Argon matrix Raman and infrared spectra and vibrational analysis of

LESTERANDREWS AND RQBERT C. SPIKER,JR.

3208

Argon Matrix Raman and Infrared Spectra and Vibrational Analysis of Ozone and the Oxygen-18 Substituted Ozone Molecules by Lester Andrews* and Robert C. Spiker, Jr. Chemistry Departmenl, University of Virginia, Charlottesville, Virginia 8 B 0 1

(Received May 50,1078)

Raman spectra of argon matrix-isolated ozone and oxygen-18 enriched ozones were obtained using reduced power argon ion laser excitation. Photodecomposition of ozone was sufficientlymoderated to obtain excellent Raman spectra, with the following leOs assignments: VI,1104 cm-I, very strong; VZ, 701 cm-l, strong; v ~ , 1038 em-', weak. Infrared spectra provided complementary data: VI, 1105 cm-l, very weak; up, 704 cm-1, weak; V S , 1040 cm-', very strong. Potential constants were calculated using vibrational fundamentals for six isotopic ozone molecules. An ozone valence angle of 116.3 f 4" was calculated from four isotopic V~ assignments, in excellent agreement with the microwave value.

Introduction

Experimental Section

Although there have been many infrared studies of the vibrational fundamentals of ozone, only one Raman spectrum has been reported to date. Gas-phase infrared measurements have yielded the fundamentals 1103.1, 1042.1, and 701.0 cm-1 for VI, v3, and v2, respectively.'r2 Infrared observations of 0 3 in solid 0xygen~3~ and liquid argon5 have been recently compared to krypton and xenon matrix frequencies of ozone produced upon passing 0 2 matrix samples through a microwave discharge.6 The primary difficulty with Raman studies of ozone has been its sensitivity to photodecomposition by the excitation source. Nevertheless, Selig and Claassen' have obtained the Raman spectrum of gaseous ozone at pressures of 2 to 4 atm using a He-Ne laser. These to 1103.3 and 702.1 workers assigned v1 and v2 of 1603 cm-l, respectively; polarization data confirmed these assignments. However, this approach is less practical for isotopic ozone species. Deglise and Giguere* erroneously attributed bands to the Raman spectrum of ozone in studies of electrical discharge products of hydrogen-oxygen systems condensed at 93" K. Giguere has recently clarified these results and privately communicateds values of 1106, 703, and 1037 cm-1 for vt, uzI and v3 of l6C):{, respectively, in a solid hydroxylic medium. The present studylo was undertaken to observe Raman spectra of isotopic ozone molecules isolated in argon matrices at 16°K. Matrix trapping may retard the photodecomposition of the ozone molecule; furthermore, small quantities of oxygen-18 enriched ozone species can be shdied using the matrix technique. In recent infrared studiesll of alkali metal atomozone reactions, infrared spectra of isotopic ozone molecules in argon matrices at 15°K were observed. These data will be reported here for comparison between infrared and Raman argon matrix spectra of ozone isotopes.

The cryogenic apparatus (Cryogenic Technology, Inc., Waltham, Mass.) and vacuum vessel used for obtaining laser-Raman matrix spectra has recently been described by Hatzenbiihler and Andrev" Ozone was synthesized by tesla coil discharge of oxygen at low pressures in a Pyrex finger partially immersed in liquid nitrogen as described by Spiker and Andrews.ll Samples of ozone (%, l8O8, or 16,1803) were outgassed a t 77"K, expanded into a stainless steel bulb, and diluted with argon in ratios ranging from argon/oxone = M / R = 50/1 to 200/l. Matrix samples were condensed on a polished, tilted copper wedge at 16°K for 4 hr at the rate of 2.5 mM/hr. Raman spectra were recorded using a Coherent Radiation Model 52 G argon ion laser (5145 and 4880 and a Spex Model 1 Ramalog spectrometer, The technique used for obtaining Raman matrix spectra has recently been described.12z13 Laser power was reduced in these studies using neutral density filters. Dielectric long-wavelength pass filters (5145 and 4880 A, Corion Instrument Corp.) were used in the regions above 900 cm--I t o suppress reflected laser light and thus eliminate grating ghosts. Spectra were calibrated by a technique

