Phase shift cavity ring-down measurement of C–H (Δv=6) vibrational overtone absorptions

9 February 2001

Chemical Physics Letters 334 (2001) 357±364

www.elsevier.nl/locate/cplett

Phase shift cavity ring-down measurement of C±H (Dv ˆ 6) vibrational overtone absorptions Ernest K. Lewis a, Dovie Reynolds a, Xiaochuan Li a, Geraud de Villele a,b, ~o a, Carlos Manzanares I a,* Charles Leduc a,b, David L. Ceden a b

Department of Chemistry & Biochemistry, Baylor University, Waco, TX 76798, USA Insititute of Theoretical and Applied Optics (Ecole Superieure d'Optique) Orsay, France Received 11 May 2000; in ®nal form 21 November 2000

Abstract Phase shift cavity ring-down absorption spectroscopy with a continuous laser is used to measure the absorption coecients and integrated cross-sections for the Dv ˆ 6 C±H stretching overtones of C2 H4 ; C2 H6 ; C3 H8 ; n-C4 H10 , and n-C5 H12 . The absorption spectrum is obtained by measuring the magnitude of the phase shift that an intensity modulated continuous laser beam experiences upon passing through an optical cavity. Sensitive absorption detection (10ÿ6 cmÿ1 ) on gas-phase samples is demonstrated. Ó 2001 Elsevier Science B.V. All rights reserved.

1. Introduction In the phase shift cavity ring-down technique the lifetime of a photon in a high-®nesse optical resonator is calculated from the measured phase shift angle between the modulated input and output light that passes through the optical cavity. This technique was originally used by Herbelin et al. [1] to measure mirror re¯ectivities. In 1996, Engeln et al. [2] used for the ®rst time the same method to obtain an electronic transition of O2 in the visible region. The phase shift method is different from the conventional ring-down technique in which the photon lifetime in the resonator is

*

Corresponding author. Fax: +1-254-710-2403. E-mail address: [email protected] (C. Manzanares I).

directly measured by monitoring the intensity decay that occurs when a laser pulse is injected into the cavity. The conventional cavity ring-down technique (CRD) has its origin in the work of Anderson et al. [3] to measure mirror re¯ectivities and the work of O'Keefe and Deacon [4] which used a pulsed-laser and the CRD technique as a spectroscopic method for absorption measurements. Since then the technique has been used in several spectroscopic and kinetic measurements [5]. The CRD technique has been used to measure absolute cross-sections and high vibrational overtone absorptions of HCN [6], HCCH [7,8], CHF3 [9], N2 O [10,11], H2 O [12], OH [13], and C6 H6 [14]. In this Letter we present an application of the phase shift cavity ring-down method. The overtone spectra, absorption coecients, and integrated cross-sections were measured for the …Dv ˆ 6† C±H stretching overtones of C2 H4 ; C2 H6 ; C3 H8 , n-C4 H10 , and n-C5 H12 .

0009-2614/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 0 ) 0 1 4 6 6 - 4

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E.K. Lewis et al. / Chemical Physics Letters 334 (2001) 357±364

