J. Phys. Chem. 1994,98, 3263-3269
3263
State-to-State Collisional Vibrational Energy Transfer in S1 pDifluorobenzene David L. Catlett, Jr.,+ Charles S. Parmenter,' and Christopher J. PurselP Department of Chemistry, Indiana University, Bloomington. Indiana 47405 Received: June 29, 19930
State-testate vibrational energy transfer from six levels in S1p-difluorobenzene (pDFB) vapor a t 300 K has been studied for single collisions with argon atoms. The levels range in vibrational energy up to 8 18 cm-l and involve quanta of US, V6, VB, and ~ 3 0 . This investigation is a continuation of a previous study concerning the zero-point level. The study is based on a laser pump-dispersed fluorescence detection method that monitors all significant one-collision channels from a given initial state. In common with results from other studies of polyatomic vibrational energy transfer, large state-to-state rate constants (up to 0.2 times hard sphere) are observed with high selectivity among possible final states. Among the 30 modes of pDFB, processes with small quantum changes in the two lowest-frequency modes, vg and ~ 3 0 ,dominate the energy transfer. Transfer to nearly resonant levels is generally too inefficient to observe. The rate constants for gaining or losing quanta of YE and of v30 are insensitive to the vibrational identity of the initial state. The collisional flow patterns from each level are semiquantitatively described by a previously developed treatment of the SSH-T vibrational energy-transfer model.
Introduction
1oO0,
An optical pump-fluorescence probe method has been used for numerous studiesof statc-to-state collisionalvibrationalenergy transfer (VET) in large polyatomic molecules ( > l o modes).' This technique selects initial vibrational levels in the S1 state by tuned laser pumpingand usts thevibrationalstructureofdispersed Sl-&fluorcscencetodetect theVETwithin the& state. Detailed information can bcextracted from these SIprobes that is difficult to acquire from ground-state studies. For example, from an initial S1vibrational level selected among several possibilities, one can obtain absolute single-collision state-testate cross sections for every important VET channel. Many of these investigations have involved aromatics, particularly benzene and its derivatives, because of their well-studied absorption and emission spectra, the accessibility of their excited states with commercial lasers, and their short fluorescence lifetimes that provide a convenient 'clock" for establishing single-collision conditions. In this paper we continue our presentation of VET characteristics in SIpdifluorobcnzene, (pDFB). In the first report,* hereafter called paper 1, we discussed VET from the S1 zeropoint level with the 300 K single-collision partners He and Ar. In the stcond,3 we described VET in the low-energy He and Ar collisions of a 30 K jet expansion. Here we return to 300 K experiments with Ar that take advantage of pDFB's unusual experimentalaccessibility from pumping a variety of higher initial vibrational levels. We have been able to describe state-to-state VET from each of six additional levels. The SIenergy level diagram in Figure 1 displays the scope of the present study and shows why pDFB is such an instructive system for polyatomic VET. The six initial levels, lying between 119 and 818 cm-1, involve two in-plane modes (YS and ug) and two out-of-plane modes (vg and UW)occurring as fundamentals, overtones, or combinations. A particularly rich array of vibrational states surrounds these pumped levels because pDFB has an unusual number of low-frequency modes. In fact, exactly half of the 30 modes occur a t or below 818 cm-l, the highest initial level of this study.' Consequently, the molecule offers f Present address: Texas Instruments, Inc., 13353 Floyd Road, PO Box 655012, Mail Stop 374, Dallas, TX 75265. t h n t addreu: Department of Chemistry, Trinity University, 715 Stadium Drive, San Antonio, TX 78212.
To whom compondmcc should be addressed. .Abstract published in Adoonce ACS Abstracts, March 1, 1994.
' Id61
8001
5'
13 (937) '25(933)
*
I
5 (818)
1651
-< ' ' --
llol
600-
400
-
6'*
15 (670)
14(666) 28(619) g(588) 7 (583) 26(558) 16(528)
29 (438) 6(410)
21 (403)
P
8'30'
*
- 22(352)
17 (274)
30'
1 1:: 8'
0
*
8 (175)
30 (120)
I
Figure 1. A display of SIpDFB vibrational levels with all levels shown to about 600 cm-l. The number of omitted levels above that region is given in braces. All fundamentals (cm-I) below 1000 cm-1 are noted. The asterisks mark levels initially pumped for VET measurements.