The Journal of Phusical Chemistry, Vol. 76, No. 88, 1978

w)

D. J. MoCaa and J. H. Shaw, J . Mol. Speetrose., 25,374 (1968). S. A. Clough and F. X. Kneizys, J . Chem. Phvs., 44, 1855 (1966). K. €3. Harvey and A. M. Bass, J . Mol. Spectrosc., 2, 405 (1958). J. L. Brumant, A. Barbe, and P. Jouve, C. Iz. Aead. Sci., Ser. B, 268, 549 (1969). (5) A. Barbe and P. Jouve, ibid.,268, 1723 (1969). (6) L. Brewer and J. L-F. Wang, J . Chem. Phys., 56, 759 (1972).

(1) (2) (3) (4)

(7) H. Selig and H. H. Claassen, 15r. J . Chem., 6, 499 (1968). (8) X. Deglise and P. A. Giguere, Can. J . Chcm,, 49, 2242 (1971). (9) P. A. Giguere, personal communication, 1972. (10) Taken in part from the thesis submitted by Robert C. Spiker, Jr., t o the Graduate School of the University of Virginia In partial fulfillment of the Ph.D. degree requirements. (11) R. C. Spiker, Jr., and L. Andrews, J . Chsm. Phys., in press. (12) D. A. Hatzenbtlhler and L. Andrews, ibid., 56, 3398 (1972). (13) L. Andrews, ibid., 57, 51 (1972).

OZONE AND THE '80-sUBSTITUTED OZONE

MOLECULES

3209

of superimposing argon fluorescence lines14on each side of a particular Raman band during a scan, which provides a frequency accuracy and reproducibility of *1 em-' for the most intense bands and A2 cm-' for the weaker lines. Polarization measurements were carried out with the use of a polarization analyzer followed by a quartz polarization scrambler. Infrared spectra were recorded during and after sample deposition on a Beckman IR-12 filter-grating infrared spectrophotometer in the 200-4000-cm-' spectral region. Deposition times for infrared experiments ranged from 12 to 22 hr. The instrument was calibrated using vibration-rotation bands of standard molecules.15 High-resolution spectra were taken using either 8 or 3.2 cm-l per min scanning speeds and either 20 or 10 cm-' per in. scale expansions. Wave number accuracy is ~ 0 . cm-l. 5

1 %

,

9

h

Results and Discussion Raman and infrared spectra were recorded for isotopic ozones in argon matrices. The observed vibrational fundamentals were used to calculate potential constants and the ozone valence angle. Raman Spectra. Four Raman investigations were performed on natural isotopic ozone-argon matrix samples. Excellent Raman spectra were obtai!ed from samples using approximately 100 mW of 5145-A excitation and approximately 15 mW of 4880-A excitation. Comparable Raman intensities for ozone were observed under these two sets of conditions. Since photodecomposition of the ozone sample was a major concern, the relative Raman intensities of 0 2 and 0 3 were monitored at intervals throughout the time of recording and calibrating spectra. As expected, the intensity ratio ( 0 2 / 0 3 ) increased gradually during the sample illumination period. After 70 min of illumination with 15 mW of 4880-A excitation, the 1104-cm-I ozone fundamental decreased to two-thirds of its original value while the 1553-.cm-' oxygen fundamental doubled its intensity. Fortunately, the ozone photodecomposition proceeded slowly eiiough to facilitate recording Raman spectra of argon matrix isolated ozone. A sample of ozone (Ar/O3 = 100) was stuced extensively using approximately 15 mW of 4880-A excitation. The initial Raman spectrum showed the 0 2 fundamental to be one-third as intense as the strong 1 6 0 3 fundamental at 1104 cm-l. Three Raman bands were observed at 1104, 701, and 1038 cm-l using blue axcitation; the spectrum was almost identical with the one in Figure 1 using green excitation. These frequencies, which were calibrated against argon fluorescence lines, are appropriate for the v 1 (symmetric 0-0 stretch), v2 (valence angle bend), and v3 (antisymmetric 0-0 stretch) fundamentals of I 6 0 3 . Relative Raman intensities of the ozone fundamentals were approximately 7/3/1, respectively. The 1038-cm-l band was observed using a dielectric long-wavelength pass filter

