J. Phys. Chem. 1996, 100, 19273-19279
19273
CH Stretching Overtone Investigation of Relative CH Bond Lengths in Pyridine Henrik G. Kjaergaard, Robert J. Proos, David M. Turnbull, and Bryan R. Henry* Department of Chemistry and Biochemistry, UniVersity of Guelph, Guelph, Ontario N1G 2W1, Canada ReceiVed: June 4, 1996; In Final Form: September 4, 1996X
We have recorded the room temperature CH stretching overtone spectra of pyridine, both in the vapor and in the liquid phase. We have used intracavity laser photoacoustic as well as conventional near-infrared absorption spectroscopy to measure these overtone transitions. Peaks corresponding to three nonequivalent CH stretching local modes are assigned in the high-energy vapor phase spectrum, as opposed to previous investigations which assigned only two. Absolute oscillator strengths are obtained from the conventional spectra and relative oscillator strengths between the observed peaks within a given overtone from the photoacoustic spectra. Oscillator strengths are calculated with an anharmonic oscillator local mode model and ab initio dipole moment functions. In the high-energy vapor phase spectrum, we have assigned the three peaks based on comparisons with ab initio calculated bond lengths and accurate overtone intensity calculations. Our simple calculations, which contain no adjustable parameters, are in very good agreement with both the absolute and relative observed intensities.
Introduction CH stretching overtone spectra can be interpreted with the local mode model of molecular vibration.1-2 The peak positions can be calculated with a harmonically coupled anharmonic oscillator (HCAO) local mode model with reasonable accuracy.3-7 The HCAO local mode model and ab initio dipole moment functions have been successful in the calculation of CH stretching overtone intensities.8-16 Recently, overtone intensities of useful accuracy have been calculated and used to facilitate spectral assignment in naphthalene.17,18 In this work we investigate the overtone spectra of pyridine. We refer to the three nonequivalent CH bonds as CHo, CHm, and CHp for the ortho, meta, and para bonds, respectively. Previous studies of the CH stretching overtone spectra of pyridine have reported only two peaks at each overtone, both in the liquid19 and in the vapor phase spectra.20 Sørensen et al.21-23 have measured and analyzed the microwave spectra of pyridine. Their analysis refines the earlier pyridine structure24 and finds the CHm bond to be slightly longer than the CHp bond, but both are predicted to be shorter than the CHo bond. In naphthalene, the two nonequivalent CH bonds are predicted by ab initio calculation to differ by 0.6 mÅ. We found that even such a small difference in CH bond length was enough to allow us to distinguish the corresponding overtone peaks in the vapor phase overtone spectrum of naphthalene in the ∆VCH ) 4-6 regions.17,18 In this work we attempt to distinguish the three nonequivalent CH bonds in the overtone spectra of pyridine. Our strategy will be to improve the resolution of the previous vapor phase overtone investigation20 and to extend the spectral range. The resolution of peaks corresponding to nonequivalent CH bonds increases with increasing overtone energy. We will also use a number of different ab initio calculations to obtain CH bond lengths in pyridine. Peak positions are very sensitive to CH bond lengths.25 The bond length frequency correlation, where the shortest bond length is expected to correspond to the highest frequency CH stretching oscillator, has proven to be very useful in the assignment of XH stretching local mode overtone spectra.25 X
Abstract published in AdVance ACS Abstracts, November 1, 1996.
S0022-3654(96)01611-5 CCC: $12.00
A principal focus of the current work will be the calculation of overtone intensities. These calculations can be very useful in facilitating spectral assignment, especially in comparisons of predicted and observed relative intensities for nonequivalent CH bonds within a given overtone. Moreover, the role of electron correlation in the dipole moment function on calculated overtone intensities is of considerable interest. Previously we have found that the inclusion of electron correlation has little or no effect on calculated overtone intensities for ∆VXH g 3 in a series of small molecules.26,27 Our intensity calculations for the CH stretching vibrational spectrum of pyridine will allow us to assess the influence of electron correlation in a relatively large molecule. Experimental Section Liquid pyridine (Fisher Certified ACS, Fisher Scientific) was used without further purification in the liquid phase spectra and was degassed by freeze-pump-thaw cycles for use in the vapor phase spectra. A conventional spectrophotometer (Cary 5e UV-vis-nearIR) was used to record the vapor phase spectrum of pyridine in the regions corresponding to ∆VCH ) 2-4 and liquid phase spectrum in the regions corresponding to ∆VCH ) 2-6. For the vapor phase spectrum the Cary 5e instrument was fitted with a White variable path length cell (Wilks variable path length cell fitted with BK7 Schott glass windows from Melles Griot). Background scans with an evacuated cell were recorded and subtracted for each region. The sample pressure in the Wilks cell was limited by the room temperature vapor pressure of pyridine.28 In the liquid phase spectrum conventional cells of varying length (see figure captions) were used with an empty cell as a reference. The wavenumber accuracy of the Cary 5e spectrophotometer is approximately (3 cm-1 in the visible region (∆VCH ) 5 and 6) and decreases from (1 to (6 cm-1 in the near-IR region (∆VCH ) 2-4). All spectra were recorded at a room temperature of approximately 23 °C. The vapor phase fundamental region was recorded on a Fourier transform infrared spectrometer (Nicolet 20 SXC). The experimental absolute oscillator strength f of an absorption band can be determined from the conventional vapor phase spectrum and the following equation11,29,30 © 1996 American Chemical Society
19274 J. Phys. Chem., Vol. 100, No. 50, 1996
f ) 2.6935 × 10-9 [K-1 Torr m cm]
T ∫A(ν˜ ) dν˜ pl
Kjaergaard et al.