2. Experimental

3. Results

The pump laser is a solid-state, frequency doubled Nd:YVO4 laser (Coherent±Verdi) providing single wavelength (532 nm) at a power level of 5 W. This laser is used to pump a continuous wave (Coherent 599-01) dye laser. The output of the dye laser is passed through an electro-optic modulator (EOM) (Conoptics modulator and driver). The laser beam is modulated as a square wave. Wavelength tuning of the (1 cmÿ1 bandwidth) dye laser is accomplished with a birefringent ®lter driven by a stepper motor. The stepper motor is controlled with a microcomputer. After passing through an iris and mode-matching optics, the modulated output of the dye laser is coupled into an optical cavity (81 cm) which consists of two highly re¯ective mirrors. The mirrors have a diameter of 25 cm and radius of curvature r ˆ 1 m. The signal is detected by a photomultiplier which is located behind the cavity. From the photomultiplier the signal is ampli®ed and connected to a lock-in ampli®er (Stanford SR 830). The zero phase shift is obtained bypassing the cavity. The lock-in ampli®er measures the amplitude and the phase di€erence between the signal passing through the cavity and the signal obtained bypassing the cavity. The phase shift of the empty cavity is around 45° with an angular modulation frequency, X ˆ …2p  15† kHz. The data are acquired with a microcomputer via a GPIB interface. The reference signal for the lock-in ampli®er is obtained from a function generator which also supplies the modulation signal to the driver input of the electro-optic modulator. We use LA B V I E W programs to control the data acquisition, dye laser wavelength scan, processing and displaying data, and output the ®nal results to a text ®le. Rhodamine 610 was used as the laser dye in the range 14,800±16,700 cmÿ1 . Absolute calibration of the dye laser lines was achieved obtaining the optogalvanic spectrum of a hollow cathode lamp ®lled with neon [15]. Samples of C2 H4 ; C2 H6 ; C3 H8 , n-C4 H10 , and n-C5 H12 were obtained from Aldrich. All experiments were performed at 22  2°C.

The spectra of the Dv ˆ 6 (C±H) absorption of C2 H4 ; C2 H6 ; C3 H8 , n-C4 H10 , and n-C5 H12 are shown in Figs. 1 and 2. The spectra show the absorption …cmÿ1 † on the left axis and the crosssection on the right axis …cm2 =molecule† as a function of the wave number. The bands have previously been assigned [16]. The single peak for the spectra of ethane and ethene in Fig. 1 arises

Fig. 1. Phase shift cavity ring-down absorption spectrum of the Dv ˆ 6 (C±H) overtone of gaseous ethene (200 Torr) and ethane (251 Torr) at 295 K.

E.K. Lewis et al. / Chemical Physics Letters 334 (2001) 357±364

359

from symmetrically equivalent hydrogen bonds. The propane, n-butane, and n-pentane spectra in Fig. 2 show the progression m…±CH3 † greater than m…±CH2 †. The ±CH2 is assigned as Hm . The …±CH3 † splits into two bands corresponding to one inplane C±H bond …Hs † and two out-of-plane CH bonds …Ha †. The spectra of propane, n-butane, and n-pentane were ®t by a computer program to a sum of Lorentzian bands. For each band, the peak positions, assignments, and integrated cross-sections are summarized in Table 1. The calculated lowest energy conformers n-pentane to be discussed in Section 4.3 are shown in Fig. 3.

4. Discussion 4.1. Absorption The phase shift …/† of the modulated beam that emerges from the optical cavity relative to the modulated input beam is related to the time that the light spends in the cavity or ring-down time …s† by the equation: tan / ˆ 2pf s;

…1†

where f is the modulation frequency. For a cavity ®lled with absorbing gas under conditions where the Beer±Lambert law is valid, the ring-down time is: s…m† ˆ

` : c‰…1 ÿ R† ‡ a…m†`Š

…2†

The lifetime is related to the re¯ectivity of the mirrors (R), the speed of light c, the absorption coecient …a† of the sample and the length (`) of the optical cavity. The absorption coecient of the sample is obtained through the relationship: a…m† ˆ

Fig. 2. Phase shift cavity ring-down absorption spectrum of the Dv ˆ 6 (C±H) overtone of gaseous propane (218 Torr), n-butane (148 Torr) and n-pentane (148 Torr) at 295 K.

1 1 ÿ : s…m†c s0 …m†c

…3†

The absorption spectrum of the background or ÿ1 empty cavity ‰s0 …m†cŠ ˆ ‰…1 ÿ R†=`Š is subtracted from the absorption spectrum of the sample plus ÿ1 the background …s…m†c† in order to obtain the absorption of the sample.

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Table 1 Peak assignments, transition wave numbers, full width at half maximum (fwhm), and integrated cross-sections for the Dv ˆ 6 (C±H) overtone transitions

a b

Molecule

Assignment

Wave number (cmÿ1 )

fwhm (cmÿ1 )

Cross-section (fm2 =molecule)a

C2 H4

CH (equiv.)

