J. Phys. Chem. 1995,99, 899-904
899
CH Stretching Overtone Spectra and Intensities of Vapor Phase Naphthalene Henrik G.Kjaergaard and Bryan R. Henry* Department of Chemistry and Biochemistry, University of Guelph, Guelph, Ontario NIG 2W1, Canada Received: August 24, 1994; In Final Form: November 7, 1994@
Room temperature vapor phase CH stretching overtone spectra of naphthalene are reported for the first time. The vibrational overtone spectra of naphthalene are recorded in the AVCH= 2 and 3 regions by conventional near-infrared spectroscopy and in the AVCH= 4 and 5 regions by intracavity titaniumsapphire laser photoacoustic spectroscopy. Absolute oscillator strengths are obtained from the conventional spectra. The photoacoustic spectra provide relative oscillator strengths between the observed peaks within a given overtone. Peaks corresponding to two nonequivalent CH stretching local modes are consistently assigned. Oscillator strengths are calculated with an anharmonic oscillator local mode model and ab initio dipole moment functions. We compare the calculated and experimental oscillator strengths. Our simple calculations, which contain no adjustable parameters, are in very good agreement with the observed intensities.
Introduction
The local mode model of molecular ~ibrationl-~ has been used extensively to explain XH stretching (X = C, N, 0, etc.) overtone spectra of various The model has been successful in assigning peak positions of the various XH bonds present in the molecule. The peak positions can be calculated with a harmonically coupled anharmonic oscillator (HCAO) local mode model with reasonable accuracy. The HCAO local mode model has recently been shown to be quite successful in the calculation of CH stretching overtone intensities in several different The HCAO local mode model neglects coupling to all lower frequency modes and approximates the coupling between CH bonds by harmonic terms. In a similar fashion to what we have observed in and 1,3-b~tadiene,~O the two different CH bonds in naphthalene are expected to be weakly coupled. We argue that it is a good approximation to neglect this coupling and treat naphthalene as two nonequivalent and uncoupled anharmonic CH stretching oscillators. The structure of naphthalene is depicted in Figure 1, which also shows the two nonequivalent CH bonds and their labeling. Thus, on basis of the local mode model, we would expect two peaks in the higher energy overtone spectra of naphthalene. This is in agreement with the fourth overtone CH stretching spectrum (AVCH= 5 ) of crystalline naphthalene measured at 1.3 K by Perry and Zewai123j24and also with our present vapor phase near-infrared (NIR) spectra in the AVCH= 3-5 regions. The AVCH= 6 overtone spectrum of naphthalene in CC4 solution shows a single broader peak.25 On the basis of the AVCH= 5 spectrum of selectively deuterated naphthalene (a-naphthalened4), Perry and Z e ~ a i assigned l~~ the lower frequency peak of the solid phase AVCH= 5 overtone spectrum of naphthalene to the CHB bond. In the present paper we argue for a different assignment in the vapor phase overtone spectra of naphthalene. Our assignment is based on ab initio bond lengths and the bond length frequency correlation. The shortest bond length is expected to correspond to the highest frequency CH stretching oscillator.1° We also use the calculated CH stretching overtone intensities to support our assignment. We give a comparison with the available experimental data on bond length^^^.^^ and fundamental intensities.28 Vibrational spectra of vapor phase naphthalene are of considerable astrophysical i n t e r e ~ t . ~ *Naphthalene -~~ is the ~~~~~~~~
'Abstract published in Advance ACS Abstrucrs, January 1, 1995.
0022-365419512099-0899$09.00/0
Y
J
Figure 1. Naphthalene at its optimized geometry (HF/6-311G**).R, = 1.0760 A, Rg = 1.0754 A, R I = 1.408 A, R2 = 1.420 A, R3 = 1.357 A, Rq = 1.416 A.