(1)
where T is the temperature, p is the sample pressure, l is the path length, A is the absorbance, and ν˜ is the frequency in cm-1. For comparisons with calculations, the liquid phase absolute intensities should be corrected for the deviation from unity of the refractive index of the liquid.31-33 Thus, the oscillator strength can be determined from a conventional liquid phase spectrum and the following equation11,29-33
f ) 4.3192 × 10-12 [mol cm-1]
1 9n A (ν˜ ) dν˜ 2 Cl ∫ liq (n + 2) (2) 2
where C is the molar concentration of the liquid sample and Aliq is the absorbance of the liquid. The refractive index of pyridine is n ) 1.51 at 20 °C and 589 nm.28 The refractive index changes slightly with wavelength (less than 10%) and temperature (less than 3%) over the range of our experiment, but we have assumed it to be constant. The room temperature vapor phase overtone spectrum of pyridine was recorded in the ∆VCH ) 4-7 regions with ICLPAS. Our version of ICL-PAS has been described in detail elsewhere.34,35 An argon ion laser chopped at 50 Hz was used to pump either a titanium:sapphire solid state broad band tunable laser (Coherent 890) for the ∆VCH ) 4 and 5 regions or a dye laser (Coherent 599-01) with the dyes rhodamine 6G or coumarin 6 for the ∆VCH ) 6 and 7 regions, respectively. As explained in detail in ref 35, the wavenumber accuracy was better than (1 cm-1. The photoacoustic cell, fitted with an electret microphone (Knowles Electronics Inc., EK3132), was filled with different pressures of pyridine (see figure captions). For the overtone ∆VCH ) 7, 100 Torr of the buffer gas argon was added to increase the signal strength. The absolute absorbance is not known, and we can only obtain the relative oscillator strengths from the ICL-PAS spectra.35 When necessary, the pyridine and the buffer gas were passed through glass tubes, which contained dried molecular sieve pellets, to extract trace amounts of H2O. The overtone spectra were decomposed into component peaks with a deconvolution program within Spectra Calc.36 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 depends on the signal-to-noise ratio of the spectrum, peak resolution, and also possible deviations from Lorentzian line shapes. We generally estimate the uncertainty to be less than 5 cm-1 for peak positions and less than 10% for intensities of well-resolved peaks. However, for the poorly resolved peaks we estimate a much larger uncertainty, especially for peak shoulders. We estimate the uncertainty for these to be less than 10 cm-1 for peak positions and as high as 30% for relative intensities, with somewhat larger values in the liquid phase spectrum due to the generally broader peaks. Theory The calculation of the CH stretching intensities of pyridine is very similar to our recent calculation of the CH stretching intensities of naphthalene, to which we refer for details,17 and here we present only a brief outline of the theory. The oscillator strength f of a vibrational transition from the ground vibrational state “g” to an excited vibrational state “e” is given by11,29,30
ferg ) 4.702 × 10-7 [cm D-2] ν˜ eg|µbe g|2
(3)
where 1tνeg is the transition frequency in cm-1 and b µeg ) 〈e|µ b|g〉 is the transition dipole moment in debye. Pyridine has three nonequivalent CH bonds, two at the 2,6 (ortho) positions, two at the 3,5 (meta) positions, and one at the 4 (para) position. Similar to naphthalene, the hydrogens in pyridine are attached to different carbon atoms, and we expect the different CH bonds in pyridine to be very weakly coupled.17 To first order this coupling is limited to potential energy coupling (force constants), and ab initio calculations show that these force constants for pyridine are similar in size to those we calculated for naphthalene.17 In naphthalene we found direct spectral evidence for this lack of coupling.17,18 We use the local mode theory of harmonically coupled anharmonic oscillators (HCAO) and neglect this small coupling. Thus, we treat pyridine as three nonequivalent isolated CH groups,10,17 each of them described by a Morse oscillator. The Hamiltonian for the para CHp oscillator can be written as
