The vibrational spectra

The vibrational spectra (100-1500 cm-') of a seriesof bicyclo[3.2.l]octanes assigned by means of scaled 3-21G ab initio harmonic force fields' THOMAS EGGIMANN, NANIBRAHIM, R. ANTHONY SHAW,A N D HALW~ESER' Department of Chetnistry, University of Calgary, Calgary, Alm., Cnnnrlo T2N IN4

Can. J. Chem. Downloaded from www.nrcresearchpress.com by KYONGGI UNIV LIB on 05/28/13 For personal use only.

Received July 3 1, 1992

THOMAS EGGIMANN, NAN IBRAHIM,R. ANTHONY SHAW, and HALWIESEK. Can. J. Chem. 71, 578 (1993). The infrared absorption (vapor phase and solution) and Raman (liquid phase) spectra of bicyclo[3.2. Iloctane, 8-oxabicyclo[3.2. lloctane, 6-oxabicyclo[3.2. lloctane, 6,8-dioxabicyclo[3.2. Iloctane, and the 7,7-dideutero-substituted derivatives of the last two compounds are reported in the region 100-1500 cm-' for the first time. The vibrational spectra are assigned almost conipletely with the guidance of ab initio 3-21G geometries and scaled force fields. A total of 14 force-field scale facors are transferred from smaller molecules, predicting the frequencies with an average error of 7.6 cm-' (1.2%) for 196 assigned transitions. After optimizing the factors in an overlay refinement involving all six molecules, the frequencies are within 5.7 cm-' (0.75%) of experiment. The nb irlitio absorption and Raman intensities are calculated with the 3-21G basis set and are demonstrated to be of such accuracy as to be useful for the spectral assignments. These intensities are calculated with uniformly and nonuniformly scaled force fields and compared to the experimental spectra. The intensities derived from the latter force fields are superior, meaning that nonuniform scaling is preferable at this level of theory for both vibrational frequencies and normal mode descriptions. THOMAS EGGIMANN, NAN IBRAHIM, R. ANTHONY SHAW et HALWIESER. Can. J. Chem. 71, 578 (1993). On a determine pour la premiere fois les spectres d'absorption (100-1500 c ~ n - ' )infrarouge (phase vapeur et solution) et Raman (phase liquide) des bicyclo[3.2. lloctane, 8-oxabicyclo[3.2. Iloctane, 6-oxabicyclo[3.2. Iloctane, 6,8-dioxabicyclo[3.2. lloctane et des dCrivCs 7,7-dideutCrCs des deux derniers composCs. On a attribuC les bandes des spectres de vibration en faisant appel presqu'uniquement aux geoniCtries nb irlitio 3-21G et aux champs de force. Utilisant des molCcules plus petites, on a transfer6 un total de 14 facteurs d'Cchelle de champs de force et on a ainsi pu prCdire les frCquences avec une erreur moyenne de 7,6 cm-I (1,2%) pour les 196 transitions attribuCes. Aprks avoir optimisC les facteurs A l'aide d'un affinement impliquant les six molCcules, les frkquences calculCes sont A 5,7 cm-I (0,7596) des valeurs expCrimentales. On a calculC l'absorption et les intensitts Raman nb itlitio A l'aide de l'ensemble 3-21G et on a dCmontrC que les valeurs calculCes sont d'une telle exactitude qu'elles peuvent &tre utiles pour attribuer des spectres. On a calcul6 ces intensitCs A I'aide de chali~psde force i echelles uniformes et non uniformes et on les a comparCes a celles des spectres expCrimentaux. Les intensitCs obtenues A l'aide des derniers champs de force sont supkrieurs, c'estA-dire que, pour les frCquences vibrationnelles ainsi que pour les descriptions des modes normaux, les Cchelles non uniformes sont prCfCrables i ce niveau de la thCorie. [Traduit par la rCdaction]

Introduction In recent years the assignment of the vibrational spectra of small molecules by means of (16 irzitio calculated geometries and harmonic force fields has become almost a routine procedure. The ub initio calculations can be performed at various levels of theory with a choice of many different basis sets. The accuracy of the results is largely limited by the size of the molecule and the available computing power. In attempting to reproduce experimental frequencies as accurately as possible, more or less severe corrections are applied to the a6 initio geometries and force fields, depending on the level of approximation. We are interested in the vibrational dynamics of monocyclic and bicyclic molecules with low symmetry and seek conceptually simple ways to interpret the experimental infrared absorption, Raman, and vibrational circular dichroism (VCD) spectra (1-6). Our approach is to calculate harmonic a6 initio force fields (3-21G, or higher if possible) from the uncorrected geometries optimized with the same basis set. The force constants are transformed to appropriate local symmetry coordinates, then scaled with a small set of factors for particular types of modes. These procedures are basically equivalent to the standard scaled quantum me'Based in part on the Ph.D. thesis of T . Eggimann, The University of Calgary, 1991. ' ~ u t h o rto whom correspondence may be addressed.

chanical (SQM) force field, originally developed and recommended by Pulay et al. (7), with the difference that we prefer not to correct the a6 initio geometries. Such scale factors, in our experience, when judiciously selected and transferred from similar moieties, lead to frequency predictions with errors well below 2% on average. Even quite complex spectra can then be assigned with high confidence. Simultaneously, the scale factors can be refined in a leastsquares fit of the frequencies in overlay refinements involving series of molecules. Finely tuned factors are thus obtained that are again suitable for transfer to the corresponding local symmetry modes of other classes of molecules with similar structural elements. Such refinements of scale factors are significant, as a dependence on the chemical or structural environment has been noted for the factors of certain modes. For the C-0 stretching mode, for example, values of 0.903 (dimethyl ether) ( I ) , 0.851 (2methyloxetane) (2u), and 0.845 (7-oxanorbomane) (5) were found, indicating unequal overestimations of the a6 initio C-0 stretching force constants for different molecules, possibly depending on the C-0-C bond angle. It is essential therefore to explore scale factors for local symmetry modes in a variety of different environments, thereby rendering them more suitable for a transfer to new structures. A good fit of the frequencies by nonuniform scaling and refining does not guarantee that the normal mode descriptions are correctly calculated. Moreover, the solutions of the refinements need not be unique. It is therefore even more

EGGIMANN ET AL.


important to start out with a set of scale factors that are already close to the optimized values and to perform the refining procedure very carefully. T o judge the quality of scaling it is essential to investigate both the frequencies and the normal m o d e descriptions of the vibrations. T h e latter cannot be observed directly, but their accuracy appears with great sensitivity in the calculated intensities of the absorption, Raman, and even more in the V C D spectra. W e demonstrate in this work that nonuniform scaling of force fields does not deteriorate the ab initio eigenvectors if enough care is taken in the process of transferring and refining the factors. It is also shown that in spite of using the primitive 3-21G basis set, the ab initio absorption and Raman intensities reflect the experimental spectra sufficiently accurately that, at the very least, the intensities can assist in the assignments. This aspect is of particular importance for this series of molecules, t w o of which have C, symmetry and the remaining four are asymmetric, as the most useful and unambiguous experimental data, namely vapor phase band shapes and Raman polarization ratios, are helpful only for very f e w bands. T h e properties that are available to guide the spectral assignments other than the frequencies are then the calculated absorption and R a m a n intensities. In addition, the method of scaling a n d simultaneously optimizing several force fields with the s a m e set of factors is indispensable for this series of sufficiently similar molecules, since the wealth of combined experimental data that can b e fitted with just a few parameters helps to resolve a number of ambiguities that otherwise would b e intractable. W e report below the vibrational spectra from 100 to 1500 c m - ' a n d corresponding assignments based o n ab itzitio 3-21G harmonic force fields for bicyclo[3.2. lloctane (BCO), and the 8-oxa (SOXA), 6-oxa ( 6 0 X A ) , 7,7-d,-6-oxa (60XA-d,), 6,s-dioxa ( D I O X A ) , and 7,7-d2-6,s-dioxa (DIOXA-d2) analogues (Figs. 1, 2). T h e investigation of the V C D spectrum of D I O X A described earlier (6) w a s based on these assignments. O f interest for further V C D studies are the vibrational spectra and assignments of several mono- and dimethyl substituted analogues of D I O X A , to b e reported in a subsequent publication.

9

17 12 18

17

12 13

Syntheses The synthesis of DIOXA has been described elsewhere (8). All the compounds were further purified to >98% by vacuum sublimation before recording their spectra. The purities were confirmed by gas chromatography.

.

Bicyclo[3.2.l]octatze (BCO) Following a known procedure (9), dichlorocarbene was added to norbornene to form exo-3,3-dichlorotricyclo[3.2.1.0'.4]octane, which upon heating rearranged to em-3,4-dichlorobicyclo[3.2.1]oct-2-ene with an overall yield of 19%. This dichloride was dechlorinated using a method recommended for a similar compound (10). A mixture of dry THF (400 mL), sodium metal (1.6 mol, cut into small pieces), and tert-butanol (0.57 mol) was stirred vigorously and heated under a nitrogen atmosphere. When reflux of the solvent started, 3,4-dichlorobicyclo[3.2.Iloct-2-ene (0.17 mol) was added dropwise. After stimng and refluxing for 40 h, the product was separated and purified as recommended (10). Bicyclo[3.2.l]oct-2-ene was obtained in 44% yield. In a hydrogenation flask were placed bicyclo[3.2.l]oct-2-ene (37 mmol), absolute ethanol (30 mL), and 5% Pd/C (100 mg). The addition was carried out in a Parr hydrogenator applying an initial pressure of 70 psi (1 psi = 6.9 kPa) of hydrogen. The pressure dropped quickly and the reaction was stopped after 4 h. The mix-

FIG. 1. Structures of bicyclo[3.2. lloctane (BCO), (top); 8-oxabicyclo[3.2. lloctane (SOXA), (middle); and 6-oxabicyclo[3.2. lloctane (60XA), (bottom). Numbers correspond to atom numbering used in Tables 7 and 8-10. ture was filtered through Celite and the BCO precipitated by adding a large volume of water. The yield of crude product after filtration was 2.4 g (59%). The structures of the products in every step were confirmed by ' H nmr. 8-Oxabicyclo[3.2 .l]octat~e (80XA) This synthesis has been reported by other workers and is therefore given in short form only. From cyclopentanone and pyrrolidine the enamine (I-(N-pyrrolidiny1)cyclopentene was prepared, which was reacted with acrolein to form 2-(N-pyrrolidiny1)bicyclo[3.2.l]octan-8-one(1 1, 12). The methyl iodide of this m i n e was converted to 4-cycloheptenecarboxylic acid by base-induced ring opening (1 1-13). Lead tetraacetate decarboxylation of the acid, followed by the reduction of the acetate with LiAIH,, gave 4-cycloheptenol (14). Ring closure to 8-oxabicyclo[3.2.l]octane-2mercurial iodide was achieved by treatment with mercury acetate (15). Treatment with iodine gave 2-iodo-8-oxabicyclo[3.2.l]octane, which, upon reduction with LiA1H4, afforded the desired


CAN. J . CHEM. VOL. 71, 1993

FIG.2. Structures of the chair (upper) and boat (lower) conformers of 6,s-dioxabicyclo[3.2. lloctane (DIOXA). Numbers correspond to atom numbering used in Tables 7 and 11.

8 0 X A (15). In all steps the yields were comparable to values reported in the stated references. The products were always checked by their 'H nmr spectra.

The iodide was reduced with LiA1H4 in ether (15). After the usual work-up, 6 0 X A was distilled at aspirator vacuum and obtained with 50% yield. Its 'H nmr spectrum was identical to the reported

6-Oxabicyclo[3.2 .I]octane (60XA) The precursor, 4-hydroxymethylcyclohexene, was obtained from cyclohexene-4-carboxaldehyde (Aldrich) by reduction with sodium borohydride in methanol, following a published procedure for a similar compound (16). The yield after work-up was 84%. Ring closure of the alcohol to the bicyclic structure was achieved analogously to 8 0 X A (15). A solution of mercury acetate (40 mmol) and sodium acetate (40 rnmol) in 50 mL of water was stirred. The alcohol (40 mmol) was added within 5 min and stirring was maintained at ambient temperature for 15 min. A solution of potassium iodide (52 mmol) and sodium hydroxide (40 mmol) in 50 mL water was added dropwise, causing the product to precipitate. After stirring for another 15 min, the supernatant liquid was decanted and the solid 6-oxabicyclo[3.2.l]octane-2-mercurialiodide was dried under vacuum at room temperature and used as such for the following step. The mercury was eliminated by stirring the mercurial iodide (40 mmol) with an equimolar amount of iodine in 250 mL of carbon tetrachloride for 28 h. The work-up was carried out as described (15), yielding 6.8 g of crude iodide (71% relative to 4-hydroxymethylcyclohexene).

7, 7-d2-6-Oxabicyclo[3 .2. Iloctnne (60X4-d2) Following a published procedure (18), m-hydroxybenzoic acid was hydrogenated with sodium in boiling absolute ethanol. When all the sodium had reacted, water was added and the mixture was neutralized with hydrochloric acid. The alcohol was evaporated and after adding an excess of hydrochloric acid the solution was extracted continuously with ether for 8 h. The extract was dried with MgSO, and the ether was evaporated to give a residue containing cis- and trans-3-hydroxycyclohexanecarboxylic acid. The mixture was heated at 170°C for 40 min to convert the cis isomer to 6-oxabicyclo[3.2. Lloctan-7-one (25% yield after distillation). 60XA-d2 was prepared by a modification of a published procedure (17). A solution of the lactone (24 mmol) in ether (50 mL) was added dropwise to a stirred slurry of LiAlD, (38 mmol) in ether (90 mL). The mixture was refluxed for 2.5 h. After work-up an oil was recovered containing the cis-3-hydroxycyclohexyl-1,l-dideuteromethanol, which was used without further purification. The crude diol and p-toluenesulfonic acid were mixed and heated to 150°C (oil bath temperature) in a distillation apparatus at aspirator vacuum. The fraction boiling at 50-80°C was collected and redistilled. The 60XA-d2 was obtained in 20% overall yield; 'H nrnr

58 1


EGGIMANN ET AL.

Wavenumbers ( l / c m )

FIG. 3. Calculated (top) and observed solution (middle) and vapor phase (bottom) absorption spectra of bicyclo[3.2. lloctane (BCO). The solution and theoretical spectra are on the same scale. For experimental conditions see text. The insert vapor phase spectrum (450-830 cm-') was recorded with 0.5 cm-' resolution (500 scans). Numbers correspond to "Band nos." in Tables 1 and 13. (Bruker AC 200, 200 MHz, CDC1,) 6: 1.5-1.9 (m, 8H), 2.36 (s, br, l H , C I - H ) , 4 . 3 1 (t, 1H,C5-H).

7,7-d,-6,8-Dioxczbicyclo[3.2. Iloctnrze (DIOXA-dz) 3,4-Dihydro-2H-pyran-2-carboxylateethyl ester (8) was reduced with an equimolar amount of LiAlD, by stirring for 2 h to yield 3,4-dihydro-2H-pyran-2-(1 ,I-dideutero)-methanol after decomposition (88% after distillation, F = 85-87"C, asp. vacuum). For cyclization, the alcohol (26 ~nmol)was refluxed for 1 h in ptoluenesulfonic acid (30 mg) and benzene (30 mL). The mixture was neutralized with sodium methanolate, filtered, and distilled. DIOXA-dZwas collected at 68-74°C (asp. vacuurn) in 79% yield; 'H nmr (Bruker AC 200, 200 MHz, CDCI,) 6: 1.5-2.0 (m, 6H), 4.49 (s, l H , C1-H), 5.51 (s, lH, C5-H).

