1094
J. Phys. Chem. 1995, 99, 1094-1100
Energy Transfer in the 31,214151 Fermi Resonant States of Acetylene. 2. Vibrational Energy Transfer Michael J. Frostt and Ian W. M. Smith* The School of Chemistry, The University of Birmingham, Edgbaston, Birmingham B15 21T, U.K. Received: July 28, 1994; In Final Form: November 3, 1994@
An infrared-ultraviolet double-resonance (IRUVDR) technique has been used to study vibrational energy transfer in CzHz-CzH2 collisions. The output of an optical parametric oscillator (OPO) at 3.04 p m was used to excite C*H2 to a single rotational level within one of the Fermi-coupled 31,214151 vibrational states. Rovibrational state populations were then probed by laser-induced fluorescence (LIF) in the AIAu-XIZg+ electronic system as collisional relaxation occurred. As the delay between the excitation and probe lasers was increased, first rapid rotational equilibration occurred, and then LIF features arising from vibrational states populated by collisional relaxation were observed. Using this IRUVDR technique, the rate constant for vibrational relaxation of the 3 1 , 2 ~ 4 ~Fermi 5' resonant states at room temperature was measured to be (7.0 f 0.3) x lo-'' cm3 molecule-' s-l. A high proportion of the molecules removed from the Fermi-coupled states were transferred by intermolecular vibration-to-vibration (V-V) energy exchange to the 2141 level, which was observed to relax with a rate constant of (2.9 & 0.2) x lo-" cm3 molecule-' s-l. The kinetic behavior of molecules in a number of other collisionally populated vibrational levels, notably 42. has been observed and is discussed.
Introduction Infrared-ultraviolet (laser) double-resonance (IRUVDR) techniques surmount many of the problems associated with the use of infrared fluorescence methods for measurements on vibrational energy transfer in collisions involving small polyatomic molecules. The narrow bandwidth of laser sources allows populations in individual vibrational states to be prepared and observed with rotational state resolution, and the fast response times of ultraviolet (and visible) detectors, coupled with the short pulse widths of excitation and probe lasers, increase the range of experiments on vibrational energy transfer which are possible. The limitations of the IRUVDR technique lie only with the specific molecules that can be studied; that is, whether there is an infrared transition of the molecule lying within the wavelength output of a tunable laser source and whether the molecule has an accessible electronic state with a suitable fluorescence lifetime and quantum yield for detection by laser-induced fluorescence (LIF). Studies of energy transfer in C2H2 have been made at both and high6-9 levels of vibrational excitation, and CzHz has become a model system for double resonance experiments. In previous papers, we described measurements of the overall' and the state-to-state? kinetics of energy transfer within and between the 31,214151 Fermi-coupled states of C2H2. The Fermi resonance between these states is different from the celebrated Fermi resonance in COz since it is largely due to the almost exact degeneracy of the zero-order, asymmetric C-H stretch, v3 fundamental level, and the combination level v2 v4 v5, rather than a large anharmonicity constant coupling the motions in the two zero-order states.1°-12 However, although these two Fermi resonances have different origins, they both lead to an almost equal mixing of the two zero-order wave functions in the eigenstates of the Fermi and in C2H2, this coupling leads to large effects in infraredL0-14and ultraviolet* transitions
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* To whom correspondence should be addressed. ' Present address: School of Chemistry, Macquarie University. N. S. W. 2109, Australia. 'Abstract published in A d w m ACS Absrrucrs. January 1. 1995. 0022-365419512099- 1094$09.0010
associated with these levels. Indeed, in the infrared spectrum of C2H2, the intensities of the transitions from the ground vibrational level to the upper (11) and lower (I) Fermi-coupled levels are almost equal," each arising from the contribution of the v3 = 1 zeroth-order state to the wave functions of the two molecular eigenstates. As already pointed out, the intrinsic coupling between the two zero-order states is actually rather small, and it has recently been found that the Fermi resonance is lifted in C2H2-Ar c ~ m p l e x e s . ' ~Consequently, ~ ' ~ ~ ~ ~ the Fermi resonance may be regarded as unlike that between the 10°O and 02OO states of CO:: where the coupling matrix element is much larger.1° However, it is reasonable to suppose that the resonance interaction in C2Hr is more like those which are generally found at higher levels of vibrational excitation, where again couplings may arise principally because of degeneracies and near degeneracies associated with different zero-order vibrational levels. For this reason, the kinetics and dynamics of energy transfer within and from the Fermi-coupled states in C2H2 are particularly important in connecting measurements made high and low in the vibrational state manifolds of small polyatomic molecules. Further, since there is a strong interaction between only two vibrational states, the effect is simplified, and the result of the resonance interaction should be highlighted. In a recent publication,* the effect of the resonance on the rate constants for state-to-state rovibrntionnl energy transfer between the Fermi dyads in C2H2 was addressed. Transfers to rotational levels within the initially excited dyad (11) were found to be preferred over transfer to the same rotational energy levels in the other dyad (I) by a factor of ca. 4. This result is consistent with the small coupling matrix between the two zero-order eigenstates but may also be due to quantum interference in the matrix element associated with the transfer between Fermi dyads.18 In this paper, we consider the effect of the Fermi resonance on the kinetics of vibrational energy transfer, other than the process linking the two Fermi dyads2 Rate constants are reported for removal of population from the Fermi resonant states and from states which are populated during relaxation of the initially excited population in collisions with C2H2.