(H - E|0〉p)/hc ) Vpω ˜ p - (Vp2 + Vp)ω ˜ pxp
(4)
˜p where E|0〉p is the energy of the vibrational ground state and ω and ω ˜ pxp are the local mode frequency and anharmonicity of the CHp oscillator. The Hamiltonian for the ortho, CHo, and ˜ is used for meta, CHm, oscillators is similar. Historically, ω the (linear) frequency of vibrations. We have added the tilde to indicate that the unit of ω ˜ is cm-1. The eigenstates of the Hamiltonians are denoted by |Vp〉, where Vp is the vibrational quantum number of the CHp oscillator. For each of the three nonequivalent CH bonds, the dipole moment function is expressed as a series expansion in the internal CH displacement coordinate, q. For the CHp oscillator, we have
µ jqpj b µ p(q) ) ∑b
(5)
j
b µj )
|
µ 1 ∂j b j! ∂q j
(6)
p e
We have limited the expansion in eq 5 to fourth-order terms.13,30 To determine the coefficients b µj, we use ab initio molecular orbital theory to calculate dipole moment values at geometries in which the CHp bond is displaced from equilibrium. We refer to previous papers for details of procedures to determine these coefficients.11,15,17 For some smaller molecules, we recently showed that an increased basis set size, beyond 6-31G(d), improved calculated absolute intensities, whereas electron correlation had only a minor effect on the overtone intensities.26,27 For the CH stretching part of pyridine, we have calculated the dipole moment function at the self-consistentfield Hartree-Fock (HF) level with the 6-31G(d), 6-311+G(d,p), and 6-311++G(2d,2p) standard basis sets and at the second-order Møller-Plesset (MP2) level with the 6-31G(d) basis set. These calculations would indicate if our previous conclusions for smaller molecules are also valid for a larger molecule like pyridine. All ab initio calculations were done with Gaussian 92.37 The vibrational wave functions and energies found from eq 4 are used in eq 3 together with the dipole moment function of eqs 5 and 6 to obtain calculated oscillator strengths. Results and Discussion The vapor phase overtone spectra of pyridine in the CH stretching regions corresponding to ∆VCH ) 4-7 are shown in Figures 1-4. The spectra of the ∆VCH ) 3-6 regions agree
Relative CH Bond Lengths in Pyridine
J. Phys. Chem., Vol. 100, No. 50, 1996 19275
Figure 1. Room temperature vapor phase overtone spectrum of pyridine in the ∆VCH ) 4 region. The spectrum was measured by ICLPAS with a sample pressure of 10 Torr. The individual Lorentzian functions and the linear base line fit to the experimental spectrum (noisy spectrum) are also shown as well as their sum (smooth lines).
Figure 3. Room temperature vapor phase overtone spectrum of pyridine in the ∆VCH ) 6 region. The spectrum was measured by ICLPAS with a sample pressure of 15 Torr. The individual Lorentzian functions and the linear base line fit to the experimental spectrum (noisy spectrum) are also shown as well as their sum (smooth lines).
Figure 2. Overtone spectra of pyridine in the ∆VCH ) 5 region. Lower trace: the room temperature vapor phase spectrum which was measured by ICL-PAS with a sample pressure of 17 Torr. Upper trace: the room temperature liquid phase spectrum which was measured with a conventional absorption spectrometer and a 10 cm path length.
Figure 4. Room temperature vapor phase overtone spectrum of pyridine in the ∆VCH ) 7 region. The spectrum was measured by ICLPAS with a sample pressure of 17 Torr and 100 Torr of argon buffer gas.
