4 Inorganic Vibrational Spectroscopy By D. M. ADAMS Chemistry Department University of L eicester Leicester LEI 7RH The development of commercial double-beam infrared spectrophotometers coincided roughly with the post-war reawakening of activity in inorganic chemistry. Coupled with the growing importance of spectroscopic measurements, generally in inorganic diagnostics this succoured the development of interest in the vibrational spectra of inorganic compounds especially in the study of skeletal modes lying generally below 500 cm-During the past decade the field has undergone a transition from what was at first largely a specialist spectroscopic area to one that is now widely contributed to by others who use vibrational spectroscopy as just one among several means to an end and very often simply to characterize a compound when used together with analytical data and its melting point.In the early years the primary objectives were to locate regions of and set up correlations for metal-ligand vibrations, such as the stretching modes of M-C M-halogen M-N etc. bonds. A product typical of this phase was the location of frequency regions characteristic of M-halogen bridging as opposed to terminal bonds. These primary objectives have now been achieved’ although much detail will doubtless continue to be added to refine our understanding. By the late 1960’s the field had become crowded to the extent that at least 400 publications per annum were appearing2 dealing with some aspect and con-siderable synthetic effort was necessary either to make new compounds or to obtain those difficult of access to provide the spectroscopist with systems of sufficient symmetry and variability for his work to result in reliable assignments.It was therefore with some relief that the advent of commercial laser-Raman instruments was viewed in some laboratories old series of compounds (recrystal-lized?) were run and the exponential growth of the spectroscopic literature was assured for at least another five years. The first flush of activity has now passed ; the diagnostic value flexibility and ease of sampling methods have assured Raman spectroscopy a continuing place in inorganic chemistry. Over-ambitious claims ’ For general reviews see D. M. Adams ‘Metal-Ligand and Related Vibrations,’ Arnold, London 1967 ; J .R. Ferraro ‘Low-Frequency Vibrations of Inorganic and Co-ordina-tion Compounds,’ Plenum Press New York 1971. See Figure 1 p. 30 in ‘Molecular Spectroscopy,’ ed. M. J. Wells Institute of Petroleum, London 1969 48 D. M. Adams have been reconsidered and the field generally has settled down to a healthy middle age. To these developments should be added the relevant comment that during the same decade there has been a general increase in the ability to handle symmetry arguments. (Indeed most chemists now graduate with a working knowledge of group theory). As a result many good spectroscopic papers are published nowa-days by those who would not classify themselves as spectroscopists. The activity in the field may be judged from the Society’s Specialist Periodical Reports in which ‘Spectroscopic Properties of Inorganic and Organometallic Compounds’ are reviewed a n n ~ a l l y .~ In consequence of the above achievements we now need to re-examine the aims of the field and ask just how far are we towards reaching them. What follows is a selective review in which an attempt is made to assess the ‘state of the art’ and to highlight certain publications which I have enjoyed reading (thereby inevitably including one’s own works!) and which I believe to be of value as much for the direction in which they point as for their particular contribution. 1 Aims Standards and Classification Now that i.r. instruments working to very low frequencies are commonplace and time is available on laser-Raman systems to all who need it,? published work must necessarily be judged both against these capabilities and against the aims of the field.The two most basic aims are : (a) Observation of complete i.r. and Raman spectra of the material from the highest to the lowest frequencies relevant to the problem in hand and under all appropriate conditions. (b) Assignment of observed transitions to their symmetry species. A great deal of derived work naturally follows thereafter (calculation of thermo-dynamic properties determination of force fields etc.) but these are the primary objectives relatively little current work meets them. In order to be quite fair we should be clear that not all work in the field sets out to meet these criteria anyway. We may identify four main reasons for the study of inorganic vibrational spectra.