-
exceptional potential to observe participation of diverse modes in the V T collisional energy exchange. Despite these opportunities, this study will show that pDFB has the most mode-specific VET yet seen among aromatics. Not surprisingly, the lowest-frequency mode ~ 3 is 0 especially active in the VET process. As with other polyatomic VET studies, large rate constants are observed. Using a previously developed treatment of the SSH-T model for VET,3we are able to describe semiquantitativelythe unique flow patterns from each initial level. Such VET processes have been described as 'collision-induced intramolecular energy transfer",S and in this sense it is fitting that the subject be included in a volume dedicated to Professor Joshua Jortner. His contributions have been central to our understandings of intramolecular processes, including specifically intramolecular vibrational dynamics. While to our knowledge
0022-3654/94/2098-3263S04.50/0 0 1994 American Chemical Society
Catlett et al.
3264 The Journal of Physical Chemistry, Vol. 98, No. 13, 1994
TABLE 1: Absorption Bands Used for Pumping SIpDFB Levels SIvibrational absorption band max level energy (cm-1) band pumped (cm-I, vac) 301 8l 302 8'30' 6l 51
119 173 238 292 410 818
30: 8; 30:
36 802 36 594 36 764 36 554 37 250 37 658
he has not extended his discussions specifically to collision-induced vibrational problems, this paper will amply demonstrate the need for such theoretical attention. This work is a continuation of our efforts to characterize polyatomic VET with the optical pump-dispersed fluorescence technique. The first such study involved benzene for which VET from V.5 at 522 cm-l in the SIstate was characterized with nine single-collision partner^."^ From this study there first emerged the dominant VET characteristics that have since been found in every aromatic studied as well as in other polyatomics. The VET was seen to be highly selective among possible final states. Small quantum changes in the lowest-frequency modes dominated the energy transfer. Large cross sections (0.01-0.1 of hard sphere values) occurred for the principal channels, and a striking similarity in the channel-to-channel competition (energy flow patterns) was seen among many collision partners. Perhaps as surprising as the high final state selectivity was the discovery that simple propensity rules developed from the SSH-Tmodel of VET were successful in replicating the flow patterns. In addition to flow patterns, the rules were able to reproduce the relative magnitudes of state-to-field rate constants for VET relaxation of 11 initial SI benzene 1evels.lO Chernoff and Rice" investigated VET by a similar approach from eight levels in SIaniline with argon as a collision partner. This work also demonstrated the highly selective nature of VET among possible final states. The study included several initial levels so that it was possible to observe VET channels with identical vibrational quantum and energy changes that originated from levels with different vibrational identities. The results established that the rate of transfer of a specific vibrational quantum may be independent of the initial state. This characteristic now seems to be general in aromatics. Additional studies of aniline using different collisional partners have also been published.12 VET studies from eight levels in SIpyrazine have been reported by McDonald and Rice.13 Many qualitative aspects of VET from SI pyrazine are identical to those of benzene and aniline. The results of this study are unique, however, in that the measured rate constants are relatively small. The difference has been attributed to the singlet-triplet coupling that enhances collisioninduced intersystem crossing, a process that competes with the SI VET." Krajnovich et al.1 have given a review of 300 K SIVET in both the aromatic systems and other molecules that have been studied by the optical pump-fluorescence probe method. Earlier reviews arecited there. Specificattention was given to theissueof whether S1 VET had special characteristics that were not applicable to VET in ground electronic state molecules. The evidence, including particularly that on SopDFB provided by Knight and co-worker~,~~ suggests that SIand SOVET differ only in the details created by vibrational frequencies, special Fermi resonances, and so forth.
Experimental Procedures The experimental procedure was identical to that used earlier from the S1 zero-point level of pDFB.2 Briefly, the frequencydoubled output of a Nd:YAG pumped dye laser was tuned to the maximum of pDFB S l S 0absorption bands to pump the initial S1level. Table 1 lists the SlSo absorption bands that were used
for pumping the S1 levels. Less than 10 mTorr of pDFB was contained in a 300 K fluorescence cell with carefully measured added Ar. SlSo fluorescence was imaged into a scanning monochromator and detected with a photomultiplier. The photomultiplier signal was monitored with a gated integrator and ratioed on a shot-to-shot basis with the signal from another detector that monitored theUV laser power. Thedispersed spectra were stored in a computer for display and manipulation.