Experimental The absorption spectra were measured with a Nicolet 8000 FT-IR interferometer using a MCT detector with a cutoff at 400 cm-I. The condensed phase spectra (400-1500 cm-I) were recorded from solutions in CS, (700-840 cm-I) and CC1, (remaining parts of the spectra) with typical concentrations of 0.5 mol/L (0.8 nlol/L for BCO) and with 0.1 mm path length. To obtain adequate signal-tonoise for Fourier self-deconvolution, 2000 scans were coadded at 1 cm-I resolution. For the mid-infrared vapor phase spectra (4001500 cm-'), the compounds were evaporated into a Wilks variable-path gas cell adjusted to approximately 5 m path length using pressures of typically 1.4 Torr (1 Torr = 133.2 Pa), except for BCO for which 12 Torr were required. In all cases 500 scans were collected with 0.12 cm-I resolution (unapodized). The water lines in

Xavenumbers ( l / c m )

FIG. 4. Calculated (top) and observed solution (middle) and vapor phase (bottom) absorption spectra of 8-oxabicyclo[3.2.1]octane (80XA). The solution and theoretical spectra are on the same scale. For experimental conditions see text. Numbers correspond to "Band nos." in Tables 2 and 14. the spectrum of BCO were diminished by subtracting a spectruln of water recorded with identical instrumental settings. The spectra are displayed in Figs. 3-8. The far-infrared vapor phase spectra (80-400 cm-I) were recorded for BCO, 8 0 X A , 6 0 X A , 60XA-d?, and DIOXA with 0.12 cm-I resolution. The spectra exhibit well-resolved sequences of Q-branches for many fundamentals resulting from skeletal anharmonicities. While the details are published elsewhere (19), peak positions of the fundamentals are included here for the sake of completeness. For BCO, the absence of significant transition dipole moments results in very weak absorptions, obscured in addition by water lines. Nonetheless, two bands located at 262.5 and 358.1 cm-.' could be identified and assigned to A' fundamentals. The Raman spectra of the neat melted compounds (Figs. 9-14) were measured between 100 cm-I and 1500 cm-I with a JarrellAsh model 25-100 double grating monochromator, utilizing for excitation the 514.5-nm line of an argon ion laser (Coherent Radiation) with 300 mW power at the sample. The photomultiplier detector was interfaced to a microcomputer, which allowed coaddition of 8 scans for each spectrum with a scanning step size of 2 cm-I and a time constant of 1 s. The slits were adjusted to an effective spectral width of 5 cm-I at 1000 cm-I. Since the samples have relatively high vapor pressures, they were sealed into capillary tubes and melted with a stream of hot air (50-150°C) in a specially designed apparatus. The laser beam was focused into the samples from the bottom of the capillary tubes. The frequencies were calibrated against the CC1, peaks. The measured intensities were not corrected for the frequency-dependent response of the photomultiplier tube. The resulting errors are estimated to be within 15% maximally over the whole reported spectral region, and


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CAN. J . CHEM. VOL. 71, 1993

Wavenumbers (l/cm) Wavenumbers (l/cm)

FIG. 5. Calculated (top) and observed solution (middle) and vapor phase (bottom) absorption spectra of 6-oxabicyclo[3.2.1]octane (60XA). The solution and theoretical spectra are on the same scale. For experimental conditions see text. Numbers correspond to "Band nos." in Tables 3 and 15. Asterisks indicate bands that are believed to arise from impurities. appreciably less in narrower regions of specific group frequencies within which intensity comparisons are invariably made in the following text for the purpose of assisting with assignments. Observed vibrational frequencies and absorption intensities (expressed as dipole strengths) are listed in Tables 1-6. Selected portions of the condensed phase absorption spectra were subjected to Fourier self-deconvolution (20) in order to resolve partially overlapped bands and to check for transitions that might be completely hidden by other bands. Accurate frequencies were thus measured for a number of bands that otherwise would have been uncertain or left unnoticed. Such bands are marked with the label "dcn" in Tables 1-6. Absorption intensities were determined from the solution spectra by fitting Lorentzian band-shape functions and measuring band heights and widths at half height. The results obtained by visual and least-squares methods and for different solutions usually varied between 2 and 10%. The errors in the experimental intensities are thus estimated to lie in this range for most bands, while for a few of the very weak and overlapped lines the errors may be above 20%.

Calculations Ab initio calculations The geometries of BCO, 80XA, 60XA, and DIOXA were fully optimized and their harmonic force fields calculated by analytical second differentiation of the energies at the equilibrium geometries. The computations were carried out at the SCF-RHF level of theory using the programs GAUSSIAN 82 implemented on a CDC Cyber 205 (STO-3G basis set), and GAUSSIAN 86 (21) running on a Convex C120 (3-21G

FIG. 6. Calculated (top) and observed solution (middle) and vapor phase (bottom) absorption spectra of 7,7-d2-6-oxabicyclo[3.2.1 ]octane (60XA-d2). The solution and theoretical spectra are on the same scale. For experimental conditions see text. Numbers correspond to "Band nos. " in Tables 4 and 16.

basis set). The atomic polar tensors and the polarizability derivatives were computed using the 3-21G basis set. BCO and 8OXA were restricted Cs symmetry. The existence of a true minimum in the potential hypersurface at the stationary point was ensured in every instance by confirming that all diagonal force constants were positive. Proof of good convergence was supplied by the fact that the lowest vibrational frequencies, which would be most affected by insufficient convergence of the energy, are calculated with an average error of 10.8 cm-' (5.7%), which is within the expected error for the unscaled force fields. Contrary to Pulay's advocated standard procedure (7, 22), according to which corrected geometries afford more accurate force fields, we prefer to obtain the force fields at the uncorrected ab initio geometries. The practice of calculating Cartesian force fields at distorted theoretical geometries would require nonlinear transformations to other coordinate systems in order to account for the non-vanishing forces. For the bicyclic structures investigated, any correctional variations of the bond lengths and angles would unavoidably lead to distortions in the ring segments, and these distortions would be dependent on the choice of the valence coordinates in which the corrections are carried out. The calculations utilizing STO-3G force fields are not presented here since they are clearly inferior to the 3-21G results. Information, however, can be obtained from the authors. Selected structural parameters and the RHF energies of all four parent molecules are given in Table 7 for the two

583


EGGIMANN ET AL.

Wavenumbers (l/cm) Wavenumbers (l/cm)

FIG. 7. Calculated (top) and observed solution (middle) and vapor phase (bottom) absorption spectra of 6,8-dioxabicyclo[3.2. lloctane (DIOXA). The solution and theoretical spectra are on the same scale. For experimental conditions see text. Numbers correspond to "Band nos." in Tables 5 and 17.

basis sets. For each of these bicyclics, two stable conformers may be expected to exist, which may be described by the chair and boat forms of the six-membered ring segment. All four structures converged to the chair conformation (Figs. 1, 2) in the geometry optimizations. To better characterize the potential surface of the ring inversion, the boat conformer of DIOXA was relaxed, converging at the 3-21G level in a local minimum higher in energy by 1577 cm-' (18.9 W / mol) compared to the chair (Fig. 2). The chair to boat inversion is accompanied by other changes, involving considerable lengthening of the bonds C 1-C2 and C4-C5, as well as an increase of the twist in the seven-membered ring segment, as expressed by the dihedral angle 6(1-7-6-5) in Table 7. The STO-3G calculation in addition proposes a remarkable expansion of the 06-C7 bond. Although no similar calculations for the other compounds were carried out, we suspect that they all possess similar highly asymmetric double minimum potentials for the inversion of the six-membered ring. The vibrational analysis of the boat conformers of the two DIOXA isotopomers revealed a number of transitions that should be observable distinctively among those of the chairs, but none were detected in the experimental spectra. This is in accord with the calculated population (0.04%, neglecting the zero-point vibrational energy) of the boat at the experimental conditions. Experimental structures have been published for 80XA from a microwave study (23) and for BCO from electron diffraction (24). In both cases the agreement with the calculated geometries is reasonably

FIG. 8. Calculated (top) and observed solution (middle) and vapor phase (bottom) absorption spectra of 7,7-d,-6,8-dioxabicyclo[3.2.l]octane (DIOXA-d,). The solution and theoretical spectra are on the same scale. For experimental conditions see text. Numbers correspond to "Band nos." in Tables 6 and 18.

good. These experimental studies confirm for both molecules the strong preponderance of the chair form at ambient temperatures. Scaling and refining of ab initio force fields These procedures, which were also described in previous publications ( 1 , 20, 4, 5), were carried out with a program developed by Shaw (25). The harmonic ab initio Cartesian force constants were transformed to a nonredundant set of local symmetry coordinates (LSCs), defined as linear combinations of internal coordinates following Pulay et al. (22) and listed in Tables 8-1 1 for the four parent molecules. The transformed force constants Kij were then scaled with factors ci and c, associated with the local symmetry modes i and j, respectively, according to Fij= ( C ~ C ~Kij, ) " ~where the F,, are the scaled force constants (26). The scale factors for the individual LSCs were transferred from similar molecules (see Table 12) and subsequently optimized stepwise in overlay refinements including all six compounds by least-squares fitting of the calculated frequency parameters, Ap = (2rcl).d2, to the observed values after weighting by (1 / ~ k " ~ ' ) ~ . Three vibrational calculations are presented here which differ in the way the ab initio force fields were scaled. The three scaling techniques were analyzed for the resulting accuracy in reproducing the experimental spectra in an attempt to find the most favorable force-field correction method. The simplest scheme, namely uniform scaling, consists of multiplying all diagonal and off-diagonal force constants by the same factor, which is subsequently refined. These results are found in column 1 under "Calculated wavenumbers" in Tables 13-18. The other two

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CAN. J. CHEM. VOL. 71, 1993

Calculated

h


4J

.4

>

.4

4J

:

Observed

Wavenumbers (l/cm) FIG. 9. Observed and calculated Raman spectra of liquid bicyclo[3.2. ]]octane (BCO). The two traces correspond to the parallel (I", upper) and perpendicular (IL, lower) polarization measurements. For experimental conditions see text. Numbers correspond to "Band nos." in Tables 1 and 13.

calculations adopt the method of nonuniform scaling, applying and adjusting several factors, separately scaling the force constants for different types of LSCs as outlined above. Tables 13-18 contain the resulting wavenumbers using 14 factors directly transferred from other molecules (column 2, see discussion below), and fully refined (column 3). The factors applied to the three scaling schemes are listed in Table 12. Intetzsity calculations The absorption and Raman intensities listed in Tables 1318 were derived from the refined nonuniformly scaled force fields. The dependence of the intensities on the scaling method is analysed below in the Discussion. The theoretical absorption intensities were computed by the standard expression for the dipole strength Di (in units of esu2 cm2) of the ith fundamental (27, 28):

where the symbols, h, c, No, and vi refer, respectively, to

Wavenumbers (l/cm) FIG. 10. Observed and calculated Raman spectra of liquid 8-oxabicyclo[3.2. lloctane (80XA). The two traces correspond to the parallel (Ill, upper) and perpendicular (IL, lower) polarization measurements. For experimental conditions see text. Numbers correspond to "Band nos." in Tables 2 and 14. Asterisks indicate bands that are believed to arise from impurities.

Planck's constant, the speed of light, Avogadro's number, and the vibrational frequency of normal mode i, in cgs units. The atomic polar tensor ( d ~ / d & is ) ~the a b initio molecular dipole moment derivative with respect to the Cartesian position vector x, of atom a , evaluated at the equilibrium geometry, and (dx,/dqi) is the Cartesian eigenvector for atom a in normal coordinate q, as obtained from the Wilson GF formalism (29). The right-hand side of the equation defines the connection to the experimentally available molar absorptivity ~ ( v if) used in units of M-' cm-I. The Raman scattering activities may be obtained to a good approximation from the derivatives of the molecular polarizability with respect to the normal coordinates dg/dqi) if the electronic ground state is nondegenerate, and iTthe Raman frequency shifts v, are small compared to the frequency vo of the incident light and compared to v, - vo, where v, is the lowest electronic absorption frequency (28a, 29). All these conditions are satisfied for the title compounds. The desired quantities can be calculated using:

EGGIMANN ET A L


Calculated

10

Observed

Wavenumbers (l/cm)

Wavenumbers (l/cm)

FIG. 11. Observed and calculated total Raman intensities (lT) of liquid 6-oxabicyclo[3.2. Iloctane (60XA). For experimental conditions see text. Numbers correspond to "Band nos." in Tables 3 and 1.5. Asterisks indicate bands that are believed to arise from impurities.

FIG. 12. Observed and calculated total Raman intensities (zT) of liquid 7,7-d,-6-oxabicyclo[3.2.Iloctane (60XA-d,). For experimental conditions see text. Numbers correspond to "Band nos. '' in Tables 4 and 16. Asterisks indicate bands that are believed to arise from impurities.

where the polarizability derivatives with respect to Cartesian atomic coordinates (dg/dz0), are generated ab initio in the GAUSSIAN86 The mean value &, and the anisotropy y: of the polarizability derivative tensors are then substituted into the standard classical equations for the Raman intensity of fundamentals (28a, 29, 30). For our experimental setup, which is collecting the scattered light at 90' from the progagation direction and perpendicularly to the electric field vector of the incident plane-polarized laser beam, these expressions are

tional to the experimental Raman activities. To allow direct comparison to observed intensities, the pertinent theoretical equations [3]-[5] must be multiplied with the factor (vo ~ ~ ) ~and / v another ; term correcting for the relative populations of the vibrational levels as derived from the Boltzmann distribution law (30, 31):

[3] [4]

sT,= 4 5 ~ 1+, ~7 ?,Z sll, = 4 5 ~ 1+, ~4

where sT,designates the total intensity of the scattered light in the stated direction, sI', and S L i are the parallel and perpendicular polarized components, respectively, and p, is the depolarization ratio of normal mode i. The Raman data listed in Tables 13-18 were calculated using eqs. [3] and [6]. These quantities, although commonly reported, are not propor-

I;

=

C

(vo - ~ i ) ~ [l - exp (-hv,/k~)]-' S;

Here, C is a constant, k is Boltzmann's constant, and T is the absolute temperature. The expression in square brackets implicitly includes a summation over the population-weighted fundamental and hot band transitions, which is significant for the lowest vibrations. Equation [7] was utilized for the theoretical Raman spectra plotted in Figs. 9-14. The constant C is irrelevant here because the Raman spectra were not measured on an absolute scale, and only the relative Raman band strengths could be compared. Basis set tests After the assignments and force field refinements described below had been completed, the ab initio geometries, force fields, and intensity parameters were also

586



!I

Calculated

Observed

Wavenumbers (l/cm)

Wavenumbers (l/cm)

FIG. 13. Observed and calculated total Raman intensities (IT) of liquid 6,8-dioxabicyclo[3.2. lloctane (DIOXA). For experimental conditions see text. Numbers correspond to "Band nos." in Tables 5 and 17.

FIG. 14. Observed and calculated total Raman intensities (IT) of liquid 7,7-d2-6,8-dioxabicyclo[3.2. lloctane (DIOXA-dl). For experimental conditions see text. Numbers correspond to "Band nos." in Tables 6 and 18.

computed for DIOXA with the basis sets 6-31G, 6-31G*, 6-31*'0.3', and 6-31G**. The 6 - 3 1 ~ * " . ~basis ' set (32) derives from the standard 6-3 lG* by reducing the exponents for the d functions from 0.8 to 0.3, thus rendering the polarization functions considerably more diffuse. This or very similar modifications have been recommended by several authors for calculating dipole moments and polarizabilities and their derivatives (7a, 32, 33). These force fields were scaled with the refined 3-21G factors (Table 12), which were then optimized again for each force field, based on the 72 assigned band positions of DIOXA and DIOXA-d,. The band assignments for the two molecules suggested by the 3-21G results (Tables 17, 18) were confirmed by the higher level calculations. To allow proper comparison, the 3-21G scale factors were also refined once more using the data of the two DIOXA isotopomers only, changing the factors by small amounts. The average error in the frequency predictions reduced to 0.52% with the 6-31G calculation as compared to 0.70% for 3-21G. The improvement of the eigenvectors was also reflected in the better agreement of the absorption and Raman intensities. However, addition of polarization functions with the 6-31G* and 6-31G** basis sets did not give rise to any further improvements in the frequencies or intensities. In fact, the last two basis sets yielded virtually

identical results after the scale factor refinements (wavenumbers agreed within 0.025%, absorption intensities within 6%, and Raman within 5%). Even the 6 - 3 1 ~ * " . ~basis ' set, although designed for absorption and Raman intensities, did not provide significantly improved results. It was found that, when employing the same eigenvectors in combination with the APTs and polarizability derivatives from the various basis sets, the theoretical absorption and Raman intensities were the same throughout. That is, the a b initio calculated intensity parameters were insensitive to the basis set applied, except for small changes in the absolute intensities (6-3 lG* intensities were largest). The distribution of the relative intensities among the vibrational modes was completely governed by the eigenvectors. The basis set dependence of the eigenvector was further traced back to the force fields. While there was also a small dependence on the geometry, the accuracy of the vibrational intensities attainable by the split-valence and the polarized basis sets was thus primarily determined by the quality of the force field. The tests also suggest that the quality of the scaled 3-21G force field closely approaches the scaled 6-31G force field, which is as accurate as the scaled 6-31G* and 6-31 ** force fields. Among the basis sets tested, the 6-31G calculation appeared to have the best performance-to-cost ratio. Compar-

EGGIMANN ET AL.

