Conformational studies by vibrational spectroscopy: a review of various methods

VlIUh 0K ELSEVIER

Vibrational Spectroscopy 9 (1995) 3-17

Conformational studies by vibrational spectroscopy: a review of various methods Peter Klaeboe Department of Chemistry, University of Oslo, P.O. Box 1033, N-0315 Oslo, Norway Received 4 June 1994

Abstract

The more important methods employed in conformational studies by infrared and Raman spectroscopy have been discussed. They include experimental methods to identify the observed vibrational bands with one or more conformers: crystallization under low temperature and high pressure conditions, variable temperature spectroscopy in the vapour and liquid states and matrix isolation spectroscopy with the hot nozzle method, including the effects of annealing and of photolysis. Differential scanning calorimetry is included, and certain molecules which have two or more solid phases each with a separate conformer are mentioned. An additional technique is spectral recordings of the compound as a solute in solvents of different polarity. Sometimes the formation of clathrates may favour one conformer. Experimental determinations of enthalpies and barriers using variable temperature studies and the analysis of torsional or puckering potentials are described. Computational methods including normal coordinate calculations, molecular mechanics and ab initio quantum chemical methods are included. The methods have been illustrated with compounds from the literature including substituted ethanes, cyclohexanes, cyclobutanes, neopentanes and related molecules. Keywords: Ab initio calculations; Conformations; High-pressure spectrometry; Infrared spectrometry; Low-temperature; Matrix isolation; Raman spectrometry

1. Introduction

The concept of conformational analysis originated with Sachse [1], who in 1890 suggested that two puckered forms of cyclohexane (flexible and chair) could be stable. Moreover, he recognised that there were two monosubstituted positions in the chair form, to day called equatorial and axial, which could be inter-converted by ring inversion. Very much later the chair form of cyclohexane and the presence of equatorial and axial bonds in cyclohexane was established by Kohlrausch et al. from Raman [2], by Hassel from gaseous electron diffraction [3] and by Beckett et al. from thermodynamic [4] measureElsevier Science B.V.

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ments. In 1950 Barton [5] pointed out the vast chemical consequences of conformations, and Hassel and Barton shared the Nobel Prize in chemistry in 1967 for their contributions to the concept of conformational analysis. A large number of physical methods have been employed for conformational studies including structural (x-ray diffraction, electron diffraction), thermodynamic (calorimetry, equilibration, pressure effects), spectroscopic [nuclear magnetic resonance (NMR), infrared (IR), Raman, ultraviolet, microwave], computational (molecular mechanics, semiempirical, ab initio calculations) and miscellaneous methods (dipole moments, Kerr effect, chirooptical, acoustical,

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P. Klaeboe/ Vibrational Spectroscopy 9 (1995)3-17

polarographic, kinetic methods). However, the majority of conformational investigations have undoubtedly been carded out using NMR and vibrational (IR and Raman) spectroscopy. The vibrational spectra can easily be interpreted and the instruments (particularly infrared spectrometers) are widespread in chemical laboratories. In the present review the various methods with which vibrational (IR and Raman) spectra of molecules with conformational equilibria can be interpreted will be discussed. The great advantage of vibrational spectroscopy compared with other techniques is the fact that the spectra can be investigated in all states of aggregation: as vapours, liquids, solutions, as amorphous and crystalline solids and in inert matrices and at high pressure. As examples various types of acyclic and cyclic molecules will be presented, many of them from the author's laboratory.

2. Why use both infrared and Raman spectroscopy? Although there are many examples of conformational studies carded out with one technique only (usually IR), it is a great advantage to combine the results of both IR and Raman spectroscopy. In molecules for which one or more conformers have a high symmetry this is evident since the different selection rules in IR and Raman can frequently establish the symmet~ of the conformers with certainty. Classic examples are the anti and gauche conformers of 1,2-dichloroethane, in which the anti has C2h and the gauche C 2 symmetry, studied by Mizushima and co-workers and reported in great detail 40 years ago [6]. Another example is 2,2-di(halomethyl)-l,3dihalopropane, in which the two most probable conformers, from six possible ones, have symmetries S 4 and D2d and can be identified from the combination of IR and Raman spectra with polarisation data [7,8]. However, the majority of conformer molecules studied have low or no symmetry in which all the modes are active in both spectra. The complementary aspects of IR and Raman spectroscopy are well known; the skeletal modes are usually intense in Raman, while vibrations involving polar groups frequently give rise to intense IR bands.

Equally important are the spectral regions covered and the different sampling techniques in the two spectra. A Raman spectrometer, either single channel, multichannel, with visible or near-infrared (NIR) laser excitation, covers the whole region of interest between 3500 and ca. 40 cm-1 using the same sample holder of glass. The IR spectra on the other hand require various beam splitters, sources and detectors as well as cells with different window materials. Moreover, because of the high water absorption, the far IR region should preferably be scanned under vacuum conditions. Certain measurements like the recording of vapours or matrix isolation spectra are more easily done in IR due to the higher sensitivity. Measurements of solution spectra in which the solvents are highly polar like water, acetonitrile, nitromethane, etc. can preferably be carried out in Raman since the solution bands are less dominating than in IR. Other experiments such as recording the same sample in various states of aggregation and recording of the low-frequency region are preferably done in Raman. Also, when the enthalpy differences between the conformers are determined by variable temperature recordings, most workers prefer to carry out these experiments in Raman rather than in IR.