(i) For characterization-often amounting to little more than a list of ob-served bands with perhaps a comment or two. (ii) Deduction or confirmation of a structural feature. For example lowering of a v(C=O) vibration in a polydentate ligand spectrum may be used to indicate co-ordination via oxygen; use of the correlation or intensity tests to prove M-NCS rather than M-SCN bonding in a complex. (iii) Study of an aspect of bonding. Quite commonly such work is restricted to observations of a single type of vibration such as v(CO) v(M-H), v(M-halogen) etc. with attempts to correlate results with bond type, ‘Spectroscopic Properties of Inorganic and Organometallic Compounds,’ (Specialist Periodical Reports) ed. N. N. Greenwood The Chemical Society London vol.1 , 1968; vol. 2 1969; vol. 3 1970; vol. 4 1971 ; vol. 5 in the press. t The comment applies to Britain and comes from ‘a usually reliable source. Inorganic Vibrational Spectroscopy 49 Taft o* and other parameters the trans-effect and perhaps with other physical parameters such as n.m.r. chemical shifts or polarographic half-wave potentials. (iu) Attempts at complete spectral observation and assignment. As with most classifications there is often overlap between the classes but the one above helps to see through the welter of published work and assists in judging each contribution against the proper objectives and standards. The majority of work in this field comes from countries in which advanced spectroscopic facilities are relatively plentiful so that even if a particular laboratory may not be fully competitive it is within reach of one that is.In other words with a bit of effort, many studies could be presented in more complete and hence more valuable form. On the other hand one recognizes the difficulties confronting colleagues in countries where they are not within reach of requisite facilities. Should their work be judged against the standard of what is possible with a basic i.r. instru-ment? I think not because the result of this is to be seen in the current literature, which has separated out into distinct classes. The standard for comparison is either that which is possible with the best currently available instrumentation or that of a restricted or specialized aim that is within reach with given facilities.For example much valuable work on band intensities could be done with simple instruments rather than using them for fragmentary studies of complexes for which the whole armoury of modern techniques is a prerequisite for success. We now take our two broad aims as a basis for discussion of some selected recent work. 2 Towards Observing the Complete Vibrational Spectrum Commercial instruments (i.r. and Raman) are now available to cover the entire vibrational frequency range and are widespread but in order to observe the complete vibrational spectrum of a material it may be necessary to use special sampling conditions or to work on a restricted timescale. Because such techniques are basic to achieving aim (a) we note some of them briefly. The low-temperature sampling problem has now been tamed and commercial equipment can be had off-the-shelf for any application.Ease of operation is being improved by the increasing use of closed-cycle cryogenic systems although these are expensive. Matrix-isolation i.r. work has been routine for a good many years but only very recently have Raman spectra been obtained from matrix-isolated species. As with solutions depolarization ratios may be rneas~red,~ giving unique symmetry-related information provided that the matrix is of good optical quality. This sampling technique is of potential value for problems in addition to the usual ones involving trapping or creation of normally unstable species. For molecular crystals internal modes often become badly mixed with external (or lattice) modes at low frequencies.By matrix-isolating molecules something approximating to the imperturbed low-frequency internal vibrational modes J. S. Shirk and H. H. Claassen J . Chem. Phys. 1971 54 3237; H. Huber G. A. Ozin, and A. Van der Voet Nature (Phys. Sci.) 1971 232 166 50 D. M . Adams should be observed I cannot recall an example of such an application but I am sure that it has quite a future. Although Raman spectra of gases have been studied since the early days of Raman spectroscopy the minute sample (ca. 10' molecules) required using laser excitation makes possible much more widespread use of gas-phase sampling conditions. In particular Beattie and co-workers have made impressive inroads into systematic application of this technique to inorganic species at temperatures