with previously reported spectra,20 apart from changes in relative intensities. The absence of corrections in the earlier spectra20 for variation in laser power during a scan is a likely explanation for these intensity differences. The liquid phase spectra of pyridine in the ∆VCH ) 2-6 regions agree well with previous spectra.19 The spectrum of liquid phase pyridine in the ∆VCH ) 5 region is shown in Figure 2 to facilitate comparison with the vapor phase spectrum. The observed frequencies, line widths, relative intensities within an overtone, and the spectral assignments of the deconvoluted peaks from the pyridine spectra are given in Tables 1 and 2 for the vapor and liquid phase, respectively. The observed frequency ν˜ of the pure local mode peaks (|V〉o, |V〉m, and |V〉p) have been fitted to a two-parameter Morse oscillator energy expression
ν˜ l(V)/V ) ω ˜ l - (V + 1)ω ˜ lxl (l ) o, m, p)
(7)
in order to obtain values of the local mode frequency ω ˜ and anharmonicity ω ˜ x of the different 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 supports our assumption of weak CH couplings. Liquid Phase Pyridine. The liquid phase CH stretching overtone spectrum of pyridine shows two broad bands in each of the overtone regions. A comparison of the pyridine spectrum with the liquid phase overtone spectrum of 2,6-dimethyl pyridine resulted in the assignment of the lower frequency band in the pyridine spectrum to the CHo oscillators and the higher frequency band to the unresolved CHm and CHp oscillators.19 Our liquid phase spectrum also shows no spectral evidence for a splitting of the high-frequency band, and we have deconvoluted each of the overtone regions into two peaks. The liquid phase local mode parameters for the two progressions agree well with the previously reported parameters.19 The higher frequency peak is consistently broader than the other peak. We attribute this increased width to the fact that the higher frequency peak consists of two peaks (CHm and CHp) which are slightly separated. The liquid phase relative intensity of the two structures within a given overtone fluctuates significantly with V (Table 2). Such
19276 J. Phys. Chem., Vol. 100, No. 50, 1996
Kjaergaard et al.
TABLE 1: Observed and Calculated Frequencies and Oscillator Strengths, Observed Line Widths, and Peak Assignments for the CH Stretching Overtone Spectra of Vapor Phase Pyridine calculatedc
observed νj/cm-1
Γa/cm-1
fb
νj/cm-1
11 398
116
1.0
11 544
87
0.81
13 942
104
1.0
14 132
113
1.03
16 373 16 578 16 632 18 687 18 939 18 993
102 92 96 98 80 114
1.0 0.42 0.65 1.0 0.26 0.96
11 390 11 510 11 558 13 942 14 101 14 154 16 374 16 578 16 632 18 689 18 939 18 993
{ {
f
assignt
1.8 × 10-9 0.6 × 10-9 1.1 × 10-9 1.7 × 10-10 0.6 × 10-10 1.1 × 10-10 1.9 × 10-11 0.6 × 10-11 1.3 × 10-11 2.6 × 10-12 0.9 × 10-12 1.8 × 10-12
|4〉o |4〉p |4〉m |5〉o |5〉p |5〉m |6〉o |6〉p |6〉m |7〉o |7〉p |7〉m
a fwhm line width. b Relative intensities within an overtone region. Calculation with the local mode parameters from Table 3 and the HF/6-311++G(2d,2p) dipole moment function. c
TABLE 2: Observed Frequencies, Line Widths, Relative Intensities, and Peak Assignments for the CH Stretching Overtone Spectra of Liquid Phase Pyridine
a
νj/cm-1
Γa/cm-1
Ibrel
assignt
8 665 8 790 11 331 11 499 13 855 14 076 16 260 16 555
127 141 183 198 198 280 193 375
1.0 1.9 1.0 1.6 1.0 2.5 1.0 4.6
|3〉o |3〉m,p |4〉o |4〉m,p |5〉o |5〉m,p |6〉o |6〉m,p
fwhm line width. b Relative intensities within an overtone region.
TABLE 3: Local Mode Frequency and Anharmonicity of the CH Stretching Modes in Vapor and Liquid Phase Pyridinea b
CHo CHpb CHmb CHoc CHm,pc
ω j /cm-1
ω ˜ x/cm-1
3144 ( 3 3164 3183 3129 ( 6 3160 ( 3
59.2 ( 0.5 57.3 58.8 59.7 ( 1.0 57.2 ( 0.5
a Uncertainties are one standard deviation. b Vapor phase values from a fit of the local mode frequencies in the ∆VCH ) 3-7 regions for CHo and in the ∆VCH ) 6 and 7 regions for CHm and CHp. c Liquid phase values from a fit of the local mode frequencies in the ∆VCH ) 3-6 regions.