Results VET in S1pDFB has now been studied from the seven levels shown in Figure 1. A report concerning VET from the SIOo level is given in paper 1. This paper describes VET from the six excited levels. Two types of measurements characterize the collisional VET. Thesimplest yields ultimately the rateconstant k4(i) that describes the destruction of an initial level i by VET into the entire field of participating SI vibrational levels. The other is associated with the rate constant k4(i-f) that describes the various stateto-state VET channels i f that occur from a given initial level i to a final state f. The procedures and the kinetic model used to determine these constants are detailed in paper 1. The state-to-field rate constant k4(i) was obtained from observations of the attenuation of an emission band from the pumped state as a function of added Ar. For example, the 5:6; emission band provides a convenient relative population monitor for the level 6l reached by pumping the band 6;. The destruction of 6l pDFB by Ar occurs entirely by VET so that the 61 level monitoring yields an accurate state-to-field VET measurement. State-to-state VET channels are identified by the growth of new spectral bands in the dispersed fluorescence spectra as Ar is added. The rate constant derivation first involves identification of the bands used to monitor the relative populations of the new SI vibrational levels. As set forth in paper 1, we then need quantitative measurement of the band intensities, a method to relate accurately these intensities to relative level populations, and a realistic kinetic model to transfer the relative level populations to the state-to-state rate constants. Since details are in paper 1, we only briefly comment on some aspects of the measurements and analysis. Spectroscopic Identification of VET Channels. We illustrate the principal issues with the example of VET from the level 6' at 410 cm-1. As described in paper 1, one can find 100-cm-l windows in the emission spectrum where bright bands from collisionally populated levels will occur. Three such regions for emission after 61 pumping are shown in Figures 2-4. The listing in Table 2 of SI pDFB levels shows the VET possibilities within 2kT below or within kT above the 6' level. All are energetically accessible by 300 K Ar collisions. Since the SOand SIvibrational frequencies and the Franck-Condon factors are known or may be ~ a l c u l a t e d ,the ~ ~positions J~ of bright emission bands are known. They are listed in Table 2. Comparison with growth bands in the collision-induced spectrum allows identification of the new levels. Some bands lie too close to each other to be resolved and produce band "clumps". Examples are labeled A-F in Figures 2-4. Many levels have bright emission bands that fall in region A of Figure 2. Only two, however, have emission band maxima that correspond to the maximum in region A, namely, 302and 6I3O1. Since the limited spectral resolution precludes distinction between the two, another region was examined where the level 61301 emits but the level 302 does not. Such a region is shown in Figure 3 where the fluorescence band 6h30; is an unambiguous flag for emission from the 61301 level. The intensity of the 6h30: band relative to the 5:6:30: band of region A indicates that emission from 61301 is responsible for 80-100% of the region A
-
Energy Transfer in SIp-Difluorobenzene
The Journal of Physical Chemistry, Vol. 98, NO. 13, 1994 3265 6'30'1 302
27130t1R 6'30'
303
35860
cm-l
\ /
3590C
Figure 2. A segment of the fluorescence spectrum after 6, excitation of pDFB in the presence of 13Torr of Ar. The markers show the calculated
positions of band maxima that would occur from the indicated levels (see Table 2). The dashed line in region A shows the contributionto intensity from the initially pumped level via the 6: band. It is determined by knowledge of the collision-free 6' spectrum. The dashed lines in regions B and C show the red tails of the rotational band contours from regions A and B, respectively.
TABLE 2 Positions of Bright Fluorescence Bands from Each SIpDFB Level up to 650 cm-* band position (cm-l)a .~ &ib level (cm-1) transition absolute (vac) relative to $6; 40 35 980 0 00 3 35 943 119 30, -206 35 734 173 8' -34 35 906 238 30' -60 35 880 275 17, -243 35 697 292 8I3OL -30 35 910 346 8' 44 35 984 353 22' -7 1 35 869 357 303 -3 35 937 391 27, -97 35 843 394 17'30,
-
6'
410
35 940
0
8'30' 29, 8l17, 8230L 22I3O1 304 27I3O1 17I3O2
41 1 438 448 465 472 476 510 513 519 526 529 530 550 557 564 567 583 584 59 1 595 61 1 617 621 626 628 629 638 645 648 649
35 660 35 911 35 634 35 857 35 947 35 832 35 900 35 806 35 647 35 738 35 903 35 623 35 780 35 873 35 690 35 597 35 693 35 820 35 910 35 795 35 664 35 764 35 794 35 663 35 884 35 863 35 610 35 700 35 866 35 586
-280 -29 -306 -8 3 7 -108
83
6'30'
\w
6'302 I
I
I
-~
I
I I
37140
37180
37220
cm-l
Figure 3. Another segment of the 6, emission spectrum under the conditions of Figure 2. In this region, only fluorescence from the levels 6'30, and 6I3O2 is expected.