up to ca.lo00 "C. Typically the dissociation of dimeric molecules such as A1,Br6 into monomers has been observed and assignments have been made for both forms.' Occasionally a gas-phase species or one of its dissociation products may exhibit resonance fluorescence. This is very intense and dominates the weak Raman spectrum. In such cases it is better to attempt a study of the gas-phase species by matrix isolation. Truly enormous strides have been made in the construction of equipment for observing transient or very unstable species by Raman techniques opening up a whole new dimension to the inorganic spectroscopist. These remarkable de-velopments are principally due to Bridoux and Delhaye and the equipment is now commercially available.As the price of an ultrafast Raman system is less than that for n.m.r. and mass spectrometers we might reasonably expect to see rapid developments in this area. To give some idea of the power of the method, spectra can be recorded using a single laser pulse to generate the effect.6 A flash-photolysis type experiment can be performed thus enabling study of the Raman spectra of transient species and their kinetics. 1.r. techniques have not yet reached down to the nanosecond level but on the basis of what is currently possible there still exists a big future Lefohn and Pimentel recently recorded the i.r. spectrum of CF,(g) in less than a millisecond, including successful resolution of rotational fine ~tructure.~ 3 Determination of Symmetry Species and Information on Specific Vibrations Totally symmetric modes of vibration are polarized in the Raman spectra of fluids and are therefore readily identified and assigned in most cases.There aye situations in which totally symmetric modes may be extremely weak (in contrast to the commonly held belief that totally symmetric modes are invariably intense) : this is generally due to cancellation of bond polarizability moments. For example, in ferrocene the C-H out-of-plane mode is very weak as is one of the A,v(CO) modes in Mn(CO),Br. In the latter case mode (1) is strong but (2) is weak as the I. R. Beattie and G. A. Ozin J . Chem. SOC. (A) 1969 2655. M. Bridoux Rev. d'optique 1967 8 389; M. Delhaye Appl. Optics 1968 7 2195. A. S. Lefohn and G. C. Pimentel J . Chem.Phys. 1971,55 1213. Inorganic Vibrational Spectroscopy 51 z-components of the polarizability changes in the approximately square-planar part cancel those of the unique carbonyl group. t 0 0 o2 O C/O O, \ ' oiT 0 c / \ 0 c / c \ I / c c\ I ,c Mn \ Mn O/ Br c / I \c c \ d ( 1 ) (2) No direct information on symmetry species can be obtained from the i.r. spectra of liquids and solutions although bandshapes half-widths and in-tensities can on occasion indicate a doubly degenerate mode among non-de-generate ones. Band structure in the i.r. spectra of gases can be used to show whether the vibration involved is of the parallel or perpendicular type. In order to make further progress it is essential to use oriented samples. Crystals obviously meet this requirement as the molecules and complex ions in them have fixed spatial orientation.By aligning the optic axes of crystals with the plane of a suitably polarized beam of radiation unique information about symmetry species can be obtained. Consider for example the square-planar PtC1,2- ion which in K,PtCl is so aligned with respect to the crystal axes that both the complex ion and the tetragonal unit cell have D, symmetry. 1.r. radiation polarized parallel to the crystal z-axis excites only vibrations with atomic motion along z viz. A,, species. Similarly radiation polarized along x (or y ) excites only vibrations occurring in the xy-plane E, species (see Figure). Experiments of this nature Z 4 4 Out-of-plane n( C1 -Pt - C1) r - - - - - -X In-plane G(C1-Pt-Cl) Figur 52 D.M . Adams were used to prove that the in-plane bend d(C1 -Pt -C1) occurs at higher frequency than the A, out-of-plane bend n(C1 -Pt -C1).8 More symmetry-related information can in general be obtained from single-crystal Raman than from i.r. spectra because Raman scattering depends upon a tensor property the derived polarizability tensor a. By choosing appropriate combinations of orientations of the stimulating linearly polarized electric field E and observations of the induced electric moment P each of the six independent tensor components can be brought into play selectively. For example taking E and P we have P = axyEy. Since aXy is uniquely associated with one sym-metry species in most of the 32 crystallographic point groups an experiment of this type yields directly symmetry-related information.In recent years