0 1995 American Chemical Society
J. Phys. Chem., Vol. 99, No. 4, 1995 1095
Vibrational Energy Transfer in Acetylene
Experimental Section The apparatus and procedures used in the present experiments have been described in detail elsewhere,ls2and therefore only a brief description will be given here. A Nd:YAG laser (20 Hz, 100 mJ per pulse, TEMm) was used to pump a lithium niobate optical parametric oscillator (OPO). Radiation at 3.04 p m (ca. 150 pJ per pulse), used for the stateselective excitation of C2H2, was generated in the idler output from the OPO, and to narrow the bandwidth of this output and hence allow excitation to a single rovibrational state, intracavity etalons were used in both the pump laser and the OPO itself. Final tuning of the output to a rovibrational transition was achieved using an optoacoustic cell containing C2H2 in an excess of Ar. LIF was excited in the AIA,-XIZg+ electronic system of C2H2 15,19 using the frequency-doubled output of an excimer pumped (Lumonics Series 400, XeCl308 nm) tunable dye laser (Lambda Physik, FL2002) operating on Coumarin dyes. This laser was scanned over the 242.5-246.1 nm wavelength range to probe the populations in a number of vibrational states in C2H2(X1Zgf) via LIF from levels in the AIAu state with appreciable fluorescence quantum yield.20 The two laser beams counterpropagated through a Pyrex cell. At the cell, the diameter of the beam from the OPO was ca. 6 mm, whereas the beam from the dye laser was 1-2 mm in diameter and probed the center of the cylindrical volume irradiated by the excitation source. LIF signals at right angles to the laser beams were detected by a photomultiplier through a combination of optical filters (Schott WG280, Cornel1 UG1). A photodiode monitored the shot-to-shot stability of the LIF probe beam for normalization purposes. The photodiode and photomultiplier signals were integrated, digitized, and transferred to a personal computer for storage and future analysis. The delay between the excitation and probe lasers was established using a synchronization pulse from the firing of the Pockels cell within the Nd:YAG laser cavity as a marker and delaying the resultant pulse with a delay generator (SRS, DG535) in order to trigger the excimer laser at a chosen delay. In the present experiments, the delays between the pulses from the excitation and probe lasers were in the range 0.5-10 ps, and the concentrations of C2H2 were between 4 x 1015 and 8 x 1015 molecules ~ m - ~Experiments . were performed on samples of either pure C2H2 or C2H2 diluted in up to 10 Torr of argon. Argon causes rapid rotational energy transfer2 but slower vibrational energy transfer from the Fermi dyads. The R(11) transition in the infrared band connecting the ground vibrational state to the upper energy Fermi dyad (state 11) in C2H2 was pumped. This strong line was chosen to ensure that a significant excited population of C2H2 was initially prepared, since it is subsequently spread over many rotational and vibrational levels as relaxation takes place. Figure 1 shows the vibrational levels in the XIZg+ ~ t a t e l l - l ~which , ~ ~ have energies corresponding to 53500 cm-’ and which are of interest in the present work. Figure 2 shows a scan of the 245.6-246.1 nm wavelength range immediately after the initial excitation, displaying the simplicity of the LIF spectrum before any collisional energy transfer occurs. LIF signals arising from individual vibrational states of C2H2 were recorded. These excited states may be divided into two categories: those which contained sufficient thermal population at room temperature for “hot bands” to be observed even in the absence of the excitation laser and those higher energy states (Elhc 2 1500 cm-’) from which transitions were only observed if the excitation laser was tuned into resonance with a rovibrational feature in C2H2. Consequently, the observed vibrational
L VI
a
P
E a C
PAl
L -.
:1
Figure 1. Vibrational energy levels in the XI&+ electronic ground state of C2H2 with values of Elhc up to cu. 3500 cm-’.
245.6
Wavelcngth / iim
246.1
Figure 2. LIF spectrum of C2H2 between 245.6 and 246.1 nm, recorded with essentially zero delay time between the pulses from (a) the optical parametric oscillator tuned to the R(11) line in the band exciting molecules to the upper (II) of the two (31,214151)Fermi dyads and (b) the dye laser exciting fluorescence. The three strong Lines in this spectrum are essentially P-, Q-, and R-branch lines in the AIA,-XIZgg+ band from the rovibrational level initially (3141,3161) (3~r214151)~) excited by the infrared pulse from the OPO. The weaker lines arise because of perturbations in the upper level of the vibronic transition.