4:6:
1
6'8'
\ I
8'27'
6'8'30'
35680
cm-l
35720
Figure 4. Another segment of the 6, spectrum under the conditions of Figure 2. The dashed line shows the 4y6; emission band intensity from
the initially pumped level. intensity. An upper limit is thus placed on the contribution of emission from the 302 level. By a similar analysis, it can be shown that 86100% of the intensities in maxima B and C of Figure 2 are due to emission from the 61302 and 6,303 levels, respectively. As an upper limit, 20% of the intensity in maxima B and C may be from the levels 303 and 304, respectively. Figure 4 shows that the expected positions of fluorescence bands from the levels 81,6181, and 6181301fall a t the maxima of the D, E, and F, respectively. Emission from four other levels would occur in the region of Figure 4. None appears to be a significant contributor to the intensity. The Single-Collision Regime. The hard-sphere collision frequency Z for a single pDFB molecule with other pDFB molecules or with Ar may be estimated from the approximate relationship Z (s-1) lO'P, where P is the pressure in Torr of pDFB or of Ar. The pDFB pressures were kept below 10 mTorr to ensure that pDFB pDFB collisions did not contribute significantly to
-
+
8'22' 6I3O1 8'303 17' 29'30' 8l27I 8'17I3O1 6l8' 8'30' 22'302 30, 8l29' 28l 8'17, 7' 17I22I 27I3O2 g3301 8l22I3O1 6'30' V3O4 a
-40
-134 -293 -202 -37 -317 -160 -67 -250 -343 -247 -120 -30 -145 -276 -176 -146 -277 -56 -77 -330 -240 -74 -354
Calculated from data listed in refs 16 and 17.
the observed VET. By the above relationship, the time between collisions established by this pressure is about l t 5s, a value far exceeding the pDFB SIfluorescence lifetime of about 10 ns.I8 Care was taken with added Ar pressures to ensure that observed VET was primarily a consequence of single-collision events. The effort was completely successful for the more efficient VET channels. Sequential collisional paths may contribute, however, to observations concerning some of the less efficient channels. Methods for correct analysis of these cases are described for 00 VET in paper 1. The corrections are more complicated for some of the low probability channels from higher levels, and a description is given e1~ewhere.I~ The VET Rate Constants. The state-testate rate constants derived from the dispersed fluorescence band intensities are collected in Table 3. We have also listed the paper 1 constants for VET from 00. Because of spectral congestion, the rates for the 61 302 and 61 303 channels represent only upper limits. For similar reasons, the 81 82 and 8130, 82301channels could not be monitored. As discussed below, the rate constant for gaining a quantum of us is independent of initial level. For later use, we have included in Table 3 the average value k = 3 X 10s T o r r ' s-1, determined from the other four initial levels.
-
- -
-
Catlett et al.
3266 The Journal of Physical Chemistry, Vol. 98, No. 13, 1994 TABLE 3 Stateto-State Vibrational Energy-Transfer Rate Constants for SI pDFB in Collisions with Argon process k4i-f). Ji) If) (lo5Torr' s-I) k4(i+f)/k4(i)* P(i-f)/CP(i--f)c 00
--
30' 81
302 8'30' 303
30'
Oo 8'
302 8'30' 303
8'
Oo
30' 302 8'30' 82 8'302
302 00 30' --L
81
-
8'30' 303 8'302 304
81301 Oo 301 81
6'
5'
-
302 303 8I3O2 8230L V303 8'
302 303 6'30' 6'8' 6'302 6W301 61303 27'29' 5'30' 5'8'
5'302 5'8'30' S303
18 f 2 (13) 2.9 0.4(13) 1.7 0.4 (12) 0.1 0.1 (2) 0.5 0.5 (4) 26 f 2 (12) 0.7 0.2 (2) 18 f 2 (12) 3.1 0.8 (2) 1.6 0.4(12) 4.5 f 1.0(10) 5.4 1.0 (10) 0.9 0.5 (2) 17 2 (10) [31d 2.1 0.5 (2) 3.7 0.8 (8) 23 2 (10) 1.3 0.4 (2) 2.1 0.5 (2) 15 l ( l 0 ) 3.3 0.5 (2) 1.8 0.4 (2) 2.3 0.3 (6) 3.5 f 0.8 (6) 29 3 (10) 3.0 f 0.7 (6) 1.0f 0.5 (2) 19 2 (10) [31d 1.5 f 0.3 (2) 0.3 f 0.1 (2)
* * *
1 .oo 0.16 0.09 0.01 0.03 0.53 0.01 0.37 0.06 0.03
0.18
[31e
0.22 0.04 0.68 0.12 0.08 0.06 0.34 0.02 0.03 0.22 0.05 0.03 0.04 0.07 0.55 0.06 0.02 0.36 0.06 0.03 0.01 0.11
[0.4Ic 15 f l(l1) 2.8 0.5 (1 1) 2.1 0.4 (1 1) 0.7 0.2(2) 0.2f 0.1 (6) 0.6 0.3 (1) 16 f 1 (13) 3.2 0.5 (2) 2.3 h 0.5(13) 0.5 0.3 (2) 0.7 0.4(2)
0.56 0.10 0.08 0.02 0.01 0.02 0.40 0.08 0.06 0.01 0.02