smallest of the polycyclic aromatic hydrocarbons (PAHs). In recent years it has been argued that the so-called unidentified infrared (UIR)bands and the diffuse interstellar bands (DIB) arise from the PAHs and their cations present in the interstellar m e d i ~ m . * ~It , has ~ ~ been suggested that the PAHs and corresponding cations might be observed in the NIR spectra from the interstellar medium.31 No absorption bands were observed in the W-NIR spectrum of neutral n a ~ h t h a l e n e . ~The ~ intracavity laser photoacoustic spectroscopy (ICL-PAS) technique is very sensitive, and it is possible to observe very weak transitions in the NIR-vis region. The NIR spectra are dominated by XH stretching overtone transitions, which have very low intensity compared to possible low-lying electronic bands. Foing and E h r e n f r e ~ n dstate ~ ~ the necessity of accurate band position, line profiles, and intensities of PAHs in the vapor phase. These spectra are needed by astronomers to identify potential DIB carriers and to derive their abundance in the interstellar medium. Perhaps the present laboratory NIR spectra of vapor phase naphthalene can help to facilitate the assignment of the DIBs in the interstellar medium.
Experimental Section Crystalline naphthalene (certified grade) was obtained from Fisher Scientific and was used without further purification except for degassing. 0 1995 American Chemical Society
Kjaergaard and Henry
900 J. Phys. Chem., Vol. 99, No. 3, 1995 Vapor phase spectra of naphthalene were recorded in the regions corresponding to AVCH= 2 and 3 with a conventional spectrophotometer (Cary 5e UV-vis-NIR) fitted with a White variable path length cell (Wilks variable path length cell fitted with BK7 Schott glass windows from Melles Griot). The wavenumber accuracy of the Cary 5e spectrophotometer is approximately f 2 cm-' in the near-infrared (NIR) region corresponding to AVCH= 2 and 3. The AVCH= 2 region was recorded at a slightly elevated room temperature (27 "C), and both AVCH= 2 and 3 regions were recorded at higher temperatures (48 and about 55 "C). Background scans with an evacuated cell were recorded and subtracted for each of the Cary spectra. Both background and sample spectra were recorded at the same temperature, because the optical transmittance of the Wilks cell changed with temperature. The temperature was measured with an electronic digital thermometer (Fisher Scientific, NIST thermometer with a YS409A probe) accurate to f 0 . 3 "C. The naphthalene vapor pressure in the cell is given by the lowest temperature of the setup (sample flask, metal hose, and Wilks cell). It is difficult to determine this temperature accurately at temperatures above room temperature. We were not able to directly measure the vapor pressure of naphthalene but have estimated it from the temperature and reference vapor pressure values of naphthalene at different temperatures (17-57 0C).32 We fitted In@) as a function of the inverse temperature and used this function to predict vapor pressures of naphthalene at different temperatures. The vapor pressure of naphthalene is 0.1 Torr at 27 "C and 0.61 Torr at 47 0C.32 It is evident that even a few degrees variation in temperature leads to a significant change in the vapor pressure of naphthalene. The Wilks cell is evacuated on a glass vacuum line pumped by a single-stage rotary pump. The typical base pressure of the Wilks cell is about 60 mTorr. The experimental absolute oscillator strength f of an absorption band can be determined from these conventional spectra and the following e q u a t i ~ n ' ~ . ~ ~
f = 2.6935 x
[K-'Torr m cm] T S A ( 0 ) dO (1) Pl
where T is the temperature, p is the sample pressure, 1 is the path length, A is the absorbance, and V is the frequency in cm-'. The room temperature vapor phase overtone spectra of naphthalene were recorded in the AVCH= 4 and 5 regions with ICL-PAS. Our version of ICL-PAS has been described in detail e l ~ e w h e r e . ~Both ~ , ~spectra ~ were recorded with an argon ion pumped titanium:sapphire (ti:sapph) solid state broad band tunable laser (Coherent 890) with the mid- and short-wave optics for the AVCH= 4 and 5 regions, respectively. The photoacoustic cell, fitted with a ceramic piezoelectric microphone (Knowles Electronics Inc., BL 1785), was filled with naphthalene and 130 Torr of krypton.36 As explained in detail in ref 19, the wavenumber accuracy was better than 51 cm-'. The absolute absorbance is not known, and we can only obtain the relative oscillator strengths in the ICL-PAS spectra.35 The overtone spectra were decomposed into component peaks with a deconvolution program with Spectra C a l ~ . ~The ' spectra were deconvoluted with a number of Lorentzian peaks and a linear base line. The deconvolution provides peak positions and areas. Uncertainty in the deconvolution is very dependent on peak resolution. We generally estimate the uncertainty to be less than 5 cm-' for peak positions and less than 10% for intensities of well-resolved peaks. However, for the poorly resolved peaks in naphthalene we estimate a much larger uncertainty, especially for the low-energy peak (vide infra) which is seen as a shoulder. We estimate the uncertainty in
the naphthalene spectra to be of the order of 10 cm-I for peak positions and 50% for intensities.