16551

132

0:30  0:01 (0.26b ; 0.39b )

C2 H6

CH (equiv.)

15823

131

0:51  0:06 (0.65b )

C3 H8

Total band Hm Ha Hs

15565 15741 15823

157 99 121

0:50  0:01 0.15 0.18 0.17

n-C4 H10

Total band Hm Ha Hs

15474 15750 15833

203 134 103

0:62  0:02 0.26 0.22 0.14

n-C5 H12

Total band Hm Ha Hs

15469 15756 15820

228 129 96

0:77  0:03 0.37 0.25 0.15

1 fm2 ˆ 10ÿ26 cm2 . Taken from Refs. [16,17].

4.2. Integrated cross-sections The absolute integrated absorption cross-sections …r† were calculated from the experimental data and the equation: Z a…m†mÿ1 dm: …4† rˆ band

The total absolute cross-sections of the bands of C3 H8 , n-C4 H10 and n-C5 H12 were obtained by using Eq. (4) and the experimental bands. The results for the integrated cross-sections (r) are shown in Table 1. The total area represents the absolute cross-section of the integrated experimental band, the integrated cross-sections of the individual deconvoluted bands are to be taken with caution because they represent the result of the deconvolution using Lorentzian bands. The areas of the component bands (Hm ; Ha , and Hs ) could change if the deconvolution is done with other functions. Comparisons can been made of the integrated cross-sections of ethane and ethene obtained with photoacoustic spectroscopy. In the acoustic method, the spectrum of a mixture consisting of a

reference absorber (r) and a sample (u) is obtained. The cross-section is calculated as: ru ˆ rr

Au qr mr ; Ar qu mu

…5†

where the subscripts u and r refer to the sample of unknown cross-section and a reference of known cross-section, respectively, r is the integrated cross-section, A is the integrated area of the band, q is the density, and m is the band center frequency. The integrated cross-section of C2 H4 [16] was calibrated against the known cross-section of the Dv ˆ 6 C±H absorption of CH4 . The absolute cross-sections of C2 H4 and C2 H6 [17] were calibrated against the known cross-section of the Dv ˆ 5 absorption of HD. Our cross-section results are in good agreement with the acoustic determination of the C2 H4 [16]. The values reported in [17] are approximately 1.3 times larger than our reported values for C2 H4 and C2 H6 , respectively. In our PS-CRD experiment, the absolute cross-section for C2 H4 is the average obtained from seven spectra ranging in pressure from 50 to 300 Torr. The cross-section obtained for C2 H6 is the average of 7 spectra ranging in

E.K. Lewis et al. / Chemical Physics Letters 334 (2001) 357±364

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photoacoustic spectroscopy [16]. Resolvable peaks were seen for each chemically or sterically equivalent C±H bond and were assigned using the local mode model. In the liquid phase, the spectra have been obtained using an NIR spectrophotometer [18]. The spectrum of gas-phase propane …Dv ˆ 1±6† was measured and relative intensities were calculated [19]. Mc Kean and co-workers [20] have studied the C±H fundamental spectra of hydrocarbons in which all but one H has been substituted by D. The lone C±H stretch is decoupled from the C±D stretching vibrations as well as the ®rst overtone of the bends. The isolated frequency is observed. These isolated frequencies correlate well with the C±H bond lengths in the vibrational ground state. High overtone peaks occur in the same sequence as the fundamental isolated frequencies and also correlate with the bond lengths [16,21]. The ab initio molecular structures of propane, butane and pentane have previously been calculated at the 421G level [22±24]. The C±H bond distances in the methylene groups are slightly longer than in methyl groups and increase with the number of adjacent C±C bonds that are staggering the CH2 group. A correlation of calculated C±H bond lengths and overtone frequencies was made by Wong and Moore [16] giving the following equation: Fig. 3. Lowest energy conformers of n-pentane calculated at the 6-31 ‡ ‡G level of theory.

rCH …calc† ˆ …0:1319  0:0022†

pressure from 50 to 250 Torr. In the acoustic determination [17], the cross-sections were obtained by integrating the band and dividing by the band center frequency instead of integrating according to Eq. (4). Considering that the acoustic technique is an indirect method to obtain cross-sections, the agreement with the PS-CRD technique is very good.