* * ** **
** * * **
0.01
0.71 0.23 0.02
0.01 0.001 0.50 0.08 0.28 0.09 0.01 0.28 0.14
0.01 0.36 0.12 0.01 0.02 0.48 0.01 0.07 0.26 0.08 0.01
0.01 0.15 0.36 0.07 0.01 0.20 0.06 0.001 0.02
0.01 0.001 0.56 0.18
0.01 0.01 0.001
0.001 0.65 0.21 0.01 0.01 0.001
The parentheses contain the number of independent measurements over which the rate constant was averaged. k4(i) represents the stateto-field VET rate constant for each initial level i (see Table 4). P(i-f) is thecalculatedstate-testate VET probability (see text). Due tospectral congestion, these rate constants are estimates based on the AVS= +1 channel from the other initial levels (see text). e These rate constantsare upper limits rather than measurements (see text).
TABLE 4 State-to-Field Vibrational Energy-Transfer Rate Constants and Comparisons with the Sums of State-to-State Vibrational Energy-Transfer Rate Constant#
00 30' 81
302 8'30' 6l 5'
0.18 0.49 0.26 0.67 0.53 0.27 0.40
0.23 0.49 0.33 0.50 0.62 0.24 0.23
1.29 1.01 1.26 0.75 1.18 0.91 0.58
Theserateconstantscanbecompared tothe hard-sphererateconstant
k b = lo7 Torr' s-I.
The state-to-field rate constants kd(i) from the six initial levels are listed in Table 4. We also include k4(00) from paper 1. The k4(i) values are compared to the summation of the state-to-state rate constants. The ratio gives an indication of whether or not all VET channels have been identified.
TABLE 5 Rate Constants Related by Microscopic Reversibility k4(i-f) / k,(f-i) process measured calculatedn 00
0.62 0.62 0.46 0.78 0.13 0.88 0.69 0.59 0.70
30'
004+81
--
0.56 0.43 0.31 0.56 0.77 0.43 0.73 0.56 0.77
00 302 30' 302 30' 8' 30' 8I3O1 8'- 302 8'- 8'30' 302 8I3O1 0 Calculated according to kd(i-f)/k4(f-i) of the states are degenerate. +
= exp(-AE/kT). None
Discussion Our central findings are the 41 absolute rate constants k4(i-f) listed in Table 3. They describe state-to-state VET in S1 pDFB in single collisions with Ar and involve seven initial SI levels. The individual rate constants are useful in their own right. When the constants from a given initial level are compared, however, they form the branching ratios or the collisional energy flow pattern that describes the competition among VET channels in single-collision encounters. A simple test informs us whether the VET flow patterns are complete. If all major channels have been observed, the sum of k4(i-f) values from a given level should match the independently measured rate constant k4(i) that describes the full state-to-field VET from that level. The &(i+f)/k4(i) comparisons are presented in Table 4. All except one are within about 25% of unity, a deviation expected from the uncertainties in the measurements. The exception concerns the highest level 51 at EY~I, = 8 18 cm-' where the ratio falls to about 0.6. The fluorescence spectrum after 5' pumping in the single-collision regime for Ar contains a poorly structured background that suggests numerous channels of low probability, none of which may be monitored individually. The known Fermi resonance16J7between 5' and 62 may lead to some of these channels. Another test of the quality of the VET measurements is derived from comparison of rate constants related by microscopic reversibility. For example, rate constants for the 8 ' - 8'301 and 8l301 8' channels have been obtained independently after pumping the respective originating states. The rate constants must be related by microscopic reversibility in the form
-
k4(8 '-4 l 301) E -
k4(8 301-8')
g(8') exp(-AE/kT) = g( 8'301)
-1 exp(-l19/206) = 0.56 1
The observed ratio is 0.59. When we include data on the 00 level, eight additional comparisons are possible. They are shown in Table 5. VET Characteristicsof Aromatic Systems. pDFB is the fourth aromatic system to bevisited with these VET methods,' the others being benzene, aniline, and the heterocyclic pyrazine. The new pDFB data add substantially to the general picture of singlecollision VET characteristics that is emerging on these systems. We have earlier presented detailed comparisons of the VET behaviors including some preliminary data on pDFB.' The comparisons showed striking similarities between the systems, and common characteristics became apparent. In the discussions below, we show how they are supported by the pDFB data that now encompass seven initial SIlevels. Efficient VET. With the exception of pyrazine,'3 the dominant state-to-state VET processes in the aromatic systems occur with rate constants that are about 0.1 of the hard-sphere value.' The