this field has exhibited increasing activity with physicists tending to study rather restricted crystal types (e.g. perovskites) which show a variety of solid-state phenomena such as piezoelectricity thermoelectricity etc. In contrast chemists have tended to work with crystals of more elaborate com-plexes often with a view to obtaining some insight into bonding. We have space to mention a very few of these results. A particularly important study of some copper (11) complexes has been re-ported by Beattie et aL9 Of special interest here is the effect of the 'long' bonds between copper and two of its ligands upon the vibrational spectrum. CuCl,, 2H,O can be considered as an assembly of planar molecules trans-[CuCl,(H,O),] linked into chains by means of long bonds between copper and chlorine atoms of neighbouring molecules.From Raman single-crystal experiments it was shown that the Cu-CI (short) bond stretch is at 216 cm- and that a line at 112 cm- ' is associated with a motion that can be described as Cu-CI (long) bond stretching plus libration of the molecules about the 0-Cu-0 axes. This interaction is apparently sufficient to lower ~(CU-CI) (short) slightly; in K,CuC1,,2H20, which also contains trans-[CuCl,(H,O),] molecules v(Cu -C1) (short) is at 228 cm- ' and the neighbouring chloride anions execute motions at wavenumbers of ca. 140 cm- ' which are effectively ionic lattice modes." An intermediate case of much interest is presented by (MeNH,),CuCI , also studied by Beattie et al.In this crystal square-planar [CUCI,]~- anions are joined in sheets such that short and long Cu-CI bonds alternate in two directions at right angles in the sequence c1-cu-c1--cu--c1-cu-c1- -cu--CI Thus any Cu -C1 short-bond stretch is automatically a 'long' bond compression. D. M. Adams and D. C. Newton J . Chem. SOC. (A) 1969 2998. I . R . Beattie T. R . Gilson and G. A. Ozin .I. Chem. SOC. (A) 1969 534. D. M. Adams and D. C . Newton J . Chern. SOC. ( A ) 1971 3507. l Inorgan ic Vibrational Spectroscopy 53 It was found that Raman lines at 286 (B2,) 248(A,) 182(A,) and 174(B2,) cm- are associated with Cu-Cl stretching ; the lower two are reasonably associated mainly with the longer bonds. A combination of i.r.and Raman single-crystal techniques is especially power-ful and has been exploited recently in the author's laboratory. Even for crystals having factor groups of low symmetry and coincident i.r. and Raman spectra the intensity differences between the two spectra can be very considerable and helpful in assignment. NiCl,(thiourea) has a strong i.r. band at 172 cm- ' of the correct symmetry to be associated with an Ni-C1 stretch. Although it is formally active in the Raman spectrum it is vanishingly weak; these pieces of evidence suggest a highly ionic bond with low polarizability (and hence low Raman intensity) but high dipole moment change.' ' 1.r. and Raman intensity differences were important also in assigning the spectrum of the square-pyramidal [InC1J2 - anion using single-crystal techniques.Interaction between vibrators can be profitably studied by single-crystal methods. Oxoanions for example are well known for the broad and complex bands associated with M-0 stretching modes when observed in the powder form. These bands are in fact due to overlap of many closely spaced bands of various symmetries as has been shown for several compounds e.g. K2Cr0,.I3 This is true both of i.r. and Raman spectra. Another recent example of an unusual interaction is CsCuC1 . The crystal contains a [Cu,Cl J 6 - helical repeat unit, for which group theory predicts a total of 12 Cu-C1 stretching modes in i.r. and Raman spectra. From single-crystal i.r. and Raman measurements nine of these were observed physically this corresponds to almost complete vibrational interaction within the very long repeat unit of the chain.', Although single-crystal spectroscopy represents a most powerful tool for making assignments it is not always possible to use this approach for a variety of practical reasons (e.g.it may not be possible to grow a crystal). More funda-mentally in many cases there is no unique way of correlating the observed symmetry species (of the crystal) with those of molecules or complex ions which may compose it. Monoclinic crystals (and a high percentage of organometallic compounds crystallize in the monoclinic system) only yield A and B symmetry species in Raman spectra. If the crystal contains molecules or complex ions of higher symmetry (e.g. C3J the relation of their symmetry species to those of the crystal is often not unique as can be seen from the following splitting scheme : Molecule C, Site C Crystal C, (2 molecules per unit cell) Raman-active 1.r.