I

1550

I

I

1500

I

l A

I

1450

"

I

I 1103

FREQUENCY

I

I

I

t

loo0

I

n

"

1

1

I

I

700

rcm-'i

Figure 1. Raman spectra of isotopic oxygen molecules in the 1420-1575-em-' region and isotopic ozone molecules in the 640-745- and 955-1150-cm-l regions a t 16'K: all spectra approximately 100 mW of 5145-A excitation a t the sample, 10 cm-l/min scanning speed, 5 em-1 resolution, suppression 0-1 X 10-9 A; top spectrum, 61 p M of Oa deposited, Ar/08 = 135/1, rise time 10 see, range 0.3 X A; middle spectrum, 166 pLM of 16,18O8deposited (55% 1 8 0 ) , h / O a = 50/1; 955-1150- and 1420-1575-em-' regions, rise time 3 see, range 0.3 X 10-9 A; 640-745-em-' region, rise time 10 see, range 0.1 X 10-9 A; bottom spectrum, 41 p M of 180adeposited (93% l80), A. Ar/Os = 200/1, rise time 10 see, range 0.1 X

to eliminate the possible interference of grating ghosts observed using higher laser power in this spectral region. The v 3 fundamental was not observed in the gas-phase Raman spectrum of ozone; however, the v1 and v 2 fundamentals were very strong.' The matrix may enhance the Raman intensity of v3. A similar strengthening of v3 was observed in the Raman spectrum13of matrix isolated OFZ. Depolarization ratios were measured for ozone an$ oxygen in this frosty argon matrix sample using 4880-A excitation. Three measurements of p , the depolarization ratio, for O2 ranged from 0.55 to 0.60; p for 0 2 in frosty argon matrices has been previously16 reported as 0.52. For ozone the following depolarization ratios were determined: pl, 0.64; pz, 0.78; p 3 , 0.89. Clearly, (14) A. R. Striganov and N. S. Sventitskii, "Tables of Spectral Lines of Neutral and Ionized Atoms," Plenum Data Corp., New York, N. Y., 1968, pp 354-356. (15) E. K. Plyler, A. Danti, L. R. Blaine, and E. D. Tidwell, J. Res. Net. Bur. Stand., 64, 1 (1960). (16) R. R. Smardzewski and L. Andrews, J. Chem. Phyls., 57, 1327 (1972). The Journal of Physical Chsmistry, Val. 76,N o . 22, 197B

LESTERANDREWSAND ROBERTC.

