Rovibrational Energy Transfer in the 4νCH Manifold of Acetylene

Apr 28, 2005 - Centre for Lasers and Applications, Macquarie UniVersity, Sydney, New South Wales 2109, Australia. ReceiVed: August 12, 2004; In Final ...
0 downloads 0 Views 250KB Size
Download PDF
8332

J. Phys. Chem. B 2005, 109, 8332-8343

Rovibrational Energy Transfer in the 4νCH Manifold of Acetylene Viewed by IR-UV Double Resonance Spectroscopy. 2. Perturbed States with J ) 17 and 18† Mark A. Payne, Angela P. Milce, Michael J. Frost,‡ and Brian J. Orr* Centre for Lasers and Applications, Macquarie UniVersity, Sydney, New South Wales 2109, Australia ReceiVed: August 12, 2004; In Final Form: NoVember 18, 2004

Collision-induced state-to-state molecular energy transfer between rovibrational states in the 12 700 cm-1 4νCH manifold of the electronic ground state Χ ˜ of acetylene (C2H2) is monitored by time-resolved infraredultraviolet double resonance (IR-UV DR) spectroscopy. Rotational J-states associated with the (ν1 + 3ν3) or (1 0 3 0 0)0 vibrational combination level, initially prepared by an IR pulse, are probed at ∼299, ∼296, or ∼323 nm with UV laser-induced fluorescence via the Α ˜ electronic state. The rovibrational J-states of interest belong to a congested manifold that is affected by anharmonic, l-resonance, and Coriolis couplings, yielding complex intramolecular dynamics. Consequently, collision-induced rovibrational satellites observed by IRUV DR comprise not only regular even-∆J features but also supposedly forbidden odd-∆J features. A preceding paper (J. Phys. Chem. A 2003, 107, 10759) focused on low-J-value rovibrational levels of the 4νCH manifold (particularly those with J ) 0 and J ) 1) whereas this paper examines locally perturbed states at higher values of J (particularly J ) 17 and 18, which display anomalous doublet structure in IR-absorption spectra). Three complementary forms of IR-UV DR experiments (IR-scanned, UV-scanned, and kinetic) are used to address the extent to which intramolecular perturbations influence the efficiency of J-resolved collisioninduced energy transfer with both even and odd ∆J.

I. Introduction Collision-induced state-to-state energy transfer in congested rovibrational energy manifolds of polyatomic molecules in the gas phase has long been of interest, both intrinsically1-10 and in other contexts such as unimolecular reaction dynamics10-13 and intramolecular vibrational redistribution.12,14-17 It remains a challenge to characterize collision-induced energy transfer involving highly excited rovibrational states of small polyatomic molecules with just a few atoms (e.g., 3-6). Such investigations provide useful comparisons (and contrasts) with corresponding studies of the more highly congested rovibrational manifolds in larger polyatomic molecules.10,12-20 This interface between the dynamics of large and small molecules is well-exemplified by the series of experiments by Flynn and co-workers on intermolecular rovibrational energy transfer between large donor molecules such as highly vibrationally excited pyrazine and a “bath” of small acceptor molecules such as CO2 21 or CO.22 Of special concern in this paper is the extent to which the rovibrational manifold of interest is affected by intramolecular perturbations and how this may affect collision-induced stateto-state rovibrational energy transfer. Previous investigations of supposedly uncomplicated small polyatomic molecules, such as CO2,7-9,23 CH3F,4,5,12,24 and formaldehyde (H2CO, HDCO, D2CO),7-9,25-27 have provided useful insights in this regard. Expectations3-6,24 that “a greatly enhanced energy transfer is invariably found”6 in the presence of strong intramolecular perturbations are not in fact always realized.7-9 It has been demonstrated7-9 that quantum-mechanical interference mechanisms can sometimes cause the probability of collision-induced energy transfer to be inhibited rather than enhanced within †

Part of the special issue “George W. Flynn Festschrift”. * Author to whom correspondence should be addressed. E-mail: brian.orr@ mq.edu.au. ‡ Present address: School of Engineering and Physical Sciences, HeriotWatt University, Riccarton, Edinburgh EH14 4AS, U. K.

moderately congested rovibrational manifolds where intramolecular perturbations prevail. This paper is the second in a series concerning collisioninduced state-to-state molecular energy transfer between rovibrational states in the 12 700 cm-1 4νCH manifold of the electronic ground state Χ ˜ of acetylene (C2H2). Such processes are monitored by time-resolved infrared-ultraviolet double resonance (IR-UV DR) spectroscopy, in which a pulsed infrared (IR) laser prepares specific intermediate states (V, J, K) in the high-energy rovibrational combination/overtone manifold of C2H2. Laser-induced fluorescence (LIF) spectroscopy, with a suitably tuned and timed ultraviolet (UV) laser pulse, is then used to probe that state preparation and to investigate the energy-transfer dynamics. The immediate predecessor of this paper focused on low-J-value rovibrational levels of the 4νCH manifold (notably those with J ) 0 and J ) 1),28 following earlier brief papers.29,30 Our initial IR-UV DR experiments on the 4νCH manifold of C2H2 were stimulated28,29 by its anomalously large Stark effect31 at a low J-value and the possibility that collision-induced mixing of g/u point-group symmetry might facilitate formally forbidden odd-∆J rovibrational energy transfer. The present paper investigates locally perturbed states with higher J-values (particularly J ) 17 and 18, which display anomalous doublet structure in infrared absorption spectra) and therefore present opportunities to reexamine the role of intramolecular perturbations in collision-induced rotational energy transfer (RET) and J-resolved state-to-state intramolecular vibration-to-vibration (V-V) energy transfer. Apart from these IR-UV DR investigations of the 12 700 cm-1 4νCH manifold of C2H2,28-30,32,33 we have also studied IR-UV DR spectroscopy and collision-induced energy-transfer dynamics in its 11 600 cm-1 (νCC + 3νCH) manifold.34-37 This complements other LIF-detected IR-UV DR studies of C2H2 and its isotopomers in overtone/combination levels with high vibrational energy (Gv > 6500 cm-1)38-43 and fundamental and