3. Experimental determination of conformers In conformational analysis we want to establish how many and which conformers are present in a pure compound and eventually to determine their symmetry and the enthalpy difference between them. These problems can be solved by spectroscopic techniques only if each of the observed bands can be assigned to one or more conformers. The crucial problem is therefore to correlate each band with one or more specific conformers. A number of experimental techniques have been employed for this purpose to identify bands disappearing or changing intensity during the process. 3.1. Crystallisation at low temperature

In almost all studies of conformational equilibria by vibrational spectroscopy it has been customary to compare spectra of the compound in the vapour, liquid, amorphous solid and solution phase on one hand

P. Klaeboe/ Vibrational Spectroscopy 9 (1995) 3-17

with those of the crystalline solid on the other. While the abundance of the conformers in the former states is determined by the AG = A H - TAS function, additional lattice energies are active in the crystal. As a consequence, the crystal usually contains one conformer only which frequently, but not always, is the conformer of lowest energy liquid state. Consequently, as reported for 1,2-dichloroethane [6], a number of bands present in the vapour and liquid states disappear after crystallisation; the vanishing bands are attributed to the gauche, the remaining bands to the anti conformer. As was observed for this molecule, the number of vanishing bands was smaller than the number of remaining bands in the crystal, revealing that a number of anti and gauche bands overlapped in these spectra. The conformer which is present in the crystal can frequently be difficult to identify if the symmetry is low. By measuring the IR dichroism in oriented polycrystalline films employing linearly polarised light, the conformers can sometimes be determined as shown for various chloromethyl and bromomethyl substituted sulphones [9]. In some cases no simplification of the IR and Raman spectra occurs after cooling and solidification; many such cases are reported in the literature. At least four explanations can be listed: (1) the solid is not crystalline, but merely a supercooled glassy or amorphous solid; (2) the solid forms a plastic crystal in which a conformational equilibrium can be maintained; (3) the conformational equilibrium in the vapour or liquid states is highly one sided and vanishing bands of the high energy conformer have very low intensities and cannot be detected in the crystal spectra; (4) the crystal can accommodate molecules of different conformations in stoichiometric ratios 1:1, 1:2, etc. in the unit cell. It is well known that certain liquids are very hard to crystallise, particularly when the freezing point is not known. Therefore case (1) is quite commonly encountered and lack of crystallinity can usually be established if lattice modes are absent in the lowfrequency IR and Raman spectra. For certain molecules crystallisation has never been obtained. However, long and tedious cooling procedures can sometimes lead to crystallisation. It was observed that allylazide [10] crystallised in a Raman capillary after numerous attempts, while no crystallisation was ever

5

achieved in an IR cryostat. Many compounds with nearly spherical symmetry form plastic crystalline phases (2), but on additional cooling anisotropic crystals containing one conformer are usually formed. A one-sided conformational equilibrium (3) can usually be observed by variable temperature observations, particularly in matrix spectra with a hot nozzle (see below). By using x-ray crystallography it has been found [11] that two different conformers are present in a 1:2 ratio in the unit cell, but such cases are very rare. Both a syn and a gauche conformer equatorial to the ring were present in the low-temperature solid in vinylcyclohexane [12], which appeared to be crystalline since a number of lattice modes were present. A 1:1 ratio of the two conformers in the unit cell agrees with the spectra and has tentatively been suggested [12]. Two or more crystals. In certain cases different crystals can be obtained by cooling the liquid, each crystal containing a different conformer. Frequently one of these crystals is metastable, meaning that when a stable crystal is formed it cannot be transformed into a metastable. These phases were often obtained by condensing the vapour on a cold window (or finger) and very careful annealing gave first a metastable crystal while annealing to higher temperatures gave a stable phase. In other cases careful cooling of the liquid below freezing can give different crystalline phases as reported by Kagarise for 1,1,2,2-tetrabromoethane nearly 40 years ago [13]. In the author's laboratory a number of such cases were found, e.g. in six different trans-l,4-dihalocyclohexanes (C1, Br, I) [14,15] a metastable crystal contained the diaxial (aa), a stable crystal the diequatorial (ee) conformer. Other examples were found in 1-cyano-3-butyne, containing the gauche conformer in a metastable and an anti conformer in the stable crystal [16], and in 1,4-dichloro-2-butyne [17], in which a stable phase contained the gauche, a metastable crystal the anti conformer. In cyclohexylallene [18], the two dominant conformers had the allene group in the equatorial (e) position as shown in the upper part of Fig. 1. A gauche conformer of the allene (right) was found in the metastable, an anti conformer (left) in the stable crystal. An additional small amount of an axial (a) conformer probably in anti (at the bottom left in Fig. 1) was detected in the matrices and by NMR spectroscopy in solution [18].

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P. Klaeboe/ Vibrational Spectroscopy 9 (1995)3-17

I

II

Fig. 1. The four possible conformersof cyclohexylallene;(top) low-energye conformers,anti to the left and gauche to the fight;(bottom) high-energya conformerswith anti to the left and gauche to the right. A very rare reversible phase transition between at least three solid phases connected with conformational changes was observed for the pure hydrocarbon dicyclohexyl [19,20], (C6Hll)2, the backbone of a series of nematic and smectic liquid crystals. The high-temperature phase (274-277 K) contained a mixture of ee, anti and gauche conformers as in the liquid state, and this phase was first believed to be plastic [19], later to be a smectic liquid crystal [20]. In one crystalline phase (256.5-274 K) only the anti conformer (Fig. 2, top), below 256.5 K only the gauche conformer (Fig. 2, bottom) was present. IR spectra of the crystals containing either the anti or the gauche conformers are given in Fig. 3. Unlike the other examples mentioned above, these phase changes were all reversible in terms of temperature and pressure changes. In all of the examples referred to in which one specific conformer can be isolated in one crystal and another conformer in a metastable or in another stable crystal, the enthalpy difference A H between the conformers measured in the liquid state was low

ee anti

ee gauche

Fig. 2. The two low-energyconformersof bicyclohexyl;ee, anti at the top; ee, gauche at the bottom.