Theory The oscillator strength f of a vibrational transition from the ground vibrational state g to an excited vibrational state e is given by15333
feCg = 4.702 x
[cm D-2] OeglFeg12
(2)
where V,, is the transition frequency in cm-' and Peg= (eljilg) is the transition dipole moment in debye. Naphthalene has four equivalent a-hydrogens (positions 1, 4, 5 , and 8) and four equivalent ,&hydrogens (positions 2, 3, 6, and 7) as indicated in Figure 1. However, the CHa and CHp bonds are nonequivalent. Since the hydrogens are attached to different carbon atoms, the coupling between the CHa and CHp oscillator will be sma11.20s22To f i s t order this coupling is given by potential energy coupling (force constant^).^,'^-^^ These force constants can be calculated ab initio. The effective coupling between neighboring CH bonds (either @ or ,9p) is calculated at the Hartree-Fock (HF) level with a 6-311G** basis set to be 3.7 cm-', which is small compared to the coupling between CH bonds attached to a common carbon but is similar to the coupling between terminal and nonterminal CH bonds in 1,3-b~tadiene.~O In 1,3-butadiene we found this latter coupling to be negligible.20 We use the local mode theory of harmonically coupled anharmonic oscillators (HCAO) and neglect this small coupling. Thus, we treat naphthalene as two nonequivalent isolated CH group^,'^,^^,*^ each of them described by a Morse oscillator. The Hamiltonian for the CHa oscillator can be written as
(H- E,,)n)/hC = valha - (vu2 + va)lhaxa
(3)
where Elo), is the energy of the vibrational ground state and 8, and 8aXa are the local mode frequency and anharmonicity of the CHa oscillator. The Hamiltonian for the CHp oscillator is similar. The eigenstates of the Hamiltonians are denoted by IVa),, and I V ~ ) ~ , where V a and vp are the quantum numbers of vibrational excitation in the CHa and CHp oscillators, respectively. These eigenstates are Morse oscillator wave functions. The vibrational wave functions and energies are used in eq 2 to obtain calculated oscillator strengths. The dipole moment function is expressed as a series expansion in the internal CH displacement coordinate, q. For the isolated CH, oscillator, we have Fa =
CZ;id i
(4)
where
and similarly for the CHp oscillator. We have limited the expansion in eq 4 to fourth-order term^.'^.^^ To determine the coefficients j i i , we use ab initio molecular orbital theory to calculate dipole moment values at geometries in which one of the CH bonds is displaced from equilibrium. This provides us with two one dimensional grids, @a(qa) and @p(qp), of the dipole moment as a function of q. For each of the two CH bonds we calculate seven points with a maximum displacement of f 0 . 3 A in steps of 0.1 A. This assures a reasonable mapping of the
CH Stretching Overtone Spectra of Naphthalene
J. Phys. Chem., Vol. 99, No. 3, 1995 901
TABLE 1: Ab Initio HF/6-311G** Dipole Moment Derivative Expansion Coefficients for CH, and CHp in Naphthalene' sa5 X z Po5 X jildDA-'
-0.109 PzdDA-' -0.120 ji3dDA-3 -0.061 -0.019
19 14 55 52
-0.539 -1.137 -0.038 -0.507
65 j&/DA-' -0.589 66 69 ji02/DA-' -1.273 50 18 jio3/DA-3 0.004 89 25 -0.454 48
Z
*30-
-0.312 -0.513 -0.031 -0.287
85 57 92 01
The indices a and B refer to the CH stretching coordinates associated with the a and ,8 hydrogens (see Figure 1). .04
6500
w
52
8650
8800
8950
91'00
WAVENUMBERS (cs' )
Figure 3. Vapor phase overtone spectrum of naphthalene in the AVCH = 3 region. The spectrum was measured at approximately 55 "C with a path length of 20.25 m. The individual Lorentzian functions fit to the experimental spectrum (noisy spectrum) are also shown as well as their sum (smooth line).