10.1021/jp0463518 CCC: $30.25 © 2005 American Chemical Society Published on Web 04/28/2005

Rovibrational Energy Transfer in Acetylene lower-energy overtone or combination levels (Gv e 6500 cm-1).44-49 Several related LIF-detected Raman-UV DR experiments have also been performed.47,50-54 There is an extensive spectroscopic database55 for the rovibrational energy states of acetylene. In particular, the 12 700 cm-1 4νCH region of the IR-absorption spectrum of C2H2 draws + most of its oscillator strength from a Σ+ u - Σg IR combination band with the (ν1 + 3ν3) zero-order label, where ν1 (σ+ g ) and ν3 (σ+ u ) denote the two normal modes for CH stretching. In terms of normal-mode basis states (V1 V2 V3 V4 V5)l, where Vi designates vibrational quanta in each of the five normal modes (i ) 1-5) and l denotes the resultant vibrational angular momentum, the upper vibrational eigenstate of this band is derived predominantly from (1 0 3 0 0)0 with Σ+ u symmetry; its corresponding local-mode designation56 is [0 4 -]. Global intramolecular perturbations lead to minor contributions from other basis states, while some values of J are affected by local perturbations such as those at J ) 17 and 18 that are of interest here. The J ) 0 level of this IR-active (1 0 3 0 0)0 / [0 4 -] Σ+ u state of the 4νCH manifold is at Gv ) 12 675.677 cm-1 (experimental57) or 12 675.0 cm-1 (calculated58). The polyad model, introduced in the context of acetylene by Kellman et al.,59 has been used extensively by groups such as those of Herman55,58,60-63 and Field63-67 to classify vibrational states of interest in C2H2. Vibrational manifolds are designated as {ns, nres, l, g/u, (}, in terms of three pseudo-quantum numbers (ns ) V1 + V2 + V3, nres ) 5V1 + 3V2 + 5V3 + V4 + V5, and l ) l4 + l5) and two customary symmetry labels, g/u and (if l ) 0) (. The 12 676 cm-1 (1 0 3 0 0)0/[0 4 -] Σ+ u manifold therefore has polyad labels {4, 20, 0, u, +}, as do other “IRbright” states of the 4νCH manifold. Additional “IR-dark” vibrational states, both g and u, have nres ) 20 and ns ) 4, 3, 2, ...; the number of bending (ν4, πg; ν5, πu) and CC stretching (ν2, σ+ g ) quanta necessarily increases as ns decreases. High V2 and V4 values enhance UV brightness in LIF-detected spectra via the Franck-Condon effect so that IR-UV DR signal strength for some IR-dark/UV-bright states may approach that of IR-bright/UV-dark rovibrational states. Rovibrational perturbations due to anhamonic mixing, lresonance effects, and Coriolis coupling are virtually ubiquitous within the electronic ground state Χ ˜ 1Σ+ g manifold of C2H2, as is evident from various spectroscopic approaches: IR absorption,55,57,58,60-63 rovibronic dispersed LIF,63,64 stimulated emission pumping (SEP),16,65 optothermally detected laser Stark effect31 and IR-IR DR,66 UV LIF-detected IR-UV DR,38-49,67 and rovibrational dispersed LIF.68 The perturbed character of rovibrational states of C2H2 is significant in more than just the spectroscopic sense or with regard to the above-mentioned tradeoff between IR-dark/ UV-bright and IR-bright/UV-dark character. For example, rovibrational perturbations are implicated in vibrationally mediated photodissociation experiments on acetylene, both spectroscopically and by molecular-action measurements.69-71 Spectroscopy at “chemically significant” energies also yields dynamical implications concerning isomerization of C2H2 to vinylidene (H2CdC:), for which the barrier is above 15 000 cm-1.66,72 In the context of this paper28-30,32 and in many of our previous investigations of acetylene8,9,34-37,44,47 and other molecules,7-9,25-27 we are particularly concerned with the role that intramolecular perturbations play in collision-induced RET and J-resolved V-V energy transfer within rovibrational manifolds of small polyatomic molecules such as C2H2. Our time-resolved, LIF-detected IR-UV DR technique uses a narrowband IR pump pulse (e.g., from a Raman-shifted tunable

J. Phys. Chem. B, Vol. 109, No. 17, 2005 8333

Figure 1. IR-scanned spectra of the 12 676 cm-1 zero-order (ν1 + 3ν3) band of C2H2. Traces a and b are LIF-detected IR-UV DR spectra; the UV probe wavelength is set at 323.791 nm to monitor the (1 0 3 0 0)0 J ) 12 rovibrational level. With P ) 0.20 Torr, IR-UV delay times t and Lennard-Jones collision numbers z are (a) t ) 10 ns, z ) 0.033 and (b) t ) 200 ns, z ) 0.66. The collision-induced spectrum in trace b is recorded with a instrumental gain double that for the collisionfree spectrum in trace a. A prominent odd-∆J R(16) RET satellite is marked by a dagger. Trace c is a photoacoustic absorption (PA) spectrum, with C2H2 pressure P ) 30 Torr.

