3081
J. Phys. Chem. 1980, 84, 3061-3065
R
= -It, aat)
$El
(
=;y AT[ 1 - exp -El-
T1
;A~)]-'
1
0.44
exp( -ElE)( TlTO
-
&) TITO
This can be reduced to a simpler form [let U 5 ElAT/ (TI To)1 AT 1- (1 + R=yT12 (1- e-U)2
0.20
---
0
80
I60
240 320 400 E(DEGK) ( x 10' 1
480
- - - -
A numerical example is plotted in Figure 10, illustrating the R dependence on E1 (0 6400 K) for y = 1, To= 300 K, Tl = 360 K. Note that for U 01, R m yAT/T12, whereas U 0, Ro yAT/2T12. References and Notes 560
Flgure 10. Energy resoluition of the TD technique as a function of the energy. Relative initial heating: ATIT,, = 0.20; T , = 360 K; To =
300 K; y = 1.
ited in spectral resolution by the weakness of the IR source and by fluctuations in laser intensity. In performing TD experiments particular attention must be given to minimize noise and drift which lead to irreproducible spectral signatures of the transient excited-state populations.
Appendix Define the sensitivity of S(tl)to El (assuming that eq 8 applies) to be the corresponding derivative:
(1) W. D. Gwinn, R. J. Anderson, and D. Stelman, presentedat the 2nd Austln Symposium on Molecular Structure, paper no. M2, 1968. (2) P. H. Turner, M. J. Corkill, and A. P. Cot, J. Phys. Chem., 83, 1473 (1979). (3) S. H. Bauer and N. S. True, J. Phys. Chem., In press. (4) L. H. Plette and W. A. Anderson, J. Chem. Phys., 30,889 (1959). ( 5 ) P. Gray and L. W. Reeves, J. Chem. Phys., 32, 1878 (1960). (6) I. M. Napier and R. G. W. Norrlsh, Proc. R. SOC.London, Ser. A , 299, 317 (1967); Nature(London), 208, 1090 (1965). (7) I. S. Zaslonko, 8. M. Kogarko, E. V. Morrukhin, Yu. P. Petrov, and A. A. Borisov, Klnef. Karal., 11, 296 (1970); A. V. Eremln, I. S. Zaslonko, S. M. Korgarko, E. V. Mouhukhin, and Yu. P. Petrov, IbM., 11, 869 (1970). (8) J. Troe, private comrnunicatlon. (9) L. Phllllps, J. Chem. SOC., 3082 (1961). (10) A. Hartford, Jr., Chem. Phys. Lett., 53, 503 (1978). (11) J. D. Lambert, J. Chem. Soc., Faraday Trans. 2, 68, 364 (1972). (12) J. Schuster, MSc. Thesls, Thermal EngineerlngDepartment, Cornell Unlverslty, Ithaca, NY, 1978; W. 0. Ll, MSc. Thesls, Thermal Engineering Depariment, Cornell University, Ithaca, NY, 1979.
Rotational Isomers of Methyl Formate, Located by the Temperature-Drlft Technique S. Ruschln and S. H. Bauer' hpertimnt of Chemlstw, Cornell University, Ithaca, New York 14853 (Received: April 14, 1980; In Final Form: June 26, 1980)
Our previously described temperature-drift (TD) technique for locating moderately excited molecular states was applied to methyl formate, which is isoelectronic with methyl nitrite, tested in our first application. The anti isomer of H3COCH0 has been found via its transient absorption at -1780 cm-', assigned to the C-0 stretching vibration. The syn conformation is more stable than the anti by 3.85 f 0.20 kcal/mol. This magnitude is conaistent with a variety of published data and the failure of prior experiments to locate the anti isomer. The theory for the TD technique was extended to experimental configurations wherein the gaseous sample is pulse heated along the core of the cell. The more difficult requirement that the cell contents be pulse heated uniformly throughout the cell need not be met. Indeed, the calibration and state-locating procedures have been Eiimplified.