.02
0 v)
3
5750
58'75
6000
61'25
A
6250
WAVENUMBERS ( c m ' )
Figure 2. Vapor phase overtone spectra of naphthalene in the AVCH = 2 overtone region at room temperature, 27 "C (lower trace), at 48 "C (middle trace) and at 55 "C (upper trace). A path length of 20.25 m was used. The vapor pressure is estimated to range from about 0.1 Torr at 27 "C to about 1.2 Torr at 55 "C. The ordinate scale of the left panel corresponds to the room temperature spectrum. For the other two spectra, the ordinate scale is 5 times larger.
dipole moment function and limits round off error^.^^,^^ The optimized geometry of naphthalene at the Hartree-Fock (HF) level of theory with a 6-3 llG** basis set is shown in Figure 1. All grid points and the optimized geometry are calculated with Gaussian 9238at the HF/6-311G** level. The 6-311G** basis set has 228 basis functions and 374 primitive Gaussians for naphthalene. The dipole moment coefficients j&are found from standard numerical differential technique^'^^'^^^^ and are given in Table 1. We have used the notation ,L&j, where the first index refers to the CH, bond and the second to the CHp bond. We also calculated the dipole moment functions with a smaller 6-31G* basis set.
Results and Discussion The vapor phase overtone spectra of naphthalene in the CH stretching regions corresponding to AVCH= 2-5 are shown in Figures 2-5. The observed frequencies, line widths, oscillator strengths, and assignments of the deconvoluted peaks are given in Table 2. The observed frequency V of the pure local mode peaks (IV)a and 1v)p) have been fitted to a two-parameter Morse oscillator energy expression v / v = I5 - ( v
+ 1) a x
(6)
in order to obtain values of the local mode frequency fi and anharmonicity h x of the two CH stretching oscillators. The local mode parameters are given in Table 3. The small size of the uncertainties in Table 3 indicates that the two-parameter fit is excellent and corroborates our assignment of a Fermi resonance in the AVCH= 2 overtone region (vide inffa).
11200
11400
11600
1lEiOO
WAVENUMBERS (cm') Figure 4. Room temperature (24 "C) vapor phase overtone spectra of naphthalene in the AVCH= 4 region. The spectrum was measured by ICL-PAS with sample pressure of 75 mTorr and 130 Torr of Kr buffer gas. The individual Lorentzian functions fit to the experimental spectrum (noisy spectrum) are also shown as well as their sum (smooth line).
Our assignment of the local mode frequencies (fia < 15p) is in accord with what would be expected based on the ab initio bond lengths (Ra > Rp) that are given in the caption to Figure 1 (the shorter the bond, the higher the local mode frequency).1° Ab initio calculations at different levels all give the same ordering of the CH, and CHp bond l e n g t h ~ . ~ O Electron -~~ diffraction study of vapor phase naphthalene cannot distinguish the two different CH bond lengths,26 and X-ray diffraction studies ,Of naphthalene crystals suggest that the CHp bond length (0.98 A) is longer than the CH, bond length (0.95 However, the uncertainty on CH bond lengths found from X-ray diffraction is generally greater than the expected difference for n a ~ h t h a l e n e .It~ is ~ of course possible that the relative ordering of the two CH bond lengths in naphthalene changes from the vapor phase to the solid phase (the crystals). The fourth overtone spectrum of crystalline naphthalene (Figure 1, ref 23) closely resembles our present fourth overtone vapor phase spectrum (Figure 5). However, the crystalline
Kjaergaard and Henry
902 J. Phys. Chem., Vol. 99, No. 3, 1995
13900
14000
i4ioo
14200