-ac t i ve E ' D.M . Adams and R. R. Smardzewski J . Chem. SOC. (A) 1971 10. D. M. Adams M. A. Hooper and M. H . Lloyd J . Chem. SOC. ( A ) 1971 946. ' * D. M. Adams and R. R. Smardzewski J . Chem. SOC. (A) 1971 714. l 4 D. M. Adams and D. C. Newton J . Chem. SOC. ( A ) 1971 3499 54 D. M . Adams An observed A mode may originate either in a molecular A or an E mode: there is no a priori way of telling which although non-symmetry-based arguments may be used to make a distinction. A similar ambiguity is associated with B,. It would therefore be most valuable to have other means of orienting molecules for spectroscopy.There is one proven possibility-and one kite that I would like Gray and co-workers have obtained oriented arrays of Mn,(CO), and Re,(CO) in nematic liquid crystals.’ Liquid crystals have complex vibrational spectra of their own but they can be used in their clear regions such as that associated with v(C0) modes of metal carbonyl compounds. Gray’s liquid crystals were oriented by rubbing and the resulting i.r. absorption v(C0) spectra, although showing some indication of anisotropy were not very convincing. Nevertheless their work is important in pointing out a means of molecular orientation. Liquid crystals can be more effectively aligned by use of electric fields,16 but so far this approach has not been applied in either i.r. or Raman work, although it is simple to do so.The basic difficulty will be whether the forces restraining the molecules in the host crystal are of sufficient strength to retain a significant degree of anisotropy in the face of thermal motion. My own ‘kite’ is really a development of this approach but designed to eliminate the complicating effect of the host crystal spectrum. It should be possible to combine molecular-beam and matrix-isolation techniques to form matrices containing oriented layers using an electric field at the matrix to ensure align-ment. The problem arises as to whether the deposited molecules would have the desired alignment. Adsorbed layers have structures determined by that of the host surface,” but what happens if molecules approach the cold matrix surface with an orientation not acceptable for preferred accommodation? All will depend upon the relative strengths of the aligning electric field and the forces of mutual interaction at the surface but if the electric field has the right strength and if the rate of deposition is such as to form a dilute matrix without significant clustering then this technique should have a future.Information on Specific Vibrations.-Even granted full information on the sym-metry species of the vibrations of a material we are left short of full understanding of the motions involved. For each symmetry species we would have a list of frequencies of vibrations but this tells us nothing about the nature of the vibra-tions ; from symmetry theory we know which internal co-ordinates contribute to each symmetry class but we are ignorant of the relative contributions of each to any given vibration.We now consider other approaches used to generate information of this sort. to fly. Spin-state Eflects. The strength of metal-ligand bonds is affected by spin state. If a particular transition-metal ion can have both high- and low-spin states and can be induced to switch from one to the other the principal effect is likely to be l 5 G. P. Ceasar R. A. Levenson and H. B. Gray J . Amer. Chem. SOC. 1969,91 772. ” G. A. Somorjai and F. J. Szalkowski J . Chem. Phys. 1971 54 389. R. Williams J . Chem. Phys. 1963 39 384 Inorganic Vibrational Spectroscopy 55 seen in vibrations that are predominantly stretching and bending modes of the metal-ligand bonds.Two examples of this effect have been reported. Konig and Madeja18 have studied the NCE part of the spectra of [Fe(phen),-(NCE),] (E = S or Se) which exist in spin-state equilibria 5T2(t24e2)++1Al(t26), and observed a decrease in the strength of Fe-NCE bonds in the ' A state as compared with 55. In the first spectroscopic study of spin-state equilibria in a d7 system Barnard and co-workers' have shown using several physical methods that bis[tri-(2-pyridy1)amine]Co1' perchlorate exists as a mixture of high- and low-spin iso-mers. Both i.r. and Raman spectra change markedly on cooling the relative band intensities of the two spin isomers being a smooth function of temperature. Owing to the higher ligand-field stabilization-energy of the low-spin state, Co-N bonds for it are expected to be stronger than for the high-spin case and this is borne out by the evidence.Thus a polarized band