dye laser)28 to selectively excite a rovibrational transition (V, J, K) r (V′′ ) 0, J′′, K′′) within the electronic ground state Χ ˜ 1Σ+ manifold of C H . A UV probe laser pulse (e.g., from a 2 2 g frequency-doubled tunable dye laser)28 excites a rovibronic transition (V′, J′, K′) r (V, J, K) in the Α ˜ -Χ ˜ absorption system, detected by UV LIF from the Α ˜ 1Au electronically excited manifold. The intermediate state (V, J, K) that is monitored by UV LIF may be either directly prepared by the IR pump pulse itself or subsequently populated by collision-induced RET and/ or V-V energy transfer. Such IR-UV DR measurements involve three key experimental factors: IR pump wavelength, UV probe wavelength, and IR-UV delay t (or collision number z). This yields three varieties of IR-UV DR experiments, each with one of the above three factors continuously varied while the other two are held fixed: IR-scanned IR-UV DR spectra (e.g., as in Figure 1), UV-scanned IR-UV DR spectra (e.g., as in section II), and IR-UV DR kinetic scans (e.g., as in section III), in which IR-UV delay t (and hence z) are scanned while the sample pressure P and the IR pump and UV probe wavelengths are held fixed. Figure 1 provides a representative preliminary illustration of results that are derived from IR-UV DR measurements in the 12 700 cm-1 4νCH manifold of C2H2. It comprises a pair of IRscanned IR-UV DR spectra in traces a and b, registered above a corresponding photoacoustic absorption (PA) spectrum in trace c of the zero-order (ν1 + 3ν3) combination band centered at 12 675.68 cm-1. The UV probe wavelength is set at 323.791 nm, which (as we shall see later in this paper) is characteristic of an intermediate rovibrational level (V, J, K) that is identified as (1 0 3 0 0)0 J ) 12; this level is of particular interest because it is understood28-30,32,33 to serve as an apparent gateway for odd-∆J collision-induced energy transfer in the 4νCH manifold

8334 J. Phys. Chem. B, Vol. 109, No. 17, 2005 of C2H2. (Here we use the term “gateway” to designate a rovibrational state with quantum-number labels V, J, K that has a remarkably high collision-induced propensity for energy transfer between that state and other rovibrational states but with odd-numbered changes of rotational quantum number J that are formally forbidden. Such odd-∆J energy transfer is understood to be possible in the presence of some forms of intramolecular and/or collision-induced rovibrational perturbations that are prevalent in the high-energy vibrational manifold of C2H2.28-30,32-37) The IR-UV DR spectrum in trace a is recorded under effectively collision-free conditions with a very small collision number z. (As before,28-30,34-37,47 values of z are referred arbitrarily to Lennard-Jones collisional rate constants kLJ that are consistent with those adopted by Crim and co-workers;38,39 for C2H2/C2H2 self-collisions at 300 K, kLJ ) 16.4 µs-1 Torr-1 ) 5.10 × 10-10 cm3 molecule-1 s-1.) The simple spectrum in trace a comprises the (ν1 + 3ν3)-band R(11) peak; it is accompanied by a single P(13) peak beyond the low-frequency limit of Figure 1, thereby confirming that the UV probe pulse is indeed monitoring the (1 0 3 0 0)0 J ) 12 rovibrational level. The IR-UV DR spectrum in trace b, with a 20-fold increase in IR-UV time delay t (and hence z, with fixed P ) 0.20 Torr), is markedly different from that in trace a. The most prominent collision-induced R(J - 1) features, with even values of J (210 and 14-22), are customary even-∆J collision-induced RET satellites, as is expected for a centro-symmetric linear molecule such as C2H2. However, there is an additional set of anomalous odd-∆J collision-induced RET satellites, R(J - 1) with odd values of J (7-21); the most prominent (marked by a dagger in Figure 1b, and remarkably strong after allowing for the 3:1 intensity alternation between even and odd J) is the R(16) feature, with the IR pump on the J ) 17 r J′′ ) 16 transition of the (ν1 + 3ν3) band. A tiny R(5) feature in trace a indicates that the (1 0 3 0 0)0 J ) 6 rovibrational level may also be weakly monitored at this UV wavelength; it is also an even-J level, and so its RET is not expected to contaminate the odd-∆J satellite structure pertaining to the probed J ) 12 level. Relatively weak odd-∆J collision-induced RET satellites centered around the (1 0 3 0 0)0 J ) 18 level have also been observed in the IR-scanned IR-UV DR spectrum that was reported in Figure 3 of ref 30, also with the (1 0 3 0 0)0 J ) 12 level monitored by the UV probe. That spectrum was obtained with a different UV probe wavelength (299.452 nm, accessing a P(12) rovibronic transition in another band of the Α ˜ -Χ ˜ electronic absorption system). The 323.791 nm UV probe wavelength used in the context of Figure 1 to monitor the (1 0 3 0 0)0 J ) 12 rovibrational level is relatively exotic, as will be discussed in section III. Finally, we note that IR-UV DR spectra associated with the (1 0 3 0 0)0 J ) 12 level have revealed unusual collision-induced quasi-continuous background (CIQCB) effects, underlying discrete IR-UV DR features that occur regularly in the 4νCH region,30,32 These will be considered in later papers of this series.33 II. The 4νCH Rovibrational States with J ) 17 and J ) 18 The central interest of this paper is not in the (1 0 3 0 0)0 J ) 12 level, as in Figure 1, but in higher-energy (1 0 3 0 0)0 J ) 17 and J ) 18 levels that are involved in the RET satellite structure of Figure 1b. It is well-known29,30,57,58,73-75 from IRabsorption spectra that the (1 0 3 0 0)0 J ) 18 rovibrational level appears as a doublet owing to a local Coriolis perturbation; this is evident in the R(17) doublet in Figure 1c and in

Payne et al.

