J . Phys. Chem. 1992, 96, 2534-2543
2534
Rotational Effects on the Overtone-Induced Isomerization Rate for CHD,NC CHDPCN
-
J. H.Gutow' and R. N.Zare* Department of Chemistry, Stanford University, Stanford, California 94305-5080 (Received: August 15, 1991; In Final Form: November 14, 1991)
CHD2NC reactant was prepared in a few rotational states, with approximately 1.7 kcal/mol of excess vibrational energy above the bamer to isomerization, by excitation of well-resolved "Q bandheads of the 5-0 C-H overtone spectrum. Experiments were performed in a static gas cell using IR absorption to monitor the progress of the reaction and a Stern-Volmer analysis to determine the rate constants. The isomerization rate constants were found to decrease significantly as the K quantum number of the excited reactants increased. Rice-Ramsperger-Kassel-Marcus calculations including angular momentum effects have been used in an attempt to simulate the observed isomerization rate constants over the small energy range of this study. Calculations using either conservationor nonconservation of the K quantum number cannot qualitatively reproduce the observed decrease in rate constant with increasing K . We are unable to establish the origin of this discrepancy.
I. Introduction Unimolecular reactions provide the basis for much of our detailed understanding of kinetics. Statistical theories, such as the Rice-Ramsperger-Kassel-Marcus (RRKM) t h e ~ r y and ~ - ~statistical adiabatic channel models (SACM),5-7have successfully described such processes. One facet of these theories not well tested experimentally is the effect of rotational excitation of the reactant on the reaction rate. Yet considerable theoretical work has shown the importance of angular momentum conservation and rotational energy in unimolecular reaction^.^^^^*-" This paper describes the experimental observation of rotational-statedependent isomerization rate constants for the reaction CHDzNC
+ hv
-
CHD2CN
Using the 5-0 C-H vibrational overtone, the reactant is prepared in a few rotational states, with approximately 1.7 kcal/mol of excess vibrational energy above the barrier to isomerization. The CHD2NC 5 - 0 overtone spectrum exhibits well-resolved AKQ bandheads, which allow selection of the K state of the excited molecules where K is the projection of the total rotational angular momentum J on the top axis. Rabinovitch and co-worker~'~-'~ began thermal studies of this reaction (CH3NC and CD,NC) almost 30 years ago. They estimated the barrier height to be 38 kcal/mol. Because the reaction is approximately 24 kcal/mol exothermic, a statistical behavior would suggest that few if any of the products can re-cross the barrier to become reactants. These early studies also included careful RRKM analyses of the data and provided impetus for ab initio and trajectory studies.1°J6-'* ( I ) Present address: Department of Chemistry, Columbia University, New York, N Y 10027. (2) Gilbert, R. G.; Smith, S. C. Theory of Unimolecular and Recombination Reactions; Blackwell Scientific Publications: Boston, 1990. (3) Forst, W. Theory of Unimolecular Reactions; Academic Press: New York, 1973. (4) Forst, W. J . Chim. Phys. Phys.-Chim. Biol. 1990, 87, 715. (5) Troe, J. An. Asoc. Quim.Argent. 1985, 73, 63. (6) Troe, J. J . Chem. Phys. 1983, 79, 6017. (7) Quack, M.; Troe, J . Ber. Bunsen-Ges. Phys. Chem. 1974, 78, 240. (8) Waage, E. V.; Rabinovitch, B. S. Chem. Reu. 1970, 70, 377. (9) Miller, J . A.; Brown, N. J. J . Phys. Chem. 1982, 86, 772. (10) Marks, A. J.; Murrell, J. N.; Stace, A. J. Chem. Phys. Lett. 1989, 154, 492. (1 I ) Troe, J . J . Phys. Chem. 1984, 88, 4375. (12) Schneider, F. W.; Rabinovitch, B. S. J . Am. Chem. SOC.1962, 84, 4215. (13) Schneider, F. W.; Rabinovitch, B. S. J . Am. Chem. SOC.1963, 85, 2365. (14) Rabinovitch, B. S.; Gilderson, R. W.; Schneider, R. W. J . Am. Chem. SOC.1965, 87, 158. (15) Chan, S. C.; Rabinovitch, B. S.; Bryant, J. T.; Spicer, L. D.; Fujimoto, T.; Lin, Y. N.; Pavlou, S. P. J . Phys. Chem. 1970, 74, 3160.