P. Klaeboe/ Vibrational Spectroscopy 9 (1995) 3-17

(typically below 2 kJ mol-1). In the case of larger A H the specific crystal energies cannot overcome the enthalpy differences and the more stable conformer will be present in all the crystal phases. Obviously, when two different conformers can be isolated in different crystal phases, the vibrational spectra can be interpreted with high certainty, since it can be concluded if a specific vibrational band belongs to the first conformer, to the second or is common to both. In the most common case of one conformer being present in the crystal(s), it can only be concluded that the bands vanishing upon crystallisation belong to one conformer while those present belong either to the other conformer or are common to both.

7

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u

m

m

Im I

m

w

m

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3.2. Differential scanning calorimetry

Fig. 4. Differential scanning (DSC) heating curve for bicyclohexyl, first cooledto 193 K, coolingand heatingrates 1 K min-~; phase 3, gauche, phases 2a and 2b, anti, phase 1, liquid crystalline or plastic, anti and gauche.

An easy technique for determining the freezing point (or more generally points of phase transitions) is differential scanning calorimetry (DSC). For unknown substances it is recommended first to record the DSC traces before carrying out the spectral measurements at different temperatures. Supercooling and hysteresis are commonly found, and the cooling and heating curves obtained from DSC are frequently quite different. They can also be influenced by the cooling or heating rate [20]. Phase transitions be-

tween various solid phases are frequently found, although it is quite rare that different solid phases accommodate different conformers (see above). A DSC heating curve (1 K min-1) for dicyclohexyl is given in Fig. 4, revealing the reversible phase transitions with their different conformers for this molecule [20]. Many molecules with conformational equilibria studied in this laboratory have plastic phases with large internal motions in which two or more conformers are present. Examples are spherical molec-

BICYCLOHEXYL

°i

I!

N

1500

II i

i

1300

1100 FREOUENCY

900 (CM-1)

Fig. 3. The IR spectra of the bicyclohexylcrystals containingthe anti conformer(solid line) recorded at 265 K and gauche conformer (broken line) recordedat 240 K.

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P. Klaeboe / Vibrational Spectroscopy 9 (1995) 3-17

ules like substituted cyclohexanes, cyclobutanes and neopentanes [C(CH3)4]. The change in A H is frequently much lower for the liquid-plastic phase transition than for the plastic phase-anisotropic crystal transition, as is apparent from the DSC curves. Moreover, it is a common experience that in compounds with a plastic phase the transition to an anisotropic crystal is slow and the vanishing of conformer bands upon crystallisation can be very difficult to achieve. It should be noted that only transitions between stable phases are seen in DSC traces. Thus, the metastable phases observed for certain compounds accompanied by changes in the conformations [14,17,18] can generally not be detected by this technique. 3.3. Crystallisation at high pressure As clearly seen from P - T diagrams, common liquids crystallise upon lowering the temperature or upon increasing the pressure. Liquids with freezing points in the range 280-300 K at atmospheric pressure typically crystallise under pressures of 2-60 kbar at room temperature, a region easily accessible in a diamond anvil cell (DAC). High-pressure crystallisation will be of particular importance when low-temperature crystallisation cannot be achieved or when the high-pressure crystal contains a different conformer from the low-temperature crystal. Brasch [21] pioneered such investigations and reported nearly 30 years ago on high-pressure crystallisation of 1,1,2,2tetrachloro- and 1,1,2,2-tetrabromoethane. Both compounds crystallised as gauche upon cooling but as anti under high pressure [21]. A number of high-pressure crystals have been prepared in a DAC in this laboratory and the IR spectra are compared with those obtained at low temperatures. In most cases the same conformer is present in the low-temperature as in the high-pressure crystals and this seems invariably to be the case when the A H value between the conformers is larger than 4 kJ mol-1. However, high pressure will favour the conformer with the smallest molar volume, and this contraction can be a deciding factor, as reported for 1,1,2,2-tetrachloro- and 1,1,2,2-tetrabromoethane [21]. In 1,1,2-trichloroethane the conformer with C 1 symmetry is present in the low-temperature, the Cs conformer in the high-pressure crystal [22].

Most of the compounds having a stable and a metastable low-temperature crystal containing different conformers (see above) were also crystallised under pressure. The high-pressure crystals of both 1,4dichloro-2-butyne [17] and 1-cyano-3-butyne [16] contained the anti conformer, and this conformer was present in the metastable crystal of the former and in the stable crystal of the latter. The six trans-l,4dihalocyclohexanes [14,15], which all have stable crystals at room temperature containing the ee conformer converted to an aa conformer (also present in the metastable crystals) under pressure. The a and the aa conformers of halogenated and dihalogenated cyclohexanes all had smaller molar volumes than the e and ee conformers. In isocyanatocyclohexane, the e conformer was present in the low-temperature, the a conformer in the high-pressure crystal [23]. trans-1Bromo-2-chlorocyclohexane crystallised also as ee at low temperature and as aa at high pressure [24]. High-pressure crystallisation can sometimes be achieved when low-temperature crystallisation is unsuccessful. Thus, in 1,1,2-trichlorotrifluoroethane (Freon 113), a plastic phase containing both conformers was observed at ca. 15 kbar, while at very high pressures (above ca. 100 kbar) a crystal was formed containing only the C 1 conformer [25]. No anisotropic crystals were ever formed for this compound by cooling in spite of many tries. Another example is provided by isocyanocyclohexane, which crystallised in the a conformer under pressure while no low-temperature crystallisation was ever obtained [26,27]. In cyanocyclohexane an "axial crystal" was first formed under pressure and after many trials the same crystal was also obtained after cooling [27]. 3.4. Molar volume determined at high pressure A molecule with two possible conformations will under high pressure preferably be present as the conformer with the smaller molar volume. The DAC was employed for this purpose using methanol as an internal standard. Quantitatively, the following relationship will be valid: AVmola~= - R T d In K / d p , in which AVmol,, is the difference between the partial molar volume of the conformers, K is equal to the (concentr. [conf(1)]/concentr. [conf (2)])and p is the pressure exerted. In 1,1,2-trichloroethane the C s conformer obviously has a smaller volume than C 1 due to the steric crowding of the three CI atoms in the