Introduction Structurally and dynamically, methyl formate is analogous to methyl nitrite; they are isoelectronic. The syn and anti conformations of the latter have been thoroughly investigated by their microwave, infrared, and NMR spectra. The two conformers of H,CONO are of comparable stability, the anti form being less stable than the syn by 275 f 40 cm-l.l Gas-phase NMR provided data for their rates of isomerization.2 We demonstrated that the interconversion follows second-order kinetics (up to pressures of 0022-3654/80/2084-3061$01 .OO/O
over 100 torr), with an activation energy of -10.5 kcal/ mol. In our first report on the temperature-drift (TD) technique,s we identified a transient IR absorption band, which was assigned to the N=O stretching vibration of the free-rotating 0-N=O species. These exist in a band of states which surmount the rotational barrier, located via TD a t 11.5 f 2.5 kcal/mol above ground level for the syn conformer, thus checking the NMR value. Structural information for H&OCHO is available for the syn conformer. The microwave spectrum4showed lines 0 1980 American Chemical Soclety
I
3062
The Journal of Physical Chemistry, Vol. 84, No. 23, 1980
due to this species only; the barrier for H3C-O rotation was reported to be 1.19 kcal/mol (compared to 2.0 f 0.1 kcal/mol for syn H3CON05). The most detailed IR including a normal mode analysis, indicated the presence of a single isomer. That in the vicinity of room temperature only the syn species is present is consistent with an early electron diffraction investigation8 and with the observation that in the analogous methyl acetate the mean dipole moment (gas phase) showed no measurable change with t e m p e r a t ~ r e .One ~ may therefore conclude that the energy of the anti conformer is at least -3 kcal/mol higher than that of the syn, such that the concentration of the former was below the detectable limits in the above experiments. Indeed, ab initio calculations indicate that AHo(syn anti) = 8 i 3 kcal/mol.1° However, sound dispersion measurements in methyl acetate by Tabuchill are best interpreted by assuming an energy difference of 2.5 kcal/mol and a barrier for syn anti conversion of 5.9 kcal. It is interesting to note that both conformers were found in tert-butyl formate, via their IR spectra, at room temperature. A complete normal mode analysis was presented for this compound.12 These observations support the postulate that the lower energy of the syn isomer is due to an attractive interaction between the terminal oxygen and suitably oriented methyl hydrogens. Here we report on the use of the TD technique for locating the anti isomer of H,COCHO. With this experiment one can discriminate between similar spectra on the basis of the level of excitation of the corresponding molecules above ground level. It depends on two facts: (i) in polyatomic molecules spectral features assigned to a specified transition are affected by the extent of excitation of the molecule as a whole, Le., [E(1,0,...,m) - (E(0,O,...,m)] # [E(1,0,...,n) - E(0,O,...,n)] for m >> n; (ii) in a system which is slowly drifting down in temperature, wherein at all times statistical equilibrium is maintained, the higher excitedstate populations decrease faster than those of low states, purely as a consequence of the Boltzmann factor. The decay constant (due to the superposed temperature drift) is therefore a signature of the extent of excitation of the state above ground level for any feature which is characteristic of that excited state. In this report we have extended the theoretical analysis to experimental configurations with nonuniform heating of the sample.
-
-
Experimental Section The methyl formate as purchased (Aldrich) had a stated purity of 97%. It was further purified by mixing it with (aqueous) 10% NaHC03 solution in a separatory funnel. After separation it was dryed with Na2S04crystals and distilled under vacuum. The experimental arrangement used previously3for the study of H3CON0 was modified in two respects: (a) a slower chopper was inserted to give longer heating pulses (9.2-ms duration); and (b) the beam was weakly focused (fl = 20 cm) at the center of the cell so that only the core of the gas sample was directly heated (Figure 1). These changes led to higher initial gas temperatures and thus increased the sensitivity of the measurements (Appendix of ref 3). However, the thermal decay function was no longer a simple exponential, necessitating a more complex analysis of the heat conduction and relaxation processes (see following section). The on/off ratio for the new chopper was 0.153. The input power was 26 W, and the beam diameter was 5 f 1mm at its waist; the cell diameter was -3 cm. Since H3COCH0 absorbs weakly in the 10-pm region, a little SF6was added (ratio 1/9). This mixture was used
Ruschin and Bauer G A S PHASE T - D R I F T
DETECTION
OF E X C I T E D
STATES:
CHOPPER LINE SELECTED
,
C O P LASER (cw)
I
/Am :--NE
POSITION I FOR CHOPPER
MONOCHROMATOR
RNS T
OLO W E R
BEAM MONITOR
,
52-
"box cor'' ELECTRONICS
F A S T DETECTOR
Flgure 1. Schematic of the experimental configuration for pulse heating the core of the sample cell.