Reddy and Berry realized that the reactants could be prepared with a narrower energy distribution by vibrational overtone excitation than by thermal activation. They studied the isomerization of CH3NC to CH3CN and observed behavior consistent with RRKM theories but with significant d i s c r e p a n c i e ~ . ' ~Subse~~~ quent calculations by Miller and Chandler,21modified to account for inefficient collisional deactivation, suggested these discrepancies may arise from the simple strong collider assumption used in Reddy and Berry's analysis as well as from a small error in the thermally determined barrier height. Trajectory calculations by Sumpter and Thompson22indicated that this isomerization process behaves statistically, although in their calculations energy redistribution in the molecule occurred in a mode-specific way that was highly dependent upon the details of the potential chosen. The CH3 overtones at room temperature are broad, unresolved features. They apparently consist of many overlapping transit i o n ~ . ~Thus, ~ no rotational-state specificity was available in Reddy and Berry's experiments. Snavely et al.24 reported the most recent overtone-induced isomerization studies of CH3NC. They determined the average energy transferred per collision for several buffer gases. For neat CH3NC, they found this energy to be approximately 1000 cm-I (-2.9 kcal/mol). Again their results appear consistent with RRKM theories. CHD2NC is an ideal system for studying rotational effects in a unimolecular reaction. Unlike its undeuterated analogue, this molecule exhibits resolved rotational structure in its high overtones. In addition, the rotationally resolved band in the region of the 5-0 C-H overtone transition is only approximately 1.7 kcal/mol above the barrier to reaction. State-dependent effects should be much more significant when close to the barrier to reaction than when high above it. In the present work, we compare the observed rotational state dependence with predictions using standard RRKM theory including rotational effect^.^-^ The experiments were performed in a static gas cell using IR absorption to monitor the reaction's progress. A Stern-Volmer analysis was used to determine the (16) Liskow, D. H.; Bender, C. F.; Schaefer, H. F., 111 J . Chem. Phys. 1972, 57, 4509.
(17) Saxe, P.; Yamaguchi, Y.; Pulay, P.; Schaefer, H. F., I11 J . Am. Chem. SOC.1980, 102, 3718. (18) Ha, T.-K. J . Mol. Sruct. 1972, 11, 185. (19) Reddy, K. V.; Berry, M. J. Chem. Phys. Lett. 1977, 52, 1 1 1 . (20) Reddy, K. V.; Berry, M. J. Faraday Discuss. Chem. SOC.1979,67, 188. (21) Miller, J. A.; Chandler, D. W. J . Chem. Phys. 1986, 85, 4502. (22) Sumpter, B. G.; Thompson, D. L. J . Chem. Phys. 1987, 87, 5809. (23) Crofton, M . W.; Stevens, C. G.; Klenerman, D.; Gutow, J. H.; Zare, R. N . J . Chem. Phys. 1988, 12, 7100 and references therein. (24) Snavely, D. L.; Zare, R. N.; Miller, J . A,; Chandler, D. W. J . Phys. Chem. 1986, 90, 3544.