Figure 2. IR photoacoustic absorption (PA) spectra of R(J - 1) and P(J + 1) features in the 12 676 cm-1 (ν1 + 3ν3) band of C2H2, with J ) 17-19. Traces a and b are recorded as in Figure 1c, with C2H2 pressure P ) 30 Torr and an optical bandwidth of ∼0.08 cm-1. Traces c and d are recorded for a 1:5 C2H2/Ar mixture (P ) 60 Torr) by a narrowband tunable source (optical bandwidth ∼0.017 cm-1). Perturbation-induced doublet structure is evident in the (1 0 3 0 0)0 rovibrational levels with J ) 17 and J ) 18. The feature marked in trace b with a dagger is discussed in the text.

corresponding IR-UV DR features in Figure 1b. It was also suggested57 that the adjacent (1 0 3 0 0)0 J ) 17 rovibrational level has a less readily resolved doublet structure. Higher-resolution PA spectra of R(J - 1) and P(J + 1) features for J ) 17-19 are portrayed in Figure 2 (first reported in ref 32). Traces a and b show IR-absorption spectra of C2H2 (P ) 30 Torr), respectively, recorded at ∼787 and ∼792 nm with moderate resolution, by tuning the output of a Raman-shifted dye laser; this yields our customary28-30,32,76 optical bandwidth of ∼0.08 cm-1. Traces c and d are recorded at ∼787 nm with higher resolution using tunable radiation from a narrowband OPO/OPA system (Continuum Mirage 3000)76 with specified optical bandwidth e 0.017 cm-1. The sample is a 1:5 mixture of C2H2 and Ar with total pressure P ) 60 Torr; the effective spectroscopic full width at half-maximum line width is estimated to be ∼0.04 cm-1, from a convolution of Doppler width, OPO/ OPA optical bandwidth, and pressure broadening.77,78 The splittings of the (1 0 3 0 0)0 J ) 17 and J ) 18 doublet features in Figure 2 are measured to be 0.08 and 0.33 cm-1, respectively. These findings are consistent with recently reported Fourier-transform intracavity laser absorption spectra (FTICLAS) of the R(16) and R(17) doublets58 and with observations of the R(17) doublet in various IR-UV DR spectra28-30,32,74,76 and in photodissociative molecular-action spectra.71 It is significant that, in both IR-UV DR and molecular-action71 spectra, the relative signal strength of the weaker “perturber” component of the (1 0 3 0 0)0 J ) 18 doublet is enhanced relative to that in corresponding absorption spectra. The (1 0 3 0 0)0 J ) 17 and J ) 18 features are also found to have “enormous cross

Rovibrational Energy Transfer in Acetylene sections” for vibrationally mediated photodissociation71 and to display anomalously large collision-induced lineshifts;75,78 however, their corresponding pressure broadening78,79 and absolute line intensities79 are regular. The feature marked with a dagger in Figure 2b is unidentified but not apparently associated with the (1 0 3 0 0)0 J ) 18 level; the same PA feature is also observed in the spectrum reported by Tobiason74 but not found elsewhere.73 No corresponding feature appears near the R(17) transitions that could be assigned to the (1 0 3 0 0)0 J ) 18 level via a ground-state combination difference. The nature of the local perturbation that causes the doublet structure of the J ) 17 and J ) 18 states in the (1 0 3 0 0)0 Σ+ u submanifold has prompted much speculation. Smith and Winn73 suggest Coriolis coupling with the (0 3 2 0 1)1 Πu submanifold, while Zhan and Halonen57 propose Coriolis resonance with an unidentified Πu (i.e., l ) 1) level. In the context of photodissociative molecular-action spectra, Rosenwaks and co-workers71 note that the {4, 20, 0, u, +} polyad, to which (1 0 3 0 0)0 belongs, may be Coriolis-coupled to the {3, 20, 1, u} or {5, 20, 1, u} polyads. This local perturbation has recently been assigned by Herman and co-workers58 to a Coriolis resonance with the (0 5 0 4 1)1 Πu submanifold, which belongs to the {5, 20, 1, u, +} polyad. This proposed perturber for the (1 0 3 0 0)0 J ) 17 and J ) 18 levels would be IR-dark (since it entails no CH stretch quanta) but UV-bright (owing to its many CC stretching and trans-bending quanta, ν2 and ν4, respectively); this is consistent with our observations. Deperturbation analysis of the observed J ) 17 and J ) 18 doublet structure58 yields a zeroorder vibrational energy Gv ) 12 678.6 cm-1 and rotational constant Bv ) 1.145 cm-1 for this IR-dark submanifold (compared to polyad model predictions58 of Gv ) 12 685.1 cm-1 and Bv ) 1.153 cm-1), such that it crosses the zero-order IRbright (1 0 3 0 0)0 submanifold (Gv ) 12 675.0 cm-1, Bv ) 1.152 cm-1)58 between J ) 17 and J ) 18. This information about the local perturbation to the (1 0 3 0 0)0 J ) 17 and J ) 18 levels establishes a useful basis for the IR-UV DR spectroscopic investigations that will be described in sections III and IV below. III. IR-UV DR Spectra for 4νCH Rovibrational States with J g 17 A key preparatory step in these investigations entails UVscanned IR-UV DR spectra, as in previous studies of the 4νCH region of C2H2 by Tobiason et al.39,74 and ourselves.28-30,32,77 The IR pump is used to prepare successive J-levels of the (1 0 3 0 0)0 submanifold by setting its wavelength on corresponding P(J + 1) and R(J - 1) features of the (ν1 + 3ν3) absorption band of C2H2. When the collision number z is small (as in Figure 1a above), the only IR-UV DR features that appear in a UVscanned IR-UV DR spectrum are those from the same rovibrational level (V, J, K) that is directly excited at the (fixed) IR pump wavelength. The resulting spectra, recorded under effectively collision-free conditions, are useful for survey purposes as a prerequisite for further IR-UV DR studies. It should be understood that vibronic bands observed in UVscanned IR-UV DR spectra are hot bands originating in high overtone/combination levels; they are not usually seen in conventional UV absorption spectra but can often be identified by combination-difference methods. Figures 3 and 4 show UV-scanned 4νCH IR-UV DR spectra for (1 0 3 0 0)0 J-levels selected by the IR pump and with UV probe wavelength ranges of ∼299 and ∼323 nm, respectively. Each set of spectra is effectively collision-free (z ) 0.016 in Figure 3 and z ) 0.032 in Figure 4). Figure 3 extends previous studies28,39,74 of selected J-levels of the (1 0 3 0 0)0 submanifold