3210

p1 and p z are much higher than expected for symmetric same reasoning applies to the 1091-cm-' band which is modes. This discrepancy can be attributed to the undoubtedly due to vl of 16-16-18. The remaining scrambling effect of the frosty matrix. Hence, these feature a t 1074 cm-l is due to the unresolved 18-16-18 p values do not represent true values for ozone; they and 16-18-16 components, whose statistical weights, are a function of the matrix environment. However, when added, compare favorably with the observed a trend is apparent; the lowest depolarization ratio was intensity of the 1074-cm-I signal. The partially redetermined for the diatomic species 0 2 . p's for the solved multiplet in the 670-710-cm-' v 2 region of ozone symmetric stretch, symmetric bend, and antisymmetric is more difficult to analyze because of the changing stretch progressively increased. The same trend has background and high noise level. This feature conbeen reported for the depolarization ratios of OF and tains six partially resolved components; the peaks a t the OF2 fundamentals in argon matricea13 and for the 682 and 688 cm-I are the most intense features. ReOFz fundamentah in liquid OFz.I7 ferring to the above statistical wei hts, the 682- and The Raman spectrum of matrixDisolatedozone using 688-cm-' signals must be assigned to the unsymmetrical approximately 100 mW of 5145-A excitation is illusozone isotopes 18-18-16 and 16-16-18, respectively. trated in the top trace of Figure 1. Oxygen produced The outside peaks at 664 and 704 cm-I are respecby ozone photolysis was observed a t 1553 em-' after and W 3 . The remaining tively assigned to v2 of scanning the spectrum. The very strong band obweaker features a t 671 and 698 cm-] are attributed to served a t 1104 I:IXI-~ is assigned to vl of argon matrixv2 of the symmetrical mixed isotopes 18-16-18 and isolated l 6 0 3 , the medium intensity signal a t 703 cm-1 16-18-16, respectively. is v2, and the weak feature a t 1039 cm-l is attributed to The frequencies assigned t o v1 and v2 of isotopic v3. The relative Raman intensities of vl/vz/va were ozones listed in Table I were taken from the scrambled respectively 6/2/1 in this green laser experiment. The third Lsacc of Figure 1 shows Raman spectra of Table I: Raman and Infrared Frequencies (cm-') Observed oxygen-18 substituted (93% '*O)Oz and 0 3 (Ar/O, = for the Fundamental Vibrations of Isotopic Ozone Molecules 200/1) using npproximately 100 mW of green excitation. in Argon Matrices a t 16'Ka The band a t 1465 cnn-I is due to l8Oz while the much weaker feature near 1510 cm-l is due to a trace oE Calcd --Obsd frequencie8--Isotopic Raman Infrared frequencies assignments lsOI8O. I n the ozone region of the spectrum, the intense feature at 1042 em-' is assigned to v1 of 1808, uz, 18-18-18 664, 7c 664b 664.3 672.9 67 1 671.8 UZ, 18-16-18 since this band shows the appropriate isotopic shift from 680.7 682 681.5 uz, 18-18-16 '$00,. Two depoliarizntion ratio measurements were ob688.9 688 688.7 u q 16-16-18 tained for this band, the first yielded a value of 0.50 and 695.8 698 697.4 u2, 16-18-16 the second 5.55. These values add further evidence 705.2 704b 704.5 uz, 16-16-16 ~ is V I of 1 8 0 3 . Weaker that the 1 0 4 2 - ~ m - feature 981.7 983 982.8 v3, 18-18-18 isotopic bands, due to 7% oxygen-16 in the sample, 991.2 d 992.0 v3, 18-18-16 were observed near 1062, 1075, and 1091 cm-l. The 1006.5 d 1006.5 ua, 16-18-16 v2 and v3 vibrations of 18Q3 appeared at 665 and 983 1017.5 d 101%.1 u3, 18-16-18 1026.2 d 1026 2 ua, 16-16-18 crn-l, respectively, as is shown in Figure 1. 1041.4 1039 1040.0 23.3, 16-16-16 The second trace displays green laser spectra of iso50% 1G0180, 30% topically scrambled oxygen (20% lG02, 1041.3 1042 1044 vi, 18-18-18 1061.7 1061 d V I , 18-18-16 1802 and ) ozone molecules (55% ISO enriched). The 1070.8 1074 d vi, 18-16-18 2/5/3 relative intensity triplet a t 1465, 1510, and 1553 1077. 1 1074 d ~ 1 ,16-18-16 cm-l is due to JaO1sO,and lGOZ,respectively. I n 1091.4 1091 d v i , 16-16-18 the ozone portion of the spectrum, two multiplets were 1104.7 1104 1105 UI, 16-16-16 seen, the higher frequency one contained five bands and a Frequencies calculated using C , potential function are listed the lower frequency multiplet showed six partially refor comparison. b Frequency measurements from 55% l8O ensolved bands. The two outermost components of the riched ?zone sample. Raman UZ of pure l 6 0 3 measured a t 701 first multiplet a t 1042 and 1104 em-' are assigned to v1 (4880 A) and 703 cm-1 (5145 A). c Input data for frequency calculations were infrared bands for vz and v3 and Raman bands of 1 8 0 3 and 1 6 0 3 , respectively, since both of these features for ut, see text. dToo weak t o be observed. match with bands observed in individual I8O3 and l 6 0 3 Raman spectra. The following intensities are predicted from statistics for the six isotopic ozone moleisotopic experiment where these frequencies were cules: 16-16-16, 0.091 ; 16-16-18, 0.222; 18-16-18, measured relative to each other, hence isotopic shifts 5.136; 16-18-16, 0.111; 18-18-16, 0.272; 18-18-18, are more accurate than absolute frequency accuracy. 0.166. Referring t o the statistical weights, the band at 1561 cm-l, which is almost twice as intense as its 1042(17) D. J. Gerdiner and J. J. Turner, J. Mol. Speclrosc., 38, 428 c1l1-l counterpart, is assigned to v1 of 18-18-16. The (1971). ~