Energy Transfer in SIp-Difluorobenzene
The Journal of Physical Chemistry, Vol. 98, No. 13, 1994 3261
lo00
800
-
5
h
-
n
P
3
.-8
6 36 2
ws
I
400
Y
E
A
= I101
600
8’303 g2301
81302 303
8’301
> 200
0
6 55 7 4
302 8l 30’ O0
Figure 5. A schematic of state-to-state VET from the initial level 8I3O1 at 292 cm-I. The levels to which VET is observed have extended lines and are identified. The number to the left of each final level is the percxntageof VET to that level asdetermined by the ratioof experimental rate anstants (k4(81301-.f)/k4(81301)) X 100.
efficiency for pyrazine is about an order of magnitude less. Reasons for this reduced value have been given.14 The efficiency of pDFB VET is seen by comparison of rate constants with the hard-sphere rate constant for pDFB + Ar collisions, khs c 1 X lo7 T o r r ’ s-I. The comparisons are immediately seen by inspection of Tables 3 and 4. The efficiency of destroying an initial state by the sum of all VET processes ranges from 0.2 to 0.6. The efficiency of the dominant channel from each initial state is 0.2-0.3. Thus, even by the standards of the other aromatic systems, VET in pDFB Ar collisions is remarkably facile. High Selectivity among Possible Final States. The selectivity of final states that occurs in S1 pDFB VET with Ar collisions is seen most clearly when those final states are viewed in their surrounding field of states. As an example, Figure 5 shows the flow pattern to the field from the initial level 81301at &b = 292 cm-1 (a combination of two out-of-plane vibrations). Despite the presence of about 20 levels within kT (over 70 levels are within 2kT), more than 50%of the transfer occurs to one level and more than 80%is encompassed by two final states. Inspection of Table 3 shows that a similar selectivity occurs for theother initial levels. For example, a display of the selectivity from the in-plane fundamental 61 at &ib = 410 cm-1 that is given elsewhere’ shows that one level among over 100 levels within 2kT accounts for more than 50% of the VET. That display is accompanied by examples showing similar behaviors for benzene, aniline, and pyrazine. Such selectivity is seen also in the single-collision VET of nonaromatic systems.’ Channel selectivity appears to be a general phenomenon for vibrational energy transfer from the lower, wellseparated vibrational levels of polyatomic molecules. It is, in fact, the most distinctive characteristic of polyatomic molecule single-collision VET. Inefficient Transfer to Nearly Resonant Levels. The high final state selectivity is obviously driven by strong propensity rules. These restrictions usually preclude efficient energy transfer to nearly resonant levels. Many examples occur with pDFB. Transfer from the 81301 level (at 292 cm-1) to the nearby level 171 (275 cm-I) is, for example, too inefficient to observe. Table 2 lists numerous levels near our pumped level 61 (at 410 cm-l)
+
that do not participate significantly in the single-collision VET. One, 81302 at 411 cm-l, is nearly degenerate. Two lower levels, also inactive, lie within 20 cm-l of 6’. The case is perhaps most impressive for VET from the pumped level 51 at 818 cm-1, occurring in a region of substantial level density. While VET with low probability to nearby levels may contribute to the poorly structured fluorescence background of the 51 VET fluorescence, the dominant VET channel involves a level relatively far away, namely, 5’301 lying 119 cm-’ above the pumped level. About 40% of the VET occurs in this single channel. DominanceofSmallAuChanges. Weconsider the VETchannel 81 302 as a Au = 3 process via the independent changes AUS = 1 and A