TABLE1. Observed band positions (cm-') and dipole strengths for bicyclo[3.2. lloctane Infrared absorption


Band nos." 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

vaporb

Solutionc

262.5/ 358.1f 525.0 709.4 726.3 755.0 764.7 795.0 (B) 812.4 872.9 876.3 892.3 963.4 979.6 1006.5 1026.9 1044.1 1050.4

523.7 709.3 724.7 758.5 765.8 790.5 811.3 863.8 872.5 874.8 890.1

w w (CS,) w (CS,) w (CS,) w, sh (CS,) m (CS,) w (CS,) w, sh, dcn m, sh, dcn m, dcn w

1167.0 1188.7 (B) 1211.3 1243.9 1259.9 1284.4 1305.2 1319.6 1329.7 1344.3 1355.5 1360.6

960.9 w 977.7 w 1004.6 m 1025.0 w 1042.2 w 1056.1 w, sh 1074.0 w 1101.2 m 1143.9 w 1164.6 m 1185.5 w 1207.7 w 1238.4 w 1256.7 m 1279.7 w 1299.8 m 1315.7 m 1325.3 m 1339.5 m 1352.4 w 1356.7 w

1453.8 1460.2 1464.2 1481.2

1449.0 s, sh, dcn 1453.7 s, dcn 1458.4 s, sh, dcn 1474.8 s

1102.5

Raman" 195 w 261 w, 332 w 361 w , 421 w , 430 w 523 w 707 m, 718 w 757 m, 763 m,

Symmetry

pol

A'

pol sh

A'

pol

A'

pol pol

809 s, pol

A' A' A" A'

869 s, pol

A'

887 w , 938 w, 959 w , 975 m, 1001 m, 1022 m 1039 m, 1052 w

sh sh sh pol pol

A' A'

pol

A'

1098 w, pol 1142 w 1161 w

A' A"

1204 w 1237 m 1253 m, pol

A'

1315 w 1349 w

Dipole strengthse

5.49 4.25 1.18 1.39 0.99 9.25 1.75 3.25 8.03 8.53 1.45 1.15 4.19 6.75 0.32 3.89 0.18 0.06 7.22 0.82 4.39 1.72 0.55 2.92 6.76 0.26 2.56 4.01 3.04 4.78 0.87 0.92

1441 m

1473 w, pol

A'

11.1 30.3 26.7 8.85

"Numbers correspond to labels in observed spectra (Figs. 3 , 9). bobserved band contours are in parentheses if discernible. 'Measured in CC1, unless labelled (CS,). Abbreviations: s = strong, m = medium, w = weak, sh = shoulder, dcn = band position measured after Fourier self-deconvolution. dMeasured from neat liquid phase. Abbreviations: s = strong, m = medium, w = weak, sh = shoulder, pol = clearly polarized band ( p < 0.75). 'Units of Io-'' esu2 cm2. 'From ref. 19.

ing these results to similar studies on smaller molecules (7a, 7 b , 34), it appears that the basis set dependencies of the vibrational intensities encountered here are less severe, partitularly for the polarized basis sets. The conclusions derived from these tests apply strictly only t~ the DIOXA isotopomers. Similar results may be found for other large molecules with related structures.

Assignments and scaling of force fields ~~~~~~lprocedure 1, general, the complexity of the spectra prevented straightforward assignments based only on observed features. The majority of the bands had to be assigned on the basis of the theoretical frequencies. In the cases where such assignments were ambiguous, the calculated absorption in-

CAN. J. CHEM. VOL. 71. 1993

TABLE2. Observed band positions (cm-') and dipole strengths for 8-oxabicyclo[3.2. ]]octane


Band nos." 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

Infrared absorption Vaporb 263.9l." 332.2s (B) 368.3" 443.5 470.8 566.0 724.0 763.2 (B) 777.5 803.7 832.7

Solution"

445.6 m 567.7 723.6 760.3 776.6 803.2 829.3

w m w w w m

(CS,) (CS,) (CS2) (CS2) (CS?)

877.2 886.9 951.5 990.5 1032.6 1049.8 1056.8 1084.6 1162.4 1192.6 (B) 1223.7 (B) 1231.9 1257.2 1275.2 (B) 1297.6(B)

871.8 s 886.1 m 950.7 m 987.1 s 1025.1 s 1045.7 w 1060.2 w 1083.1 m 1160.2 m 1189.4 w 1222.7 w, sh, dcn 1229.3 m 1252.3 m 1273.4 w 1295.1 w

1327.3

1324.3 m

1347.1 1361.0

1343.0 m 1357.6 w 1421.5 w 1439.2 w 1447.8 m 1456.3 w, dcn 1459.9 w, sh, dcn 1473.4 m

1444.5 1453.7 1460.6 1465.0 1478.6

Raman" 184 w 263 w, pol 337 w 371 m, pol 446 w 471 w 567 w , pol 722 m, pol 758 w, sh 775 s, pol 809 w 828 s, pol 856 w 870 w 885 s, pol 949 w 984 m, pol 1023 m 1043 m, pol 1081 m 1159 m 1186 w 1220 w , sh 1226 m 1250 m 1268 w, sh 1312 w 1323 w, 1333 w, 1341 w, 1355 w 1416 w , 1436 m

sh sh pol

Dipole Symmetry strengths' A' A A'

93.6 A' A' A" A' A' A' A'

A'

A" A" A A

175 27.8 37.7 124 170 25 .O 2.72 54.3 44.7 7.60 5.41 29.4 20.8 3.08 4.62 32.2

A'

sh

1456 w, sh 1472 w, pol

30.8 30.3 24.2 10.3 1.93 27.6

A'

22.0 6.67 4.94 15.0 15.4 16.4 3.86 29.8

"Numbers correspond to labels in observed spectra (Figs. 4, 10). bobserved band contours are in parentheses if discernible. 'Measured in CCI, unless labelled (CS2). Abbreviations: s = strong, m = medium, w = weak, sh = shoulder, dcn = band position measured after Fourier self-deconvolution. dMeasured from neat liquid phase. Abbreviations: s = strong, m = medium, w = weak, sh = shoulder, pol = clearly polarized band (p < 0.75). 'Units of lo-'' esu2 cm'. 'From ref. 23. T r o m ref. 19.

tensities, and Rarnan activities and polarization ratios turned out to be very helpful guides, assuming that at least the order of magnitude of the calculated intensities was correct. The validity of this assumption will be demonstrated in the Discussion. In general, therefore, band assignments were initially based on the mode symmetries as deduced from Raman polarization ratios and gas phase absorption band shapes where applicable, and on the frequencies, which are the most reliable theoretical predictions with the 3-21G basis set. The intensities usually were consulted only for transitions that were observed or calculated less than 10 cm-' apart (which

is in the same range as the uncertainly in the predicted band positions) and only on a semi-quantitative basis, that is, if the absorption or Raman intensities of the involved bands were sufficiently different, to provide a safe criterion to differentiate between them. A few bands were assigned despite remaining uncertainties, if the predicted frequencies were in good agreement with the frequencies of observed bands that appeared to correspond to the normal modes in question. This was done to ensure that there were sufficient data to guarantee stability in the refinement of the force field. Even if a few of these assignments were incorrect, the ef-

EGGIMANN ET AL

TABLE3. Observed band positions (crn-') and dipole strengths for 6-oxabicyclo[3.2. lloctane


Band nos."

Vapor

Infrared absorption solution"

Rarnan'

Dipole strengthsd

429.8 w 470.3 w 554.1 w 718.5 w (CSJ 741.6 rn (CS,) 796.0 w (CS?) 813.0 m (CS,) 850.8 s 878.9 s 884.4 m, sh, dcn 903.0 m 932.8 m 942.9 w, sh, dcn (br 955.1 w 987.3 s 1013.0 m 1047.7 m, sh, dcn 1051.4 s, dcn 1080.6 m , dcn 1085.5 m , sh, dcn 1099.7 s 1106.8 m 1154.8 w 1171.4 m 1222.0 w 1233.9 m 1265.0 m 1285.1 w 1301.1 w 1317.2 w, sh 1320.0 m 1332.5 m 1348.0 w 1355.7 w, sh, dcn 1361.7 w 1437.6 w , dcn 1445.8 w, sh, dcn 1454.7 m, dcn 1458.1 m, sh, dcn 1460.9 m , dcn 1486.4 w "Numbers correspond to labels in observed spectra (Figs. 5 , 11). 'Measured in CCI, unless labelled (CS,). Abbreviations: s = strong, m = medium, w = weak, sh = shoulder, dcn = band position measured after Fourier self-deconvolution. 'Measured from neat liquid phase. Abbreviations: s = strong, m = medium, w = weak, sh = shoulder. esu' cm'. "Units of 'From ref. 19.

fect on the optimized scale factors was negligible because the frequency errors were always small. Initially, the force fields were scaled with 11 factors, 10 of which (factors 1, 2, and 4-1 1 in Table 12) were transferred from the norbornane series (4) (from refinement "A" in that reference, where the ring out-of-plane deformation factor of norbornane was used) and applied to the corre-

sponding local symmetry modes of the bicyclo[3.2.11octanes. The C-0 stretching factor (3 in Table 12) was taken from 7-oxanorbornane (5). Previous experience from the assignment of the vibrational spectrum of 2-methyloxetane (2a) suggests that different scale factors may be required for certain methylene deformation modes if the CH, group is located next to an oxygen atom, and for methyne


TABLE 4. Observed band positions (cm-') and dipole strengths for 7,7-d2-6-oxabicyclo[3.2. lloctane Band nos."

Infrared absorption Vapor

solutionb

Ramanc

Dipole strengthsd


-

-427 w 458.5 w 550.7 w 714.6 w (CS,) 726.0 w (CS,) 745.3 m (CS,) 802.2 m (CS,) 81 1.7 w, sh (CS2) 855.7 s 867.9 w, sh 876.7 w, sh 885.7 m

187 w 240 w 322 w 355 w 423 w 456 w 549 w 712 m 723 w 742 m 800 m, sh 808 s

] 1.

sh (broad)

903.0 s 983.5 s 997.6 w, sh 1004.7 w 1035.0 s 1040.0 m, sh, dcn 1047.3 m 1061.9 s 1075.0 m 1102.2 s 1 106.4 s 1127.3 w 1167.7 w 1199.5 m 1234.0 w (broad) 1264.3 w 1289.7 w 1305.4 w 1317.4 m 1321.6 w , 1335.3 w 1354.6 w, 1359.1 w, 1438.1 w , 1444.5 w, 1451.7 m,

sh, dcn sh, dcn dcn sh, dcn sh, dcn dcn

1457.9 m, sh, dcn 1465.2 m, dcn "Numbers correspond to labels in observed spectra (Figs. 6 , 12). "Measured in CC1, unless labelled (CS2).Abbreviations: s = strong, m = medium, w = weak, sh = shoulder, dcn = band position measured after Fourier self-deconvolution. 'Measured from neat liquid phase. Abbreviations: s = strong, m = medium, w = weak, sh = shoulder. dunits of lo-"' esuZcm'. 'From ref. 19.

deformations if an adjacent C-0 bond is located approximately in the plane of the CH bend. Two special factors for the CH, wag and twist (12 and 13 in Table 12) were therefore transferred from 2-methyloxetane (2a) and used for the corresponding modes on C7 of 60XA, DIOXA, and their

isotopomers. Factor 14 was taken from the same source and used for all "in-plane" (i/p) and "out-of-plane" (o/p) methyne CH bends for which an adjacent oxygen atom lies approximately in the plane of the motion of the hydrogen atom (C1 and C5 o/p in 80XA, C5 i/p in 60XA and

EGGIMANN ET AL

TABLE5. Observed band positions (cm-I) and dipole strengths for 6,8-dioxabicyclo[3.2. lloctane


Band nos." 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

Infrared absorption Vapor 188.2' 252.3' 338.6' 372.8' 445.2 506.4 610.0 746.5 779.8 808.8 833.5 858.9 886.4 896.8 942.0 962.5 1000.4 1030.3 1035.0 1076.7 1092.5 1129.1 1158.9 1181.3 1190.1 1213.1 1242.7 1276.6 1310.5 1320.7 1333.5 1340.4 1343.7 1352.3 1364.7 1437.3 1439.3 1442.7 1462.7 1469.5 1488.5

Solutionb

Ramanc

447.7 m 508.3 w 611.4 m 743.9 w (CS2) 776.8 w (CS2) 808.8 w (CS*) 832.2 w 856.7 s 882.1 s 893.1 m 938.5 m 962.1 m 992.6 s 1022.4 s 1032.8 m 1075.6 w 1088.7 m 11 18.6 s, sh, dcn 1123.9 s, dcn 1156.5 s 1182.2 w 1210.7 w 1240.0 w 1275.7 w 1309.5 m 1314.8 w , sh, dcn 1330.6 m, dcn 1338.2 m, dcn 1342.6 m, dcn 1349.1 w, dcn 1362.2 w, dcn 1364.9 w, dcn 1429.6 w , sh, dcn 1434.6 w, sh, dcn 1438.3 w, dcn 1457.6 m 1469.1 w 1483.5 w

196 w 251 w 342 w 376 w 446 w 506 m 609 w 741 w 773 w 807 s 828 s 853 m 885 w, sh 890 m 935 w 960 w 987 m 1019 m 1031 m 1073 m

]

y:

:

1153 w 1179 w 1208 m 1237 m 1274 w 1313 w 1328 w 1335 w, sh

y:i

I

,; sh

1435

1455 m 1482 w

Dipole strengthsd

79.1 8.14 49.9 8.51 6.14 21.2 26.1 175 216 120 120 32.6 249 191 77.4 17.0 33.4 206 172 126 34.4 11.5 0.78 28.1 5.84 37.6 11.4 21.8 8.33 14.9 11.1 6.72 5.81 11.9 20.7 3.92 13.1

"Numbers correspond to labels in observed spectra (Figs. 7, 13). bMeasured in CCI, unless labelled (CS,). Abbreviations: s = strong, m = medium, w = weak, sh = shoulder, dcn = band position measured after Fourier self-deconvolution. 'Measured from neat liquid phase. Abbreviations: s = strong, m = medium, w = weak, sh = shoulder. "Units of lo-*' esuZ cm'. 'From ref. 19.

60XA-d,, C1 o/p, C5 i/p and o/p in DIOXA and DIOXAd2). The frequency predictions that resulted from this first correction of the force field with the 14 factors led to the unambiguous assignment of 55 bands for the six molecules in the methylene scissoring (1400-1500 cm-l) and the low frequency (100-600 cm-') regions. The assignments in the latter were straightforward. Except for BCO, the seven lowest modes for each molecule were identified in either or both the

absorption and Raman spectra simply by consulting the frequencies. Additional confirmation was obtained for BCO and 80XA from the Raman polarization ratios, clearly establishing A' symmetry for a number of vibrations. The factors for the dominant local symmetry modes (factors 4, 10, and 11) were then refined. Next, bands from 600 to about 1050 cm-I were included and the factors 1, 3, and 5 were floated together with 4, 10, and 11, fitting a total of 123 frequencies. The assignment of the rest of the spectra turned

CAN. J. CHEM. VOL. 71. 1993

TABLE 6. Observed band positions (cm-') and dipole strengths for 7,7-d,-6,8dioxabicyclo[3.2.1]octane


Band n0s.O

Infrared absorption Vapor

solutionh

Ramanc

Dipole strengthsd

445.7 m 491.4 w 607.2 m 728.9 w (CS,) 752.2 w (CS2) 764.6 w (CS,) 802.3 m (CS?) 829.3 w (CS,) 866.4 s 877.1 m 884.4 m 896.5 w sh 910.1 w 975.5 m, sh, dcn 979.9 m dcn 1012.8 m 1021.9 s 1054.8 w 1075.1 m 1098.1 w, sh, dcn 1 1 16.5 s 1133.6 m 1162.1 m 1198.8 m 1239.7 w 1280.6 w 1312.8 w, sh, dcn 1318.0 m, dcn 1322.0 w , sh, dcn 1333.8 w 1342.9 m 1357.2 w, sh, dcn 1363.5 w, dcn 1369.6 w, sh, dcn 1432.8 w 1438.0 w 1456.0 w, sh, dcn 1462.4 w , dcn "Numbers correspond to labels in observed spectra (Figs. 8, 14). bMeasured in CCI, unless labelled (CS,). Abbreviations: s = strong, m = medium, w = weak, sh = shoulder, dcn = band position measured after Fourier self-deconvolution. 'Measured from neat liquid phase. Abbreviations: s = strong, m = medium, w = weak, sh = shoulder. "Units of esu2 cm'.

out to be more difficult because of congested bands. However, it was possible to assign with relatively high confidence a number of bands in the remaining parts of the spectra, followed by the third refinement cycle including the factors 6-9 and 12-14. With a total of 196 assigned transitions, all the factors except the one for the C-H stretch were finally optimized simultaneously, converging to the set listed in Table 12 as "Refined factors" with an average error of 5.7 cm-' (0.75%). Tables 13-18 list in bold lettering the assignments included in the refinements, and the frequencies calculated with

the three scaling methods. Also listed are dipole strengths, Raman intensities and depolarization ratios, and the strongest contributors to the potential energy distribution (PED) of the normal modes, all of which have been calculated with the fully refined, nonuniformly scaled force fields. The following paragraphs contain an outline of the rationales used for the most problematic band assignments, as well as discussions about spectral details that are interesting for other reasons. In some instances, plausible assignments are suggested for bands that were not included in the refinement cycles; they are listed in Tables 13-18 in italic lettering.