0022-365419212096-2534%03.00/0 0 1992 American Chemical Society
Rotational Effects on CHD2NC
-
CHD2CN Isomerization
The Journal of Physical Chemistry, Vol. 96, No. 6, 1992 2535
U
rate constants. The distribution of laser-excited rotational states is based on simulations of the observed overtone spectra. The observed results do not appear to be consistent with calculations based on standard RRKM theory. 11. Experimental Section A. CHD2NC Synthesis. The CHD2NC was synthesized by
dehydration of CHD2NHCH0, N-(dideuteriomethyl)formamide, using p-toluenesulfonyl chloride and quinoline as described by Casanova, Schuster, and Wernerzs
+
CHD2NHCHO p-C6HdM&02Cl+ 2CgH7N -, CHD2NC p-C6H4Me.SO3- + 2C9H7N+
+
+ c1-
The yield of the whole synthesis was 80-90%. As suggested by Casanova, Schuster, and Werner,25 the quinoline was distilled to avoid contamination of the product. Also, the reactants and products were handled so that they did not contact anything other than glass, teflon, stainless steel, or silicone-based vacuum grease. The product reacts with and dissolves readily most other plastics and forms a scale on brass. Even with care, CHD2CI/CH3Cl,CH30H, and H 2 0contaminated the final product. The methyl chloride was removed by freezing out the CHD2NC as the gaseous reaction products were pumped through a trap cooled in an ethyl acetate slush bath (-84 "C), with a backing pressure of 100-200 mTorr. This procedure was repeated until the methyl chloride peak disappeared from the gas chromatogram of the sample. On most gas chromatography (GC) columns, methyl chloride comes off faster than methyl isocyanide. Purification typically took four to six cycles. The methanol and water were removed by transferring the sample to a vacuum finger containing sodium hydride.26 After the sample stopped evolving hydrogen, the isocyanide was transferred to a storage finger, leaving behind unreacted N a H and the solid products NaOH and NaOCH3. The methanol comes out of many GC columns at about the same time as the isocyanide. Infrared spectroscopy was used to judge the degree of water and methanol contamination. We estimate that the final chemical purity of the product was greater than 99%. The isotopic purity was estimated to be as good as specified for the deuterated precursor (see below), approximately 99%, by gas chromatography-mass spectrometry. The CHD2NCsample was stored in a glass vacuum finger with two all-teflon valves in series to prevent significant leakage of air into the sample. B. CHD2NHCH0 Synthesis. The reagent CHD2NHCH0 is not available commercially and was synthesized as follows. CHD2NH2gas was released from -2.5 g of CHD2NH3Cl(98.6 atom 9% purity, MSD Isotopes division of Merck, Sharp & Dohme), dissolved in -4.5 mL of distilled H 2 0 by the addition of a saturated solution of KOH in H 2 0 (- 18 mL); KOH pellets were then added until the stirred reaction mixture appeared saturated. The evolved gas was collected in a liquid-nitrogencooled trap after it passed through a short drying tube packed with KOH pellets. The whole apparatus was evacuated to -25 Torr. After collection of the evolved deuterated methylamine, the contents of the trap were defrosted and re-cooled with an ethylene glycol slush bath (-15.6 "C). This procedure limited the amount of water transferred by trapto-trap distillation to a vacuum finger that was cut in half so that the end of the finger and its contents could be removed. The top and bottom of the finger were held together by a stainless steel Cajon Ultra-Torr fitting with teflon O-rings. The amine was frozen down into the removable part of the finger with liquid nitrogen. The removable bottom part was transferred into a pressurizable reaction vessel made of stainless
+
15.Wcm
Figure 1. Isomerization cell.
-
steel Swagelock fittings and teflon tubing and containing methanol (Aldrich 99+%) and an excess, 13 mL, of methyl formate (Aldrich 99+%). The vessel was then sealed, pressurized with dry nitrogen to 3 atm, shaken vigorously, and allowed to sit for at least 48 h before the pressure was released. The N-methylformamide was recovered by using a rotovap to remove the methanol. Approximately 2 mL of the deuterated N-methylformamide was recovered at this stage. C. Kinetics. A sample of CHD2NC was degassed by freezepump-thaw cycles with liquid nitrogen. If the presence of C 0 2 was evident in the IR spectrum, additional degassing was done using a dry ice/acetone slush bath (-78 "C). Then a known amount of the isocyanide (0.8-6.2 Torr) was introduced into a glass photolysis cell. The cell was constructed in an X configuration with CaF2 windows at opposite ends of one slash of the X and fused-silica windows a t Brewster's angles on the other slash (seeFigure 1). The windows were attached to the