fluctuations are smaller in our vapor phase results (Table 1) and are not significant. We believe that the fluctuations are due largely to uncertainties in the deconvolutions. Comparison of the liquid and vapor phase spectra (Figure 2) shows, not surprisingly, a red shift in peak positions from the vapor to the liquid phase. The red shift from vapor to liquid phase is also apparent from the observed local mode parameters (Table 3). The local mode frequencies are lower in the liquid phase spectrum whereas the anharmonicities do not change significantly. It is apparent and not surprising that the line widths of the CH stretching transitions increase significantly from vapor to liquid phase spectra. Vapor Phase Pyridine. The previous CH stretching overtone vapor phase spectra of pyridine20 reported two bands in each of the overtone regions. The higher frequency band was assigned to unresolved CHm and CHp transitions and the lower frequency band to CHo transitions. This assignment was based
TABLE 4: Ab Initio CH Bond Lengths and Dipole Moments in Pyridinea bond lengthsa/Å method
CHo
CHm
CHp
dipole/D
HF/STO-3G HF/6-31G(d) HF/6-31G(d,p) HF/6-311+G(d,p) HF/6-311+G(2d,p) HF/6-311++G(2d,2p) MP2/6-31G(d) MP2/6-31+G(d,p) MP2/6-311+G(d,p) QCISD/6-31G(d) exptb
1.0869 1.0760 1.0767 1.0765 1.0757 1.0738 1.0887 1.0840 1.0881 1.0903 1.0865
1.0817 1.0743 1.0746 1.0743 1.0734 1.0715 1.0865 1.0825 1.0860 1.0881 1.0826
1.0833 1.0754 1.0759 1.0757 1.0748 1.0728 1.0872 1.0829 1.0865 1.0890 1.0818
2.059 2.314 2.310 2.375 2.317 2.308 2.316 2.473 2.415 2.268 2.215
a The indices o, m, and p refer to the CH stretching coordinates associated with the ortho, meta, and para hydrogens. b Experimental bond lengths and permament dipole moment from the microwave analysis in refs 21 and 22.
in part on the microwave21 CH bond lengths and the bond length frequency correlation (the shorter the bond, the higher the local mode frequency).25 The higher frequency peak consists of transitions to both CHm and CHp oscillators and as we would expect was observed to be wider than the lower frequency peak.20 In Table 4 we show CH bond lengths in pyridine that we have calculated with different ab initio approaches. The calculations at the HF level agree with previous HF results, with regard to both the magnitude38 and the relative ordering of the three CH bond lengths.38,39 We have extended our calculations to include electron correlation, both at the MP2 level with basis sets as large as 6-311+G(d,p) and at the QCISD level with a 6-31G(d) basis set. It is significant that although the absolute magnitudes of the bond lengths change, the relative ordering of the ab initio CH bond lengths is consistently Rm < Rp < Ro, from which we would expect the local mode frequencies to be ˜p < ω ˜ m. ordered: ω ˜o < ω Thus, in the overtone spectra the CHo peak is expected at a significantly lower frequency as compared to the CHp and CHm peaks, in agreement with what was previously observed.20 In our previous work on vapor phase naphthalene,17,18 we were able to use deconvolution to distinguish peaks corresponding to CH bonds with bond lengths that were calculated to differ by only 0.6 mÅ. On the basis of the calculated CH bond length differences in pyridine (Table 4), we expected to distinguish the peaks arising from the CHp and CHm bonds, at least at the highest overtones. The vapor phase spectrum of pyridine in the ∆VCH ) 6 and 7 regions (Figures 3 and 4) clearly shows the higher frequency band to consist of two peaks. We have deconvoluted the ∆VCH ) 6 and 7 vapor phase overtone spectra of pyridine with one peak for the lower frequency band and two peaks for the higher frequency band. The higher frequency band has not been deconvoluted into two peaks in the ∆VCH ) 4 and 5 regions. The vapor phase local mode parameters for the three CH oscillators (Table 3) are smaller in magnitude than the previously reported values.20 As expected, we observe the splitting between the CHp and CHm peaks to increase from the ∆VCH ) 6 region to the ∆VCH ) 7 region (Table 1). The splitting is 54 cm-1 at ∆VCH ) 6, which is significantly smaller than the splitting we observed in the vapor phase spectrum of naphthalene in the ∆VCH ) 6 region.18 The ab initio CH bond lengths in Table 4 predict Rm < Rp with a bond length difference (discounting the HF/STO-3G result) in the range 0.4-1.4 mÅ. Thus, we have assigned the highest frequency peak at each overtone to the CHm oscillator.
Relative CH Bond Lengths in Pyridine
Figure 5. Observed relative intensities for the ∆VCH ) 6 region of the vapor phase spectrum of pyridine and calculated relative intensities with different dipole moment functions. The last column is the sum of the meta and para intensities. The ortho peak intensity has been set to unity.