TABLE 7. Selected a b ir~itio3-21G and STO-3G structural parameters and energies of BCO, 8 0 X A , 6 0 X A , and DIOXA" BCO

80XA'

60XA

DIOXA (chair)


Structure

"Structures are displayed in Figs. 1.2. "and lengths (A), angles, and dihedral angle 6 (deg). For definitions of atom numberings and angles 'P, 8 , and @, see F ~ g s .1, 2. 'See also ref. 23. dHartree-Fock SCF energies in units of hartrees.

DIOXA (boat)

CAN. J. CHEM. VOL. 7 1 . 1993

TABLE8. Definitions of local symmetry coordinates for bicyclo[3.2. l]octanea C-C

stretch


CH, scissor

CH, rock

CH, twist

CH, wag

C-H

def. (i/p)

C-H

def. (o/p)

Ring def. (i/p) Ring def. (o/p)

A' A' A" A' A'

A Bridge wag Bridge twist Bridge rock

A' A" A"

c ( 1)-(c(2) C(2)--C(3) C(3)-C(4) C(4)--C(5) C(5)-C(6) C(6)-C(7) C(7)-C( 1) C( l)-C(8) C(5)-C(8) C(2) 5a(10-2- 11) + a( 1-2-3) C(3) 5a(12-3- 13) + a(2-3-4) C(4) 5a(14-4-15) + 43-4-5) C(6) 5a(17-6- 18) + a(5-6-7) C(7) 5a(19-7-20) + a(1-7-6) C(8) 5a(21-8-22) + a(1-8-5) C(2) 410-2-1) + a(10-2-3) - a(l1-2-1) - a(11-2-3) C(3) a(12-3-2) + a(12-3-4) - a(13-3-2) - a(13-3-4) C(4) a(14-4-5) + a(14-4-3) - a(15-4-5) - a(15-4-3) C(6) a(17-6-5) + a(17-6-7) - a(18-6-5) - a(18-6-7) C(7) a(19-7-1) + a(19-7-6) - a(20-7-1) - a(20-7-6) C(8) a(21-8-1) + a(21-8-5) - a(22-8-1) - a(22-8-5) C(2) a(10-2-1) - a(10-2-3) - a(l1-2-1) + a(11-2-3) C(3) a(12-3-2) - a(12-3-4) - a(13-3-2) + a(13-3-4) C(4) a(14-4-5) - a(14-4-3) - a(15-4-5) + a(15-4-3) C(6) a(17-6-5) - a(17-6-7) - a(18-6-5) + a(18-6-7) C(7) a(19-7-1) - a(19-7-6) - a(20-7-1) + a(20-7-6) C(8) a(21-8-1) - a(21-8-5) - a(22-8-1) + a(22-8-5) C(2) 410-2-1) - a(10-2-3) + a(11-2-1) - a(l1-2-3) C(3) a(12-3-2) - a(12-3-4) + a(13-3-2) - a(13-3-4) C(4) a(14-4-5) - a(14-4-3) + a(15-4-5) - a(15-4-3) C(6) a(17-6-5) - a(17-6-7) + a(18-6-5) - a(18-6-7) C(7) a(19-7-1) - a(19-7-6) + a(20-7-1) - a(20-7-6) C(8) a(21-8-1) - a(21-8-5) + a(22-8-1) - a(22-8-5) C(1) a(9-1-2) - a(9-1-7) C(5) a(16-5-4) - a(16-5-6) C(l) 2a(9-1-8) - a(9-1-2) - a(9-1-7) C(5) 2a(16-5-8) - a(16-5-4) - a(16-5-6) a(1-8-5) - a(8-5-4) + 45-4-3) - a(4-3-2) + a(3-2-1) - a(2-1-8) 2a(1-8-5) - a(8-5-4) - 45-4-3) + 2a(4-3-2) - a(3-2-1) - a(2-1-8) a(8-5-4) - a(5-4-3) + a(3-2-1) - a(2-1-8) ~(3-2-1-8)- ~(2-1-8-5) ~(1-8-5-4)- ~(8-5-4-3) ~(5-4-3-2)- ~(4-3-2-1) ~ ( 21-8-5) - ~(1-8-5-4)+ ~(5-4-3-2)- ~(4-3-21) 2~(3-2-1-8)- ~(2-1-8-5)- ~(1-8-5-4)+ 2~(8-5-4-3)- ~(5-4-3-2)- ~(4-3-2-1) a(7-1-8) + a(6-5-8) - a(7-1-2) - a(6-5-4) a(7-1-8) - a(6-5-8) - a(7-1-2) a(6-5-4) a(1-7-6) - a(5-6-7)

+

+

+

"For atom numbering see Fig. 1. C-H stretching coordinates nos. 10-23 are omitted. Labels i/p and o/p refer to deformations inplane and out-of-plane with respect to the six-membered ring segment.

Bicyclo[3.2 .l]octane (BCO) There are only four CH2 scissoring modes apparent in the spectrum of BCO. Band 44 is separated from the rest and exhibits strong polarization in the Raman spectrum (Figs. 3 and 9). It clearly corresponds to v,, (Table 13). The remaining three observed bands (41-43) can be assigned to v,,, v,,, and v,, by noting that the last two scissoring modes, v,, and v,,, are predicted with much smaller absorption intensities by comparison. The latter two transitions, not included in the refinement, are predicted to give rise to the strongest Raman lines of all scissoring modes, and are therefore likely to be the principal if not the only significant contributors to band 40 in Fig. 9. The region between 1050 and 1400 cm-' is quite congested. The modes v,, and v,, cannot be found in the spec-

trum. They are both predicted with very low infrared intensities near prominent fundamentals (32 and 26, respectively) and are therefore likely to be completely hidden. There is one unassigned band (25 in Fig. 3) that could be identified with v,,, but the large discrepancy in frequency makes this assignment problematic. Some of the bands in the wagging region (1280-1350 cm-') were assigned, although not with absolute confidence. Band 34 with the lowest frequency and band 37 with the highest intensity were ascribed to v, and v42,respectively. For the three fundamentals predicted between these two, namely v,,, v16, and v,,, there are only two observed absorptions (bands 35 and 36). One plausible assignment is suggested in Table 13. The remaining two bands at the highest frequencies in this region (38 and 39) were included in the refinement by virtue of their

595

EGGIMANN ET AL.


TABLE 9. Definitions of local symmetry coordinates for 8-oxabicyclo[3.2. I]octanea 1 2 3 4 5 6 7 8 9 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

C-C

stretch

C-0

stretch

CH2 scissor

CH2 rock

CH2 twist

CH2 wag

C-H

def. (i/p)

C-H

def. (o/p)

Ring def. (i/p) Ring def. (o/p) Bridge wag Bridge twist Bridge rock

A' A' A" A' A' A" A' A" A

c ( 1)-(c(2) C(2)--C(3) C(3)-C(4) C(4)-C(5) C(5)-C(6) C(6)--c(7) C(7)-C( 1) c (1 C(5)-0(8) C(2) 5a(10-2-11) + a(1-2-3) C(3) Sa(12-3-13) + a(2-3-4) C(4) Sa(14-4- 15) + 43-4-5) C(6) 5a(17-6-18) + a(5-6-7) C(7) 5a(19-7-20) + a(1-7-6) C(2) a(10-2-1) + a(10-2-3) - a(l1-2-1) - a(l1-2-3) C(3) a(12-3-2) + a(12-3-4) - a(13-3-2) - a(13-3-4) C(4) a(14-4-5) + a(14-4-3) - a(15-4-5) - a(15-4-3) C(6) a(17-6-5) + a(17-6-7) - a(18-6-5) - a(18-6-7) C(7) a(19-7-1) + a(19-7-6) - a(20-7-1) - a(20-7-6) C(2) 410-2-1) - a(10-2-3) - a(l1-2- 1) + a(11-2-3) C(3) a(12-3-2) - a(12-3-4) - a(13-3-2) + a(13-3-4) C(4) a(14-4-5) - a(14-4-3) - a(15-4-5) + a(15-4-3) C(6) a(17-6-5) - a(17-6-7) - a(18-6-5) + a(18-6-7) C(7) a(19-7-1) - a(19-7-6) - a(20-7-1) + a(20-7-6) C(2) a(10-2-1) - a(10-2-3) + a(11-2-1) - a(l1-2-3) C(3) a(12-3-2) - a(12-3-4) + a(13-3-2) - a(13-3-4) C(4) a(14-4-5) - a(14-4-3) + a(15-4-5) - a(15-4-3) C(6) a(17-6-5) - a(17-6-7) + a(18-6-5) - a(18-6-7) C(7) a(19-7-1) - a(19-7-6) + a(20-7-1) - a(20-7-6) C ( l ) a(9-1-2) - a(9-1-7) C(5) a(16-5-4) - a(16-5-6) C(l) 2a(9-1-8) - a(9-1-2) - a(9-1-7) C(5) 2a(16-5-8) - a(16-5-4) - a(16-5-6) a(1-8-5) - a(8-5-4) + 45-4-3) - a(4-3-2) + a(3-2-1) - a(2-1-8) 2a(l-8-5) - a(8-5-4) - a(5-4-3) + 2a(4-3-2) - a(3-2-1) - a(2-1-8) a(8-5-4) - a(5-4-3) + a(3-2-1) - a(2-1-8) ~(3-2-1-8)- ~(2-1-8-5)+ ~(1-8-5-4)- ~(8-5-4-3)+ ~(5-4-3-2)- ~(4-3-2-1) ~(2-1-8-5)- ~(1-8-5-4)+ ~(5-4-3-2)- ~(4-3-2-1) 2~(3-2-1-8)- ~(2-1-8-5)- ~(1-8-5-4) 2~(8-5-4-3)- ~(5-4-3-2)- ~(4-3-2-1) a(7-1-8) + a(6-5-8) - a(7-1-2) - a(6-5-4) a(7-1-8) - a(6-5-8) - a(7-1-2) + a(6-5-4) a(1-7-6) - a(5-6-7)

+

"For atom numbering see Fig. 1. C-H stretching coordinates nos. 10-21 are omitted. Labels i/p and o/p refer to deformations inplane and out-of-plane with respect to the six-membered ring segment.

predicted positions and infrared intensities as corresponding to v,, and v,,, respectively, although their ordering may be reversed. Many assignments in the 600-1050 cm-' region were guided by the Raman spectrum, which exhibits intense, strongly polarized lines. The two fundamentals vZ8(A') and v,, (A") were not assigned as there are three observed bands (9-1 1) in the vicinity. The predicted frequencies would suggest bands 10 and 11 as the fundamentals. This is contradicted by the Raman spectrum, which shows both as strongly polarized. Accordingly, band 9 should be assigned to the A" fundamental v,,, while the bands 10 and 11 may possibly result from Fermi resonance involving vZ8 (A'). Although the three bands near 870 cm-' (14-16) were not included in the refinement, a plausible assignment may be suggested. Of the three fundamentals v,,, vZ6,and v,,, the second is predicted to give rise to a polarized Raman line with much greater intensity than the other two, while the first

should have the highest infrared intensity. Accordingly, v26 most likely corresponds to band 15, and bands 16 and 14 to vZ5and v,,, respectively. 8-Oxabicyclo[3.2 .l]octane (80XA) The highest and the lowest frequency CH2 scissoring bands 39 and 35 (Figs. 4, 10) are assigned to v, (A') and v36 (A"), respectively (Table 14). Besides the clear separation from others, band 39 is readily distinguished by the relatively high infrared intensity, and the low Raman depolarization ratio, as predicted for v,. The assignment of band 35 is supported mainly by the pronounced observed and calculated Raman intensities. The remaining three scissoring modes cannot be clearly assigned, but must correspond to bands 36-38. They have therefore not been included in the refinements. Also left unassigned was v,,, as it may correspond either to band 20, in which case the calculated frequency and intensity would be completely wrong, or it may coincide with v,, (band 21). The second alternative is consistent with the

CAN. 1. CHEM. VOL. 71, 1993


TABLE10. Definitions of local symmetry coordinates for 6-oxabicyclo[3.2. l]octanea 1 2 3 4 5 6 7 8 9 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

C-C

stretch

C-0

stretch

C-C

stretch

CH2 scissor

CH, rock

CH2 twist

CH2 wag

C-H

def. (i/p)

C-H

def. (o/p)

Ring def. (i/p) Ring def. (o/p) Bridge wag Bridge twist Bridge rock

C(l)-(c(2) C(2)-C(3) C(3)-C(4) C(4)-C(5) C(5)-0(6) 0(6)-C(7) c(7)-c( 1) C( 1)--C(8) C(5)-C(8) C(2) 5a(10-2-11) + a(1-2-3) C(3) 5a(12-3-13) + a(2-3-4) C(4) 5a(14-4-15) + a(3-4-5) C(7) 5a(17-7-18) + a(1-7-6) C(8) 5a(19-8-20) + a(1-8-5) C(2) a(10-2-1) + a(10-2-3) - a(l1-2-1) - a(11-2-3) C(3) a(12-3-2) + a(12-3-4) - a(13-3-2) - ~(13-3-4) C(4) a(14-4-5) + a(14-4-3) - a(15-4-5) - a(15-4-3) C(7) a(17-7-1) + a(17-7-6) - a(18-7-1) - a(18-7-6) C(8) a(19-8-1) + a(19-8-5) - a(20-8-1) - a(20-8-5) C(2) 410-2-1) - a(10-2-3) - a(l1-2- 1) + a(11-2-3) C(3) a(12-3-2) - a(12-3-4) - a(13-3-2) + a(13-3-4) C(4) a(14-4-5) - a(14-4-3) - a(15-4-5) + a(15-4-3) C(7) a(17-7-1) - a(17-7-6) - a(18-7-1) + a(18-7-6) C(8) a(19-8-1) - a(19-8-5) - a(20-8-1) + a(20-8-5) C(2) a(10-2- 1) - a(10-2-3) + a(l1-2-1) - a(l1-2-3) C(3) a(12-3-2) - a(12-3-4) + a(l3-3-2) - a(13-3-4) C(4) a(14-4-5) - a(14-4-3) + a(15-4-5) - a(15-4-3) C(7) a(17-7-1) - a(17-7-6) + a(18-7-1) - a(18-7-6) C(8) a(19-8- 1) - a(19-8-5) + a(20-8-1) - a(20-8-5) C(1) a(9-1-2) - a(9-1-7) C(5) a(16-5-4) - a(16-5-6) C(l) 2a(9-1-8) - a(9- 1-2) - a(9-1-7) C(5) 2a(16-5-8) - a(16-5-4) - a(16-5-6) a(1-8-5) - a(8-5-4) + a(5-4-3) - a(4-3-2) + a(3-2-1) - a(2-1-8) 2a(1-8-5) - a(8-5-4) - a(5-4-3) + 2a(4-3-2) - a(3-2-1) - a(2-1-8) a(8-5-4) - a(5-4-3) + a(3-2-1) - a(2-1-8) ~(3-2-1-8)- ~(2-1-8-5)+ ~(1-8-5-4)- ~(8-5-4-3)+ ~(5-4-3-2)- ~(4-3-2-1) ~(2-1-8-5)- ~(1-8-5-4)+ ~(5-4-3-2)- ~(4-3-2-1) 2~(3-21-8) - ~ ( 21-8-5) - ~(1-8-5-4)+ 2~(8-5-4-3)- ~(5-4-3-2)- ~(4-3-2-1) u(7-1-8) + a(6-5-8) - a(7-1-2) - a(6-5-4) a(7-1-8) - a(6-5-8) - a(7-1-2) + a(6-5-4) a(1-7-6) - a(5-6-7)

"For atom numbering see Fig. 1. C-H stretching coordinates nos. 10-21 are omitted. Labels i/p and o/p refer to deformations in-plane and out-of-plane with respect to the six-membered ring segment.