J. Phys. Chem. B, Vol. 109, No. 17, 2005 8335

Figure 3. UV-scanned IR-UV DR survey spectra for C2H2 prepared by the IR pump in (1 0 3 0 0)0 rovibrational levels with J ) 17-22. The UV probe is scanned through the Α ˜ -Χ ˜ 101 313 510 rovibronic band at ∼299 nm, exciting the (ν′3 + ν′5) upper vibronic state. All spectra are recorded with C2H2 pressure P ) 0.10 Torr, IR-UV DR delay t ) 10 ns, and z ) 0.016.

via the 299 nm Α ˜ -Χ ˜ 101 313 510 rovibronic absorption band of C2H2. These spectra are relevant to results presented later in this paper. As before,28 reduced term value plots32,74,82 have been used to label P, Q, and R branches of the rotational structure and identify K′ in the upper vibronic state (ν′3 + ν′5), which combines the ag CC stretching and bu CH stretching modes. The primary subbands in Figure 3 are K10 (i.e., K′ ) 1 r K ) l ) 0), but even-K′ features with K′ ) 0 and K′ ) 2 also occur. This is attributable to axis switching,52,82,83 which is prevalent at high values of J, and/or global Coriolis perturbations that introduce Π (K ) l ) 1) character in the (1 0 3 0 0)0 submanifold as J increases. The UV-scanned IR-UV DR spectra observed in Figure 4 are most probably due to high-K′ portions (e.g., Ka′ ≈ 7) of the Α ˜ -Χ ˜ 101 303 (40 60)1 rovibronic band, in view of combination differences with the previously ˜ -Χ ˜ 303 (40 60)1 rovibronic band. analyzed81 Α Assignment of the spectra in Figure 4 is less straightforward than of those in Figure 3. First, the tentatively assigned upper vibronic state (ν′4/ν′6) comprises a Coriolis-coupled dyad combining the nearly degenerate au torsional and bu CH inplane bending modes of the nonlinear Α ˜ 1Au electronically excited manifold; this has previously been characterized by Utz et al.81 Second, it was considered possible that 4νCH IR-UV DR spectra in the UV-scanned region from 322 to 328 nm might contain additional underlying contributions from other upper vibronic levels, ν′2 or ν′3, that are of gerade vibrational symmetry (rather than ungerade, as is customary in the upper state of IR-UV DR excitation schemes for C2H2). A hypothesis was advanced that participation by such “forbidden” vibronic states of opposite g/u symmetry might help to explain some of the apparently anomalous aspects of our 4νCH IR-UV DR

8336 J. Phys. Chem. B, Vol. 109, No. 17, 2005

Figure 4. UV-scanned IR-UV DR survey spectra for C2H2 prepared by the IR pump in (1 0 3 0 0)0 rovibrational levels with J ) 0, 12, and 14-24. The UV probe is scanned through the 323 nm region of the Α ˜ -Χ ˜ absorption system. As discussed in the text, the observed UVscanned spectra are assigned tentatively to the Α ˜ -Χ ˜ 101 303 (40 60)1 rovibronic band, accessing high-K′ portions of the ν′4/ν′6 Corioliscoupled dyad that were previously characterized by Utz et al.81 All spectra are recorded with C2H2 pressure P ) 0.20 Torr, IR-UV DR delay t ) 10 ns, and z ) 0.032.

observations, such as odd-∆J RET and CIQCB effects.28-30,32 However, reduced term value plots derived from UV-scanned IR-UV DR spectra in the region from 322 to 328 nm have failed to provide any support for this hypothesis.32 It is remarkable that the 4νCH IR-UV DR spectra UVscanned at ∼323 nm in Figure 4 are of appreciable signal strength only for J g 12 and that they gain signal strength as J increases; we note a similar J-dependence in photodissociative action spectra.71 (A very weak feature at ∼323.1 nm, in the bottom trace of Figure 4, is apparently associated with J ) 0, but this cannot be confirmed by combination differences since (1 0 3 0 0)0 J ) 0 can only be prepared by P(1) IR pump excitation in the (ν1 + 3ν3) band; moreover, J ) 0 reduced term values generated for this feature do not match any predicted subbands for ν′2, ν′3, or ν′4/ν′6, so that the feature is possibly due to an accidental overlap of the IR pump with another intermediate level (V, J, K), as has been found in other instances.)28,29,32 Reduced term value plots32 have been used to tentatively assign the rovibronic features for J ) 12 and 14-24 in Figure 4 as P, Q, or R. However, assignment of K′ is omitted, since that quantum number is not a well-defined label for the Α ˜state rovibronic levels accessed in these IR-UV DR spectra (owing primarily to b-axis Coriolis coupling).32,81 The right-