The Journal of Ph@aE

Chemistry, V o l . Y6,No. $8, IQYQ

--

OZONEAND THE 1 8 8 0 - SOZONE ~ ~ MOLECULES ~ ~ ~ ~ ~ ~ ~ ~

3211

enriched ozone clearly shows that the 1017-cm-' absorption is more intense than the 1006-cm-l band; since the 18-16-18 isotope has a greater statistical weight, 5Ea@1 the 1017-cm-1 band is assigned to v3 of 18-16-18 ozone and the 1006-cm-1 band to v3 of 16-18-16 ozone. Further statistical evidence supporting this z o assignment is seen in the 93% lSO enriched ozone spectrum, where the 1 0 1 7 - ~ m -feature ~ was the only one of r ln these two bands detected, as is shown in the bottom 2 EO $, spectrum of Figure 2 . Kote that the 18-18-16 component is double the intensity of the 18-16-18 feature. The present spectra show six clearly resolved v3 2 ; $80 60 isotopic components for the scrambled ozone isotopes as expected. I n recent discharge experiments, Brewer and Wang6 passed xenon containing 1602and W z through a microwave discharge arid trapped the 2 40 effusing products at 20°K. These workers resolved only four isotopic bands; the 18--16-18 and 18-18-16 v3 *o-.-L-------L components were missing. Clearly, matrix deposition 1120 lOLl0 1040 of presynthesized ozone, as in the present work, proFREQUENCY (cm-'i duces better resolved, sharper spectra. Figure 2 . Infrared spectra recorded in the 630-720- and The bending mode region was examined after 940-1130-cm-1 spectral regions for isotopic samples of ozone in sample; the spectrum is inset depositing more 1e,1803 argon (Ar/Oa = 200/1) deposited at 15°K: top spectrum from the middle spectrum of Figure 2 . Also present in 1 6 6 0-~,: middle sDectrum 1e,1*Oa. 55% ox~qen-18: bottom spectrum, , "W a , 937, oxygen-18. Inset spectra were recorded from this scan are traces of C16~1802 causing the trio of thicker samples. doublets centering a t 663, 658, and 653 cm-l. The COZdoublet a t 663 obscures v2 of 180in 3 this spectrum. The five remaining bands are asbigned to v2 of the The Raman assignments to v3 were measured in the scrambled ozone isotopes in Table 1. It is important pure isotopic experiments. to note that the two central features are the most Infrared Spectra. Typical infrared spectra for three intense components; hence, these bands must be isotopic ozone samples in argon matrices (M/R = 200) assigned to the most abundant isotopes, the unare illustrated in Figure 2 . The sharp, intense v3 symmetrical species 16-16-18 and 16-18-18. of 1603 is immediately obvious a t 1039.6 cm-' as the Weak bands in the l 6 0 3 spectrum at 2109 cm-' and most prominent feature of the infrared spectrum; a in the I8O3spectrum a t 1997 cm-l (not shown in Figure weak shoulder is resolved at 1033.5 em-', which is 2 ) are assigned to the v 1 v3 combination band of probably due to a matrix site splitting. The weaker l 6 0 3 and ' * 0 3 , respectively. band at 704.4 em-' is assigned to v z ; the very weak, The same ozone isotopic species were studied. in nitrobroader feature a t 1105 cm-' in the indented spectrum gen matrices. For the 1 6 0 3 isotope vl, v2 and v3 were obrecorded fsorn st thicker sample is likely the argon served a t 1109, 704.5, and 1042.5 cm-l, respectively. matrix v1 fundamental of 1603.An estimate of the nitrogen matrix spectrum, the v3 comI n the 1a,1803 relative infrared intensities of v3/ v Z / v I is 70/7/1. ponents were observed 3.0 cm-l higher than the corSimilarly, the very intense, sharp band in the l 8 0 3 responding argon matrix isotopic frequencies. spectrum a t 982.8 cm-' and the resolved shoulder a t Potential Constants. The vibrational assignments 976.8 em-' are asaigned to v3 of l803. Great care was listed in Table I provide ample basis lor normal cotaken to minimize C02 in this experiment to avoid ordinate calculations for the isotopic ozone molecules. ambiguity with v2 of leos;the weaker band at 664.3 The force constant adjustment program FADS written species. The very cm-' is assigned t o v 2 of the 1803 by Schachtschneider was used for matrix calculations meak, broad feature at 1044 cm-' in the indented trace which were performed in the usual VC'ilson FG-matrix i,q attributed to vl of 1803. format. The middle spectrum in Figure 2 was recorded of an First, the four symmetrical isotopes were analyzed ozone sample prepared from 55% oxygen-18 enriched in CZvsymmetry by factoring the secular equation ac012. The sharp six-component multiplet is appropriate cordingly. Since the VI Raman band at 1074 em-' for a nondegenerate vibration of a three oxygen atom was not resolved into 16-18-16 and 18-16-48 isotopic species, with two equivalent oxygen atoms, namely, components, frequencies of 1078 and 1070 em-', Cpl, ozone. The relative intensities of the six bands respectively, were used for these assignments. Raman are appropriate for the statistical weights of the isotopes as assigned in Table I. The spectra of 55% l80 bands for v l and infrared frequencies for v:! and v3 IO0 _I_T----