Raman spectrum where band 20 has no analog. A similar situation holds for v,, (left unassigned) and v,, both of which likely contribute to band 22 in the infrared and Raman spectra. The ordering of v,, and vd2 (bands 25 and 24, respectively) was reversed based on the absorption intensities and the apparent B-type contour of band 24 (not visible in Fig. 4). In the wagging region, band 30 can be assigned confidently to v,, based on the observed and calculated infrared intensities, while band 33 must correspond to v , , by virtue of the observed and calculated positions. Mode v,, is absent in the absorption spectra, but is observed in the Raman (band 29). The last remaining A' wagging mode, v,,, must correspond to the partially polarized Raman line 32, while the remaining two A" frundamentals, v,, and v,,, cannot be assigned unambiguously. The former may give rise to band 3 1 (in the Raman only), while the latter may be hidden under band 32. Although v2, and v,, are predicted in the wrong order,

their assignment is unambiguous based on the apparent B-type contour of the latter (band 9 in gas phase infrared) and the clearly polarized Raman line 10 corresponding to the former. The location of vd8remains uncertain as evidently it is too weak to be observed in the absorption spectra. The slight asymmetry of Raman band 16 may indicate the presence of v4, there. Band 17 probably contains v,, (A') and v,, (A"), both of which are calculated with equally strong absorption intensities. Moreover, v,, is predicted to give rise to a dominant polarized Raman line, which is consistent with the observed spectrum, justifying inclusion of v,, in the refinement, while v,, was not added to the certain assignments. 6-Oxabicyclo[3.2 .l]octane (60XA) a n d 7, 7-d2-6oxabicyclo[3.2. Iloctane (60XA-d2) The spectra of these two isotopically related molecules are similar in several respects and are therefore discussed

EGGIMANN ET A L


TABLE 1 1. Definitions of local symmetry coordinates for 6,8-dioxabicyclo[3.2. lloctane" 1 2 3 4 5 6 7 8 9 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

C-C

stretch

C-0

stretch

C-C C-0

stretch stretch

CH, scissor

CH2 rock

CH, twist

CH2 wag

C-H

def. (i/p)

C-H

def. (o/p)

Ring def. (i/p) Ring def. (o/p)

c ( 1)-(c(2) C(2)-C(3) C(3)-C(4) C(4)-C(5) C(5)-0(6) 0(6)-C(7) c(7)-c( 1) c ( 1)-0(8) C(5)--0(8) C(2) 5a(10-2-11) + a(1-2-3) C(3) 5a(12-3- 13) + a(2-3-4) C(4) 5a(14-4- 15) + a(3-4-5) C(7) 5a(17-7- 18) + a(1-7-6) C(2) 410-2-1) + a(10-2-3) - a(l1-2-1) - a(l1-2-3) C(3) a(12-3-2) + a(12-3-4) - a(13-3-2) - a(13-3-4) C(4) a(14-4-5) + a(14-4-3) - a(15-4-5) - a(15-4-3) C(7) a(17-7-1) + a(17-7-6) - a(18-7-1) - a(18-7-6) C(2) 410-2-1) - a(10-2-3) - a(l1-2-1) + a(11-2-3) C(3) a(12-3-2) - a(12-3-4) - a(13-3-2) + a(13-3-4) C(4) a(14-4-5) - a(14-4-3) - a(15-4-5) + a(15-4-3) C(7) a(17-7-1) - a(17-7-6) - ~~(18-7-1) + a(18-7-6) C(2) a(10-2- 1) - a(10-2-3) + a(l1-2- 1) - a(ll-2-3) C(3) a(12-3-2) - a(12-3-4) + a(13-3-2) - a(13-3-4) C(4) a(14-4-5) - a(14-4-3) + a(15-4-5) - a(15-4-3) C(7) a(17-7-1) - a(17-7-6) + a(18-7-1) - a(18-7-6) C ( l ) a(9-1-2) - a(9-1-7) C(5) a(16-5-4) - a(16-5-6) C(l) 2a(9-1-8) - a(9-1-2) - a(9-1-7) C(5) 2a(16-5-8) - a(16-5-4) - a(16-5-6) a(1-8-5) - a(8-5-4) + a(5-4-3) - a(4-3-2) + a(3-2-1) - a(2-1-8) 2a(1-8-5) - a(8-5-4) - 45-4-3) + 2a(4-3-2) - a(3-2-1) - a(2-1-8) a(8-5-4) - 45-4-3) + a(3-2-1) - a(2-1-8) ~(3-2-1-8)- ~(2-1-8-5)+ ~(1-8-5-4)- ~(8-5-4-3)+ ~(5-4-3-2)- ~(4-3-2-1) ~(2-1-8-5)- ~(1-8-5-4)+ ~(5-4-3-2)- ~(4-3-21) 2~(3-2-1-8)- ~(2-1-8-5)- ~(1-8-5-4) 2~(8-5-4-3)- ~(5-4-3-2)- ~(4-3-2-1) a(7-1-8) + a(6-5-8) - a(7-1-2) - a(6-5-4) a(7-1-8) - a(6-5-8) - a(7-1-2) + a(6-5-4) a(1-7-6) - a(5-6-7)

+

Bridge wag Bridge twist Bridge rock

"For atom numbering see Fig. 2. C-H stretching coordinates nos. 10-19 are omitted. Labels i/p and o/p refer to deformations in-plane and out-of-plane with respect to the six-membered ring segment.

together. Of the methylene scissoring modes of 60XA, v,, is separated from the rest and must correspond to band 46 (Figs. 5, 11, Table 15). It clearly disappears on deuteration (Figs. 6, 12, Table 16), confirming the assignment to C7 scissoring. Another prominent feature in the congested region is the strong Raman line labelled as 41 and 42 for the two compounds, respectively (Figs. 11 and 12). For 60XA a connection between this band and v,, is readily made with confidence. For the isotopomer, the infrared band is not as neatly separated and therefore was not included in the refinement, although the assignment to v I 6 is nonetheless reasonable by comparison. Since v,, and v I 5 in the two compounds, respectively, also are predicted to exhibit relatively strong Raman lines, they probably contribute significantly to lines 41 and 42, respectively, while being clearly resolved in the absorption spectra and labelled as band 42 in Fig. 5 and band 43 in Fig. 6. The last relatively certain assignment in this region is band 47 in the infrared spectrum of 60XA-d2 (Fig. 6) that we believe must correspond to v,, in this compound. By comparison, the same mode in 60XA, v,,, can probably be associated with band 45 in Fig. 5 . For the last scissoring mode in both

compounds, several choices of observed bands are possible and the fundamental cannot be located unambiguously. The abundance of bands with undistinguished intensities in the region of 1280-1380 cm-' seemingly confuses their assignment. The region contains the CH, wagging and CH bending modes variously coupled. Their predicted intensities are not expected to be very reliable, since small differences in force constants may subtly alter the eigenvectors. Nonetheless, a one-to-one correspondence between predicted and observed band positions exists for both derivatives. The assignment, therefore, of v,,-v2, to bands 40-33, respectively, in 60XA, and vI7-vz3 to bands 41-35 in 60XA-d,, can be made with little hesitation, although for the sake of refining the scale factors only v,,, vz4, and v2, in 60XA, and v,, and v2,-v2, in 60XA-d2, were included as firm. For v , ~of 60XA, the predicted position and intensities provided reasonable grounds for association with band 22. The predicted intensities for v3,-v,, appeared unreasonably different from those of bands 24-27 to which presumably these modes should correspond. They were therefore not

C A N . J. CHEM. VOL. 71, 1993

TABLE12. Sets of force field scale factors


Nos."

Local symmetry coordinate"

Transferred factorsC

C-C stretch 0.907 C-H stretch 0.82 C-0 stretch 0.845 CH, scissor 0.78 CH, rock 0.81 CH? wag 0.776 CH2 twist 0.768 C-H bend i/p 0.78 C-H bend o/p 0.773 Ring bend 0.812 Ring torsion 0.989 CH, wag (C7)' 0.802 CH, twist (C7)' 0.797 C-H bendf 0.822 All coordinates (uniform scalirzg)

Refined factorsd

(uncertainties)

0.925 [O.821 0.838 0.771 0.802 0.763 0.765 0.784 0.799 0.886 0.853 0.802 0.768 0.814 0.827

(07) (not refined) (13) (05) (10) (09) (08) (25) (30) (06) (06) (26) (25) (1 1) (03)

"Numbers as used in text. bDefinitions of coordinates are found in Tables 8-1 1 'As described in text. dFollowing the procedure explained in text. 'When adjacent to oxygen. 'If oxygen atom is in plane of bend.

TABLE13. Assignments and calculated vibrational wavenumbers (cm-') and intensities for bicyclo[3.2. lloctane Calculated (3-2 1G) Observed

v

Band position"

Wavenumbers' Band nos.b

1481.2 1464.2 1460.2

44 43 42

1441.0 (R)

40

1360.6

39

1329.7 1319.6

36 35

1259.9 1211.3 1167.0 1102.5 1044.1 1006.5 979.6 892.3

32 30 28 26 23 21 20 17

876.3 872.9

16 15

812.4

13

755.0

10

709.4 525.0

8 7

(1)

(2)

Raman

(3)

Dipole Intenstrengths\itiesr

Approximate PEDs"

0.72 0.46 0.03 0.34 0.58 0.28 0.32 0.40 0.26 0.32 0.71 0.73 0.75 0.69 0.70 0.68 0.73 0.73 0.75 0.67 0.61 0.70 0.63 0.56 0.72 0.11 0.04 0.05 0.12 0.69

0.5 C6/C7 sci + 0.3 C3 sci 0.5 C3 sci + 0.3 C8 sci 0.5 C6/C7 sci + 0.4 C2/C4 sci 0.6 C8 sci + 0.3 C2/C4 sci 0.3 C2/C4 wag 0.3 CH bend o/p 0.2 CH bend o/p + 0.2 CH bend i/p 0.4 C2/C4 wag 0.3 C-C str. (1+4) 0.2 C6/C7 wag 0.6 C2/C4 twist 0.2 C-C str. (5+7) 0.5 C6/C7 wag 0.1 CH bend o/p 0.5 C6/C7 twist 0.2 C2/C4 rock + 0.2 CH bend i/p 0.3 ring def. i/p (52) + 0.1 C-C str. (1+4) 0.2 C6/C7 twist + 0.1 C8 rock 0.2 C-C str. (6) + 0.2 C3 rock 0.3 C8 rock + 0.2 C-C str. (5+7) 0.5 C-C str. (8+9) + 0.2 C-C str. (6) 0.4 C-C str. (6) + 0.2 C-C str. (5+7) 0.4 C-C str. (2+3) + 0.2 C6/C7 rock 0.6C6/C7rock + 0.1 C-Cstr. (1+4) 0 . 3 C 3 r o c k + 0.2C2/C4rock 0.5 ring def. i/p (53) + 0.3 ring def. i/p (52)

+

+ + + +

599

EGGIMANN ET AL.

TABLE 13 (concluded) Calculated (3-2 1G) Observed

v 31 32 33

Band position"

Wavenumbers' Band nos.'

(1)

(2)

Raman

(3)

Dipole strengths"

358.1 262.5

Intensities'

p1

Approximate PEDs"

0.2 0.6 0.1

0.70 0.34 0.43

0.7 ring def. o/p (55) + 0.3 ring def. i/p (53) 0.7 bridge wag (58) + 0.2 ring def. i/p (53) 2.0 ring def. o/p (56) + 0.8 ring def. o/p (55)

77.9 14.1 63.1 31.1 37.5 2.4 31.6 0.0 0.3 3.8 1.7 0.2 2.8 25.2 2.2 10.7 2.1 6.4 8.4 1.8 0.7 0.5 0.4 2.4 1.1 0.1 0.1

0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75

0.6 0.6 0.3 0.5 0.3 0.3 0.5 0.3 0.5 0.2 0.3 0.3 0.4 0.2 0.4 0.5 0.7 0.4 0.5 0.7 0.7 0.6


A" 34 35 36 37 38 39 1453.8 40 1441.0 ( R ) 41 1355.5 42 1344.3 43 44 1305.2 45 1284.4 46 47 1243.9 48 1188.7 49 1143.9 (sol) 50 51 1050.4 52 1026.9 53 963.4 54 938.0 (R) 55 863.8 (sol) 56 795.0 57 726.3 58 59 332.0 60 195.0 Average error of calculations

C6/C7 sci + 0.4 C2/C4 sci C2/C4 sci + 0.4 C6/C7 sci C3 wag + 0.3 CH bend i/p C2/C4 wag + 0.1 C3 wag C3 wag + 0.1 CH bend o/p C6/C7 wag + 0.2 C8 wag C6/C7 wag + 0.2 CH bend o/p C-C str. (8-9) + 0.2 C2/C4 twist C6/C7 twist + 0.2 C3 twist C6/C7 twist + 0.2 C6/C7 rock CH bend i/p + 0.2 C8 twist CH bend o/p + 0.2 C2/C4 wag C-C str. (2-3) + 0.3 C8 twist C2/C4 twist + 0.2 C6/C7 rock C6/C7 rock + 0.3 C-C str. (8-9) C-C str. (5-7) + 0.2 C-C str. (1-4) C2/C4 rock + 0.1 bridge rock (60) C-C str. (1-4) + 0.2 C-C str. (5-7) bridge rock (60) + 0.2 C-C str. (8-9) ring def. i/p (54) + 0.4 bridge twist (59) bridge twist (59) + 0.4 ring def. o/p (57) ring def. o/p (57) + 0.1 bridge twist (59)

"Measured from vapour phase absorption unless designated sol (absorption of solution) or R (Raman). 'As listed in Table 1 and Figs. 3 and 9. 'Calculated with uniformly scaled force field (I), transferred scale factors (2), and fully refined scale factors (3); see text. "In units of lo-" esu' cm', from fully refined force field. 'ST, (eq. [3] in text) in units of A' amu-', from fully refined force field. lDepolarization ratios p, Ceq. [6] in text), from fully refined force field. fiMost important contributors to potential energy distribution (PED) of the normal modes. Numbers in parentheses refer to coordinate definitions in Table 8.

TABLE14. Assignments and calculated vibrational wavenumbers (cm-I) and intensities for oxabicyclo[3.2.~]octane Calculated (3-2 1G) Observed

v

Band position"

Wavenumbers' Peak nos."

(1)

(2)

Raman

(3)

Dipole strengthsd

Intensities'

p1

Approximate PEDs8

600

C A N . J . C H E M . VOL. 71, 1993

TABLE14 (concluded) Calculated (3-2 1G) Observed


v

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

Band position"

Wavenumbers' Peak nos.h

1478.6

39

1361.0 1347.1 1327.3 1257.2 1231.9

33 32 30 26 25

1049.8 990.5 951.5 886.9 877.2 832.7 777.5 724.0 566.0 443.5 368.3 263.9

19 17 16 15 14 12 10 8 7 5 4 2

Raman

(1)

(2)

(3)

Dipole strengths"

Intensities'

2917.3 1527.6 1509.7 1498.2 1395.5 1371.6 1345.2 1287.2 1248.0 1199.0 1092.3 1052.9 963.7 936.2 857.7 846.9 804.5 752.9 703.0 545.2 420.9 356.5 261.5

2904.7 1483.4 1466.4 1455.1 1367.8 1350.6 1320.2 1254.9 1233.2 1169.4 1097.8 1055.0 981.7 948.4 873.8 865.1 816.9 770.7 723.0 550.2 434.3 355.1 282.9

2904.8 1475.2 1458.4 1447.5 1363.6 1341.8 1322.8 1252.0 1220.9 1168.0 1090.8 1065.7 991.1 957.3 879.5 865.1 819.9 770.9 720.3 553.6 430.6 367.6 265.7

7.93 33.50 16.16 10.92 2.23 4.59 48.81 22.96 30.72 9.64 28.24 14.23 21.98 36.73 21.56 101.97 12.07 20.19 42.36 20.18 115.17 24.65 14.45

59.7 2.2 17.0 10.8 1.6 0.7 1.2 16.0 5.5 10.8 4.4 4.2 17.5 4.6 9.6 0.8 20.0 6.3 5.4 0.6 0.4 0.7 0. I

0.51 0.34 0.75 0.70 0.50 0.48 0.63 0.74 0.74 0.75 0.74 0.46 0.69 0.59 0.19 0.75 0.04 0.08 0.15 0.50 0.68 0.24 0.11

0.5 C6/C7 sci + 0.5 C3 sci 0.5 C6/C7 sci + 0.5 C3 sci 1.0 C2/C4 sci + 0.1 C3 sci 0.5 CH bend o/p + 0.2 C2/C4 wag 0.3 CH bend i/p + 0.3 C2/C4 wag 0.4 C2/C4 wag + 0.3 C-C str. ( l + 4 ) 0.6 C2/C4 twist + 0.2 C6/C7 wag 0.6 C6/C7 wag + 0.1 C-C str. (5+7) 0.5 C6/C7 twist + 0.1 CH bend o/p 0.2 C2/C4 rock + 0.2 ring def. o/p (49) 0.3 ring def. i/p (46) + 0.2 C2/C4 rock 0.3 C-C str. (1+4) + 0.2 C-C str. (6) 0.3 C-C str. (6) + 0.2 C3 rock 0.3 C-C str. (6) + 0.3 C-C str. (5+7) 0.6 C-0 str. 0.2 C-C str. (2+3) 0.4 C-C str. (2+3) 0.2 C6/C7 rock 0.5 C6/C7 rock + 0.1 C-C str. (1+4) 0.2 C3 rock + 0.2 C-C str. (5+7) 0.4 ring def. i/p (46) + 0.2 bridge wag 0.7 Ring def. i/p (47) + 0.6 ring def. o/p (49) 0.7 bridge wag + 0.2 ring def. o/p (50) 1.8 ring def. o/p (50) + 0.8 ring def. o/p (49)

2990.8 2976.9 2958.3 2943.9 2920.7 1499.2 1488.0 1382.5 1381.3 1348.8 1338.1 1285.7 1264.0 1205.8 1201.2 1088.9 1043.0 994.9 928.2 864.8 775.7 754.7 459.3 319.4 166.5

2977.9 2964.1 2945.4 2931.2 2908.1 1456.1 1445.0 1347.8 1342.0 131 1.4 1305.3 1274.7 1226.3 1183.3 1174.5 1096.8 1044.8 997.1 956.8 859.3 798.1 760.4 456.6 326.1 175.3