for all of the measurements. Three pressures were tested 19,11, and 5 torr. Most of the data were taken with the lowest pressure, because then the temperature decay was fastest so that we were certain that the cell contents returned to the wall temperature by the end of the dark period. The boxcar integrator was operated at 50-ms scanning time. Fluorescence Spectra. With the chopper in position no. 1and the Nernst glower off, the infrared fluorescence was scanned (resolution 9 cm-l). Clear peaks appeared at 2970 cm-' (assigned, v3, sym str CH3), 1783 cm-l (assigned; v4, C=O str), and 1183 cm-l (probably an overlap of vg, C-0 str, with out of plane CH3 rock). Since the emission at 1783 cm-l was the strongest, its decay curve was used to evaluate the principal parameters which appear in the expression for the signal intensity, i.e., the ratio lhn(ab)(t)/llm(ab)(t
['
= 0) =
exp z 2 ( t ) =1/2 z
- erf z(t) - 1 2
I/
, U 3 Ep. El (meawhere, z(t) (Ue-rt)112,zo W 2 and sured in degrees) is the energy of the state from which absorption or emission occurs. T1 is the temperature at the end of the heating period while Tois the ambient (wall) temperature. The best fit (least-squares) of the observed decay curve to eq 1 for v4 was obtained with w = (6.3 f 0.3) X deg-l and I? = 14.5 f 0.5 s-l. This is illustrated in Figure 2 for a run at 5 torr. To check on the validity of eq 1, we reinserted these magnitudes into eq 1and evaluated the corresponding El values from the recorded decay curves for the other two frequencies. Figure 3 shows the fit obtained for the v3 band; the derived value is El = 2790 f 140 cm-l; Figure 4 is a similar plot for the overlap band (vg; vI5). Here the derived value is El = 1067 f 54 cm-l. Absorption Spectra. The conventional absorption curve was obtained with the chopper in position no. 2 and the laser off. The transient absorption over the spectral range 1650-1850 cm-l (resolution 9 cm-') was obtained with the chopper in position no. 1and both sources on, but with the monochromator entrance slit displaced 40 cm from the cell window. Nevertheless some contribution from fluorescence was present; its magnitude was measured (glower off) and substracted from the signal with the glower on. The spectral distribution for pure fluorescence (dashed curve) and that for the transient absorption (full curve) are plotted in Figure 5 (vertical scales are arbitrary). The transient absorption has a dip at -1780 cm-l, which
The Journal of Physical Chemistry, Vol. 84, No. 23, 1980 3063
Rotational Isomers of Methyl Formate
'3
I .o
LL
I
I
I
I
1
0.24 0.32 t (sec)(x IO-')
0.16
0.00
0
0.40
0.40
Figure 4. The recorded decay In relative fluorescence Intensity at 1183 cm-'. Wcth the values for I? and o derived in Figure 2, the best fit was obtained for El = 1007 f 54 cm-'.
I
1.00-
'0.
-*.*
/
fluorescence
0
0
'
3 0.6
--20 IO1
LL
-
\o 0.41
0.21
\
-30L
l
1650
1
j
I
I
1
I
I
1750
1700
1
1
'
1
I
I
'
1850
I800
I
I
cm-'
Flgure 5. The dependence of ac absorption on frequency, compared with the fluorescence intensity.
ow ,\o', I
0
-e transient absorption
0.04
0.08
I
I
1
0.12
0.16
0.20
J
0.24
t (sec) (x IO-')
Flgure 3. The recorded decay in relative fluorescence intensity at 2970 cm-'. With the values for I'and o (Figure 2) the best fit was obtained for E, = 2790 :k 140 cm-'.
corresponds to the peak in the fluorescence curve; also enhanced absorptions appear at both the high- and lowfrequency sides of the central frequency. The decay functions for these side bands were fitted to eq 1 by using the previously determined values for I' and (J.The graph for the enhanced absorption at 1727 cm-l gave El = 1352 f 70 cm-I (Figure 6); the graph for 1815 cm-l (not the peak frequency) gave El = 1320 f 70 cm-l (Figure 7). (The larger estimated errors were allowed because of the need to correct the observed signals for the fluorescence contributions.) We conclude that these transient side bands originate at the same energy level, which is 3.85 f 0.20 kcal/mol above the ground level of the syn conformer, Pressure Dependence of the r and w Parameters. The theoretical analysis (next section) requires that the inverse temperature parameter (0)be independent of pressure and that the cooling rate factor (I')be inversely dependent on pressure. To check these predictions, we measured the decay of fluorescence at 1783 cm-l at three pressures and fitted the curves to eq 1. The derived parameters are liited in Table I. The results of this experiment are in accord with expectations. The magnitudes of r can be compared with a value reported for sulfur hexafluoride by Bates et
0 I
0
0.04
0.08
I
I
I
1
0.12
0.16
0.20
0.24
t (sec) ( x IO-') Flgure 6. The decay in enhanced absorption at 1727 cm-' and the best fit curve for E, = 1352 f 70 cm-' (corrected for the fluorescence contribution); p = 5 torr.
TABLE I
5 w (deg-')
r
(s-I)
6.3 x 14.5
P, torr 11 6.8 x 10.0
19 7.1 x 6.7
al.13 They measured the decay in thermal fluorescence from low-lying states of SFB in a cell with dimensions
3064
The Journal of Physical Chemlstry, Vol. 84, No. 23, 1980 1.2r
isomer. In contrast, the TD technique not only has a much higher sensitivity14 ( N O 4 ) but also provides the needed discrimination.
I
I .oo
A0
Derivation of Eq 1 Consider heat transport in a long, round cylinder (length much greater than diameter) with an initial temperature distribution: T(r;t = 0 ) = T1 for 0 5 r 5 b =Toforb