I icoL

iz ~~~

~

I

+

The Journal

of

Physical Chemistry, Vol. 7 6 , N o . 293 1972

LESTER ANDREWS AND ROBERT C. SPIKER,JR.

3212 were used as input data to calculate potential constants. The potential constants obtained in symmetry coordinates are listed in Table 11; their internal coordinate counterparts are readily obtained to be Fo-o = 5.829 f 0.100, Fo-O,O-o = 1.664 f 0.100, and Fo-o,, = 0.565 f 0.054. These numbers can be compared. to the results of the C, calculations to follow.

Table XI: Vibrational Potential Constants and Potential Energy Distribution for Isotopic Ozone Moleculesa Potential energy ---distribution, *eOa----Potential constants

Y1

Ye

Y8

C%,,Symmetry. Four Isotopes

F,,,

= = Fa = Pantrsym= Av =

Fey,,,

*

7.493 0.091b 0.800 f 0.050 2.036 f 0.015 4.166 A: 0.010 0 . 8 cm-'1

0.988O -0.169 0.181 0.000

0.054 0.086 0.860 0.000

0.000 0.000 0.000 1.000

C, Symmetry. Six Isotopes

Po-o Po-o,o-0 Fo-o,, Fo-o Fo-o,, Fa Av

= 5.879 =k 0.09tib = 1.662 0.039

*

= = = = =

0.483 =k 0.076 5.978 I 0.074 0.520 A: 0.054 2.038 i 0.012 0 . 7 cn1-l

0.409O 0.219 -0.092 0.360 -0.078 0.182

0.015 0.012 0.038 0.029 0.048 0.860

0.684 -0.398 -0.006 0.713 -0.006 0.001

Ro-O = 1.278, 0-0-0 angle = 01 = 116.8". b Units: stretching, mdyn/A ; stretch-bend, mdyn/rad; bend, mdyn A/rad2; error limits provided by program FADJ. c Fraction of v1 in indicated force constant.

