a meaningful mathematical modelling of these systems. References 1 (a) A.Whitaker and J. W. Jeffery, Acta Crystallogr., 1967, 23, 977; (b) B. Rees and A. Mitschler, J. Am. Chem. Soc., 1976, 98, 7918. 2 N. J. Hawkins, H. C. Mattraw, W. W. Sabol and D. R. Carpen-ter, J. Chem. Phys., 1955, 23,2422. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 1269 3 4 (a) F. A. Cotton and C. S. Kraihanzel, J. Am. Chem. SOC.,1962, 84, 4432; (b) L. H. Jones, R. S. McDowell and M. Goldblatt, Inorg. Chem., 1969,8,2349. D. M. Adams, W. S. Fernando and M. A. Hooper, J. Chem. SOC., Dalton Trans., 1973,2264. 10 11 12 U. A. Jayasooriya, S. F. A. Kettle and S. Mahasuverachai, J. Chem. Phys., 1987,86, 3127 and references therein. H. Poulet and J. P. Mathieu, Vibrational Spectra and Symmetry of Crystals, Gordon and Breach, Pans, 1976. E. B. Wilson, J. C. Decius and P. C. Cross, Molecular Vibrations, 5 6 7 8 D. A. Kariuki and S. F. A. Kettle, Inorg. Chem., 1978,17, 141. W. Scheuermann and K. Nakamoto, J. Raman Spectrosc., 1978, 7, 341. W. Rudorff and U. Hofmann, 2. Phys. Chem. B,1935,28,351. D. M. Adams and I. D. Taylor, J. Chem. SOC.,Faraday Trans. 2, 1982,78,1051. 13 The Theory of Infrared and Raman Vibrational Spectra, McGraw-Hill, London, 1955, ch. 3. Y. S. Jain and R. Bhattacharjee, J. Phys. C., Solid State Phys., 1985,18,5299. 9 A. Kastler and A. Rousset, J. Phys. Radiat., 1941, 2, 49; Vibra-tional Intensities in Infrared and Raman Spectroscopy, ed. W. B. Person and G. Zerbi, Elsevier, Amsterdam, 1982. Paper 3/07305J;Received 10th December, 1993.