WAVENUMBERS (cm') Figure 5. Lower traces: room temperature (25 "C) vapor phase overtone spectra of naphthalene in the AVCH= 5 region. The spectrum was measured by ICL-PAS with sample pressure of 82 mTorr and 130 Torr of Kr buffer gas. The individual Lorentzian functions fit to the experimental spectrum (noisy spectrum) are also shown as well as their sum (smooth line). Upper trace: the spectrum calculated as the sum of two Lortentzians with a line width of 97 cm-' and frequencies and relative intensity from the calculations in Table 2. TABLE 2: Observed and Calculated Frequencies and Oscillator Strengths, Observed Line Widths, and Peak Assignments for the CH Stretching Overtone Spectra of Vapor Phase Naphthalene observed calculated iVcm-' I'u/cm-l f b ikm-' f' assignment 5823 55 0.09 comb 5910 25 0.06 comb 5956 41 1.0 5957 2.8x lo-' 12)a 5978d 36 0.39 5989 3.9x lo-' 12)p 5998d 24 0.47 6040 26 0.12 I1)aI 1 ) ~ 6133 40 0.09 I1)all)a 8762 86 1.0 8759 3.3 x lo-* 13)a 8807 58 0.72 8806 5.0x lo-* 13)p 11442 84 1.0 11445 4.5X 14)a 11501 82 1.64 11506 6.6x 14)p 13898 101 0.09 watef 14016 115 1.0 14014 6.6x lo-'' IS), 14092 79 0.84 14088 9.4x lo-'' 15)~ 16467 1.1 x lo-'' 16)a 16553 1.5x lo-'' 16)~
Fwhm line width. Relative intensities within an overtone region. Local mode calculation with the parameters from Tables 1 and 3. Fermi resonance with a calculated center frequency of 5989 cm-'. e Residual water absorption. TABLE 3: Local Mode Frequency and Anharmonicity of the CH Stretching Modes in Vapor Phase Naphthalene"
CHa CHB
3154 i2 3171 zk 2
58.5i 0.4 58.9z t 0.5
a Uncertainties are one standard deviation. From a fit of the local mode frequencies in the AVC"= 2-5 regions.
spectrum shows broader peaks and a larger splitting. The latter can be associated with a larger difference in CH bond lengths in the crystals. The solid phase spectrum also shows a significant down shift compared to our vapor phase spectrum. Perry and Z e ~ a i observe l ~ ~ the two peaks at 13 952 and 14 055 cm-'. The high-frequency peak is broader, 133 vs 90 cm-',
and more intense (3:l ratio) than the low-frequency peak. Perry and also recorded the AVCH= 5 overtone spectrum of a-naphthalene-& (naphthalene-l,4,5,7-4 crystals and saw a significant decrease in intensity of the high-frequency peak. Thus, they assigned the high-frequency peak to the CH, stretching vibrations and the low-frequency peak to the CHp bond, in agreement with the relative X-ray determined CH bond lengths.27 The calculated frequencies and oscillator strengths of the local mode stretching states in naphthalene are given in Table 2. We have only shown the intensities obtained with the HF/6-311G** dipole moment function, given in Table 1. The intensities with the smaller HF/6-31G* dipole moment function show similar relative intensities within a given overtone but have larger absolute intensities. We see in Table 2 that our calculated frequencies are in excellent agreement with the observed values. This is even the case in the AVCH= 2 region where we expect larger effective coupling to lower frequency modes (localnormal mode combinations) and between the local modes (local mode combinations). The larger number of peaks observed in the AVCH= 2 region is an indication of this larger coupling. The peaks to the high-energy side of the pure local mode peaks are assigned as local mode combinations. Naphthalene has a large number of normal mode vibrations with frequencies about half the CH stretching and thus the likelihood of local-normal mode mixing is high. One example of this local-normal coupling is the Fermi resonance observed for the 12)~peak. All these states will carry some intrinsic intensity but also steal intensity from the pure local