In order to get a closer agreement with the experimental distances, the correlation plot of Wang and Moore used calculated distances at the 4±31G level that were corrected by adding a factor 0.0011 nm [25]. The measured frequencies given Table 1 and Eq. (6) are used to predict the following average C±H distances (nm) for propane: (C±Hm ˆ 0:1097…0†, C±Ha ˆ 0:1094…5†, and C±Hs ˆ 0:1093 …4†), butane: (C±Hm ˆ0:1098…3†, C±Ha ˆ0:1094…5†, and C±Hs ˆ0:1093…2†), and pentane: (C±Hm ˆ 0:1098…4†, C±Ha ˆ0:1094…3†, and C±Hs ˆ0:1093 …4†). A calculation of C±H bond lengths allows then to make observations related to the observed bands.

4.3. Propane, butane, and pentane The overtone spectra of the C±H stretching vibrations of gas-phase propane, butane, and pentane have been previously observed using laser

ÿ …1:426  0:134†  10ÿ6 mvˆ6 :

…6†

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E.K. Lewis et al. / Chemical Physics Letters 334 (2001) 357±364

Table 2 Ab initio calculated C±H bond lengths (nm) and minimum energies (Hartree) of conformers of propane, butane, and pentane using a 6-31 ‡ ‡G basis set Propane

Butane

Pentane

Conformer

E (hartree)

E (kJ/mol)

A

)118.277

)310536.407

Bond C1H4 C1H5 C1H6 C2H7 C2H8 C3H9 C3H10 C3H11

A 0.1086 0.1087 0.1087 0.1087 0.1087 0.1086 0.1087 0.1087

Conformer

E (hartree)

E (kJ/mol)

DE (kJ/mol)

anti (180) gauche (60)

)157.315 )157.313

)413030.793 )413026.407

0 4.38

Bond C1H5 C1H6 C1H7 C2H8 C2H9 C3H10 C3H11 C4H12 C4H13 C4H14

anti 0.1086 0.1087 0.1087 0.1088 0.1088 0.1088 0.1088 0.1086 0.1086 0.1086

Conformer

E (hartree)

E (kJ/mol)

DE (kJ/mol)

AA AG+ G+G+ G+G)

)196.353 )196.351 )196.350 )196.347

)515524.958 )515520.681 )515516.928 )515508.697

0 4.28 8.03 16.26

Bond C1H6 C1H7 C1H8 C2H9 C2H10 C3H11 C3H12 C4H13 C4H14 C5H15 C5H16 C5H17

AA 0.1086 0.1086 0.1086 0.1088 0.1088 0.1089 0.1089 0.1088 0.1088 0.1086 0.1086 0.1086

G+G+ 0.1086 (1) 0.1087 (3) 0.1085 (6) 0.1087 (9) 0.1087 (4) 0.1089 (2) 0.1089 (2) 0.1087 (4) 0.1087 (9) 0.1086 (1) 0.1087 (3) 0.1085 (6)

G+G) 0.1086 (3) 0.1087 (1) 0.1085 (1) 0.1088 (2) 0.1088 (9) 0.1089 (6) 0.1087 (5) 0.1087 (3) 0.1088 (8) 0.1086 (5) 0.1084 (2) 0.1086 (9)

(2) (0) (0) (8) (9) (1) (0) (0)

(1) (0) (0) (9) (9) (9) (9) (1) (9) (9)

(1) (9) (9) (7) (7) (8) (8) (7) (7) (1) (9) (9)

gauche 0.1086 (1) 0.1087 (5) 0.1085 (1) 0.1089 (2) 0.1087 (8) 0.1089 (2) 0.1087 (8) 0.1086 (1) 0.1087 (5) 0.1085 (1)

AG+ 0.1086 0.1087 0.1086 0.1086 0.1089 0.1088 0.1090 0.1089 0.1087 0.1086 0.1087 0.1085

(1) (0) (9) (9) (1) (9) (0) (0) (9) (1) (3) (3)