U ~=O 2. Similarly, the 81301 8’ channel is a Au = 1 process, where we are interested in the magnitude as opposed to the sign of the quantum change. When the VET processes listed in Table 3 are so classified, it is seen that processes with small Au dominate the VET. That table contains 17 channels with Au = 1, 17 with Au = 2, and 7 with Au = 3. None with a larger ALJis seen. The bias to small Au channels emerges even more clearly if we limit attention to the important channels, say those with at least 10% of the total VET probability. By this accounting, 14 of the 16 dominant channels are Au = 1 processes. A similar tabulation has been presented for VET in the other aromatic systems.’ All show a bias to processes with small Au. Dominant Activity of Low-Frequency Modes. Inspection of Figure 1 shows that the two lowest-frequency modes in SIpDFB are v j ~ ’= 119 cm-’ and vg’ = 173 cm-1. Only two of the 41 observed state-to-state VET channels listed in Table 3 involve quantum changes in modes other than v{ and ~30’. Additionally, the two channels containing change in other modes are relatively minor, occurring at the few percent level. This situation is the rule among polyatomic molecules. Perhaps no VET study has shown the propensity for lowfrequency mode changes more clearly than the crossed molecular beam explorations of Hall, Giese, and GentryZoon SOpDFB. They monitored vibrationallyinelastic scattering in collisionswith He as the collision energy was increased from a small value to over 2500 cm-I. Thus, most fundamentals were energetically accessible. Only the lowest-frequency mode, ~ 3 0 ”= 158 cm-I, was found active in a specific search for activity among seven modes. The lowest-frequency modes of aromatic systems are usually out-of-plane, and interest centers on whether the low frequency or thekinematicnatureofthevibrational motion ismost influential with respect to VET. The issue has been explored in a clever way by Claryz1with three-dimensionalquantal scattering calculations on the system SOpDFB He. The calculations were run with the frequency of the lowest six modes reduced to the ~ 3 0 ”value. Under such a change, all modes acquired the efficient VET characteristics of v30 with little distinction (a factor of 2) for their in-plane vs out-of-plane character. There is a distinction between Soand SI pDFB on the issue of low-frequency mode activity. In SOpDFB, a large energy gap separates the lowest mode (VSO” = 158 cm-1) from the next mode (~22”= 353 cm-I), and this gap contributes to the unique activity of vj,,”. In SIpDFB, two modes, V ~ O ’= 119 cm-l and US’ = 173 cm-l, have reasonably low frequencies relative to the next mode, VI,’ = 275 cm-l. Hence, ~ 3 0 ’dominates VET activity but it does not stand alone. Separated Modes. The data contained in Table 3 provide good opportunityfor comparisons of VET channels that involve identical quantum changes. For example, the VET processes 0’ 301, 81301 8’302, and 6l 6’301 are all exclusively A U ~ = O +1 processes. This A U ~=O + 1 channel is seen also from four other initial levels. To the extent that v3ooperates in VET as a separate, independent oscillator, the rate constantsfor these processes should match.
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3268 The Journal of Physical Chemistry, Vol. 98, No. 13, 1994
Catlett et al.
TABLE 6 Comparison of Virational Energy-Transfer Rate Constants for State-testate Processes with Identical Quantum Changes quantum k4-W quantum k4(i--f)" change (lo5Torr' s-l) change (lO'Tor1-1 s-1) All30
AV30
AV30
+1
= -1 +2
18 18 17 15 19 15 16 26 23 29 1.7 1.6 2.1 1.8 1.5
AV8
+1
A v ~ -1
3
2.9 3.1 3.3 2.8 3.2 4.5 3.5
0
100
200
300
400
500
IAEI (cm") Figure 6. I(AE) plotted against 1 4for collisions of SI pDFB with argon. AE is a negative quantity since the plot is given for exoergic (V T) processes. For endoergic (T V) processes the Boltzmann factor exp(-AE/kT) must be included as a multiplicative factor to I(M).
-
L. I
2.3 a The rate constants within each group are listed in order of initial level energy, Le., 00,301,8l, 302,8'301,6', 5l.