mode states. Due to this coupling, we do not expect the intensity calculation to perfectly match the observations at the fiist overtone, but usually the most intense features are predicted ~ e l l . l ~ - As ~ l can be seen from Table 2 , the calculation predicts the relative intensity of the 12)p transition to be 50% larger than observed. In the overtone spectra in the region of AVCH= 3-5, only two peaks are observed. The calculated intensity of the higher energy transition to Iv)p is 1.5 times larger than the transition to Iv),. In all three spectra (Figures 3-5) the two peaks are heavily overlapped with the maximum absorbance to the highenergy side. Thus, the calculations agree with the observed relative peak heights. The line widths obtained from deconvolution are larger than the observed splitting between the two peaks. Thus, as mentioned in the Experimental Section, deconvolution is connected with considerable uncertainty. The deconvolutions show the CHp stretching peak to be more intense (factor of 1.6) in the AVCH= 4 region and less intense (factor of 0.7-0.8) in the AVCH= 3 and 5 regions. This is in good agreement with the calculated intensities for AVCH= 4 but not for AVCH= 3 and 5. Of these three spectra, the spectrum of the AVCH= 4 region is not surprisingly the one with the best signal-to-noise ratio and the flattest base line. It is also the one with the best deconvolution (see Figure 4). It is the only spectrum where the difference in peak intensities from the deconvoluted areas exceeds our estimate of the experimental uncertainty. For each overtone, we calculated spectra as the sum of two Lorentzians with equal line width (taken as the average of the two observed values) and peak positions and intensities taken from the calculations in Table 2. These calculated spectra are in quite good agreement with the observed spectra. We have only shown the result for the AVCH= 5 region (Figure 5 ) . Thus, we claim that the present spectra are in reasonable agreement with the calculation of relative peak intensities. As expected, we observe the splitting between the CH, and CHp peaks to increase with increasing overtone. The splitting
CH Stretching Overtone Spectra of Naphthalene
J. Phys. Chem., Vol. 99,No. 3, I995 903
TABLE 4: Observed and Calculated Total Oscillator Strengths of the CH Stretching Fundamental and First Two Overtone Regions in Vapor Phase Naphthalene" V obs" HF/6-31G*b HF/6-3 1lG**b DHc 1 2 3 4
1 x 10-5 6x 9x
3.5 x 10-5
7.9 x 15.3 x
1.9 x
3.1 x 10-5 6.7 x 8.4 x 1.1 x
2.7 x 10-5
Fundamental intensity from ref 28 in AI matrix at 12 K. Estimated for v = 2 and f 3 x for v = 3. Calculated accuracy is f 2 x with the local mode parameters of Table 3. ' A b initio frequency calculation at HF/6-3 1G** level, double-harmonic approximation.
milliangstrom. However, the two observed peaks overlap which makes deconvolution difficult, and thus the relative experimental oscillator strengths have quite high uncertainties. Our calculated intensities, calculations which contain no adjustable parameters, are in reasonable agreement with the observed relative intensities of the overtone spectra. Our assignment of the CH, and CHBstretching transitions is different from that observed in the spectra of naphthalene crystals. This may indicate that the relative bond lengths of the CH bonds in naphthalene change from the crystal to the vapor phase. We have observed room temperature overtone spectra in the regions corresponding to AVCH= 4 and 5 of a sample with a very low vapor pressure, less than 0.1 Torr. To our knowledge, these are the fist room temperature vapor phase overtone spectra of naphthalene.
