7371
J. Phys. Chem. 1995,99, 7371-7380
Collisional Flow of Vibrational Energy into Surrounding Vibrational Fields within S1 p-Difluorobenzene. Rate Constants for Initial Levels with High Vibrational Excitation David L. Catlett, Jr.,? Charles S. Parmenter,* and Christopher J. Pursell* Department of Chemistry, Indiana University, Bloomington, Indiana 47405 Received: July 29, 1994; In Final Form: December 21, 1994@
State-to-field vibrational energy transfer from optically pumped vibrational levels in S 1 pDFB by single collisions with Ar at 300 K has been characterized for 18 initial levels whose energies range from 0 to about 2500 cm-l where the density of levels is about 200 per cm-'. The rate constants vary according to the zero order identity of the initially pumped level, even for the highest levels that are of extensively mixed vibrational character. In the midst of these variations, the constants gradually increase as higher energy levels are pumped, but the energy regime where the rate constants level off has apparently not yet been reached. The largest rate constants are about 60% of the Lennard-Jones value. Transfers involving single quantum changes in the lowest frequency mode, Y ~ O = ' 120 cm-l, are the dominant single channels for all levels. These channels result in elevated rate constants for initial levels that contain quanta of 13;. If the state-to-state 1301contributions are subtracted from the state-to-field rate constants, the entire set of rate constants has close similarity to that for benzene i- CO over the same SI energy range. Attempts to model the state-to-field rate constants using propensity rules that describe well many S1 pDFB state-to-state transfers are only partially successful. The modeling shows, however, that increase of state-to-field rate constants at higher energies is primarily a consequence of increasing numbers of state-to-state channels that involve larger vibrational quantum number changes (Av I3).
Introduction We continue our investigation of single-collision state-selected vibrational energy transfer (VET) in large molecules with further study of S1 p-difluorobenzene (PDFB>.I-~In this work, we report measured rate constants for the collisional destruction of an initially pumped S1 vibrational level by collisional energy transfer into the neighboring field of S1 vibrational levels. These state-to-field VET rate constants (k4(i) in our parlance) have been characterized for each of 18 initial SI levels in the energy range 0 I6 v i b l 2500 cm-'. As enumerated in Figure 1, the levels are fundamentals, overtones, or combinations of six modes. This work complements a similar study with S1 benzene for levels lying in the same energy range,4 as well as a study of state-to-field relaxation from four levels in SO pDFB5 that provides an instructive comparison with the S1 data. The extension from benzene to pDFB is an important step since it provides an entry to a fundamental issue in chemical reactivity, namely, the collisional activation and deactivation of polyatomic molecules. This problem was recognized over 70 years ago in the Lindemann mechanism for thermal unimolecular reactions,6and it still remains under active study as new experimental approaches are brought into use. Most of the work concerns collisional deactivation of molecules with high vibrational energy ('20 000 ~ m - l ) . Interest ~ has focused on the magnitudes of vibrational energy change per collision and on the relative deactivation efficiencies of various collision partners. The more recent studies have probed the state-resolved deactivation of small molecules8-10as well as the internal excitation of small molecules in collision with highly excited large molecules.1 ~ 1 Abundant theoretical efforts complement the experimental studies.l2
* To whom CorresDondenceshould be addressed.
Present address: Texas Instruments, 13353 Floyd Road, M/S 374, Dallas, TX 75265. Present address: Chemistry Department, Trinity University, 715 Stadium Dr., San Antonio, TX 78212. Abstract published in Advance ACS Abstracts, May 1, 1995.
*
@
0022-365419512099-7371$09.0010
2500
STATE
cm-'
32 53
2502 2454
3'5'30' n
e
2000
8
3'5'
2189 2069
51
1758 1638
w"-
3'30'
1371
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1251
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818
W
x on
3
52301
1500
cd
E
500
6' 8'30' 17' 30'
8' 0
30' 00
410 295 274 240 175 120
ooo
Figure 1. SIpDFB energy levels for which state-to-field vibrational energy transfer constants have been measured. The approximate state density is taken from ref 36.