Second, calculations were done for all six ozone isotopes using intend coordinates in C, symmetry. The six force constants determined are given in Table 11; calculated frequencies are listed in Table I for each isotopic assignment. The frequency fit is excellent (Av = 0.7 cm-l) for 18 vibrational frequencies. Anharmonicity is likely the major contribution to this discrepancy. When average isotopic force constants are used to calculate isotopic frequencies, the effect of normal cubic contributions to anharmonicity is to make calculated lighter isotopic values exceed the observed while calculated heavier isotopic values fall below the observcd. Such is the case for these isot>opic ozone calculations. It is of interest to compare the two Fo-0 force constants and the two Fo-o,, force constants which, by symmetry, should be the same. These force constants agree, within the error limits of the calculations, for the ozone molecule with two equivalent oxygen-oxygen bonds. In fact, the average of the two Fo-0 force constants obtained for G, symmetry agrees exactly with the Fo-o obtained from symmetry coordinates. I n the only other report of ozone potential constants, The Journal of Physical Chemistry, Vol. 76, No. 88, 1978

Pierce determined vibrational potential constants from centrifugal distortion effects by requiring compatibility between the infrared vibrational and microwave rotational spectra for the 1 6 0 3 isotope.18 The potential constants of Pierce are in excellent agreement with the present values calculated from isotopic data. Pierce's values (converted t o Table I1 units) were reported as follows: Fo-o = 5.70, Fo-o,o-o = 1.52, F o - o , ~= 0.424, F , = 2.09. The observed frequencies for the 16-18-16 and 16-16-18 isotopes are in good agreement with the values calculated by Pierce.'* Potential energy distributions, the fraction of each frequency contributing to each force constant, are also given in Table I1 for each potential function. It is clear that v l contains a small amount of bending character; as would be expected, the symmetric vl and v 2 modes interact to a small degree. This is particularly evident in the unsymmetrical isotopes, which causes a rearrangement of mixed ozone v2 frequencies from the order predicted from diagonal valence angle bending G-matrix elements alone. Consistent with symmetry, v3 has negligible bending character, even for the unsymmetrical ozone isotopes. Oxone Valence Angle. Matrix frequencies for antisymmetric vibrational fundamentals of CzV molecules have been widely used in recent years to calculate bond angles for these molecules. Since v3 is alone in its antisymmetric irreducible representation, in principle the valence angle can be calculated directly from the fundamental frequencies. The v 3 assignments reported here for the four symmetrical ozone isokopes provide a good test of the angle calculation procedure, since the ozone valence angle is accurately known from microwave spectra. The 16-16-16/18-18-18 isotopic frequency ratio cannot be used to calculate the ozone valence angle because the G-matrix elements contain a single isotopic mass, and hence, the angular dependence cancels, leaving a frequency ratio depending only on mass. Using the four combinations of symmetrical isotopes 16-18-16/ 16-16-1 6,18-16-18/ 18-18-18, 18-1 6-18/ 1616-16, 16-18-16/18-18-18, the v2 assignments listed in Table I produce the ozone valence angle cosines -0.32188, -0.30987, -0.55349, and -0.56827, respectively. These cosine values place the ozone valence angle lower limit a t 108.4 f 0.4" and the upper limit a t 124.1 k 0.5" with an average value of 116.3'. AS has been discussed previously for 802 isotopic calculations, the upper limit and lower limit average represents an excellent determination of the bond angle for isotopes whose anharmonicities are nearly the same. l9 The 116.3 f 4" bond angle for ozone determined from (18) L. Pierce, J . Chem. Phys., 24, 139 (1956). (19) M.Allavena, R.Rysnik, D. White, V. Calder, and D. E. Mann, ibid,, 50, 3399 (1969).