In the ∆VCH ) 6 and 7 regions, where the splitting of the CHp and CHm peaks is spectroscopically evident, the deconvolution shows the intensity of the CHm peak to be larger than the CHp peak (Table 1). Since there are two CHm bonds and only one CHp bond, we would expect the CHm peak to be more intense. We have recently shown that our overtone intensity calculations, which use HCAO vibrational wave functions and ab initio dipole moment functions, are a very useful tool in spectral assignments.17,18 We have calculated CH stretching overtone intensities for pyridine (Vide infra), and these calculations predict the CHm transitions to be approximately 1.7 times more intense than the CHp transitions, in close agreement with what we have observed (see Figure 5). Thus, the overtone intensity calculations support our assignment. On the basis of these intensity calculations (Vide infra) and the ab initio bond lengths, we are confident of our assignment of the three peaks in the pyridine overtone spectra. The fundamental spectra of C2V deuterium-substituted pyridines have been measured by DiLella and Stidham.40-42 From these spectra it is possible to obtain transition frequencies for isolated CH bonds in the ortho, meta, and para positions. The observed frequencies of the isolated CH oscillators increase from ortho to para to meta, in agreement with the local mode frequencies from our overtone spectra. Both the local mode frequencies and the isolated CH frequencies are in agreement with the ab initio CH bond lengths and the bond length frequency correlation.25,43 The CH bond lengths from the microwave analysis predict Rp > Rm with a bond length difference of 0.8 ( 0.5 mÅ.21 Thus, if the frequency bond length correlation is valid, the microwave CH bond lengths would suggest that the highest frequency peak be assigned to the CHp oscillator. However, this assignment would lead to complete disagreement between the observed and calculated intensities for the higher overtones at ∆VCH ) 6 and 7. In a critical review of microwave structures, Harmony et al.44 report an uncertainty of the CH bond lengths in pyridine at least 3 times larger than the uncertainty in the earlier original analysis22 which they reviewed. One of the problems with substitution structures in microwave analysis is the difference between CH and CD bond lengths.45 The average bond length of a CH oscillator in the vibrational ground state is about 4
J. Phys. Chem., Vol. 100, No. 50, 1996 19277 mÅ longer than that of a CD oscillator. Thus, it appears that the uncertainty in the CH bond lengths in pyridine is likely to be somewhat larger than the reported 0.4 mÅ21 and that the CHm and CHp bond lengths are within the uncertainties of the microwave analysis. The only other explanation consistent with our assignment and the microwave bond lengths is a breakdown of the bond length frequency correlation.25,43 Relative Overtone Intensities. Our intensity calculations rely on an ab initio calculated dipole moment function, which is calculated for an isolated molecule. Thus, our intensity calculations are best compared to vapor phase spectra where intermolecular interaction is weakest. In the liquid phase considerable interaction between the molecules might alter the dipole moment function and thus alter the intensities. In Table 1 we compare our calculated intensities with the relative observed vapor phase intensities. We have only shown the intensities calculated with the HF/6-311++G(2d,2p) dipole moment function. The calculated intensities with the smaller basis set dipole moment functions show similar relative intensities within a given overtone. Since the observed splitting of meta and para peaks is much smaller than the observed line widths of the peaks, the deconvolution has considerable uncertainty. The intensities are much more sensitive to deconvolution than are the peak positions. In Table 1 we see that the agreement between experimental and calculated relative intensities is good for the higher overtone regions, ∆VCH ) 6 and 7. In the ∆VCH ) 4 and 5 spectra (Figures 1 and 2), the CHm and CHp peaks are not well resolved and have not been deconvoluted as two peaks. The first three clusters of columns in Figure 5 show a comparison of observed and calculated relative intensities of the ortho, meta, and para peaks in the ∆VCH ) 6 region. On the basis of the quality of the spectra (resolution, signal-tonoise ratio, and laser power), we expect that the spectrum of the ∆VCH ) 6 region has the best deconvolution. Figure 5 shows that the calculated relative intensities within the overtone are predicted very well with all four ab initio dipole moment functions. Thus, if only relative overtone intensities are of interest, even the HF/6-31G(d) calculation seems to be sufficient. To avoid the problems associated with the deconvolution of the meta and para peaks, we compare the intensity of the ortho peak to the sum of the intensities of the meta and para peaks. The first and the last clusters of columns in Figure 5 show that the agreement is excellent. The small differences in the meta and para peak intensities in the two center clusters are thus most likely due to errors in deconvolution. For the overtone regions ∆VCH ) 4-7, the ratios of the intensity of the meta plus para peaks to the intensity of the ortho peak are close to unity, in very good agreement with the calculated ratios (Table 1). The calculated permanent dipole moment of pyridine (Table 4) is within 10% of the experimental value. Only the HF/STO3G calculation obtains a value that is smaller than the experimental value.22 Absolute Intensities. Absolute intensities are more difficult to calculate and to measure than relative intensities. In Table 5 we compare the observed and calculated absolute total CH stretching oscillator strengths for the ∆VCH ) 1-6 CH stretching regions in pyridine. We have obtained experimental oscillator strengths from the conventionally recorded spectra for the ∆VCH ) 1-4 regions of the vapor phase spectrum and for the ∆VCH ) 2-6 regions of the liquid phase spectrum. Absolute intensities cannot be derived from our ICL-PAS spectra. We expect the uncertainty of the oscillator strengths from the liquid phase spectra to be somewhat larger than the those from the vapor phase spectra due to variation of the refractive index of
19278 J. Phys. Chem., Vol. 100, No. 50, 1996
Kjaergaard et al.