cell with 5-min epoxy (any brand available). We used two all-teflon valves in series to prevent leakage into the cell, which we found to be significant with a single valve. Because the sample sticks well to glass, the filled cell was allowed to equilibrate for a t least 1 h. After equilibration, an FTIR spectrum of the sample was taken in the region between 500 and 4ooo cm-' using an IBM 98 (Bruker IFS 113) spectrometer. The path length in the gas cell was 15 cm. Each spectrum was the average of 128 interferometer scans at a resolution of 2 cm-I, measured using a HgCdTe (MCT) detector. This spectrum was used to verify that the sample was free of water, COz, and other organic contaminants. This measurement was also used to calibrate the amount of isocyanide in the vapor phase by integrating the band associated with the N e stretch (2097-2233 cm-I). Because the optical bench of the FTIR was maintained a t approximately 30 "C, the sample cell was allowed to sit in the bench for at least 10 min to reach thermal equilibrium before the FTIR spectrum was taken. A photolysis run was performed by placing the cell inside the cavity of a home-built dye laser with the same optics geometry as a Coherent 590 laser and with the output coupler replaced by a high reflector, as in previous experiments performed in this l a b o r a t ~ r y . ~ ~ *The ~ ' , ~dye * laser using LD700 laser dye (Exciton and Lambda Physik) was pumped with about 4-W multiline red from a Kr' laser (Spectra Physics 171). The frequency of the dye laser was controlled with a three-plate birefringent filter and an uncoated thin quartz etalon with a free spectral range (FSR) of approximately 3.2 cm-I. The bandwidth of the laser in this configuration is approximately 0.34 cm-' (seebelow). In addition to narrowing the bandwidth below the 1.0 cm-' level provided by the birefringent filter, the thin etalon prevented the laser frequency from drifting significantly as the temperature in the laboratory changed. To further insulate the laser and sample cell from the surrounding environment, they were enclosed in a Lucite box. The laser frequency was monitored with a Burleigh wavemeter using an external battery-biased photodiode detector (EG&G PV-1OOA photodiode) amplified with a variable-gain amplifier (Tektronix AM-502). During the course of a photolysis, the laser frequency drifted in a 0.5 cm-' wide band centered at the photolysis frequency; thus,
( 2 5 ) Casanova, J., Jr.; Schuster, R. E.; Werner, N. D. J . Chem. SOC.1963, 4280.
(26) Butler, J. N.; Jasinski, R. J.; Cogley, D. R.;Jones, H. L.; Synnott, J. C.; Carroll, S . Purification and Analysis of Organic Nonaqueous Solvents; AFCRL: Bedford, MA, 1970; p 7.
(27) Chuang, M. C.; Baggott, J. E.; Chandler, D. W.; Farneth, W. E.; Zare, R. N. Faraday Discuss. Chem. Soc. 1983, 75, 301. (28) Segall, J.; Zare, R. N. J . Chem. Phys. 1988, 89, 5704.
Gutow and Zare
2536 The Journal of Physical Chemistry, Vol. 96, No. 6, 1992 in
- eiponenual f i t to the data Neat CHD2NC staning sample 0 A
09
-6.010m -09IOn
2784
270A1 (1
I
200
l
400
,
600 8M) Time (mmulcr)
I
,
loo0
12w
1
Figure 2. Integrated intensity of the N e stretching band of CHD2NC versus time for a sample left sitting in the isomerization cell. The slight upward drift in the intensity for the 50 O C data is caused by an instability in the temperature control for the FTIR spectrometer. This instability was repaired.
although the laser bandwidth is approximately 0.34 cm-I, 0.5 cm-' probably better represents the time-averaged excitation bandwidth. The laser power was monitored with an N R C 815 power meter and digitized at 0.2-1 Hz for future integration using a microcomputer (IBM PC) equipped with a 12-bit, analog-to-digital converter. The 0.1-Hz square-wave output of a Hewlett Packard function generator (Model 3300A) was digitized simultaneously on another channel to verify the time base. The sample cell was periodically removed from the dye laser, and an FTIR spectrum was taken of the sample using the IBM 98. This cycle was repeated until 2040% of the sample was converted to CHDzCN from CHD2NC. During a run, five to seven FTIR spectra were collected. A spectrum was taken roughly every 2 h for the first 8-10 h of photolysis. Subsequent spectra were taken at intervals varying between 3 and 9 h. A single run lasted about 30 h. Occasionally, a t the end of a run, a gas chromatogram was taken of the gas sample to check for contamination and other products. The column was a Superox I1 15- X 0.53-mm column (Alltech). The G C runs were programmed runs starting a t 60 OC for 3 min followed by a ramp of 20 'C/min to 210 OC using He carrier gas at 10.4 mL/min. The isocyanide and cyanide retention times were approximately 2.1 and 3.4 min, respectively, but both had long tails. No other products were observed. We checked for background reactions by allowing samples to sit for one day without being photolyzed (see Figure 2). 