Payne et al. hand Q-branch feature at 323.791 nm in the J ) 12 trace of Figure 4 was used for UV probe excitation in the IR-scanned IR-UV DR spectra presented in Figure 1. UV-scanned IR-UV DR spectra for (1 0 3 0 0)0 rovibrational states prepared by the IR pump with J g 17, as depicted in Figures 3 and 4, have served as necessary preparation for IRscanned IR-UV DR experiments on specific high J-states in the 4νCH rovibrational manifold. These include J ) 17 (see section IV below), J ) 19 (see Figure 8 of ref 76, where use of narrowband IR pump and UV probe sources yield no fresh insight into odd-∆J RET), and J ) 23 and 24.32,33 As in previous experiments,28-30,34-37 it is always important to ensure that a given IR-UV DR rovibronic feature is uniquely characteristic of its designated rovibrational J-state, avoiding accidental coincidences that might lead to spectroscopic ambiguities and thereby hinder reliable interpretation. Apart from the 299 and 323 nm regions, explored in Figures 3 and 4, respectively, and elsewhere,28-30,32,74 we have recorded additional UV-scanned IR-UV DR spectra for (1 0 3 0 0)0 rovibrational J-states in the vicinities of 296-298 and 324328 nm. The former spectra are assigned to the Α ˜ -Χ ˜ 101 210 0 1 3 3 5 0 rovibronic band and the latter to lower-K′ portions of the Α ˜ -Χ ˜ 101 303 (40 60)1 rovibronic band, extending the spectrum shown in Figure 4. Despite (or perhaps because of) its spectroscopic complexity, the Α ˜ -Χ ˜ 101 303 (40 60)1 band at 322-328 nm provides superior IR-UV DR signal strength (and hence improved signal-to-noise ratios) for high J-levels (e.g., J > 20) relative to the 299 nm Α ˜ -Χ ˜ 101 313 510 and 296 nm Α ˜ -Χ ˜ 101 210 303 510 bands. The UV-scanned IR-UV DR spectra for J ) 18 in Figures 3 and 4 pertain to IR pump preparation of the (1 0 3 0 0)0 J ) 18 main level but not of its accompanying J ) 18 perturber level. In fact, UV-scanned IR-UV DR spectra for the J ) 18 perturber level are virtually identical (apart from minor intensity variations) to those for the main J ) 18 level, with corresponding spectral features offset by the 0.33 cm-1 doublet separation. This was confirmed in both the 299 and 323 nm regions, as illustrated in Figure 5 for the 323 nm region. Both traces a and b of Figure 5 were sequentially recorded under effectively collision-free conditions (z ) 0.033) with C2H2 sample pressure P ) 0.20 Torr and IR-UV DR delay t ) 10 ns. All experimental conditions were identical for each trace of Figure 5, apart from switching the IR pump wavelength from one component of the perturbed (1 0 3 0 0)0 J ) 18 doublet to the other. This allows the absolute signal strengths of IR-UV DR features to be reliably compared between the two traces. It is notable that most of the IR-UV DR features associated with the J ) 18 perturber level are stronger than those of the J ) 18 main level, from which the perturber level “borrows” its intensity in IR absorption; such an effect clearly demonstrates the tradeoff between IR- and UV-brightness discussed briefly in section I above. The average “perturber/main” ratio of signal strengths for the five IR-UV DR peaks in Figure 5 is 1.5 ( 0.6, with an as-yet inexplicable factor-of-two variation from one pair of peaks to another. This perturber/main ratio differs markedly (by a factor of 3) from the corresponding ratio of ∼0.45 ( 0.05 for the R(17) and P(19) doublets observed in various IR-absorption spectra,28-30,32,73,74,77 including Figure 2 (but excluding the ratio of ∼0.6 from FT-ICLAS,58 in view of the uncertain response linearity of such an intracavity technique). Collision-induced R(17) doublet features in various IR-scanned 4νCH IR-UV DR spectra28-30,32,33 have a J ) 18 perturber/main ratio of ∼0.65

Rovibrational Energy Transfer in Acetylene

Figure 5. UV-scanned IR-UV DR spectra of C2H2 recorded with the IR pump preparing (a) the (1 0 3 0 0)0 main J ) 18 level and (b) the (1 0 3 0 0)0 J ) 18 perturber level. The IR pump wavelength is set at either component of the (ν1 + 3ν3)-band R(17) doublet (see Figure 2), while the UV probe scans the 323 nm region (see Figure 4). Traces a and b are sequentially recorded with z ) 0.033, and all experimental conditions are identical. Features of trace b lie ∼0.33 cm-1 above (i.e., ∼0.003 nm below) those of trace a, consistent with the J ) 18 doublet separation.