TABLE 5: Observed and Calculated Total Oscillator Strengths of the CH Stretching Fundamental and Overtone Regions in Pyridine calculateda V
c
HF
1 2 3 4 5 6 7
1.8 5.0 9.5 11.9 15.5 22.4 36.4
c
observedb
MP2
d
e
HF
HF
vapor
1.1 3.7 8.2 10.8 14.3 20.9 34.2
1.4 4.3 4.8 5.4 6.8 10.0 16.5
1.3 4.5 4.2 3.5 3.4 3.9 5.3
1.2 4.6 5.4 3.4
liquid
exponent
2.8 3.9 3.5 4.0 5.4
10-5 10-7 10-8 10-9 10-10 10-11 10-12
a Calculated with the local mode parameters of Table 3. b Estimated accuracy is 30% for vapor phase and 40% for liquid phase. c With the 6-31G(d) basis set. d With the 6-311+G(d,p) basis set. e With the 6-311++G(2d,2p) basis set.
the liquid with wavelength. Due to possible changes of the dipole moment function in the liquid phase, we do not expect the liquid and vapor phase absolute oscillator strengths to agree perfectly. However, we assume the liquid phase intensities to be of the right order of magnitude. Comparisons of the observed liquid and vapor phase intensities in the ∆VCH ) 2-4 region indicate reasonable agreement. Our earlier investigation suggested that a HF/6-311++G(2d,2p) calculated dipole moment function would lead to overtone intensities in good agreement with experimental intensities.26 The results in Table 5 show that the agreement between the measured and HF/6-311++G(2d,2p) calculated oscillator strengths is indeed very good. Comparison of the HFc and MP2c columns in Table 5 illustrates the effect of electron correlation on the calculated overtone intensities. In agreement with what we have observed previously for some smaller molecules,26,27 it is apparent from Table 5 that electron correlation in the ab initio dipole moment function has little effect on the intensities of overtone transitions with ∆VCH g 3. Electron correlation has a significant effect on the intensity of the fundamental transition and to a lesser extent also on the intensity of the first overtone transition. The HF/6-31G(d) ab initio frequency calculation of pyridine gave a fundamental CH stretching oscillator strength (double harmonic approximation) of 2.0 × 10-5 compared to our calculated fundamental intensity of 1.8 × 10-5 (Table 5), thus in reasonable agreement. In earlier investigations we have found that the total absolute overtone intensities decreased as the basis set size in the HF ab initio dipole moment function calculation was increased.17,26 It is clear from Figure 6, that an increase in basis set significantly improves the agreement with the experimental absolute total CH stretching oscillator strengths. The agreement extends over 6 orders of magnitude with calculations that contain no adjustable parameters. Conclusion We have measured the vapor and liquid phase overtone spectra of pyridine and have extended the range of the previous vapor phase spectra20 to include the ∆VCH ) 7 region. Furthermore, our vapor phase spectra have improved resolution and relative intensities, both of which are essential for the spectral assignment. We have based our assignment on both ab initio bond lengths and calculations of relative CH stretching overtone intensities. The oscillator strengths of the CH stretching transitions have been calculated with a Taylor expanded ab initio dipole moment function and vibrational wave functions and eigenenergies from an anharmonic oscillator local mode model. These calculated
Figure 6. Observed and calculated absolute intensities summed over each vibrational manifold in the CH stretching spectra of pyridine.