is 33, 45, 59, and 76 cm-' for the AVCH= 2-5 regions, respectively. We also observe the average line width to increase with increasing overtone. Line broadening due to the increase in temperature in the AVCH= 2 spectrum was not observed. Acknowledgment. We are grateful to Knowles Electronics In Table 4 we compare the observed and calculated absolute Inc. for providing us with samples of their microphones and total oscillator strengths for a given overtone region. Since we helpful discussions regarding microphone characteristics. Fundcan only measure absolute absorbance in the Cary spectra, we ing for this research has been provided by the Natural Sciences could only obtain experimental values for the AVCH= 2 and 3 and Engineering Research Council of Canada. regions. Furthermore, due to the low room temperature vapor pressure of naphthalene and thus a weak signal, these measured References and Notes total oscillator strengths have significant uncertainties. None(1) Hayward, R. J.; Henry, B. R. J . Mol. Spectrosc. 1975, 57, 221. theless, as can be seen from Table 4, the agreement with our (2) Henry, B. R. Acc. Chem. Res. 1977, 10, 207. best intensity calculation (HF/6-311G**) is excellent. In earlier (3) Watson. I. A.: H e m . B. R.: Ross. I. G. SDectrochim. Acta. PartA investigations of total absolute overtone intensities, a decrease 1981, 37, 857. (4) Mortensen. 0. S.: H e m . B. R.: Mohammadi. M. A. J. Chem. Phvs. in total intensity was found as the basis set size was in1981,75, 4800. ~ r e a s e d . ~ 'This . ~ ~ is also seen in the present calculation. In (5) Child, M. S.; Lawton, R. T. Faraday Discuss. Chem. SOC.1981, the fundamental region, our local mode calculations and ab initio 71, 273. frequency calculations at different level^^-^^ (double harmonic (6) Sage, M. L.; Jortner, J. Adv. Chem. Phys. 1981, 47, 293. (7) Child, M. S.; Halonen, L. Adv. Chem. Phys. 1984, 57, 1. approximation) agree quite well. The observed oscillator (8) Sage, M. L. J. Chem. Phys. 1984, 80, 2872. strength28obtained from the fundamental spectrum of naphtha(9) Child, M. S. Ace. Chem. Res. 1985, 18, 45. lene in the Ar matrix at 12 K is somewhat lower than these (10) Henry, B. R. Ace. Chem. Res. 1987,20,429 and references therein. (11) Mortensen, 0. S.; Ahmed, M. K.; Henry, B. R.; Tam, A. W. J. values. Electron correlation is expected to improve the calcuChem. Phys. 1985, 72, 3903. lated intensities, especially for the fundamental transition, but (12) Tarr,A. W.; Swanton, D. J.; Henry, B. R. J. Chem. Phys. 1986, to have a much smaller effect on the overtone i n t e n s i t i e ~ . ~ ~ 85, ~ ~3463. ~ On the basis of these intensity calculations and the ab initio (13) Findsen, L. A.; Fang, L.; Swofford, R. L.; Birge, R. R. J. Chem. Phys. 1986, 84, 16. bond lengths, we feel comfortable with assigning the high(14) Tarr, A. W.; Zerbetto, F. Chem. Phys. Lett. 1989, 154, 273. frequency peak to the CHB stretching local mode. This (15) Kjaergaard, H. G.; Yu, H.; Schattka, B. J.; Henry, B. R.; Tarr, A. assignment is in contrast to the assignment given for the AVCH W. J. Chem. Phys. 1990, 93, 6239. = 5 overtone spectrum of naphthalene crystal^.^^,^^,^ This shift, (16) Kjaergaard, H. G.; Henry, B. R.; Tarr, A. W. J. Chem. Phys. 1991, 94, 5844. if real, would indicate a significant change in bond lengths from (17) Kjaergaard, H. G.; Henry, B. R. J. Chem. Phys. 1992, 96, 4841. vapor phase to crystals. (18) Kjaergaard, H. G. Ph.D. Thesis, Odense University, Denmark, 1992. (19) Niefer, B. I.; Kjaergaard, H. G.; Henry, B. R. J . Chem. Phys. 1993,
Conclusion
99, 5682.
We have measured the vapor phase overtone spectra of naphthalene in the regions corresponding to AVCH= 2-5 and have determined experimental peak positions and oscillator strengths. We have used vibrational wave functions and eigenenergies from an anharmonic oscillator local mode model and a Taylor expanded ab initio dipole moment function to calculate frequencies and oscillator strengths of the pure local mode CH stretching transitions. The observed and calculated frequencies of the pure local modes (Iv), and Iv)& are in very good agreement. The oscillator strengths were calculated with two different ab initio dipole moment functions (HF/6-31G* and HF/6-31 lG**). Both calculations give approximately the same relative intensity of the transitions to the and ( v )states. ~ However, comparison with observed absolute total oscillator strengths shows the larger basis set calculation to be closer to and in very good agreement with the observed values. The overtone spectra AVCH= 3-5 can distinguish between CH bonds that from ab initio geometry optimizations are predicted to have bond lengths that differ by less than a
1993, 99, 9438.
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