P. Klaeboe/ VibrationalSpectroscopy9 (1995)3-17

G

700

•

650

600

550

700

A CM-t

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Fig. 5. Raman(left) and IR curves(right)of tetrafluoroneopentane [(C(CH2F)4].(A) In acetonitrile,(B) pure liquid and (C) in carbon tetrachloride.Bands with asterisks are enhancedin polar solvents. former. Values of AVmolar equal to 1.8 + 0.4 and 3.8 + 1 cm 3 mol-1 were obtained in CS 2 solution and in the neat liquid, respectively [28]. It appears that in monosubstituted as well as in trans-l,4-dihalo- and trans-l,2-dihalocyclohexanes the a or aa conformers regularly have smaller volumes than the corresponding e or ee conformers, since the former are more spherical and the latter more ellipsoidal in shape. In CS 2 solution chlorocyclohexane, trans-l,4-dichlorocyclohexane and trans-l,4-dibromocyclohexanes have partial molar volumes AVmolar equal to 1.87 + 0.14, 2 . 8 _ 0.2 and 3.8 + 0.2 cm 3 mol -I, respectively [29]. In fluorocyclohexane the AVmolar value was smaller, ca. 1 cm 3 mol-1 [30]. The differences AVmolar between various dimethylcyclohexanes have been measured by Gardiner et al. [31].

3.5. Solvents of different polarity In some molecules with conformational equilibria there is a large variation in thermodynamic functions A H and AG between the conformers when measured in the vapour and in the liquid states. An extreme example is provided by 1,2-dicyanoethane which contains ca. 70% of the anti conformer in the vapour at 443 K as studied by electron diffraction technique [32], whereas the gauche conformer is much more abundant than the anti in the liquid and is present in the crystal [33]. This effect is due to the stabilisation of the highly polar gauche molecule in the condensed states, whereas the anti conformer with a symmetry center has no dipole moment. Even larger displacements of the conformational equilibrium are observed when the molecules are dissolved in a series of solvents with increasing polarities, e.g. from the non-polar carbon tetrachloride over the neat liquid itself to the highly polar acetoni-

9

trile, nitromethane or dimethylsulphoxide. Such studies were pioneered by Mizushima and co-workers [6] on 1,2-dichloroethane and 1,2-dibromoethane and correlated with the Onsager dielectric theory [34]. Many studies of solvent effects on conformational equilibria have been reported and the older data have been reviewed [35]. Whenever two (or more) conformers have very different dipole moments the spectral measurements in solvents of different polarities are very useful. The results can be used to attribute the vibrational bands to the appropriate conformer according to the intensity variations observed. Since the highly polar solvents all have very intense IR spectra, it is our experience that such solution studies are more easily carried out in Raman. The Raman and IR spectra of tetrafluoroneopentane [8] dissolved in acetonitrile and carbon tetrachloride are shown in Fig. 5. The bands with asterisks are enhanced in polar solvents and belong to a polar conformer C1" or C 1 (see Fig. 6). Quantitative thermodynamic results can also be extracted from spectral measurements in different solvents. From IR measurements in various solvents the thermodynamic functions AG °, A H ° and AS ° between the ee and aa conformers of trans-l,2-dichlorocyclohexane and trans-l-bromo-2-chlorocyclohexane were determined [36]. Corresponding results for various other systems have recently been reviewed [37].

3.6. Forming of clathrates which favour one conformer It was reported by Nishikawa [38] from mid-IR and verified by far-IR [39] and by Raman [40] spectroscopy that certain halogenated cyclohexanes existed predominantly in the axial conformer in thiourea clathrates. Apparently the axially substituted cyclo-

Fig. 6. The six possibleconformersof tetrafiuoroneopentane.

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P. Klaeboe/ VibrationalSpectroscopy 9 (1995)3-17

hexanes are more effectively accommodated in the channels than those with equatorial substituents. An IR study of various monohalo- (including also CN and NCO), trans-l,2-dihalo- and trans-l,4-dihalocyclohexanes has been carded out. It was observed in the 1000-800 and 500-300 cm -1 regions that in trans- l,4-dichloro- and trans- l,2-dichlorocyclohexanes the equilibria were nearly completely displaced towards the aa conformers, while a partial displacement was observed for the monohalocyclohexanes [41]. In ethynyl cyclohexane (C6H11CCH) the equilibrium was also displaced towards the a conformer but the clathrate was decomposed at ambient temperature [42]. No clathrate was obtained for trans-l,4-dicyanocyclohexane [43]. In favourable cases the clathrates can be used to assign conformer bands and to decide which conformer is e- and a-substituted. This was the case in cyano- and isocyanocyclohexane [27], which are rare examples of monosubstituted cyclohexanes in which the a conformers have lower energy in the liquids and are preferred both in the crystals and in thiourea clathrates. The cross-sectional dimension of adducts in thiourea is 5.8-6.8 ,~ [44], which is very suitable for the cyclohexane dimension. Attempts to form thiourea clathrates with halogenated cyclobutanes were unsuccessful except for the bulky 1,1,2-trichloro-2,3,3-trifhorocyclobutane, apparently forming an unstable clathrate in which the conformer with an axial fluorine and equatorial chlorine (opposite from the conformer in the crystal) was slightly preferred [45]. Urea clathrates have smaller dimensions of the channels and various linear hydrocarbon chains (C10-C12)will be accommodated in a preferred zigzag (all anti) conformer as observed in the Raman spectra by Fawcett and Long [46].