The vibrational fields of these highly excited molecules differ fundamentally from the low-energy level structure generally involved in the state-resolved studies. With high vibrational excitation, the large state densities create a vibrational quasicontinuum without preservation of individual level identities or characteristics. Discussions of the deactivation necessarily use the language of statistics. In contrast, the S1 state-resolved studies concern individual levels near the bottom of the vibrational manifold. Here the levels are well separated, and they can often be well described with the zero order picture of 0 1995 American Chemical Society
7372 J. Phys. Chem., Vol. 99, No. 19, 1995 separated harmonic modes. Discussions of these results usually invoke single-level identities, complete with propensity rules for single-collision state-to-state processes. With both benzene4 and SO PDFB,~even the state-to-field VET results were reconciled by modeling based on such individual level propensity rules. The present work with pDFB now begins to bridge these dissimilar vibrational domains. The upper reaches of these pDFB state-to-field experiments concern regions of the S1 manifold where the individual level harmonic model description has become poor and the level structure is beginning to attain some of the high level characteristics. As one climbs the pDFB S1 manifold, indication of abundant mixing among adjacent levels f i s t appears13near 1600 cm-' where the state density is about 10 per cm-'. At the 2500 cm-' upper limit of the present pDFB study, the state density is approaching 200 per cm-', and the mixing is so severe that the dispersed S1-So fluorescence spectrum contains only vestiges of structure.13 In fact, time-dependent intramolecular vibrational redistribution (IVR), the hallmark of high vibrational levels, has been observed in fluorescence chemical timing experiments14 for many pDFB levels with 1600 cm-' IEvib I2500 cm-'. The contrast between pDFB and benzene is important. While the state-to-field VET study in benzene4 also extended to Evib 2500 cm-l, the level structure of the molecules is fundamentally different at that energy. In benzene, the state density is only about 10 as opposed to 200 for pDFB, and there is little evidence for extensive state mixing. Thus, all of the benzene experiments would seem to pertain to states with reasonably well defined zero-order identities. The greater abundance of low frequency modes in pDFB establishes the critical difference between these molecule^.^^^^^ These low-frequency modes create the relatively high level density and lead to the severe level mixing at Evib % 2500 cm-l.17 In the present studies, we will be particularly interested to see whether pDFB state-to-field VET characteristics undergo change as we climb the vibrational ladder from unmixed to severely mixed initial states. With benzene, the VET rate constants continue to rise as the initial level energies i n ~ r e a s e , ~ but do so always with level-to-level variation in recognition of the initial level harmonic mode identities. One would anticipate different behavior when the pDFB vibrational field is dominated by severely mixed states. Here the quantal distinctions between states become blurred so that the level-to-level sensitivity should disappear. Additionally, the drift to increasing rate constants at higher energies must eventually stop. The present experiments use the laser pump-dispersed fluorescence probe technique that has been so effective with 300 K thermal systems as well as with the cold molecules of crossed molecular beams.16~18~19 Initial S1 states are selected by S1-So absorption of a laser tuned to appropriate absorption bands. The vibrational structure of the ensuing &-So fluorescence is used to monitor depletion of the pumped level as increasing added gas pressures cause the state-tofield VET. The built-in molecular clock of fluorescence lifetimes ensures that collision partner pressures remain in the one-collision regime. The known free-molecule fluorescence lifetimes allow calculation of absolute values of the rate constant. It is surprising that systematic explorations of state-to-field VET rate constants from a variety of vibrational levels in large molecules are apparently available only for S1 benzene," SO PDFB,~and, with the present study, S1 pDFB. Several complementary studies are, however, relevant to this work. One has provided state-to-field rate constants for more than a dozen
Catlett et al. gases in collision with S1 benzene excited to a mix of several levels with Evib x 1970 cm-1.20 Another is a study of SO pDFB providing similar information with 23 collision partners using completely different experimental techniques.21 It concerns a level with Evib x 2040 cm-' where the state density is 6-8 per cm-'. In addition, room temperature explorations of state-tostate VET in S1 b e n ~ e n e and ~ ~ St , ~ pDFB2s3 ~ also bear on this work. State-to-state VET studies of these and other aromatic molecules are summarized in a review.16
Experimental Procedures The experimental apparatus is similar to that used in a previous study.2 Gas samples were contained in a specially designed cross-shaped fluorescence cell with quartz windows. The pDFB pressures, 20-200 mTorr, were low enough to prevent pDFB-pDFB collisions from occumng within the -10 ns fluorescence lifetime. Argon pressures up to 6 Torr were used, which represent the single-collision regime. The pressures were measured at the sample cell with a capacitance manometer. The excitation source was the frequency-doubled output of a Nd:YAG pumped dye laser. This system gives 6-7 ns pulses at 10 Hz with about 2 cm-' band-pass. The UV radiation was tuned to the maximum of a pDFB absorption band contour to prepare the initial S1 level. Molecular fluorescence was collected at a right angle to the excitation radiation, imaged into a scanning monochromator, and detected with a photomultiplier whose output was fed to a boxcar averager. The monochromator was tuned to an S1 +. SO emission band from the initially prepared level that was chosen to avoid overlap with emission from collisionally populated levels. The bands are listed in Table 1. The monochromator was used with 40 cm-' resolution, a value sufficient to filter out broadening effects due to rotational energy transfer.