2978.0 2964.0 2945.5 2931.4 2908.1 1448.3 1437.4 1346.0 1333.3 1309.1 1296.2 1271.0 1224.8 1186.8 1173.4 1100.3 1046.5 996.9 962.3 859.3 805.0 780.4 473.9 326.8 170.2

75.58 17.99 12.93 21.37 58.05 9.71 7.74 3.92 2.55 0.52 11.23 1.23 9.57 7.14 48.31 53.39 157.65 22.1 1 0.18 2.49 5.99 8.62 0.60 4.14 2.03

108.9 16.2 44.2 24.8 37.5 5.7 27.7 0.9 0.9 10.1 1.4 1.2 14.0 5.1 2.9 2.8 8.2 0.6 2.2 1.6 0.1 3.8 2.6 0.0 0.0

0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75

0.9 C6/C7 sci + 0.1 C2/C4 sci 0.9 C2/C4 sci + 0.1 C6/C7 sci 0.4 CH bend i/p + 0.3 C3 wag 0.6 C2/C4 wag + 0.2 C3 wag 0.2 C3 wag + 0.2 CH bend i/p 0.9 C6/C7 wag 0.1 C-C str. (5-7) 0.6 CH bend o/p 0.1 C-C str. (5-7) 0.7 C6/C7 twist + 0.1 C3 twist 0.2 C3 twist + 0.2 C-C str. (2-3) 0.4 C2/C4 twist + 0.1 C-0 str. 0.2 C-C str. (1-4) + 0.2 C-0 str. 0.4 C-0 str. + 0.2 C2/C4 twist 0.4 C6/C7 rock + 0.1 C-C str. (2-3) 0.5 C-C str. (5-7) + 0.2 C-C str. (2-3) 0.7 C2/C4 rock + 0.2 bridge rock 0.4 C-C str. (1-4) + 0.2 C-C str. (5-7) 0.4 bridge rock + 0.1 C-0 str. 0.7 ring def. i/p (48) + 0.3 bridge twist 0.7 bridge twist + 0.4 ring def. o/p (51) 0.6 ring def. o/p (51) + 0.2 bridge twist

7.5 (1.3%)

7.0 (1 .O%)

Approximate PEDsP

+

+

A" 30 31 32 33 34 35 36 1444.5 37 38 39 1312.0 (R) 40 1297.6 41 1275.2 42 1223.7 43 1192.6 44 1162.4 45 1084.6 46 1032.6 990.5 47 48 856.0(R) 49 50 803.7 763.2 51 470.8 52 332.2 53 184.0 (R) 54 Average error of calculations

35

29 28 27 24 23 22 21 18 17

13 11 9 6 3 1

-3 3 .-

3

(2.6%)

+ +

"Measured from vapour phase absorption unless designated R (Raman). bAs listed in Table 2 and Figs. 4 and 10. 'Calculated with uniformly scaled force field (I), transferred scale factors (2), and fully refined scale factors (3); see text. esuZ cm" from fully refined force field. "In units of 'ST, (eq. [3] in text) in units of A.' amu-', from fully refined force field. '~epolarization ratios p, (eq. [6] in text), from fully refined force field. gMost important contributors to potential energy distribution (PED) of the normal modes. Numbers in parentheses refer to coordinate definitions in Table 9.

60 1

EGGIMANN ET AL.

TABLE 15. Assignments and calculated vibrational wavenumbers (cm-') and intensities for 6-oxabicyclo[3.2. lloctane Calculated (3-2 1G) Observed


v

Band position"

I 2 3 4 5 6 7 8 9 10 11 12 13 1492.9 14 1466.0 15 16 1450.0 17 1442.8 18 1364.6 19 1355.7(sol) 20 1348.0 (sol) 21 1336.1 22 1323.7 23 1319.8 24 1303.9 25 1288.5 26 1267.6 27 1236.0 28 1224.0 29 1172.6 30 1160.1 31 1102.5 32 1109.9 33 1085.8 34 35 1056.5 36 1015.2 993.5 37 38 942.6 933.8 39 905.5 40 882.8 41 885.8 42 852.5 43 814.1 44 796.7 45 743.2 46 719.7 47 551.3 48 467.7 49 426.0 (R) 50 51 363.6 338.3 52 249.5 53 54 198.8 Average error of calculatio~zs

Wavenumbers' Peak nos.h

46 45 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 26 27 24

22 20 19 17 16 15 13 14 12 11 10 9 8 7 6 5 4 3 2 1

Rarnan

(I)

(2)

(3)

2990.0 2988.6 2983.4 2977.4 2969.6 2953.6 2937.4 2935.9 2932.6 2932.2 2917.6 2906.1 1542.7 1516.6 1510.7 1500.1 1494.1 1389.1 1387.9 1383.2 1371.6 1355.2 1336.2 1330.7 1306.7 1283.6 1262.7 1238.6 1184.9 1175.8 1138.8 1125.0 1086.4 1062.1 1026.5 1013.0 988.4 948.0 910.7 902.2 883.6 849.1 838.4 782.3 756.2 728.5 707.6 543.2 461.0 421.6 356.8 331.0 248.9 191.8 17.6 (1.9%)

2977.2 2975.9 2970.4 2964.5 2956.9 2940.8 2924.8 2923.2 2919.9 2919.6 2905.0 2893.6 1498.4 1473.0 1467.3 1456.9 1451.4 1367.9 1354.9 1351.2 1336.9 1320.5 1311.6 1301.6 1288.1 1258.2 1234.6 1216.5 1164.2 1153.6 1130.1 1102.3 1082.0 1059.6 1045.6 1019.7 996.8 957.8 929.3 914.9 884.2 873.4 845.0 812.9 786.4 733.0 715.1 541.6 460.9 438.2 353.9 336.2 270.2 203.5 6.9 (1.2%)

2977.2 2976.0 2970.5 2964.6 2956.8 2940.9 2924.8 2923.3 2920.1 2919.7 2905.1 2893.6 1490.8 1464.8 1459.4 1449.1 1443.8 1361.8 1358.1 1347.3 1330.7 1319.3 1316.5 1299.5 1286.0 1266.3 1233.4 1217.5 1157.8 1143.1 1119.4 1103.5 1086.0 1077.2 1051.8 1025.1 1000.0 959.8 933.3 911.6 886.3 879.0 843.8 817.9 793.7 750.3 719.6 555.3 474.9 428.6 367.8 340.2 252.7 195.9 4.9 (0.65%)

Dipole strengths"

Intensitles'

pJ

41.44 64.31 61.01 24.58 75.01 29.81 65.09 4.32 115.73 20.99 29.03 37.87 0.17 11.53 37.68 9.52 6.22 5.06 6.38 7.39 5.49 1.76 10.71 4.70 21.19 15.54 14.75 12.57 21.89 25.92 149.71 2.43 45.69 41.35 8.25 34.56 119.96 7.31 36.59 48.38 26.07 10.66 36.07 15.32 12.39 41.68 1.78 6.17 19.15 1.90 8.88 61.33 3.59 156.43

60.9 173.6 92.4 28.6 108.2 75.1 64.8 196.1 18.3 77.1 50.9 63.3 10.7 8.0 4.5 17.7 24.0 2.7 2.0 0.5 0.7 2.9 3.3 2.1 1.4 2.6 19.0 16.2 11.8 8.7 3.0 2.4 8.4 2.2 9.7 7.8 11.9 2.8 3.2 1.4 2.5 5.9 3.2 10.4 16.2 2.0 3.7 1.8 1.1 0.2 0.7 0.1 0.2 0.2

0.49 0.16 0.68 0.70 0.17 0.66 0.36 0.23 0.65 0.34 0.51 0.31 0.58 0.67 0.73 0.75 0.75 0.66 0.74 0.74 0.75 0.73 0.70 0.74 0.75 0.73 0.71 0.75 0.75 0.75 0.60 0.74 0.73 0.42 0.75 0.70 0.63 0.60 0.74 0.75 0.57 0.13 0.49 0.09 0.05 0.69 0.08 0.67 0.74 0.35 0.50 0.70 0.43 0.71

Approximate PEDs4

C7 sci 0.6 C3 sci + 0.2 C4 sci 0.4 C3 sci + 0.3 C8 sci 0.6 C2 sci + 0.2 C4 sci 0.5 C4 sci + 0.4 C8 sci 0.5 C5 CH bend i/p + 0.2 C7 wag 0.4 C7 wag + 0.2 C5 CH bend o/p 0.3 C1 CH bend i/p + 0.3 C3 wag 0.4 C2 wag + 0.2 C4 wag 0.2 C1 CH bend o/p + 0.2 C3 wag 0.3 C4 wag + 0.2 C-C str. (4) 0.3 C8 wag + 0.1 C2 wag 0.3 C7 wag + 0.2 C5 CH bend i/p 0.2 C-C str. (8) + 0.1 C-C str. (9) 0.3 C4 twist + 0.2 C2 twist 0.3 C3 twist + 0.2 C7 twist 0.2 C8 twist + 0.1 C5 CH bend i/p 0.5 C7 twist + 0.1 C7 rock 0.2 ring def. o/p (49) + 0.1 C-0 str. (5) 0.2 C1 CH bend o/p + 0.2 C3 wag 0.2 C7 rock + 0.1 bridge wag 0.4 ring def. i/p (46) + 0.1 C8 rock 0.2 C-C str. (2) + 0.2 C-C str. (3) 0.2 C-C str. (9) + 0.1 C2 twist 0.3 C-0 str. (6) + 0.2 C-C str. (8) 0.2 C7 rock + 0.2 C-C str. (7) 0.2 C-C str. (7) + 0.2 C7 rock 0.3 C8 rock + 0.2 C-0 str. (6) 0.2 C-0 str. (5) + 0.1 C2 rock 0.2 C-C str. (8) + 0.1 C3 rock 0.2 C-0 str. (6) + 0.2 C4 rock 0.3 C-C str. (4) + 0.3 C-C str. (3) 0.3 C-C str. (1) + 0.3 C-C str. (2) 0.5 bridgerock+ 0.1 C-Cstr. (9) 0.3 C3 rock + 0.1 C2 rock 0.5 ring def. i/p (47) + 0.3 bridge wag 0.5 ring def. i/p (48) + 0.4 bridge twist 0.7 ring def. o/p (49) + 0.3 ring def. i/p (47) 0.6 bridge wag + 0.2 ring def. i/p (47) 0.5 bridge twist + 0.3 ring def. o/p (51) 2.2 ring def. o/p (50) + 1.0 ring def. o/p (49) 0.7 ring def. o/p (51) + 0.1 bridge twist

"Measured from vapour phase absorption unless designated R (Raman). b ~ listed s in Table 3 and Figs. 5 and 1 1 . 'Calculated with uniformly scaled force field ( I ) , transferred scale factors (2). and fully refined scale factors (3); see text. esu' cm', from fully refined force field. "In units of amu-', from fully refined force field. 'ST, (eq. [3] in text) in units of 'Depolarization ratios p, (eq. [6] in text), from fully refined force field. M o s t important contributors to potential energy distribution (PED) of the normal modes. Numbers in parentheses refer to coordinate definitions in Table 10.

602


TABLE 16. Assignments and calculated vibrational wavenumbers (cm-') and intensities for 7,7-d2-6-oxabicyclo[3.2. lloctane Calculated (3-2 1G) Wavenumbers'

Observed


v

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

Band position"

Dipole strengths"

Intensities' 53.8 162.6 49.4 99.5 75.3 59.3 155.6 64.6 50.6 64.5 34.7 50.2 5.6 5.4

1448.7 1442 7

1362.7 1354.6 (sol) 1338.4 1327.3

1319.7 1308.2 1293.4 1266.2 1238.5 1202.9 1168.8 1129.3 1110.7 1104.7 1077.5 1064.7 1049.1 1041.5 997.6 (sol) 988.3 900.8 904.9

887.1 876.1 860.0 860.0

811.7 804.7 45 746.3 46 726.8 47 715.3 48 549.7 49 455.6 50 423.0 (R) 51 353.6 52 320.1 53 245.5 54 184.5 Average error of calculations 44

Peak nos."

Raman

Approximate PEDs" 0.55 0.19 0.67 0.25 0.66 0.40 0.22 0.37 0.52 0.31 0.75 0.15 0.53 0.73

0.5 C3 sci + 0.2 C2 sci 0.5 C3 sci + 0.3 C8 sci 0.6 C2 sci + 0.2 C4 sci 0.6 C4 sci + 0.4 C8 sci 0.2 C5 CH bend o/p 0.4 C5 CH bend i/p 0.3 C3 wag + 0.2 C1 CH bend i/p 0.3 C2 wag + 0.3 C4 wag 0.3 C5 CH bend o/p + 0.1 C4 twist 0.2 C1 CH bend o/p + 0.2 C3 wag 0.2 C4 wag + 0.2 C1 CH bend i/p 0.4 C8 wag + 0.2 C3 twist 0.2 C-C str. (8) + 0.1 C2 twist 0.3 C4 twist + 0.2 C2 twist 0.2 C8 twist + 0.2 C3 twist 0.2 C3 twist + 0.2 C1 CH bend i/p 0.3 C-C str. (7) + 0.2 C7 wag 0.5 C7 sci + 0.1 ring def. o/p (49) 0.2 C1 CH bend o/p + 0.2 C3 wag 0.2 ring def. i/p (46) + 0.1 C2 rock 0.2 ring def. i/p (46) + 0.1 C8 rock 0.3 C8 twist + 0.2 C-C str. (3) 0.2 C7 wag + 0.2 C-0 str. (5) 0.2 C-C str. (9) + 0.1 C8 wag 0.2 C-0 str. (6) + 0.2 C3 rock 0.2 C-0 str. (6) 0.3 C8 rock 0.1 C7 wag + 0.1 C-C str. (1) 0.2 C-C str. (8) + 0.1 C-C str. (2) 0.1 C-C str. (9) 0.2 C4 rock 0.2 C7 rock + 0.2 C-0 str. (6) 0.4 C7 twist + 0.3 C7 rock 0.3 C-C str. (3) + 0.2 C-C str. (4) 0.2 C7 twist + 0.2 C2 rock 0.2 C-C str. (1) + 0.1 C7 rock 0.5 bridge rock + 0.1 C-C str. (8) 0.3 C3 rock + 0.1 C-C str. (1) 0.4 ring def. i/p (47) + 0.2 bridge wag 0.5 ring def. i/p (48) + 0.3 bridge twist 0.7 ring def. o/p (49) + 0.3 ring def. i/p (47) 0.6 bridge wag + 0.1 ring def. i/p (47) 0.5 bridge twist + 0.4 ring def. o/p (51) 2.1 ring def. o/p (50) + 1.0 ring def. o/p (49) 0.6 ring def. o/p (51) + 0.1 bridge twist

+

+

+

"Measured from vapour phase absorption unless designated sol (absorption of solution) or R (Raman). bAs listed in Table 4 and Figs. 6 and 12. 'Calculated with uniformly scaled force field (I), transferred scale factors (2). and fully refined scale factors (3); see text. units of lo-* esu2 cmZ,from fully refined force field. 'ST (eq. [3] in text) in units of A4 amu-', from fully refined force field. 'Depolarization ratios p i (eq. [6] in text), from fully refined force field. SMost important contributors to potential energy distribution (PED) of the normal modes. Numbers in parentheses refer to coordinate definitions in Table 10.

603

EGGIMANN ET AL.

TABLE17. Assignments and calculated vibrational wavenumbers (cm-I) and intensities for 6,8-dioxabicyclo[3.2. lloctane Calculated (3-21G) Observed


v

Band position"

1 2 3 4 5 6 7 8 9 10 11 1488.5 12 1462.7 13 1442.7 14 15 1364.7 16 1352.3 17 1343.7 18 1340.4 19 1333.5 20 1320.7 21 1310.5 22 1276.6 23 1242.7 24 1190.1 25 1158.9 26 1129.1 27 1118.6(sol) 28 1092.5 29 1076.7 30 1030.3 31 1035.0 32 1000.4 33 962.5 34 942.0 35 896.8 36 886.4 37 858.9 38 833.5 39 808.8 40 779.8 41 746.5 42 610.0 43 506.4 44 445.2 45 372.8 46 338.6 47 252.3 48 188.2 Average error of calculations

Wavenumbers' Peak nos."