4. Experimental determinations of enthalpies ( ~ H °) and barriers 4.1. Vapours, liquids or solutions studied at various temperatures

Spectral recordings of vapours, liquids or solutions at different temperatures have been a standard method for conformational studies for two reasons: if there is an enthalpy difference between the conform-

ers, intensity variations with temperature will be observed between the low- and the high-energy conformer bands. Thus, a qualitative evaluation of intensity variations is an added criterion for selecting which vibrational bands belong to which conformer. However, quantitative recordings of the intensity variations with temperature give data leading to a determination of the enthalpy difference between the conformers from the simple van 't Hoff equation: A H = - R T In (11/12) + constant, in which 11 and 12 are the absorbances (in IR) or intensities (in Raman) of bands belonging to conformer 1 and 2, respectively. It should be noted that since the extinction coefficients of the proper bands are not known, the functions AG, AS and K cannot directly be determined by this method. However, if the difference in entropy between the conformers can be neglected (apart from the statistical weight difference e.g. between anti and gauche conformers) the Gibbs energy AG will be equal to A H and the relative abundance can be determined. Numerous determinations of A H have been made based upon IR and/or Raman spectra, and these measurements are most easily carded out in the liquid state. In spite of modem Fourier transform (FF) spectrometers in IR and Raman near-infrared FF instruments as well as multichannel Raman spectrometers with charge coupled devices, most workers still prefer conventional monochannel Raman spectrometers for these measurements. These spectrometers use excitation in the visible region (generally argon ion lasers) and cooled photomultipliers as detectors, with very good linear response. The sampling of liquids or solutions is much easier in Raman than in IR since a glass capillary surrounded by a transparent Dewar cooled by a stream of cold nitrogen gas works very efficiently in Raman [47]. Much more sophisticated cryostats are required for variable temperature studies in IR, requiring double sets of IR transparent windows under vacuum and they have a large potential leaking problem. Variable temperature studies of vapours are probably more easily carded out in IR and particularly above room temperature a standard 10-cm vapour cell surrounded by a thermostatted box of hot air can be employed. Corresponding Raman studies usually require vapour cells with Brewster windows illuminated in a multiple reflection unit to increase the excitation energy, and this system can-

P. Klaeboe / Vibrational Spectroscopy 9 (1995) 3-17

not easily be studied except at ambient temperature. However, Mohamad et al. [48] in their very comprehensive conformational studies have frequently reported A H values in the vapour phase obtained by Raman spectroscopy. It is a prerequisite for determining the enthalpy difference from this method that the bands of conformers 1 and 2 both have reasonably high intensities, are situated on a flat background and do not overlap other bands in the spectra. Particularly important is the requirement that the bands employed in the van 't Hoff plots must be "pure", meaning that their intensities must be due to one conformer only, with no contribution from the other conformer(s). With the large number of combination bands or overtones possible, some of which might be enhanced by Fermi resonance, it is very difficult to decide if the bands are pure. If a band completely vanishes in the crystal it is probably a pure band of the high-energy conformer. The bands remaining in the crystal, however, can easily be overlap bands of both conformers. Only in the rare cases when the spectra of each conformer can be isolated in different crystals (discussed above) can the IR and Raman bands be assigned to the conformers with high certainty. It is highly recommended that more than one pair of bands should be employed and independent calculations of A H should be made for each band pair. Frequently, considerable discrepancies occur between A H values obtained from different band pairs, indicating that each band of the pair is not pure. Raman or IR spectra recorded digitally can be manipulated by various techniques, using curve resolution, flattening of the background and calculation of the band areas between defined limits. No such spectral improvements can make up for poorly defined bands. It has been argued [49] that at least for symmetric molecules, the Raman trace scattering cross sections from the vapour phase offer advantages compared with ordinary Raman vapour spectra for calculating A H differences between conformers. The Raman trace spectrum consists of only Q-branch transitions of totally symmetric vibrations and can be separated from the anisotropic scattering. Since only the totally symmetric vibrations are present, Raman bands of the trace spectrum have less chance of overlap with bands from other conformers. A temperature study of these bands might therefore give more reliable AH values.

11

In n-butane this method [50] gives a A H value of 2.9 + 0.4 kJ mol-1. Ordinary Raman data of the vapour obtained in a very thorough investigation [51] give 4.55 + 0.5 from one band pair, 4.71 + 0.66 for another pair and 4.41 + 0.8 kJ mo1-1 from a band pair of n-butane-d10. The lower value of 2.9 kJ mo1-1 agrees well with those obtained by electron diffraction [52], IR matrix studies [53], NMR investigations [54] and high resolution (diode laser) temperature studies [55]. This example reveals the inherent difficulties in finding vibrational bands which are not contaminated by the other conformer. It should be mentioned that infrared or Raman band contours in the vapour phase depend upon the moments of inertia and are therefore different for the conformers. In 1,5-hexadiyne (bipropargyl) a thorough vapour phase analysis was important for the assignments of bands to the anti and gauche conformers [56].