at 170 cm- ' (low-spin state) in the Raman spectrum increases in intensity with cooling whereas one at 130 cm- ' (high-spin state) weakens and eventually vanishes this is v(Co-N),. Similarly a band sensitive to change of metal at 263 cm- ' in the high-spin state becomes a doublet 301 and 3 12 cm- ' upon cooling it is v(Co-N), . Isotope Shifts. The use of isotopic substitution has always been important in spectroscopy but there have recently been several inorganic applications of particular precision and beauty. Junge and MUSSO in a paper which ranks as a classic,20 report the i.r. spectra of metal acetylacetonato-complexes in which the ligands are labelled with l3C.l80 and ,H in a variety of permutations. Despite the large number of i.r. studies of acetylacetonato-complexes ('supported' by at least two discordant normal-co-ordinate analyses) pre-dating their work Junge and Musso's assignments are the first to be supported by really substantial experimental evidence. The use of metal isotopes to assign metal-ligand modes has been developed by Nakamoto and co-workers in a series of papers. The method is of value owing to the fortunate accident that many such vibrations can be described principally in terms of a restricted set of internal co-ordinates. A study of 58NiX,(PR3), and 104PdX2(PR3) (X = C1 or Br; R = Et or Ph) series together with 62Ni and "Pd analogues showed up bands sensitive to metal-isotope change.,' In particular the following v(M -P) assignments were deduced and are of especial importance in that the greatest uncertainty in the metal ligand-field is still con-nected with metal-pnicnide vibrations v(Ni -P) 260-274 cm- ' (one band) for truns-[NiX,(PEt,),] but two bands in the range 16&190cm-' are found for tetrahedral complexes NiX,(PPh,) .For trans-[PdX,(PR,),] v(Pd -P) is at 232-235 cm-' for R = Et but drops to ca. 190 cm-' for R = Ph. '' '' 2 o H. Junge and H. Musso Spectrochim. Acta 1968 24A 1219. E. Konig and K. Madeja Spectrochim. Acta 1967 23A 45. P. F. B. Barnard A. T. Chamberlain G. C. Kulasingham W. R. McWhinnie and R. J . Dosser Chem. Comm. 1970 520. K . Shobatke and K . Makamoto J. Amer. Chem. SOC. 1970,92,3333 56 D.M. Adams Use of s4Fe and s7Fe "Ni and 62Ni and 64Zn and 68Zn showed up two or three metal-sensitive bands in the i.r. spectra of tris-complexes of these metals with 2,2'-bipyridyl and o-phenanthroline the ranges (in cm- ') 360-375 (Fe), 240-300 (Ni) and 175-240 (Zn) follow the order of M-N bond strength.22 A study of several acetylacetonates turned out to be of especial interest.23 For Pd(acac) bands at 677.8 466.8 297.1 and 265.9 cm - (' 04Pd) were metal-isotope-sensitive indicating quite substantial mixing of several types of internal co-ordinate with the consequent deduction that no one or two vibrations cor-respond to v(Pd -0). Earlier P i n c h a ~ ~ ~ had used "0-substitution in Cr(acac) to locate v(Cr -0) modes Nakamoto's work shows that Pinchas' interpretation of his "0-shift data was erroneous as both v(Cr-0) and ligand internal modes are affected owing to coupling.4 Theoretical Work Interpretation of any spectrum depends upon knowledge of the selection rules applicable. Two developments in this area are particularly worth noting. Non-rigid Molecules.-Increasing attention has been directed towards the study of flexible molecules [e.g. BMe HgMe Fe(Cp),] for which selection-rule predictions depend upon the molecular configuration chosen. Longuet-Higgins laid down a basic approach in 1963.2s Altman26 introduced the concept of an 'isodynamic operation' which has since been misunder~tood~~ and clari-fied.28 A good example of the use of these rules is ferrocene for which the very simple observed solution spectra29 are better fitted by the highly restrictive non-rigid-molecule rules3' than those for an assumed staggered-ring D, configura-tion.Further work to test the theory is desirable. Unit-cell Analysis (UCA).-A method for working out vibrational selection rules for crystals was laid down in 1939 by Bhagavantam and Venkataray~du.~~ Basically the method takes the appropriate primitive cell and treats it as a large molecule having 3N modes of vibration. Although by no means difficult applica-tion does present pitfalls for those not familiar with space groups and not all of the snags are clearly described in the review literature. This has undoubtedly slowed up diffusion of unit cell analysis (not factor group analysis32) into general use in chemical spectroscopy.2 2 J . Takemoto and K. Nakamoto J . Amer. Chem. SOC. 1970 92 3335. " K. Nakamoto C. Udovich and J. Takemoto J . Amer. Chem. SOC. 1970 92 3973. 