( 0.1; molecular-action spectra for vibrationally mediated photodissociation71 yield a corresponding ratio of ∼0.75. It is evident that the relative efficiency of the main and perturber (1 0 3 0 0)0 J ) 18 rovibrational states in several molecular processes (UV-brightness, collision-induced RET and V-V transfer, and vibrationally mediated photodissociation) varies substantially in comparison with relative intensities observed for the (ν1 + 3ν3)-band R(17) and P(19) doublets in IR-absorption spectra. The physical implications of these contrasting results are not yet well-understood. Nevertheless, it is clear that the main (1 0 3 0 0)0 J ) 18 state and its perturber are strongly coupled by a local intramolecular perturbation, most likely58 Coriolis resonance at J ≈ 18 between the (1 0 3 0 0)0 Σ+u and (0 5 0 4 1)1 Πu submanifolds as explained in section II above. The outcome is that these two (1 0 3 0 0)0 J ) 18 states are effectively inseparable in many experiments. The virtual indistinguishability of UV-scanned IR-UV DR spectra for the main (1 0 3 0 0)0 J ) 18 state and its perturber has foiled our original intention to measure collision-induced stateto-state ∆J ) 0 energy transfer between them and to test the effect of intramolecular perturbations on this energy-transfer channel. IV. Collision-Induced Energy Transfer from the 4νCH J ) 17 Rovibrational State The 0.08 cm-1 splitting of the J ) 17 doublet in the (1 0 3 0 0)0 submanifold has been resolved with narrower optical bandwidth, as in Figures 2c and 2d and in recently reported FT-ICLAS experiments.58 However, as in Figures 2a and 2b, rovibrational features for the main (1 0 3 0 0)0 J ) 17 level and its perturber are not separately resolvable with the 0.08 cm-1

J. Phys. Chem. B, Vol. 109, No. 17, 2005 8337

Figure 6. IR-scanned spectra of the 12 676 cm-1 zero-order (ν1 + 3ν3) band of C2H2. Traces a and b are LIF-detected IR-UV DR spectra with the UV probe wavelength set at 298.973 nm to monitor both levels of the (1 0 3 0 0)0 J ) 17 doublet. The IR-UV delay times t and Lennard-Jones collision numbers z are (a) t ) 10 ns, z ) 0.033 and (b) t ) 200 ns, z ) 0.66 with P ) 0.20 Torr. The collision-induced spectrum in b is recorded with instrumental gain a factor of 10 above that for the collision-free spectrum in a. Note that the odd-∆J satellites in trace b are centered around the daggered R(11) IR-UV DR feature in which the IR PUMP prepares the (1 0 3 0 0)0 J ) 12 level. Trace c is a PA reference spectrum, with C2H2 pressure P ) 30 Torr.

optical bandwidth of IR pump radiation from the Raman-shifted dye laser used28 in our regular IR-UV DR experiments. Both (1 0 3 0 0)0 J ) 17 levels (main and perturber) are therefore simultaneously prepared in such IR-UV DR experiments. Given that J ) 17 and J ) 18 are affected by a common local Coriolis perturbation,58 we infer that the (unresolved) J ) 17 doublet will have IR-UV DR properties (e.g., virtually identical UVscanned IR-UV DR spectra) that are similar to those of the (resolved) J ) 18 doublet, as discussed in section III above. Both main and perturber J ) 17 doublet levels are thus expected to be simultaneously monitored by the excimer-pumped, frequency-doubled dye-laser UV probe,28 with optical bandwidth ∼0.2 cm-1. Figures 6 and 7 show IR-scanned spectra in which the (1 0 3 0 0)0 J ) 17 levels (main and perturber) are unresolved, as explained above. In each figure, traces a and b are IR-scanned IR-UV DR spectra of C2H2 (P ) 0.20 Torr), with the UV probe wavelength set at 298.973 nm (Figure 6) and 323.321 nm (Figure 7). For reference purposes, Figures 6c and 7d show inverted IR-absorption spectra of the (ν1 + 3ν3) band of C2H2 (P ) 30 Torr). The IR-scanned IR-UV DR spectra in Figure 6 were obtained with the UV probe wavelength set at 298.973 nm, corresponding to the Q(17) K′ ) 2 feature of the Α ˜ -Χ ˜ 101 313 510 rovibronic band (see the bottom trace of Figure 3 above). This arrangement monitors population in the (1 0 3 0 0)0 J ) 17 doublet levels either under effectively collision-free conditions (as in Figure 6a, with z ) 0.033) or after a 20-fold increase in IR-UV delay and a 10-fold increase in signal gain (as in

8338 J. Phys. Chem. B, Vol. 109, No. 17, 2005

Figure 7. IR-scanned spectra as in Figure 6, except that the UV probe wavelength is now set at 323.321 nm to monitor both levels of the (1 0 3 0 0)0 J ) 17 doublet.