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bands could be assigned with a knowledge of the spectroscopic parameters for each state,15J9an estimate of the Franck-Condon factors for transitions between the upper and lower vibrational states, and a knowledge of the thermal population of individual vibrational states. It was found that the LIF signals arising from those states with observable thermal populations increased when the excitation laser was on and the time delay between the excitation and probe lasers was such that significant vibrational relaxation from the Fermi-coupled states had occurred. Consequently, kinetic measurements could be made on all the observed vibrational states. These measurements were made by tuning the probe laser to a rotational line from the vibrational level of interest and recording the rise and decay of the LIF signals. In general, these traces were fitted to functions involving the difference of two exponentials to yield first-order constants characterizing the rise and fall of the signals. If these two first-order constants were sufficiently well-separated, then the smaller of the two first-order constants could be determined by fitting a single-exponential decay to the data starting at a delay time longer than that at which the signal reached its maximum value. Of course, it was necessary to exercise the usual care2* when attributing the derived first-order constants to the processes creating and relaxing population in the level under observation.
Frost and Smith
1096 J. Phys. Chem., Vol. 99, No. 4, I995 TABLE 1: Summary of Rate Constants for the Collisional Self-Relaxationfrom Different Vibrational Levels of CzH2 initial ref state final state kkm3molecule-' s-' ca. 2.5 x 1O-Io 2 I I1 7.4 x 10-11 23 I, I1 total this work (direct) I, I1 total 7.0 x lo-" 2.9 x lo-" this work (direct) 2141 total 2141 total 4.7 x 10-11 5 5.5 x lo-" this work (inferred) I, 11 2141 ~~~~~~
I, I1
+ 51
other than 2141+ 51
1.5 x lo-"
this work (inferred)
Results and Discussion (a) Vibrational Relaxation from the 31,214151 Fermi Resonant Dyads. In order to measure the rate of vibrational self-relaxation from the lower energy Fermi resonant dyad, (31,214151)1, LIF signals were monitored in two bands of the AIAu-XIEgelectronic system of C2H2: the 43,63 (31,214151)1 band at ca. 243 nm and the 3141,3161 (31,214151)1band at ca. 245 nm. At each concentration of C2H2, after a period had been allowed for equilibration over the rotational levels and between the Fermi-coupled vibrational levels, the LIF signals in these bands decayed exponentially. The pseudo-first-order rate constants obtained from these single-exponential fits varied linearly with the concentration of C2H2, yielding a second-order rate constant for removal of molecules from the (31,214151)1state of kl = (7.0 i 0.3) x lo-" cm3 molecule-'s-l. As the comparison in Table 1 shows, our value of kl is in excellent agreement with that derived by Smith and W a d 3 from time-resolved infrared fluorescence experiments. Smith and Warr were unable to distinguish infrared emission arising from the individual Fermi dyads, and their work therefore related to some undetermined distribution over these two levels. The present work, together with that reported in refs 1 and 2, confirms that the populations in the two Fermi resonant levels I and I1 are coupled somewhat faster by collisions with other C2H2 molecules than they are removed to other, lower levels. Consequently, despite the difference in the measurement techniques, these two sets of experiments both measure the same quantity: the rate of self-relaxation of population which is distributed thermally over the two Fermi resonant levels. Figure 1 shows the energies of the zero-order vibrational levels up to and including those which are coupled by Fermi resonance. There are clearly a number of energetically accessible mechanisms by which the population in the Fermi resonant dyads can relax. The observed rate constant for self-relaxation is appreciably larger than those for relaxation by the noble gases23and corresponds to a collisional probability as high as 0.12. Given this high collision probability, and the evidence from a wealth of studies of vibrational energy transfer in systems involving diatomic and small polyatomic molecules,10~18~24-26 it seems certain that vibrational self-relaxation from the C2H2 Fermi dyads occurs by processes with only small changes in the combined vibrational energy of the collision partners and collision products. Since the wave functions for the Fermi resonant states I and I1 both contain large contributions from the wave functions for the zero-order combination state jv2 vj vs), an efficient route is provided by which these states can undergo vibrational self-relaxation by processes in which single vibrational quanta can be transferred between the collision partners, leading to removal of the Fermi resonant states by near-resonant intermolecular vibration-to-vibration (V-V) en-
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+
-
+
245.6
246.1
Wavelength I nm Figure 3. LIF spectra of C2H2 between 245.6 and 246.1 nm. In recording the spectrum in the lower panel, the delay between the excitation and probe laser pulses was set to allow ca. 20% of the molecules initially excited to relax from the I and I1 Fermi dyad states, (31,214151)1) band are and lines in the AIAu-XIXg+ (3l4l,3l6I assigned. For the spectrum in the upper panel, the delay time was increased to allow for abouj 95% relaxation from the I and I1 Fermi dyad states, and lines in the A1A,-X1Zgf (3l- 2141) band are assigned.
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ergy exchange, according to the equations
Of these routes to relaxation, both experimental and theoretical evidence suggest strongly that (la) is the predominant mechanism for self-relaxation from the Fermi dyad vibrational states. To confirm the occurrence of process la, LIF spectra were recorded over the wavelength range 245.6-246.1 nm. At time delays short enough for the probability of a collision to be