2 4 S. Pinchas B. L. Silver and I . Laulicht J . Chem. Phys. 1967 46 1506. 2 5 H. C. Longuet-Higgins Mol. Phys. 1963 6 445. 3 6 S. L. Altmann Proc. Roy. SOC. 1967 A298 184. 2 7 J . K. G. Watson Mol. Phys. 1971 21 577. 2 8 S. L. Altmann Mol. Phys. 1971,21 587. 29 D. Hartley and M. J. Ware J . Chem. SOC. ( A ) 1969 138. 3 0 P. R. Bunker Mol. Phys. 1965,9 247. 3 1 S. Bhagavantam and T. Venkatarayudu Proc. Indian Acad. Sci. A 1939,9 224. 3 2 J. E. Bertie and J. W. Bell J . Chem. Phys. 1971,54 160; J . E. Bertie and R. Kopelman, J . Chem. Phys. 1971,55 3613 Inorganic Vibrational Spectroscopy 57 These difficulties have now been entirely removed by publication of a set of Tables33 which lists explicit results of all possible unit cell analyses by breaking down each problem into the contributions from individual sets of symmetry-related (Wyckoff) sites.Given a list of atom sites in a crystal it is necessary only to sum appropriate rows of the Tables in order to have the complete vibrational representation of the unit cell automatically reduced (in the case of non-primitive cells) to that for the primitive cell. In addition related Tables allow treatment in terms of internal co-ordinates and a new and general method for determining the symmetry species of external modes for polymers and sheets is given. Others were working on the same problem (i.e. UCA) simultaneously using an ascent in symmetry-correlation method.34 Although the same end is achieved the pub-lished Tables are simpler to use.Normal-co-ordinate Analysis (NCA).-Wherever spectroscopists meet dis-cussion of NCA readily generates an atmosphere more akin to that of theological debate than scientific enquiry. Beliefs range from profound disbelief to uncritical faith in the technique. In large measure the attendant disrepute has been brought upon the method by practitioners making use of it without regard to the inherent limitations and by claims that NCA ‘supports’ assignments when it does nothing of the sort. The increasing availability of computer programs for NCA has happily focussed attention upon some of the real problems of NCA as compared with such mediaeval minutiae as definition of abstruse redundancy conditions.In short NCA now falls into perspective as one of a general group of refinement problems drawing upon a common basis in numerical analysis. Almost without expection NC analysts have used the Gauss-Newton-Raphson method (GNR), of refinement which has its limitations and quirks. What is remarkable is that it has taken so long for any other refinement method to be used in NCA. In important publications G a n ~ ~ ~ has recently employed the highly-regarded Fletcher-Powell minimization method in NCA; it is too early to see how this approach will compare with the GNR method but there should be interesting developments. It is wrong to disregard NCA entirely used in conjunction with really reliable assignments and with supporting information (of the types discussed above) to monitor the calculation it is a means of quantifying the description of vibrations in terms of internal co-ordinates and a way in to other derived informa-tion such as intensity calculations.We note four recent contributions of some interest . ( a ) After a lapse of some years Heath and Linnett’s orbital valency force field (OVFF)36 is slowly coming back into favour owing to the way in which force constants may be related by our understanding of orbital hybridization and other 3 3 D. M. Adams and D. C . Newton ‘Tables for Factor Group and Point Group Analysis,’ 3 4 W. G . Fateley N. T. McDevitt and F. F. Bentley Appl. Spectroscopy 1970 25 155. 3 5 P. Gans Chem. Phys. Letters 1970,6 561; 7 396; J . Chem.SOC. ( A ) 1971,2017. 3 h Beckman-RIIC Ltd. Croydon 1970. D. C . Heath and J . W. Linnett Trans. Faraday SOC. 1948 44 873 878 884; 1949 45, 264 58 D. M. Adams attractive features. Thus the angular parts of potential-energy functions are expressed in terms of angles between actual positions of ligand atoms and their preferred positions where orbital overlap would be maximal. This avoids intro-duction of redundancies that inevitably occur when interbond angles are used in the potential-energy function ; further it allows a physical interpretation to be placed upon the associated force constants. Claassen and co-workers have performed some excellent refinements with it.37 More recently they have ex-plicitly included the effects of lone pairs in NCA by treating them as ligands of very small mass.This results in the appearance of very high frequencies in the calculation which are then neglected but retains the physically important features upon