1. Kinetics at Elevated Temperature. For the photolyses performed at 50 OC, the cell was mounted in the laser cavity using a form-fitted block of foam insulation. This insulating block was created by casting the cell into place with expanding foam insulation (Geocel Co.). The resulting block was cut into three pieces, a bottom and two top sections, so that the cell could be removed. The temperature was maintained to within 0.6 OC, using an Omega 9000 temperature controller with a type J thermocouple sensor, but the accuracy of the temperature is only *2 O C . The cell was heated using about 12 V ac through 0.4-mm-diameter nichrome wire wrapped around the body of the cell in a spiral of approximately 0.5-cm spacing. The low voltage, which was slightly more than enough to maintain the desired temperature, prevented formation of hot spots in the cell, which might have caused a thermally induced background reaction. As shown in Figure 2, no s i d i c a n t background reaction occurred under these conditions, as indicated by the stability of the integrated N S stretch band intensity. 2. k r Bandwidth Measurement. The bandwidth of the laser was measured using a piezo-scanned plane Fabry-Perot etalon (Spectra-Physics 58 1A) modified using plastic adaptors to hold 0.5-in.-diameter optics. The mirrors used were 95% reflective and were centered at 13793 at-'(725 nm) with antireflection coatings on their backsides (CVI Corp.). The FSR of the scanning etalon
(I
IoiituI !iuw ~ H Y I 4r" I ~ m + \ i w 01 I t ~ r l m U ' L l ~[ nc l~l c ~ l i v ephololyw lime1
~IUXXI
Figure 3. Effect of pressure on the observed reaction rate constants. The curves are single exponential fits to the data. The isomerization frequency was 13 850.4 cm-I (RQ2).
was measured by putting an additional thick, uncoated quartz etalon with a FSR of 0.934 cm-I into the laser cavity and adjusting the laser to lase on two modes of this etalon. The major uncertainty in this calibration method was the measurement of the separation in volts between the modes on our oscilloscope. Once the wavenumbers scanned per volt were known, the voltage required to scan one FSR was measured. The scanning etalon was used at two mirror spacings, which gave FSRs of 6.5 f 0.1 and 2.5 f 0.04 cm-I. Both configurations gave roughly the same laser bandwidth (0.34 f 0.02 cm-I), but for the 6.5-cm-I FSR, the theoretical maximum resolution of the etalon would be only 0.1 cm-l ,29 which is barely adequate to measure a bandwidth of approximately 0.3 cm-I. Based on measurements of the fwhm of the beating modes observed at the 2.5-cm-l FSR, we estimate the finesse of the etalon to be between 35 and 40, when properly aligned. This finesse means the resolution is approximately 0.2 cm-I for a FSR of 6.5 cm-I and is 0.07 cm-I or somewhat better for a FSR of 2.5 cm-I. We believe that the resolution at the smaller FSR was adequate for this measurement because we observed the multiple laser modes within the laser bandwidth profile. 3. End Mirror Transmission Measurement. One check of the validity of the kinetics analysis is to calculate spectroscopic absorption crm sections from the data. To do this check, the relative intracavity laser power must be known. Because the laser power was monitored through the end mirror of the laser cavity, the transmission coefficient of the end mirror is needed to calculate the intracavity power. The transmission coefficient was measured at various laser frequencies using the laser as the light source for a home-built dual-beam spectrometer, which had a photodiode detector and an Hewlett Packard 8540A diode array spectrometer, with a resolution of approximately 38 cm-I. We estimate that the fractional transmission coefficient for the mirror used in this experiment was (5.1 f 0.3) X over the frequency range of the experiment, where the uncertainty represents the range of values measured. D. V i b r a t i d overtow Spectroscopy. The laser photoacoustic apparatus used to record the 5-0 C-H vibrational overtone spectra of CHD2NC has been described p r e v i o ~ s l y . ~The ~ sample consisted of approximately 10 Torr of CHD2NC buffered in approximately 300 Torr of Xe. The spectroscopic assignments and analysis will be detailed el~ewhere.~' 111. Data Analysis
A. Stern-Volmer Analysis. The raw data from a run consisted of a series of five to seven FTIR spectra of the contents of the (29) Demtrader, W.Laser Specrroscopy;Springer-Verlag: New York, 1982. (30) Davidsson, J.; Gutow, J. H.; Zare, R. N. J . Phys. Chem. 1990, 94, 4069. (31) Gutow, J. H.; Hollenstein, H.; Quack, M. Manuscript in preparation.