Table 6 provides the comparisons. The seven A U ~=O +1 rate constants agree within experimental error. Similar comparisons are possible for processes with AU30 = -1, Au30 = +2, bug = +1, and Aus = -1. They support the operation of v3g as an independent oscillator and show additionally that vs behaves similarly. The extent to which vibrational modes operate independently in the collisional interactions was considered in the early aromatic VET studies. The question was addressed indirectly in the first benzene study by the successful modeling of flow patterns with the assumption of separated modes.7 Explicit exploration9 subsequently affirmed the separability of the lowest-frequency mode in SIbenzene ( ~ 1 6 )by comparisons such as discussed above for pDFB. VET explorations with SI aniline supported the occurrence of independent oscillators in that molecule as well.'' SSH-TModeling. Clary has developed a three-dimensional quantal scattering treatment using vibrational close coupling (VCC) with the rotational infinite-order sudden approximation (10s) for application to polyatomic VET.22 The pDFB He system is among the numerous polyatomics to which these calculations have been Much of the effort was directed toward the So crossed beam experiments of Hall et al.," for which extremely good agreement was obtained. Rate constants for two 300 K SI channels with He were also calculated, namely, 00 301 and 00 8l. The agreement with the experimental values reported in paper 1 is impressive, with respect to both the ratio of the two constants and, more importantly, their absolute values. The scattering treatment of Clary is the only alternative to a highly simplified modeling of polyatomic VET that has been developed from Schwartz, Slawsky, and Herzfeld's (SSH) quantum mechanical treatment of atom-diatom colli~ions.~3 All modeling for aromatic systems derives from Tanczos' adaption to polyatomics (SSH-T).24 The use of SSH-T models for the SI VET experiments has focused entirely on replications of flow patterns and other comparisonsinvolving the relative magnitudes of VET rates. SSH-T modeling has not provided a successful account of the large absolute magnitudes of the constants. A review of the applications to aromatic systemsis given elsewhere.' The use of SSH-T with aromatics began with benzene.7.9 A simple and reasonably successful set of propensity rules was developed based on the quantum changes Au and the V-T energy gap AE of the VET channels. Variations on this theme subsequently emerged as the rules were tailored to individual aromaticsystems. For example,our first application to SIpDFB2 involved, additionally,steric factors dependent on mode identities that were introduced by McDonald and Rice." In our later
+
-
250 200
-+
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discussion of VET occurring in low-energy collisions of SIpDFB with He and Ar,3 we developed modified rules involving only Au and AE that had closer fidelity to the original SSH-T presentation. This treatment gave a superior account of both the 300 K and the low-energy collision experiments despite being based on parameters determined independentlyfrom our VET data. Since a discussion of this SSH-T treatment has been given? we provide here only a brief description. The basic relationship for the state-to-state VET probability in a polyatomic is
in which, say, two modes v, and Vb undergo quantum changes between the initial and final states. The v2 terms are squared vibrational matrix elements appearing independently for each normal mode. The Z(AE) term is primarily dependent on the amount of energy exchanged V T during the collision, the temperature, and the reduced mass of the collision pair. As was shown previ~usly,~ v2 can be written as
-
where Au is the change in vibrational quantum number and v, is the vibrational frequency of mode a. fl is a parameter related to the steepness of the intermolecular potential and the displacement of atoms along the normal coordinate per unit change in the normal coordinate. This parameter is 35 cm-1 for all modes, as has been determined previously3from data independent of our VET results. The vibrational matrix elements are calculated with eq 2 using only the quantum change and the vibrational frequency. The Z(M)term for SIpDFB collisions with argon at room temperature was derived previ~usly.~It is dependent on the steepness and well depth of the intermolecular potential, the temperature, and the reduced mass of collision pair. It involves numerical integration over the velocity distribution. To aid discussion, Z ( M ) for St pDFB with argon is reproduced in Figure 6. For endoergic (T V) VET, the Boltzmann factor exp(AE/kT) must be included as a multiplicative factor to Z(AE). Individual probabilities P(i-4) from each initial level to all final levels within 2kT have been calculated using the above expressions for v2 and Z(AE). The summation of the calculated probabilities cP(i-f) from a level represents the total VET from that level and is analogous to the experimental k,(i). The calculated flow patterns P(i-+f)/cP(i-+f) for each initial level are presented in Table 3 for comparison with the experimental flow patterns k4( i-+f)/k4(i).
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Energy Transfer in SIp-Difluorobenzene 1.0
0.8
-
0.6
-
30'
I '0
0.4
8'
3d
8'30'
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The Journal of Physical Chemistry, Vol. 98, No. 13, 1994 3269
observed calculated
302
-
0
3d
0'
30'
E' 8'30' 303-8'3d