4.2. Matrix isolation spectroscopy, hot nozzle,

photolysis The matrix isolation technique is used for trapping and producing chemical species and preserving them in a rigid host (often the inert gases Ar, Kr, Xe or N 2 at high dilution, e.g. in a 1:1000 ratio) at low temperatures, typically at 4-15 K. This technique can be applied to various spectroscopic techniques; it is particularly well suited for IR spectroscopy but can also be used in Raman. With the introduction of closed-cycle cryostats capable of reaching ca. 10 K with two stage systems or ca. 4.5 K with an additional Joule-Thomson stage, matrix isolation spectroscopy (MIS) is convenient and economical since no liquid helium is required. The method is within the reach of most laboratories and MIS, which was introduced in 1954 [57], has become a very common technique for studying unstable species. Matrix isolation spectroscopy in IR has been employed in numerous studies of conformational equilibria starting with the hot nozzle technique around 20 years ago [58]. A rapid cooling of the sample mixed with inert matrix gases to 4-15 K prevents equilibration of the conformational mixture if the barrier is higher than 3-6 kJ mol-1. Thus, a non-equilibrium condition regarding conformational equilibria, not generally obtained by other techniques, can frequently be seen in the matrix spectra. The enthalpy

P. Klaeboe / Vibrational Spectroscopy 9 (1995) 3-17

12

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<

0 9C

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J /i

B

C i

1200

1100

1000

6/.,0

600

560

WAVENUMBER (CM -t)

Fig. 7. The MIS spectra of tetrafluoroneopentane in nitrogen at 14 K. (A) unannealed, 700 K nozzle temperature; (B) unannealed, 450 K nozzle temperature; (C) annealed at 34 K for 1.5 h, nozzle temperature 700 K.

difference can be measured from spectra recorded in a large temperature interval (e.g. 300-900 K). Moreover, by selective annealing of the matrices to defined temperatures, thermodynamic equilibrium can frequently be achieved and the barriers of conformational transitions can be calculated. The matrix technique is particularly useful in studies of conformational equilibria involving not only two but three and more conformers separated by different A H values as discussed for 2,2-di(fluoromethyl)-l,3-difluoropropane (tetrafluoroneopentane) [8]. The six possible conformers are given in Fig. 6 and MIS spectra in nitrogen, showing the effect of variation of nozzle temperature and annealing, appear in Fig. 7. Another example is discussed for allylazide [10]. The conformers in these compounds are also separated by barriers of different heights. Some examples of matrix isolation spectroscopy applied to conformational problems have been discussed in two reviews [59,60]. It is a prerequisite for MIS studies of conformations that the thermodynamic equilibrium in the vapour phase is maintained on the cold window after quenching. A very recent investigation on methyl nitrite reveals a very good agreement between the enthalpy difference A H ° observed in the vapour phase with that observed in argon matrices being equal to 3.5 + 0.2 kJ mo1-1 [61]. When the barriers are below 4-5 kJ mo1-1, however, the A H ° values obtained from the matrix spectra can be much too low as demonstrated for some haloacetyl halides [62]. In

other instances the conformers may have a specific interaction with the matrix materials as recently demonstrated for 1,1,2-trichloro-2,3,3-trifluorocyclobutane [45]. Here the equilibrium was displaced towards one conformer in argon and towards the other conformer in nitrogen in unannealed matrices when deposited at 13 K. After annealing to 25-30 K the opposite equilibria in the two matrices were even more pronounced. When the argon matrix was "contaminated" by ca. 3% nitrogen, the effect on the conformational equilibrium on this halogenated cyclobutane was quite large, demonstrating the important role of nitrogen in this case [45]. When the enthalpy difference between the conformers is quite low, the barrier height cannot be determined assuming a simple first order reaction A ---*B and then applying the Arrhenius equation. Instead the reverse reaction must also be taken into account and the kinetics must satisfy two differential equations for the left to right and the right to left reactions. Employing these procedures the barrier from anti to gauche of azidoethane [63] was determined to be 9 kJ mo1-1 in the nitrogen matrix while in 1,1,2-trichloro-2,3,3-trifluorocyclobutane [45] the two barriers were determined to be 8.7-9.0 and 8.8-9.3 kJ mo1-1 in the nitrogen matrix, with A H ° being equal to - 0 . 3 kJ mo1-1. Conformational changes leading to an increased population of one or more high-energy conformers can frequently be obtained by photolysis of the matrices, using radiation ranging from UV to IR as first

P. K laeboe / Vibrational Spectroscopy 9 (1995) 3-17

more accurate spectroscopic, photochemical and thermodynamic data.

1.0 J 11 tn i--

A.,,

laJ o z

J;2.

<

ID IZ

,c (

I

2175

13

2160 21~5 W^VENUMBER/CM "1

Fig. 8. The MIS spectra of isopropylthiocyanate (CH3)2SCN in argon, deposited at 13 K; solid curve, annealed to 20 K, anti and gauche; dotted curve annealed to 35 K, predominantly anti conformer.

demonstrated by Hall and Pimentel [64]. There are examples of the radiation causing transitions from the low-energy to higher-energy conformers as well as in the opposite direction. If filtered radiation or tunable lasers are used for irradiation one can decide which normal modes in the molecule are photo sensitive. Very recent examples of these techniques have been reported for oxalic acid [65] and for fluoro- and chloroacetic acids [66] and combined with very extensive ab initio calculations (see below). Other examples of the effects of IR radiation on the conformational composition in matrices are given by R~isiinen and Murto [67]. The sharp peaks of the matrix spectra make it possible to observe more bands belonging to different conformers than can be studied in the vapour or liquid phases where many bands overlap. IR spectra of isopropylthiocyanate in the ~ N stretching region in an argon matrix are given in Fig. 8, showing the spectrum after annealing to 20 K (both conformers) and to 35 K (only anti conformer) [68]. Changing the temperature of the sample matrix gas prior to condensation makes it possible to isolate different conformational mixtures. This can for example be achieved with a heated nozzle or a Knudsen cell. Typically, infrared matrix isolation spectroscopy is often applied to conformational problems already studied by using other techniques in order to obtain