INFLUENCE OF INTEERNAL MOTION ON CARBON-13

RELAXATION

argon matrix isotopic v 3 frequencies is in excellent agreement with the 116.8 & 0.5"microwave valueOz0 Hence, reliable angles can be calculated from va matrix frequencies. Clearly, the precision of these crilcula,tions depends upon accurate frequency measurem ent and isotopic arrharmonicities being nearly the same. It is also helpful to have data for both terminal and central atom isotopic substitutions.

Conclusions The vibrational fundamentals of ozone in argon m&rices are in very good agreement with gas-phase values The intense infrared mode v3 is two wave numbers lower in the matrix phase; the bending mode v2 occurs 2--3 cm-l higher. The intense Raman active fundamental va agrees within one wave number with gas-phase values. It i s interesting to note the extraordinary infrared intensity of v3 and weakness of v l

Influence

of'

3213

of ozone and the complete reversal of this intensity relationship in the Raman spectrum. The technique of laser-Raman matrix isolation spectroscopy is useful for obtaining Raman spectra of relatively small amounts of sample molecules. For photolytically unstable molecules such as ozone, the matrix cage apparently retards photodecomposition such that excellent Raman spectra of the trapped molecule can be obtained.

Acknowledgments. The authors gratefully acknowledge financial support for this research by the National Science Foundation under Grant No. GP-28582 and a Governor's Fellowship for R . 6.8., Jr. We acknowledge helpful discussions with Dr. Alfred Arkell on ozone Bynthesis. (20) R.H . Hughes, J. Chem. Phys., 24, 131 (1956)

nternal Motion on the Carbon-13 Relaxation

Times of Methyl Carbons y James R. Lyerla, Jr., and David M. Grant* Department of Chemistry, University of Utah, Salt Lake City, Utah 84118

(Received May 1 , 1978)

PuEslication costs assisted by the National Instit Utes of Health

The carbon-13 spin-lattice relaxation times, T I , and lac- { 'H ] nuclear Overhauser enhancements have been determined at 38' for 14.1 and 23.5 kG fields for various methyl carbons subject to internal reorientational motion. The contributions of the C-H dipolar and spin-rotation mechanisms to T1have been separated from the overall relaxation rate. The influence of methyl internal rotation on the C-H dipolar and spin-rotation relaxation rates has been discussed and C-H dipolar rates have been used to estimate the magnitude of methyl rotational barriers.

Introduction The use of nuclear magnetic relaxation times as a means of investigating molecular dynamics in liquid systems has been well established.lV2 Although the precise details of the microdynamic behavior of the liquid are not readily available from these relaxation data,3 the results do allow semiquantitative evaluation of the molecular motion. While the majority of reports relating relaxation times to a system's dynamics have been carried out cia proton magnetic resonance, several recent studies have focused on the determination of carbon-13 spin-lattice relaxation times ( T I ). 4 - 1 2 I n particular, work from this has concentrated on simple molecular systems with the purpose of elucidating the relaxation mechanisms governing 13C

relaxation. By separating the C-H dipolar part from the overall 13C relaxation rate, these workers have (1) N. Bloembergen, E. M. Purcell, and R . V. Pound, Phys. Rev., 73, 679 (1948). (2) J. S. Waugh in "Molecular Relaxation Processes," Academic Press, London, 1966. (3) W. T.Huntress, Jr., 1.Phys. Chem., 73, 103 (1969). (4) K. T. Gillen, M. Schwartz, and J. H . Noggle, Mol. Phys., 20, 899 (1971). (5) D. Doddrell and A. Allerhand, J. Amer. Chem. Hoc., 93, 1558 (1971). (6) H . Jaeckle, U. Haeberlen, and D. Schweitzer, J. Magn. Resonance, 4, 198 (1971). (7) K. F. Kuhlmann, D. M. Grant, and B. K. Harris, J. Chem. Phys., 52, 3439 (1970). (8) T. D. Alger, S. W. Collins, and D. M . Grant, ibid., 54, 2820 (1971).

The Journal of Physical Chemistry, Vol. 76, N o . 28,is73