which the Gillespie-Nyholm molecular-shape approach is based. Typical of their results is a calculation on XeOF .38 (b) Computers make it possible to undertake some really large calculations that were otherwise prohibitively lengthy and complex. An important ‘first’ has been scored by Cyvin Briinvoll and Schafer with a calculation on Cr(n-C6H,), which treated the molecule as a whole :39 all previous calculations on organo-metallics have treated the ligands separately or in interaction with some reduced mass representing the rest of the molecule. One of the classic features associated with n-co-ordination of a cyclic aromatic hydrocarbon to a metal is a large rise in the wavenumbers associated with C-H out-of-plane bending; e.g.the A, 673 cm- mode in benzene rises to 794 cm-in Cr(n-C,H&. What comes out of Cyvin’s calculation so beautifully is that this rise is not due to electronic effects but to kinematic coupling. (c) In NCA it is common to select a set of force constants and then proceed with refinement taking the final fit as representing the best available. As the number of interaction constants that can be included is usually severely restricted by the relatively smaller number of observed frequencies those included are usually chosen as most important on the basis of chemical intuition. A variant of this approach which may appeal to male practitioners not willing to trust their chemical intuition is as follows.4o Starting with a diagonal force field add groups of symmetry-related force constants and proceed with refinement include statistical tests to determine the effect of each new force constant upon the refinement discarding any that are ineffectual.Applying the ‘data-determined force field’ concept to diborane yielded a slightly better refinement than previous ones with the curious feature that a B-H terminal bond stretch-stretch interac-tion constant was ineffectual and was apparently being looked after by other interaction constants. The really gratifying feature of this approach is that when it was applied independently to the data for the molecular dihalides M2X6 (X = C1 Br or I ; A4 = Al Ga or In) an almost identical force field resulted in each case.37 J. Tyson H. H. Claassen and H. Kim,J. Chem. Phys. 1971,54,3142; H . H. Claassen 3 8 P. Tsao C. C. Cobb and H. H. Claassen J . Chem. Phys. 1971,54 5247. 3 9 S. J. Cyvin J . Briinvoll and L. Schafer J . Chem. Phys. 1971,54 1517. 40 D. M. Adams and R. G. Churchill J . Chem. SUC. ( A ) 1970 697. and J. L. Huston ibid. 1971 55 1505 Inorganic Vibrational Spectroscopy 59 ( d ) Now that full assignments for single crystals are becoming more common, a corresponding increase is developing in NCA of complete unit cells. Shimanouchi showed the way in 1961 with calculations on diamond and fl~orite.~' Since then he and his co-workers have made some fascinating calcula-tions of unit-cell vibrations for systems such as M',PtC14 M',[MC1,],42 and M' [Co(NO,),] .43 Very recently a particularly interesting calculation by Swanson and Jones has shown that in Cs,LiCo(CN) the low-frequency CMC deformations of the complex ion are inextricably mixed in with lattice modes.44 This quantifies conclusions reached qualitatively on the basis of i.r.and Raman studies by the same authors and for K,Fe(CN) by 0the1-s.~' The majority of the changes in frequency of the vibrations of [Co(CN),I3- on passing from solution to the dicaesium lithium salt can be reproduced without changes in intramolecular force constants other than a slight rise in k(C-N). 5 Conclusions This brief review is concerned principally with section (iu) work and no attempt has been made to outline some of the very fine work being done that is classified under sections (ii) and (iii) because the development of any field is determined by the availability and knowledge of appropriate techniques. Application of the methods discussed above will lead to improved understanding in depth whilst the slow acquisition from physicists of still subtler aids to assignment can be expected to lead to increased precision. Our field of study is of age and powerful techniques are to hand although admittedly the complexity and cost of the re-quisite hardware are increasing steadily. We may reasonably expect a period of real development in understanding. " 4 2 J . Hiraishi and T. Shimanouchi Spectrochim. Acta 1966 22 1483. 43 I . Nakagawa and T. Shimanouchi Spectrochim. Acta 1966 22 1707. 44 B. I . Swanson and L. H. Jones J . Chem. Phys. 1971,55 4174. 4s D. M. Adams and M. A. Hooper J . C . S. Dalton 1972 160. T. Shimanouchi M. Tsuboi and T. Miyazawa J . Chem. Phys. 1961,35 1597