4.3. Analysis of asymmetric torsional or puckering potential The conformers are typically separated by torsional barriers due to restricted rotation around C-C, C-O, N-C, P-O and other single bonds. In other cases inversion of ring systems causes conformational equilibria, particularly well studied are small rings such as in cyclohexanes, cyclopentanes and cyclobutanes. Common to these systems is the fact that they give rise to large amplitude inharmonic vibrations, usually of low wave numbers. These lowfrequency vibrations are of course not restricted to molecules having different conformers, but are present in methyl torsions, bending of linear molecules, puckering of ring systems, etc. They can be studied by various techniques such as microwave spectroscopy, NMR spectroscopy, electron diffraction, calorimetry and neutron scattering. However, IR and Raman spectroscopy give direct information about the transitions and are the preferred methods. The molecules should be present in the vapour phase where liquid or solid state interactions are absent, although broad bands connected with these modes can be observed in the liquid, in solution, in the plastic phase and in amorphous solids. Since these vibrations are the lowest in frequency within a molecule they have a large number of populated excited states and give rise to a series of transitions and hot bands. Also, they give the largest contribution to the thermodynamic functions. Although overtones and combination bands are generally weak in Raman, series of overtones of these fundamentals with sharp Q-branches have been observed in many cases. Frequently the low-frequency transitions for two conformers have been observed. From these data the barriers for both conformers, the conformational enthalpy difference and the dihedral angle between the conformers can be obtained and compared with the results from variable temperature spectra. The far IR spectra (typically below 150 cm-1) are weak and the region has a number of very intense rotational water bands while the Raman vapour spectra require high powered lasers. The experimental work is therefore quite difficult. However, very important information can be extracted about conformer stability and bar-

14

P. Klaeboe/ VibrationalSpectroscopy9 (1995)3-17

rier heights making these investigations very rewarding. The older IR and Raman investigations of these low-frequency vibrations have been reviewed [69]. A large part of these studies have been carded out by Dudg and his group and reviewed [70,71]. They have for a long time described the anharmonic vibrations of a vast number of molecules with conformational equilibria, of which a few newer examples will be mentioned. In 1,2-difluoroethane, which has been studied by numerous workers, the asymmetric torsional frequencies of the stable gauche and the less stable anti conformers were recorded of a vapour in the far-IR region and in Raman and observed at 147.0 and 116.7 cm -1, respectively [72]. The potential function corresponds to an enthalpy difference of 3.35 kJ mol-1, a gauche dihedral angle of 71.0 ° and anti-gauche, gauche-gauche and gauche-anti barriers of 8.9, 23.9 and 12.2 kJ mol-1, respectively, and compared to the results of ab initio calculations. Another recent example is provided by 2-methylpropionyl fluoride [(CH3)2CHCFO]. The more stable gauche and less stable anti conformers in this compound was separated by barriers of 2.6 (anti-gauche), 5.3 (gauchegauche) and 7.5 kJ mo1-1 (gauche-anti) derived from far-IR and microwave spectra [73]. In 2-bromo3-fluoropropene the more stable syn conformer had a torsional transition at 112.6 cm -1 with four excited states falling to lower wave numbers and a gauche torsion at 93.0 cm -1. These values gave barriers of 12.0, 12.3 and 9.5 kJ tool -1 for the syn-gauche, gauche-gauche and gauche-syn barriers, respectively [74].

5. Computational determinations of conformers With the development of digital computers during the last 30 years it has become increasingly common for spectroscopists to combine their experimental resuits with various types of calculations. They include normal coordinate calculations for determining the frequencies of the fundamental vibrations, molecular mechanics calculations, semiempirical calculations and ab initio quantum mechanical computations. The last three methods have been used to determine the structure (distances and angles) of the molecules, the relative energies of conformers and eventually the

frequencies and intensities of the fundamental modes in IR and in Raman. Such computations are valuable in many spectroscopic studies, but are particularly important when a mixture of conformations is being investigated. When the spectra of two or more conformations are superimposed in the vapour and liquid states, these calculations are often essential for dependable assignments.

5.1. Normal coordinate calculations Based upon the Wilson G and F matrix methods [75], normal coordinate calculations have been carried out for many thousands of molecules in the last 40 years. In these calculations the various G and F matrix elements are used as input and should therefore be known. The G matrix elements depend upon the geometry of the molecule and can be determined when the bond distances and angles are known (or they can be guessed). The force constants which are the elements of the F matrix depend upon the bond strengths and their values are often very uncertain. The diagonal elements can frequently be assumed or transferred from similar molecules but the off-diagonal elements (the interaction terms) are very uncertain and are often put equal to zero. If many related compounds are being investigated the force constants can be transferred between the molecules as demonstrated for hydrocarbons by Snyder and Schachtschneider [76]. In the series of six different trans-l,4-dihalocyclohexanes mentioned above, the ee and aa conformer spectra of each compound were determined with considerable accuracy since the pure ee and aa conformers were isolated in the stable and metastable crystal phases [14,15]. In each compound the two conformers had both C2h symmetry in the case of equivalent halogen substituents or they had C s symmetry in the molecules with two different halogens. In all together 12 separate conformer spectra the wave numbers of ca. 600 bands were determined; with a modified overlay program [77] all 12 conformers were treated simultaneously and 49 independent force constants were determined by a least-squares program. A good fit between the observed and calculated wave numbers of most bands was obtained, and a quite reliable assi~ment could also be made for overlapping and uncertain bands in this series. Moreover, a simple relationship Kr 2 = constant [15,77], in