Rotational Effects on CHD2NC
-
The Journal of Physical Chemistry, Vol. 96, No. 6, 1992 2537
CHD2CN Isomerization
TABLE I: Relative Isomerization Rate Constants (k)Corrected for the Laser Power and Absorption Cross Sections. AU Constants Are Normalized to tbe
woTransition
k final K
transition
4 3
pQS
0
'Qia
pQ4
QQ"
? 1 2 3
"These
RQO RQ~ RQ2
fractional change
298 K 0.78 f 0.03 0.95 f 0.04 0.85 f 0.03 1.20 f 0.05 1.00 f 0.05 0.81 f 0.02 0.41 f 0.01
E, cm-' 13 809.3 13 815.4 13 833.6 13 835.9 13 839.3 13845.1 13 850.4
323
K
((k323
- k298)/k298)
1.21 f 0.08
0.27 i 0.02
1.41 f 0.09 1.19 f 0.06
0.41 f 0.03 0.47 0.03
two bandheads overlap. The assignment is only approximate.
photolysis cell along with digitized traces of the laser output power. The integrated cross section for the N z C absorption band was plotted versus the time-integrated laser output power, to yield a single exponential decay. The observed decay rate depends upon the starting pressure of CHD2NC. At higher pressures, the decay rate decreases because the higher collision rate deactivates more of the excited molecules (see Figure 3). The decay rate was interpreted using a Stern-Volmer analysis and a kinetic model for overtone-induced isomerization of CH,NC, suggested by Reddy and Berry.19920 The approximate expression for the expected rate constant, derived from a Taylor expansion of the solution, is kapp(v)
e kiso(v)
-kiso(v)ka(v) [hvl + kd(v)[Ml + ka(v)[hvl
(1)
Here v is the photolysis frequency, ka&) is the observed first-order decay rate constant, ka(v) is the rate constant for excitation of molecules by the laser (proportional to the absorption cross section), kiso(v)is the rate constant for isomerization of excited molecules in the absence of collisions, [hv] is the concentration of photons (proportional to the laser power), k&) is the deactivation rate constant, which describes the rate at which molecules lose sufficient energy through collisions to make them unreactive, and [MI is the concentration of gas in the sample cell (proportional to the pressure). The Stern-Volmer analysis consists of noting that 1/kapp(u) is linearly proportional to the collider density, [MI:
The sum of the first two terms in this expression is the zeropressure intercept. Since kiso(v)= lo8 s-', the first term is negligible; hence the intercept is the second term, the inverse of the excitation rate (ka(u)[hv] s-]). Dividing expression 2 by the intercept yields an expression for a line with a slope that is proportional to the ratio of the collisional deactivation rate constant divided by the reaction (isomerization) rate constant (see Figure 4): (3) The value of kiSo(v)/kd(v) (l/slope) normalized to kjso(V)/kd(v) a t 13 839.3 cm-I (RQo)is the value reported in this work (see Figure 5 and Table I). Variations in this value reflect changes in ki,(v) or k&). The deactivation rate constant, k&), however, is expected to change little under the conditions of this e~periment'~ (see the discussion below). B. Error Analysis and Propagation. All errors reported in this work represent 95% confidence levels (f2u). The errors were propagated from the estimated errors in measuring the N=C stretch cross section using the covariance matrix generated in the program IGOR (Wavemetrics) from a least-squares fit to the exponential decay and then propagating the errors through the Stern-Volmer analysis. The error in the measured Ncross sections was determined by a statistical analysis of the data that was collected to test whether background reaction occurred (see
Figure 4. Reduced Stern-Volmer plot for isomerization via the RQ2and RQobandheads (see eq 3). 0.8 l 4
? 3
3.0
RQ
PQ 4 5
i 2
O I
I O
2 I
3 2
4 3
5 4
-
2.5
R