Results and Kinetic Analysis We use the kinetic model and the experimental approach that was developed for the earlier benzene study.22 The tunable W laser radiation pumps pDFB, here designated B, to a single Si vibrational level
B
+ hv - B*(i)
Under collision-free conditions this initial level may decay by radiative and nonradiative processes
k2(i)
B*(i)
nonradiative decay
. I
(2)
Vibrational energy transfer from the initial level into the neighboring field of SI vibrational levels may occur by collisions with ground electronic state pDFB or with added argon gas (M),
+ B -B* + B B*(i) + M -B* + M B*(i)
k,(O
(3)
k&)
(4)
B* designates S1 pDFB in vibrational states other than state i. Under our experimental conditions (pDFB pressures of 20200 mTorr), process 3 may be ignored. Additionally, electronic state quenching of B*(i) by pDFB or argon collisions may be ignored.
J. Phys. Chem., Vol. 99, No. 19, 1995 7373
Collisional Flow of Vibrational Energy within SIpDFB
TABLE 1: Emission Bands Used for Monitoring State-to-FieldVibrational Enerev Transfer level transition band max (cm-l, vac) 00 35 980 35 943 301 81 35 734 35 906 302 35 880 17l 35 697 8I3O1 35 940 6l 51 37 208 5I3O1 37 170 37 132 5I3O2 31 37 231 3I3O1 37 193 38 026 52 37 988 52301 3151 38 459 38 421 3151301 53 38 844 38 085 32 Using the emission bands listed in Table 1, it is possible to adjust the monochromator to a region free from B* emission. The monitoring of B*(i) is therefore blind to B* fluorescence. for emission The B*(i) fluorescence intensities and with and without argon, respectively, are given by the steady state expression
7
I
,
I
1
*
32 (2502)
3' 0251)
J
I
34000
1
I
1
38000
cm-' (vac) Figure 2. Collision-free SI-SO fluorescence spectra from three SI pDFB levels (E\ib in cm-l). The bands used to monitor emission intensity from the pumped levels are marked.
c
where [MI is the pressure of argon. A plot of versus [MI should be linear with a slope S = k4(i)/(kl(i) kz(i)). The quantity (kl(i) h(i))-'= zfneeded to obtain k4(i) from the slope is determined in principle from experimental measurements of the fluorescence lifetime. While values are available" for a selection of levels up to 3310 cm-l, many of the levels of our study are not represented. We have obtained values that can be used with eq 5 by interpolation from a fit to the experimental values plotted against the S1 level energy. The decrease of tfwith increasing vibrational energy is approximately linear. The emission bands used for monitoring the collisional destruction of the initial levels were chosen such that emission from the field of collisionally populated levels would not interfere. Figure 2 shows an example of the dispersed fluorescence spectra from the levels Oo, 3l, and 32. An m o w indicates the emission band used for monitoring the energy transfer for each level. The state-to-field rate constants h(i)were determined for plots of versus argon pressure according to eq 5 . Examples of such data for the levels Oo, 3l, and 32 are presented in Figure 3. The band intensities were measured for about six Ar pressures to establish the slope. Three to five slopes from plots of separate experiments were averaged to establish the rate constant for each level. Rate constants were obtained for 18 initial levels with vibrational energy up to 2500 cm-'. The constants are listed in Table 2. The constants are plotted as a function of vibrational energy in Figure 4. A 15% precision of the rate constants is established by the reproducibility of the slopes. Absolute errors may be larger if for some (unsuspected) reason the fluorescence lifetime of a given level has a larger deviation from our approximate value.
@e
+
+
M (torr) Figure 3. Stern-Volmer plots of fluorescence intensity in a selected band from each of three S1 pDFB levels that are being destroyed by state-to-field VET in Ar collisions (M).
Discussion The central results of this study are the rate constants k4(i) listed in Table 2 and displayed in Figure 4 that describe the destruction of the initially pumped SI vibrational level by collisions with Ar. The destruction occurs entirely by vibrational energy transfer to the field of S1 levels surrounding the level. These state-to-field VET rate constants concern 18 initial levels ranging up to Evib = 2500 cm-' where the level density is approaching 200 per cm-'. Those levels are fundamentals, overtones, or combinations involving six SI modes, of which two are out-of-plane ( ~ 3 0 ' and Q') and four are in-plane (vg', Y