E.K. Lewis et al. / Chemical Physics Letters 334 (2001) 357±364

In this Letter, the most stable conformers of propane, butane, and pentane were calculated at the 6-31 ‡ ‡G level of theory. The results at this level of theory are similar to the calculation at the 4-31G level except that the minimum energies of the conformers are lower and the correction for C± H internuclear distances is 0.0008 nm (instead of 0.0011 nm) to get a closer agreement with the experimental distances. The results of the calculation are given for the most stable conformer of propane, two stable forms of butane, and four conformers of pentane (Table 2). The four lowest energy conformers of pentane are shown in Fig. 3. The lowest energy corresponds to the AA form. The energy of the conformers allows to estimate their relative population at room temperature using a Boltzman distribution. At room temperature, there is approximately 82% of AA, 15% of AG‡ and 3% of G‡ G‡ . The calculated average C±Hm distance of methylene groups for the lowest energy form (AA) of pentane is 0.1097(2) nm. Other pentane conformers show methylenic C±H average distances of (AG‡ ) 0.1096(6) and (G‡ G‡ ) 0.1096(2) nm. The strength of the methylene bonds for di€erent conformers translates into a distribution of absorption frequencies. The lowest frequency corresponds to the contribution of most stable form AA (82%). Increasing in energy within the band are the contributions from the AG‡ conformer (15%) and the G‡ G‡ conformer (3%). These results qualitatively agree with an asymmetry of the methylenic band on the high energy side of the maximum at 15,469 cmÿ1 . The average distance of the methyl bonds C±Ha (out-of-plane) for the AA conformer is 0.1094(9) nm and the average methyl C±Hs (inplane) is 0.1094(1). Again the congestion of the bands in the C±Ha and C±Hs regions for pentane is due to the fact that the conformers show di€erences in bond length with respect to the lowest energy form and an appreciable percentage of them contribute to the absorption. Several conformers of butane were calculated. Using a Newman projection the most stable form (anti) shows terminal methyl groups 180° from each other. In the second most stable form

363

(gauche) the terminal methyl groups are 60° apart from each other. According to their relative energies, the major contribution to the absorption at room temperature comes from the anti (80%) and the gauche (13%). Two other calculated conformers contribute with 4% and 2%. The average distance C±Hm of methylene groups for the lowest energy form (anti) of butane is 0.1096(9) nm. The average C±Ha (out-of-plane) distance is 0.1095 nm. The average methyl C±Hs (in-plane) calculated distance is 0.1094(2) nm. As with pentane, higher energy conformers contribute to the absorption increasing the width of the main bands. The average C±Hm distance of a methylene group of propane is 0.1095(9) nm. The average C±Ha (outof-plane) distance is 0.1095 nm and the methyl C±Hs (in-plane) calculated distance is 0.1094(2) nm. The calculations show a pattern when compared with the results of the correlation equation. For all calculated average values of the lowest energy form of propane, butane, and pentane, the average C±Hm length is around 0.0001 nm below the value obtained with the correlation. The calculated C±Ha and C±Hs distances are 0.0001 nm or less higher than the values obtained from the correlation. Although absolute bond lengths (or frequencies) cannot be predicted, the bond length di€erences derived from overtone data are useful as a ®rst approximation in re®ning structures based on microwave data. In addition to rotational congestion, there are other mechanisms that will change the shape and width of the bands. A resonance of the 6mCH stretching mode with the combination band of a lower energy stretching overtone and the ®rst overtone of the bending mode (5mCH ‡ 2mB ) is usually assumed for C±H overtones of hydrocarbons. This resonance is expected to show in propane but they are probably more dicult to observe in an absorption band of pentane where several conformers are absorbing the laser radiation. The (Dv ˆ 6) overtone spectrum of propane obtained by Crofton et al. [26] showed very small changes when the temperature was lowered from 298 to 189 K. The minimal change was attributed to a small reduction in the rotational congestion

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but it could also re¯ect a change in the percentage of conformers.