P. Klaeboe/Vibrational Spectroscopy 9 (1995) 3-17

which K and r are the C-Hal stretching force constant and distance, respectively, was employed for the series, reducing the number of force constants considerably. Later, the force field derived for the substituted cyclohexanes [15] was transferred to cyanoand isocyanocyclohexane [27], to bicyclohexyl [19,20] and to ethynylcyclohexane [42]. In all these molecules essentially the same force constants were used for both the e and the a conformers of cyclohexane. Numerous force constant calculations with different degree of sophistication have been carded out on conformer molecules, and often the calculated frequencies give the final clue to determine the structure and symmetry of the various conformers. However, until recently the limiting factor in such calculations was always the number of unknown force constants which made the calculations on single systems uncertain. With the development of very large, rapid (and comparatively cheap) computers in the last 5-10 years the situation has completely changed. The ab initio quantum chemical calculations can now give quite reliable force constants for molecules of moderate size (see below). 5.2. Molecular mechanics calculations

Molecular mechanics (MM) simulations use the classical laws of physics to predict the structure and properties of molecules. There are many different methods within molecular mechanics and each one is characterised by its own particular force field. Unlike the quantum chemical methods, molecular mechanics do not treat the electrons in a molecular system, but the computations are based upon interactions among the nuclei. The MM calculations are cheap in computer time and allow very large systems containing many thousands of atoms (e.g. biological systems) to be treated. Particular MM force fields achieve good results for a limited class of compounds, but they cannot be generally used for every molecular system. Many chemical properties depend upon molecular orbital interactions and cannot be predicted from MM calculations. MM calculations can be applied to molecules with conformations and the number of stable conformers, the structures of each conformer, their relative energies (and in certain programs the vibrational spectra

15

of each conformer) can be calculated. A number of MM programs are available (HyperChem, Quanta, Sybyl and Alchemy), the most comprehensive ones being undoubtedly the MM1, MM2 and MM3 developed by Allinger et al. [78]. The MM3 with many examples for conformations is described in three comprehensive articles. The conformational energies for a number of halogenated alkanes derived from gaseous electron diffraction and spectroscopic data have successfully been computed by St¢levik and his results have recently been reviewed [79]. For this limited series of molecules the calculated energies agree well with the experimental values. 5.3. A b initio quantum chemical calculations

Thirty years ago quantum chemical calculation was an esoteric activity for a few specialists. The rapid development in performance and price of computers has revolutionised the field and made such calculations within reach of most experimentalists. A large development in computer programs has been a contributing factor: first semiempirical programs (CNDO, INDO and MINDO) then ab initio programs (HONDO, IBMOL, POLYATOM and GAUSSIAN). Particularly, the Gaussian programs [80] (from version 70 to the newest 92) are available in many laboratories, and experimental spectroscopic work is strongly supported by such calculations. The calculations can be carried out with increasing sophistication depending upon the number of electrons in the molecule and the accuracy required [81]. The minimal basis sets are STO-3G in the Hartree Fock (HF) limit without polarisation and electron correlation, requiring the shortest time. Approximately a thousand times longer computing time depending upon the molecule may be required when using the very large Gaussian basis set MP2/6311G** (including electron correlation with the M¢ller-Plesset 2nd order perturbation) [80]. This very large basis set has been used for the calculation of conformational energies in small molecules like oxalic acid [65], fluoroacetic and chloroacetic acid [66] with supercomputers. For conformational studies of larger molecules smaller basis sets like 3-21G, 631G and 6-31G * have been employed in many laboratories. The ab initio results using these basis sets can greatly support the experimental work. Among the most useful parameters are the relative conforma-

16

P. Klaeboe / Vibrational Spectroscopy 9 (1995) 3-17

tional energies, the height of the barriers to internal rotation or ring conversions and a complete set of force constants. It is the experience of the author that the relative energies and barriers calculated with the 6-31G * or similar basis sets have considerable uncertainties (of the order of + 2 kJ mol- 1 ). We can therefore not decide from these data which conformer is the more stable if the enthalpy difference is low. At the HF limit the force constants are always too high; they can be scaled with factors typically 0.7-0.95 and transformed to internal coordinates. These force constants are used in the normal coordinate analyses (see above). A remarkably good agreement between the experimental and calculated wave numbers (particularly in the low-frequency region) was found for a number of systems: 2,2-di(fluoromethyl)-l,3-difluoropropane [8] and for the halogenated cyclobutanes 1-chloro- 1-fluorocyclobutane, 1-chloro- 1,2,2,-trifluorocyclobutane [81] and 1,1,2-trichloro-2,3,3-trifluorocyclobutane [45]. The normal coordinate calculations showed that the bands belonging to the more stable conformer should be F(equatorial), Cl(axial). This conclusion was quite uncertain from the calculated conformer energies using the 6-31G * basis set [82]. Many calculations with the Ganssian basis sets 631G* or 6-31G * * have been made on conformational equilibria the last years, among others by Durig and co-workers [71-73], leading to more reliable calculated frequencies for each conformer. It is probable that with the larger basis sets going beyond the Hartree Fock limit and including polarisation and electron correlation, e.g. MP2/6-31G * * or M P 2 / 6 311G * * [64,65], the conformational energies and the barriers will be determined with quite good accuracy compared with the experiments. It is significant that the scaling factors used to fit the ab initio force constants are now closer to 1 (0.956 and 0.957 for fluoroacetic and chloroacetic acid, respectively), indicating a more realistic model of the electronic energies.

Acknowledgements The author wants to thank his colleagues, coworkers and students who were engaged in the ex-

perimental work referred to in this paper. He is grateful to Professor David L. Powell, Wooster College, USA for reading and correcting the manuscript.

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