43 41 40 37 35 34 33 32 31 30 29 28 26 24 23 22 21 20 18 19 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

(1)

(2)

Raman

(3)

Dipole strengths"

Intensities' 156.7 109.1 66.5 38.3 57.2 109.3 72.7 158.2 43.7 65.7 9.6 10.8 11.7 19.0 2.4 2.2 0.9 0.8 2.1 10.5 1.7 2.0 19.1 8.4 4.4 7.1 .5.9 6.1 6.3 3.5 7.7 11.7 3.5 4.1 7.0 0.9 1.7 11.1 16.1 2.1 3.6 1.8 2.3 0.3 0.5 0.2 0.1 0.3

Approximate PEDss 0.17 0.45 0.48 0.75 0.71 0.37 0.37 0.07 0.75 0.36 0.64 0.74 0.72 0.75 0.66 0.74 0.73 0.74 0.52 0.75 0.64 0.66 0.74 0.75 0.75 0.72 0.69 0.66 0.75 0.56 0.72 0.60 0.72 0.75 0.31 0.39 0.72 0.14 0.05 0.73 0.19 0.52 0.75 0.75 0.40 0.40 0.20 0.60

C7 sci C3 sci 0.6 C2 sci + 0.3 C4 sci 0.6 C4 sci + 0.4 C2 sci 0.3 C5 CH bend i/p + 0.3 C5 CH bend o/p 0.4 C7 wag + 0.2 C5 CH bend i/p 0.3 C1 CH bend i/p + 0.3 C3 wag 0.4 C2 + wag 0.2 C4 wag 0.3 C4 wag + 0.1 C2 wag 0.3 C3 wag + 0.2 C3 twist 0.4 C7 wag + 0.2 C-C str. (7) 0.3 C5 CH bend o/p + 0.3 C1 CH bend o/p 0.3 C4 twist + 0.2 C2 twist 0.3 C3 twist + 0.2 C7 twist 0.2 C2 twist + 0.2 C4 twist 0.3 C7 twist + 0.1 C1 CH bend i/p 0.2 C-0 str. (5) + 0.1 C4 twist 0.2 C4 rock + 0.2 ring def. o/p (43) 0.2 C-C str. (1) + 0.1 C-C str. (2) 0.3 ring def. i/p (40) + 0.1 C7 rock 0.2 C-0 str. (8) + 0.2 C-0 str. (9) 0.5 C-0 str. (6) + 0.1 C-0 str. ( 5 ) 0.3 C-C str. (7) + 0.2 C7 rock 0.2 C-C str. (2) + 0.1 C-0 str. (5) 0.2 C-C str. (5) + 0.2 C3 rock 0.3 C-0 str. (8) + 0.2 C-0 str. (9) 0.3 C-0 str. (9) 0.2 C4 rock 0.3 C-C str. (3) + 0.2 C-C str. (4) 0.3 C-C str. (2) + 0.3 C-C str. (1) 0.5 bridge rock + 0.1 C-0 str. (8) 0.2 C3 rock + 0.1 C-0 str. (5) 0.2 bridge wag + 0.2 ring def. i/p (40) 0.4 ring def. i/p (42) + 0.3 bridge twist 0.8 ring def. i/p (41) + 0.5 ring def. o/p (43) 0.6 bridge wag + 0.2 ring def. o/p (44) 0.7 bridge twist + 0.3 ring def. o/p (45) 2.0 ring def. o/p (44) + 0.9 ring def. o/p (43) 0.7 ring def. o/p (45) + 0.1 bridge twist

+

"Measured from vapour phase absorption unless designated sol (absorption of solution). bAs listed in Table 5 and Figs. 7 and 13. Talculated with uniformly scaled force field (1). transferred scale factors (2), and fully refined scale factors (3); see text. units of 10-j0 esu2 cm2, from fully refined force field. 'ST, (eq. [3] in text) in units of A4 amu-', from fully refined force field. 'Depolarization ratios p, (eq. [6] in text), from fully refined force field. RMostimportant contributors to potential energy distribution (PED) of the normal modes. Numbers in parentheses refer to coordinate definitions in Table 11.

604


TABLE 18. Assignments and calculated vibrational wavenumbers (cm-') and intensities for 7,7-dz-6,8-dioxabicyclo[3.2. ]]octane Calculated (3-2 1G) Observed

u


...

.

.

Band position"

1 2 3 4 5 6 7 8 9 10 11 1466.4 12 1441.9 13 1436.8 14 1365.9 15 1345.6 16 1336.5 17 1323.2 18 1319.4 19 1315.5 20 1280.5 21 1242.7 22 1202.0 23 1163.5 24 1137.2 25 1122.8 26 1098.1 (sol) 27 1079.4 28 1056.4 29 1026.8 30 1016.1 31 987.1 913.6 32 33 897.3 888.6 34 879.8 35 870.1 36 37 830.1 805.0 38 39 764.4 755.9 40 41 729.1 42 605.8 43 489.4 443.6 44 45 369.0 (R) 46 325.0 (R) 47 246.0 (R) 48 180.0 (R) Average error of calcularior~s

Wavenumbers" Peak nos.b

42 40 39 37 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

Raman

(1)

(2)

(3)

3023.3 3012.3 2989.2 2973.9 2958.8 2945.3 2936.5 2923.3 2238.6 2151.5 1516.9 1495.9 1487.3 1397.5 1386.1 1380.8 1362.7 1341.9 1328.0 1286.4 1271.0 1210.3 1197.6 1148.7 1124.1 1102.2 1091.4 1045.4 1032.8 1001.0 979.1 899.7 887.2 871.8 859.7 851.7 803.6 789.7 748.1 737.1 705.3 587.7 474.6 426.6 350.4 313.1 253.6 171.9 20.4 (2.3%)

3019.2 2999.4 2976.3 2960.9 2946.0 2932.7 2923.9 2910.7 2228.8 2142.7 1473.2 1452.9 1444.6 1379.3 1352.0 1349.9 1342.9 1319.6 1308.0 1276.6 1244.3 1189.1 1174.1 1145.2 1125.0 1 1 11.2 1089.3 1051.4 1036.6 1007.8 983.5 907.4 891.8 876.7 860.0 854.6 818.6 803.0 762.8 736.2 723.7 589.9 474.6 438.6 349.8 320.6 273.2 181.2 9.0

3019.4 2999.5 2976.3 2961 .O 2946.1 2932.8 2923.9 2910.7 2229.1 2143.4 1465.0 1445.2 1436.8 1372.2 1347.5 1341.5 1334.1 1316.9 1307.9 1272.3 1240.3 1191.8 1172.4 1141.0 1126.8 1108.3 1088.0 1052.6 1037.5 1027.7 984.2 910.9 890.8 875.6 859.4 848.3 823.5 803.4 762.8 749.6 722.2 599.7 486.7 437.0 360.6 320.1 257.7 175.6 5.8 (0.82%)

(1.3%)

Dipole strengths"

Intensities'

59.58 41.58 53.44 14.43 17.72 39.47 33.62 28.93 34.96 54.09 24.91 11.42 12.42 37.72 8.12 15.34 7.28 65.27 6.29 4.99 12.60 45.28 117.04 164.27 130.96 36.20 39.14 27.73 193.28 98.59 226.65 20.63 1.89 74.86 84.03 38.12 1.83 54.47 25.26 53.92 14.46 48.31 3.44 126.33 105.16 8.80 0.79 142.39

150.1 97.6 43.4 60.9 77.8 166.5 44.8 67.9 32.6 49.1 8.4 12.4 17.9 3.2 0.7 1.3 0.7 3.0 11.3 1.4 18.3 6.4 1.8 3.0 3.3 2.4 6.9 3.7 9.6 7.3 7.9 4.4 1.3 2.2 6.6 4.1 22.8 3.4 4.3 0.9 6.8 2.0 2.3 0.3 0.2 0.1 0.2 0.2

Approximate PEDs" 0.20 0.37 0.75 0.70 0.71 0.07 0.74 0.35 0.74 0.15 0.71 0.72 0.75 0.67 0.74 0.57 0.75 0.72 0.75 0.51 0.74 0.75 0.73 0.45 0.69 0.72 0.65 0.74 0.75 0.70 0.64 0.75 0.72 0.26 0.50 0.61 0.06 0.75 0.49 0.48 0.17 0.55 0.72 0.75 0.43 0.37 0.20 0.54

C3 sci 0.6 C2 sci + 0.3 C4 sci 0.7 C4 sci + 0.4 C2 sci 0.4C5CHbendi/p+ 0.3C5CHbendo/p 0.3 C3 wag + 0.2 C1 CH bend i/p 0.2 C5 CH bend o/p 0.2 C4 wag 0.3 C2 wag + 0.3 C4 wag 0.2 C4 wag 0.2 C2 wag 0.3 C1 CH bend i/p + 0.3 C3 twist 0.4 C1 CH bend o/p + 0.3 C5 CH bend o/p 0.4 C4 twist + 0.2 C2 twist 0.2 C3 twist + 0.1 C-C str. (2) 0.2 C3 twist + 0.1 C4 twist 0.1 C-0 str. (5) + 0.1 C2 twist 0.2 C7 wag + 0.2 C-C str. (7) 0.6 C7 sci + 0.1 C-0 str. (6) 0.2 C4 rock + 0.2 C2 rock 0.2 C7 wag + 0.1 C-C str. (2) 0.3 C-0 str. (8) + 0.2 C-0 str. (9) 0.3 ring def. i/p (40) + 0.1 C-C str. (4) 0.5 C-0 str. (6) 0.2 C-0 str. (5) 0.2 C7 wag + 0.2 C-C str. (4) 0.2 C4 rock + 0.1 C2 rock 0.2 C-0 str. (8) + 0.1 C-0 str. (9) 0.2 C-0 str. (9) + 0.2 C-C str. (7) 0.4 C7 twist + 0.3 C7 rock 0.3 C-C str. (3) + 0.2 C-C str. (2) 0.2 C2 rock + 0.1 C-0 str. (9) 0.2 C7 twist + 0.1 C-C str. (1) 0.5 bridge rock + 0.1 C-0 str. (5) 0.2 C3 rock + 0.2 C-C str. (7) 0.2 bridge wag + 0.2 ring def. i/p (40) 0.4 ring def. i/p (42) + 0.2 bridge twist 0 . 8 r i n g d e f . i / p ( 4 1 ) + 0.5ringdef.o/p(43) 0.5 bridge wag + 0.2 ring def. o/p (44) 0.6 bridge twist + 0.4 ring def. o/p (45) 1.8 ring def. o/p (44) + 0.8 ring def. o/p (43) 0.6 ring def. o/p (45) + 0.1 bridge twist

+

+

+

"Measured from vapour phase absorption unless designated sol (absorption of solution) or R (Raman). bAs listed in Table 6 and Figs. 8 and 14. 'Calculated with uniformly scaled force field (I), transferred scale factors (2), and fully refined scale factors (3); see text. esuZcm2, from fully refined force field. d ~ units n of 'ST, (eq. [3] in text) in units of A" amu-', from fully refined force field. IDepolarization ratios p, (eq. [6] in text), from fully refined force field. RMostimportant contributors to potential energy distribution (PED) of the normal modes. Numbers in parentheses refer to coordinate definitions in Table 11.

605


EGGIMANN ET AL.

included in the refinement. Bands 24, 27, and 26 may be ascribed to v,,, v3,, and v,,, respectively, based on approximately matching intensities. The location of v,, is left uncertain unless it gives rise to band 22, in which case v,, could be reassigned to band 21; however, the calculated frequency of v,, appears unreasonably high. Evidently, band 23 and possibly band 25 are not fundamental transitions. 'The corresponding normal modes v , ~ - v ~ ,in 60XA-dz are readily assignable to bands 28-22, respectively, from the point of view of the frequencies, but appreciable differences in the absorption intensities emerge. A similar competition between position and intensity is found also for th8 in the same compound (band 29 in Fig. 6). From the point of view of the former, the assignment given in Table 16 seems the most reasonable and was adopted as firm only in the very last refinement cycle on that basis. The scale factors as a result changed very little. From the point of view of the intensities, however, it would seem better if 1.'28,v , ~ ,and v,, were assigned to bands 28, 27, and 30, respectively, thereby clearly introducing major discrepancies in the frequencies. This dilemma remains unresolved. Bands 13 and 14 in 60XA, which must correspond to one or the other of v,, and v,?, were originally not assigned and hence not included in the refinement. In retrospect, v,, is predicted to be the stronger of the two in absorption, while v4, should be stronger in the Raman (Figs. 5 and 1 I). The assignment suggested in Table 15 is based on the relative intensities in the infrared spectra. The corresponding fundamentals in 60XA-d, are thought to be nearly coincident, together giving rise to band 13 (Fig. 6). The last remaining ambiguity concerns bands 17 and 18 for both compounds. Only one normal mode (~38)is at disposal for assigning the two bands for 60XA. While band 17 appears prevalent in the infrared, the Raman experiment suggests band 18 as the fundamental. Bands 17 and 18 in the isotopomer may be as8 a nearly coincident pair. cribed to v,, and ~ 3 as 6,8-Dioxabicyclo[3.2 .l]octane (DIOXA) and 7,7-d,-6,8dioxabicyclo[3.2 .l]octane (DIOXA-d2) The methylene scissoring bands 43, 4 1, and 40 of DIOXA (Figs. 7, 13) were readily assigned to v,, , v,,, and v,,, respectively (Table 17). Near the predicted position of v,,, the two bands 38 and 39 are observed with about equal intensities, preventing fm identification of the fundamental. One of the bands 38 or 39 and also 42, therefore, are likely to arise from higher order transitions. The normal mode descriptions for the three methylene scissors v,,-v13 of DIOXA-d, (Table 18) are essentially the same as for the corresponding modes (v,,-v,,) in DIOXA. The vibrations are identified for DIOXA-d, as bands 39, 40, and 42 (Figs. 8, 14) by comparison with the spectrum of DIOXA, and confirmed by the predictions of the frequencies and intensities. The methylene wagging and methyne bending regions for both molecules were completely assigned on the basis of the good agreement of predicted frequencies and intensities with the observed absorption spectra, although some ambiguities remain. The band ordering may be wrong for the modes v,, and v,, and for v,, and v,, for DIOXA, and for v,, and v,, for the isotopomer. The C5 C-H bending vibration of DIOXA (vI5)is observed to be split into the two bands 36 and 37, while the corresponding mode of DIOXA-d, (v,,) has shoulders on either side (bands 36, 38) that are not fundamentals. The Raman spectra confirm the assignments to a satisfactory degree.

Presuming that bands 22 and 23 are both fundamental transitions, the calculations suggest bands 22-24 of DIOXA - v ~ ~large errors in the frequento correspond to v ~ ~ despite cies, but leave uncertain the correct ordering of v2, and v2& Bands 25 and 27 cannot be fundamentals. Bands 25 and 26 of DIOXA-d, must be attributed to v,, and ~~4 even though their calculated intensities are in error in absorption and Raman scattering. Similar discrepancies were encountered in the same region for DIOXA (bands 23 and 22, Fig. 7), 60XA-d, (bands 28 and 29, Fig. 6), and 6 0 X A (bands 26 and 27, Fig. 5). None of these bands was assigned firmly. The region 600-1050 cm-I is reproduced unambiguously by the theory for both molecules except for a few congested lines. For DIOXA, the pair of bands 18 and 19 (v3,, v3,), which are calculated only 1.6 cm-' apart, are tentatively assigned in the reverse order using the Raman intensities as a criterion. The correct ordering of v,,, v,,, and v,, for the deuterated isotopomer cannot be resolved due to the differences between experiment and the predictions of frequencies and intensities in both the absorption and Rarnan spectra, preventing any firm interpretation of bands 13-15. The transition v,, of DIOXA-d, involving C-0 stretching is split into a doublet (bands 18 and 19) with about equal inensities in the solution absorption spectrum, while the splitting is not evident in the gas phase and Raman.