5. Conclusion The phase shift cavity ring-down technique was used to measure the absorption spectrum of the C± H …Dv ˆ 6) overtone transition of several alkanes. By measuring the magnitude of the phase shift that an intensity modulated continuous laser beam experiences upon passing through an optical cavity, it is possible to measure weak overtones and to determine their absolute cross-sections. Several conformers of pentane were calculated and at least three of them contribute to the shape of the absorption band.

Acknowledgements This work was supported by the Robert A. Welch Foundation under Grant NO AA-1173. Partial support from the Baylor University Research Committee is also acknowledged.

References [1] J.M. Herbelin, J.A. McKay, M.A. Kwok, R.H. Ueunten, D.S. Urevig, D.J. Spencer, D.J. Benard, Appl. Opt. 19 (1980) 144. [2] R. Engeln, G. von Helden, G. Berden, G. Meijer, Chem. Phys. Lett. 262 (1996) 105. [3] D.Z. Anderson, J.C. Frisch, C.S. Masser, Appl. Opt. 23 (1984) 1238.

[4] A. O'Keefe, D.A.G. Deacon, Rev. Sci. Instr. 59 (1988) 2544. [5] K.W. Busch, M.A. Busch, Cavity Ringdown Spectroscopy, American Chemical Society, Washington, DC, 1999. [6] D. Romanini, K.K. Lehmann, J. Chem. Phys. 99 (1993) 6287. [7] D. Romanini, A.A. Kachanov, N. Sadeghi, F. Stoeckel, Chem. Phys. Lett. 264 (1997) 316. [8] J.J. Scherer, D. Voelkel, D.J. Rakestraw, J.B. Paul, C.P. Collier, R.J. Saykally, A. O'Keefe, Appl. Chem. Phys. Lett. 245 (1995) 273. [9] D. Romanini, A.A. Kachanov, F. Stoeckel, Chem. Phys. Lett. 270 (1997) 546. [10] D. Romanini, A.A. Kachanov, F. Stoeckel, Chem Phys. Lett. 270 (1997) 538. [11] Y. He, M. Hippler, M. Quack, Chem. Phys. Lett. 289 (1998) 527. [12] A. O'Keefe, O. Lee, Am. Lab. 21 (1989) 19. [13] J.J. Scherer, D. Voelkel, D.J. Rakestraw, Appl. Phys. B 64 (1997) 699. [14] D. Kleine, S. Stry, J. Lauterbach, K. Kleinermanns, P. Hering, Chem. Phys. Lett. 312 (1999) 185. [15] K.C. Smyth, P.K. Schenck, Chem. Phys. Lett. 55 (1978) 466. [16] J.S. Wong, C. Bradly Moore, J. Chem. Phys. 77 (1982) 603. [17] J.H. Gutow, J. Davidsson, R.N. Zare, Chem. Phys. Lett. 185 (1991) 120. [18] W.R.A. Greenlay, B.R. Henry, J. Chem. Phys. 69 (1978) 82. [19] H.G. Kjaergaard, B.R. Henry, A.W. Tarr, J. Chem. Phys. 94 (1991) 5844. [20] D.C. McKean, Chem. Soc. Rev. 7 (1978) 399. [21] R.J. Hayward, B.R. Henry, Chem. Phys. 12 (1976) 387. [22] J.N. Scarsdale, C. Van Alsenoy, L. Schafer, J. Mol. Struct. 86 (1982) 277. [23] L. Schafer, K. Siam, J.D. Ewbank, E. Osawa, J. Mol. Struct. 139 (1986) 125. [24] N.L. Allinger, L. Schafer, K. Siam, V.J. Klimkowski, C. Van Alsenoy, J. Comput. Chem. 6 (1985) 331. [25] C.E. Blom, P.J. Slingerland, C. Altona, Mol. Phys. 31 (1976) 1359. [26] M.W. Crofton, C.G. Stevens, D. Klenerman, J.H. Gutow, R.N. Zare, J. Chem. Phys. 89 (1988) 7100.