oscillator strengths are compared to the oscillator strengths obtained from the vapor phase overtone spectra. The oscillator strengths were calculated with four different ab initio dipole moment functions (HF and MP2/6-31G(d), HF/6-311+G(d,p), and HF/6-311++G(2d,2p)). All four calculations give approximately the same relative intensity of the three CH stretching peaks and agree well with the observed relative intensities in the spectral regions where three peaks are clearly evident. The larger basis set HF calculation of the absolute total oscillator strengths is closer to and in very good agreement with the observed values. Our intensity calculations contain no adjustable parameters. Electron correlation in the ab initio calculation of the dipole moment function does not have a significant effect on the higher overtone intensities, in agreement with our earlier observations for some smaller molecules. On the basis of the ab initio relative bond lengths and the bond length frequency correlation, we assign the three peaks to the CHo, CHp, and CHm bonds, in order of increasing frequency. This assignment is supported by our intensity calculations which correctly predicts the transition associated with the CHm bonds to be stronger than the CHp peak. The assignment is also supported by fundamental spectra of selectively deuterated pyridines. Acknowledgment. We are particularly grateful to Prof. Deanne Snavely both for communicating her research results on pyridine and for valuable discussions. Funding for this research has been provided by the Natural Sciences and Engineering Research Council of Canada. References and Notes (1) Hayward, R. J.; Henry, B. R. J. Mol. Spectrosc. 1975, 57, 221. (2) Henry B. R. Acc. Chem. Res. 1977, 10, 207. (3) Watson, I. A.; Henry, B. R.; Ross, I. G. Spectrochim. Acta, Part A 1981, 37, 857. (4) Mortensen, O. S.; Henry, B. R.; Mohammadi, M. A. J. Chem. Phys. 1981, 75, 4800. (5) Child, M. S.; Lawton, R. T. Faraday Discuss. Chem. Soc. 1981, 71, 273. (6) Sage, M. L.; Jortner, J. AdV. Chem. Phys. 1981, 47, 293. (7) Child, M. S.; Halonen, L. AdV. Chem. Phys. 1984, 57, 1. (8) Mortensen, O. S.; Ahmed, M. K.; Henry, B. R.; Tarr, A. W. J. Chem. Phys. 1985, 72, 3903. (9) Findsen, L. A.; Fang, H. L.; Swofford, R. L.; Birge, R. R. J. Chem. Phys. 1986, 84, 16. (10) Tarr, A. W.; Zerbetto, F. Chem. Phys. Lett. 1989, 154, 273. (11) Kjaergaard, H. G.; Yu, H.; Schattka, B. J.; Henry, B. R.; Tarr, A. W. J. Chem. Phys. 1990, 93, 6239.
Relative CH Bond Lengths in Pyridine (12) Kjaergaard, H. G.; Henry, B. R.; Tarr, A. W. J. Chem. Phys. 1991, 94, 5844. (13) Kjaergaard, H. G.; Henry, B. R. J. Chem. Phys. 1992, 96, 4841. (14) Niefer, B. I.; Kjaergaard, H. G.; Henry, B. R. J. Chem. Phys. 1993, 99, 5682. (15) Kjaergaard, H. G.; Turnbull, D. M.; Henry, B. R. J. Chem. Phys. 1993, 99, 9438. (16) Turnbull, D. M.; Kjaergaard, H. G.; Henry, B. R. Chem. Phys. 1995, 195, 129. (17) Kjaergaard, H. G.; Henry, B. R. J. Phys. Chem. 1995, 99, 899. (18) Kjaergaard, H. G.; Henry, B. R. J. Phys. Chem. 1996, 100, 4749. (19) Bini, R.; Foggi, P.; Della Valle, R. G. J. Phys. Chem. 1991, 95, 3027. (20) Snavely, D. L.; Overly, J. A.; Walters, V. A. Chem. Phys. 1995, 201, 567. (21) Mata, F.; Quintana, M. J.; Sørensen, G. O. J. Mol. Struct. 1977, 42, 1. (22) Sørensen, G. O.; Mahler, L.; Rastrup-Andersen, N. J. Mol. Struct. 1974, 20, 119. (23) Sørensen, G. O. J. Mol. Spectrosc. 1967, 22, 325. (24) Bak, B.; Hansen-Nygaard, L.; Rastrup-Andersen, J. J. Mol. Spectrosc. 1958, 2, 361. (25) Henry, B. R. Acc. Chem. Res. 1987, 20, 429 and references therein. (26) Kjaergaard, H. G.; Henry, B. R. Mol. Phys. 1994, 83 1099. (27) Kjaergaard, H. G.; Daub, C.; Henry, B. R. Mol. Phys., in press. (28) CRC Handbook of Chemistry and Physics, 73rd ed.; Chemical Rubber: Boca Raton, FL, 1992. (29) Atkins, P. W.; Molecular Quantum Mechanics, 2nd ed.; Oxford University: Oxford, 1983. (30) Kjaergaard, H. G. Ph.D. Thesis, Odense University, Denmark, 1992. (31) Bulanin, M. O. J. Mol. Struct. 1973, 19, 59.
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