Discussion The detailed analysis of the absorption spectra described above revealed the presence of a number of transitions that cannot be fundamentals, many of them with considerable intensities, likely due to mixing with fundamentals by Fermi resonance. Such bands have repeatedly confused definitive identifications of fundamentals in this study. Recurring examples are the lines in the CH, scissoring region at approximately 1440 and 1465 cm-' and a mode around 1080 cm-'. While an investigation of the origin of these transitions would be of great interest, such endeavor is beyond the scope of this work as it would require anharmonic force fields. Some vapor phase bands exhibit series of Q-branches that probably arise from coupling to excited vibrational states of low energy vibrations of anharmonic skeletal deformations. This observation and the occurrence of Fermi resonances are evidence for high anharmonicity in the potentials of certain vibrations, in particular the ones involving skeletal deformations. Force-jield scaling and refining The average errors of the frequency predictions for all six bicyclo[3.2.l]octanes after uniform scaling is 20.4 cm-I (2.2%), which is lowered to 7.6 cm-I (1.2%) and 5.7 cm-I (0.75%), respectively, upon nonuniform scaling with the transferred and refined sets of factors (see Table 12). Tables 13-18 contain the corresponding errors for the six individual molecules, among which 80XA has the largest deviation in the frequency predictions after refinement (1.0%), and also has the worst fit after uniform scaling (2.6%). The excellent fit of the frequencies in general and the qualitative agreement of the intensities strongly support the assignments listed in Tables 13-18 in bold letters as fm, except for a small number of bands that are discussed in the previous section. Difficulties were encountered especially for clusters of closely spaced bands with similar intensities. In some cases, such modes were tentatively assigned to cal-


606


culated transitions despite uncertainties and may therefore be incorrect. Nevertheless, the success of the spectral assignments is also reflected in the refined scale parameters, which deviate only slightly from the transferred values, demonstrating as well the validity of transferring the parameters. The comparatively large changes for the ring bend (+9.1%) and ring torsion (- 13.8%) factors may be rationalized by the smaller ring strain of the bicyclo[3.2. lloctane system compared to the bicyclo[2.2. lloctane (norbornane) system from which these parameters were taken, and also by the presence of one or two oxygen atoms in the rings, since and the C-C-C bending force constants the C-0-C were not scaled differently. Vibrational anharmonicities may also account in part for the differences as they influence the magnitudes of the scale factors. The necessity of special scale factors for deformations of methylene groups adjacent to oxygen atoms is confirmed for the wagging mode, but not for the twisting mode. The "normal" CH, wagging and twisting factors converge to similar values as observed previously for norbornane (2a). The "special" factor for wagging does not change upon refinement and is found still considerably higher than the normal value. However, the "special" twist factor converges back to its original value. Whether this trend is real or not is not clear at this stage as the uncertainty of the refined value is relatively large. The most ambiguous scale factors in this work are the ones used for the methyne deformations. The problem apparently lies in their strong dependence on neighboring substituents and bonding, necessitating three separate factors that are then supported only by a relatively small number of experimental data. This naturally leads to large uncertainties in the refinement process. Removal of any one of the CH bending factors leads to appreciably worse frequency fits. Intensities In general, the calculated absorption intensities and, perhaps even more surprisingly, the Raman activities and depolarization ratios of the title compounds are predicted very satisfactorily using the 3-21G basis set. All intensity data are certainly accurate enough to be useful in a qualitative manner for spectral interpretations. Other workers have reported before that simple split-valence basis sets afford absorption intensities that are correct in the order of magnitude (7b, 22, 26, 35). The calculated absorption intensities in this study appear to surpass this order of magnitude accuracy as will be demonstrated below with a statistical analysis of the data. Raman activities have been reported to be even more susceptible to basis set truncation (7b, 22, 36). Large a b initio basis sets extended by polarization functions were deemed necessary for reasonable predictions (37). In this study, the relative intensities agree in the order of magnitude or better (Figs. 9-14). The calculated relative Raman intensities and depolarization ratios appear to be about as accurate as the absorption intensities. With theoretical predictions of such quality at hand, it would be worthwhile now for the purpose of spectral assignments to measure Raman depolarization ratios even for asymmetric molecules, as these properties can be calculated with reasonable accuracy. Furthermore, our results for DIOXA and DIOXA-d2 from various a b initio calculations indicate that the APTs and polarizability derivatives are only slightly basis-set dependent in the domain of the split-valence and the 6-31G*,

)/IIfully refined

transferred

0uniform scaling

relative frequency errors (%)

FIG. 15. Error distributions of the calculated frequencies for all six molecules using the three different force fields (fully refined nonuniform, transferred nonuniform, and uniform scaling).

6-3 IG*''-~', and 6-3 1G** basis sets. The relative absorption and Raman intensities were found to be governed only by the accuracy of the normal mode descriptions. Accuracy of eigenvectors Some recently reported analyses of vibrational spectra have adopted uniform scaling methods, multiplying the entire force field by only one parameter. In the same studies, the nonuniform correction procedures used for SQM force fields were found to deteriorate the a b initio vibrational eigenvectors (38). Uniform scaling was preferred by these authors because it does not change the composition of the a b initio normal modes. These observations conflict with the findings by other workers that different local symmetry coordinates need different scale factors to obtain good frequency fits, which originally led to the idea of nonuniform scaling (39). The abundance of data for the series of molecules in this work permits a statistical analysis of the errors in the calculated intensities which rely partly on the underlying eigenvectors. This should allow some conclusions to be drawn about the preferable approach to scale force fields. To reexamine the validity of our approach and to gauge the accuracy of the scaled force fields, tests were carried out based on the assignments of the bicyclo[3.2.:I]octanes as outlined above, probing the quality of our scaling method against uniform scaling. Figure 15 displays histograms that compare the distributions of the relative errors in the calculated frequencies for the force fields obtained by scaling with the fully refined and transferred multiple set of factors, and with the uniform parameter, respectively. The standard deviations of the errors of the 196 firmly assigned transitions are found at 1.1%, 2.0%, and 2.6%, respectively, assuming Gaussian distributions. The apparent superiority of the nonuniformly scaled force field in predicting the vibrational frequencies does not guarantee that the eigenvectors also are calculated more accurately. To judge the effect of nonuniform vs. uniform scaling on the normal mode compositions, the accuracy of the calculated absorption intensities was also investigated. Due to the large error margins on the intensities, distributions using relative errors for the abscissa of the histograms are not symmetric. The error in absorption intensity for every assigned transition is therefore mea-

EGGIMANN ET AL.


fully refined

transferred

0uniform scaling

log (intensitycalc/intensityeXp)

FIG. 16. Error distributions of the calculated absorption intensities for all six molecules using the three different force fields (fully refined nonuniform, transferred nonuniform, and uniform scaling).

sured here by the ratio of the calculated and the experimental intensity of the band (f, = I,'""/I,'"~). A histogram using log(h) for the abscissa is approximately symmetric and does reflect a Gaussian distribution (Fig. 16). The standard deviations calculated in this fashion are then found a t h = 2.5, 2.7, and 3.2, respectively, for refined nonuniform, transferred nonuniform, and uniform scaling. The error distributions demonstrate clearly that nonuniform scaling certainly does not deteriorate but rather slightly improves the intensities. The Raman spectra did not allow a similar test as the experimental absolute intensities were not measured. However, a qualitative comparison of the relative calculated Raman intensities with the spectra leads to the same conclusion. Conclusions It appears that for these compounds and probably also for a large set of other moieties the a b initio eigenvectors are generally not deteriorated by nonuniform scaling if the factors are transferred from appropriate molecules and then carefully refined. This statement holds for the 3-21G basis set that was utilized here and can probably be extended to all split-valence basis sets. Even the intensities predicted by the transferred, unrefined set of scale parameters are notably superior to the calculations based on the uniformly scaled force field. It is known that similar calculations closer to the Hartree-Fock limit utilizing large basis sets require fewer scale factors. Consequently, if more sophisticated basis sets are used, uniform scaling~willgive more favorable results compared to this study, or may even be superior to nonuniform scaling (40). Some very recent theoretical work suggests that the Hartree-Fock-limit force field for a given molecule can be corrected with one factor only (41). HOWever, due to basis set truncation, calculations at the 3-21G level are significantly less accurate and require nonuniform scaling as demonstrated theoretically (41) and confirmed here. In principle, the errors in the intensities originate from two possible sources, firstly from deficiencies in the eigenvectors and secondly from inaccurate atomic polar tensors and polarizability derivatives. If a principal part of these inten-

607

sity deviations originates from poor eigenvectors, some degree of correlation between the frequency errors and the intensity errors would be expected. However, linear regression of the errors from the above analysis shows no correlation at all, meaning that the intensity errors encountered here are basically independent of the remaining inaccuracies of the force field. When properly scaled force fields are utilized, the deviations from the observed values of the intensities must therefore originate from deficiencies in the APTs and polarizability derivatives, and cannot be substantially improved with more accurate force fields. Deficiencies in the force fields would obviously become more evident if the APTs and polarizability derivatives were obtained with sophisticated basis sets. However, the scaled force fields developed here are probably almost as accurate as any other harmonic a b initio force field, except if very large basis sets or electron correlation methods were used, which in any case are not yet feasible or are very expensive for molecules of this size. The basis set tests carried out with the DIOXA isotopomers not only demonstrate that the intensity parameters remain largely unchanged up to the 6-31G:" basis set, but also that, after scaling, the 3-21G force field is only slightly inferior to the force fields from the considerably larger basis sets. This study fully justifies using the 3-21G basis set for the vibrational calculations for the title compounds. Application of the 6-31G basis set may be recommended, which appears to produce improved force constants without much increase of computational costs. In connection with reports that favor uniformly scaled harmonic ab initio force fields, the following comments seem appropriate. It is crucial to realize that the fine tuning of several scale factors is important for large molecules with low symmetry, as even very small frequency shifts of normal modes will cause considerable remixing among modes of similar energies and hence subtle redistributions of intensities, more so than for small and highly symmetric molecules where the modes perturb each other to a lesser degree. For the latter, scaling with a very small set of independent factors may be preferable for the sake of simplicity or because of lack of sufficient experimental data, but the eigenvectors will almost certainly be less accurate than they could be using a full set of scale factors. Such inaccuracies in the predicted normal modes, if present for large molecules, will likely prevent or confuse numerous band assignments in the congested regions of the spectra. A judicious nonuniform scaling with a full set of factors, as demonstrated above, will yield more reliable predictions, allowing for firmer band assignments. Finally, according to the standard deviation of the intensity errors, 95.5% of the calculated absorption intensities lie within a factor of 5 of the measured values. This validates the approach to utilize theoretical intensities from 3-21G a b initio calculations as an aid for spectral assignments, especially if only orders of magnitude are required. The theoretical relative Raman intensities are judged qualitatively to be comparably accurate. The 3-21G intensities are particularly gratifying when compared to the calculations carried out with the polarized and diffuse basis sets, all of which are only marginally more accurate. The successful performance of the 3-21G basis set for the absorption and Raman intensities may be connected to the large size of these molecules. Despite the small number of basis functions per atom, the overall sum of the functions applied in these molecules is considerable


608

CAN. J . C H E M . \

and m a y permit a sufficiently detailed description of the electron densities and the connected properties. In terms of the accuracy of the theoretical predictions, applying a simple split-valence basis set to large molecules may therefore b e equivalent to utilizing more sophisticated basis sets for small molecules.

ter Committee of the University of Calgary t o access the Honeywell Multics, the Convex C 1 2 0 , and the Cyber 205 supercomputer. W e are further indebted to Drs. A . Rauk and R . Dutler for their assistance with the mainframe computers and the associated programs.

Summary

1. R. A. Shaw, C . Ursenbach, A. Rauk, and H. Wieser. Can. J. Chem. 66, 1318 (1988). 2 . ( a ) R. A. Shaw, N. Ibrahim, and H. Wieser. J. Phys. Chem. 93, 3920 (1989); ( b ) J . Phys. Chem. 94, 125 (1990). 3 . ( a ) R. A. Shaw, C . Castro, N. Ibrahim, and H. Wieser. J. Phys. Chem. 92, 6528 (1988); (b) R. A. Shaw, N. Ibrahim, and H. Wieser. Can. J . Chem. 68, 90 (1990); (c) Can. J. Chem. 69, 345 (1991). 4 . R. A. Shaw, C. Castro, R. Dutler, A. Rauk, and H. Wieser. J. Chem. Phys. 89, 716 (1988). 5 . R. A. Shaw, N. Ibrahim, and H. Wieser. Can. J. Chem. 67,

W e have assigned 196 observed bands a s fundamental transitions in the vibrational spectra (100-1500 cm-') of six bicyclo[3.2. I ]octane analogs. M o r e assignments are suggested that could not b e unambiguously confirmed b y the available data. All assignments were based o n the theoretical ab initio R H F geometries, harmonic force fields, and absorption and Raman intensities calculated with the 3-21G basis-set. T o correct for the deficiencies in the ~ r e d i c t e d frequencies, three methods for scaling force constants were tested, namely, multiplication by a uniform optimized factor, scaling with a set of parameters originally transferred from other molecules, and, finally, optimization b y leastsquares fitting of the frequency parameters. T h e three procedures produced frequency predictions with average errors of 2.2%, 1.2%, and 0.75%, respectively. T o assess the accuracy of the vibrational eigenvectors resulting from the differently scaled force fields, the errors in the theoretical absorption intensities were analyzed i n detail. T h e error distributions demonstrate that the absorption intensities are reproduced most accurately with nonuniformly corrected force fields and after refining the scale factors. A qualitative inspection of the theoretical R a m a n spectra indicates a similar trend. W e conclude that for the most accurate predictions of frequencies and normal m o d e descriptions, scaling with multiple factors followed by refinementis preferable provided that the scale parameters are judiciously selected and transferred from other molecules and then refined with great care. W e believe that this applies to all ab initio R H F force fields derived from split-valence basis sets. Accurate predictions of vibrational frequencies and intensities are crucial, particularly for large molecules, since the spectra become considerably more congested, which aggravates the problem of identifying the vibrations. In addition, the mixing of the modes is more pronounced such that even small deviations of the frequencies may result in erroneous normal m o d e descriptions and intensities. T h e 3-21G calculated absorption intensities and the Raman data agree very satisfactorily with the experiments. T h e o b served intensities are reproduced b y the theory considerably better than just in order of magnitude. T h e intensity predictions are therefore extremely valuable in guiding the spectral assignments. The theoretical Raman deblarization ratios are particularly useful for this purpose since they c a n b e applied to molecules with n o symmetry. While a better force field for D I O X A w a s obtained b y applying the 6-31G basis set, the intensity parameters remained essentially unchanged. Calculations using the 6 - 3 1G * and 6-3 1G** basis sets did not further improve the 6-3 1 G frequencies and intensities

Acknowledgements This work w a s supported b y a n Operating Grant from the Natural Sciences and Engineering Research Council of Canada. W e gratefully acknowledge the generous support from the Academic Computing Services and Supercompu-

535 (1989). 6 . T . Eggimann, R. A. Shaw, and H. Wieser. J. Phys. Chem. 95, 591 (1991). 7 . ( a ) P. Pulay, G . Fogarasi, X. Zhou, and P. W. Taylor. Vib. Spectrosc. 1, 159 (1990); ( b ) G . Fogarasi and P. Pulay. Irz Vibrational spectra and structure. Vol. 14. Edited by J . R. Durig. Elsevier, Amsterdam. 1985. pp. 125-2 19; (c) Annu. Rev. Phys. Chem. 35, 191 (1984). 8 . N . Ibrahim, T. Eggimann, E. A. Dixon, and H. Wieser. Tetrahedron, 46, 1503 (1990). 9. W. R. Moore, W. R. Moser, and J. E. Laprade. J. Org. Chem. 28, 2200 (1963). 10. P. G. Gassman and J. L. Marshall. Org. Synth. (Collect. Vol.) V, 424 (1973). 11. G . Stork and H. K. Landesman. J. Am. Chem. Soc. 78, 5129 (1956). 12. R. A. Appleton, K. H. Baggaley, C . Egan, J. M. Davies, S. H. Graham, and D. 0. Lewis. J. Chem. Soc. (C), 2032 (1968). 13. A. C . Cope and G. L. Woo. J. Am. Chem. Soc. 85, 3601 (1963). 14. A. C. Cope, C. H. Park, and P. Scheiner. J. Am. Chem. Soc. 84, 4862 (1962). 15. L. A. Paquette, I. R. Dunkin, J. P. Freeman, and P. C. Storm. J. Am. Chem. Soc. 94, 8124 (1972). 16. F. Sweet and R. K. Brown. Can. J. Chem. 46, 2289 (1968). 17. S. W. Baldwin, R. J. Doll, and S. A. Haut. J. Org. Chem. 39, 2470 (1974). 18. E. J. Boorman and R. P. Linstead. J. Chem. Soc. 258 (1935). 19. (a) T. L. Smithson. Ph.D. Thesis, The University of Calgary. 1982; ( b ) T . L. Smithson and H. Wieser. Unpublished re-

sults. 20. J. K. Kauppinen, D. J. Moffatt, H. H. Mantsch, and D. G. Cameron. Appl. Spectrosc. 35, 27 1 (198 1). 21. M. J . Frisch, J. S. Binkley, H. B. Schlegel, K. Raghavachari,

22. 23.

24. 25. 26. 27.

C. F. Melius, L. R. Martin, J. J. P. Stewart, F. W. Bobrowicz, C. M. Rohlfing, L. R. Kahn, D. J. Defrees, R. Seeger, R. A. Whiteside, D. J. Fox, E. M. Fluder, and J . A. Pople. Carnegie-Mellon Publishing Unit, Pittsburgh, Pa. 1984. P. Pulay, G . Fogarasi, F. Pang, and J. E. Boggs. J . Am. Chem. Soc. 101, 2550 (1979). T. Eggimann, T. L. Smithson, H. Wieser, P. LorenEak, P. Bergquist, H. Badawi, S. P. Sibley, and R. L. Kuczkowski. Can. J. Chem. 68, 267 (1990). V. S . Mastryukov, E. L. Osina, L. V. Vilkov, and R. L. Hilderbrandt. J. Struct. Chem. 22, 190 (1981). R . A. Shaw. Ph.D. Thesis, The University of Calgary. 1986. P. Pulay, G . Fogarasi, G . Pongor, J. E. Boggs, and A. Vargha. J. Am. Chem. Soc. 105, 7037 (1983). W. B. Person and J. H. Newton. J. Chem. Phys. 61, 1040

(1974). 28. (a) G. Zerbi. In Vibrational intensites in infrared and Raman

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