Figure 6b, with z ) 0.66). Figure 7 differs from Figure 6 in that the IR-scanned IR-UV DR spectra in Figures 7a and 7b were obtained with the UV probe wavelength set at the central 323.321 nm P-branch feature in the J ) 17 trace of Figure 4, which is assigned to a high-K′ portion of the Α ˜ -Χ ˜ 101 303 (40 1 60) rovibronic band. As in Figure 6a, the collision-free spectrum in Figure 7a comprises a single J ) 17 feature (with its underlying doublet structure unresolved). The collision-induced spectra in Figures 6b and 7b exhibit satellite structure, similar to that in Figure 1b, due to both regular even-∆J RET and supposedly forbidden odd-∆J RET. In each case, the former is more prominent, while the latter appears to peak around the R(11) feature (marked with a dagger), which corresponds to the (1 0 3 0 0)0 J ) 12 level. As explained in the context of Figure 1, this level is an apparent gateway for odd-∆J collision-induced energy transfer in the 4νCH manifold of C2H2.28-30,32,33 The same (1 0 3 0 0)0 J ) 12 level has previously been found to dominate collision-induced odd-∆J RET satellite structure via R(11) and P(13) features in IR-scanned IR-UV DR spectra with the UV PROBE set at 299.10528-30 or 296.032 nm,28,30 thereby monitoring population in the (1 0 3 0 0)0 J ) 1 level. Subtle differences,28 between IR-UV DR spectra and kinetic curves obtained in these two UV probe situations, were attributed to a highly efficient rotationally resolved V-V transfer channel that is observable with the UV probe set at 299.105 nm to excite LIF via the (ν′3 + ν′5) upper state, whereas that channel is not readily monitored at 296.032 nm via (ν′2 + ν′5).28 A similar situation seems to apply in the context of Figures 6b and 7b. Close examination indicates that, within experimental error, the even-∆J RET satellite structures have comparable IRUV DR intensity envelopes, if the spectra are normalized to parent peak intensity. However, the same is not true of the odd∆J satellite structure, which is more prominent in Figure 6b than in Figure 7b. It appears that “J ) 12 to J ) 17” odd-∆J RET, which yields the daggered R(11) features in those spectra, contains a fast kinetic component that is more prominent when the UV probe is at 298.973 than at 323.321 nm. The rovibrational levels probed (particularly J ) 12) are likely to have vibra-

Payne et al. tional basis states with stronger vibronic transition probability to the (ν′3 + ν′5) upper state than to high-K′ portions of the (ν′4/ν′6) manifold. There is evidence28,30 that more than just a single discrete set of (1 0 3 0 0)0 J-states contributes to IR-UV DR spectra and kinetics of the 4νCH manifold, particularly when the UV probe is set at ∼299 nm to monitor the (ν′3 + ν′5) upper state. It is possible that odd-∆J RET proceeds predominantly to only one of the (1 0 3 0 0)0 J ) 17 doublet levels; for example, the LIF detection cross section for the J ) 17 perturber level may be favored via the 298.973 nm UV probe transition relative to that of the 323.321 nm UV probe transition. Speculation about such amplitude anomalies and possible mechanisms must be regarded with caution, since many of the IR-UV DR features involved are weak and some of the spectra were not sequentially recorded. However, these results indicate a further “even J to J ) 17” odd-∆J RET pathway in the 4νCH rovibrational manifold (additional to that postulated to account for transfer between even-J levels and J ) 1) in which the (1 0 3 0 0)0 J ) 12 level plays a key mechanistic role. Allowance must also be made for unusual CIQCB effects comprising collision-induced rovibrational transfer to a “bath” of quasi-continuous background states,28,30,32 apparently associated primarily with the (1 0 3 0 0)0 J ) 12 gateway level. These underlie discrete IR-UV DR features that are regularly observed in the 4νCH region and will be considered in more detail in later papers of this series.33 In the meantime, we note that CIQCB bath effects may account largely for odd-∆J RET satellite structure of IR-UV DR spectra as in Figures 1b and 7b, Figure 1c of ref 30, or the lower IRUV DR kinetic curve in Figure 1c of ref 28. IR-UV DR kinetic scans are able to provide insight into collision-induced energy transfer, additional to that gained from IR-scanned and/or UV-scanned IR-UV DR spectra. Figure 8 shows a set of IR-UV DR kinetic curves, in which the UV probe set at 298.973 nm monitors both levels of the (1 0 3 0 0)0 J ) 17 doublet and the IR pump prepares various J-levels via appropriate R(J - 1) transitions in the (ν1 + 3ν3) band of C2H2. The curves are arranged in two columns, with the even∆J RET on the left and odd-∆J RET on the right. It is notable that the “J ) 12 to J ) 17” odd-∆J RET channel (labeled “J ) 12” in the right-hand column of Figure 8) is prominent, with an IR-UV DR kinetic efficiency comparable to that for even∆J RET with |∆J| g 6; this is consistent with the IR-scanned IR-UV DR spectrum presented in Figure 6b. Other odd-∆J RET features fall away monotonically from the kinetic curve for J ) 12, as if from a secondary parent peak. Both levels of the J ) 18 doublet (main and perturber, labeled “J ) 18” in the right-hand column of Figure 8) display similar kinetic growth and decay rates, consistent with aspects of section III above; their growth rates are higher than expected from the “monotonic fall-off” pattern mentioned above, indicating their possible collision-induced gateway role. The corresponding kinetic curve showing collision-induced decay of the J ) 17 parent levels of the (1 0 3 0 0)0 doublet is presented in the upper half of Figure 9. A similar parent decay curve for the (1 0 3 0 0)0 J ) 12 level is shown (for completeness) in the lower half of Figure 9. The ordinate axes of Figures 8 and 9 (and all other kinetic curves in a large global date set for this investigation) are calibrated carefully in selfconsistent “IR-UV DR relative intensity units” to facilitate mechanistic comparisons and modeling of IR-UV DR kinetic results and interpretation of corresponding spectra. Exponentially decaying kinetic curves such as these, recorded over a pressure range up to ∼0.20 Torr (where beam-flyout

Rovibrational Energy Transfer in Acetylene

J. Phys. Chem. B, Vol. 109, No. 17, 2005 8339

Figure 8. Averaged IR-UV DR kinetic curves for C2H2 (P ) 0.20 Torr), with the UV probe wavelength set at 298.973 nm to monitor both levels of the (1 0 3 0 0)0 J ) 17 doublet and the IR pump set to monitor the kinetics of both even-∆J RET (left-hand column) and odd∆J RET (right-hand column) over the range J ) 1-19.

effects are the dominant type of relatively minor mass-transport loss effects), yield a second-order rate constant k or cross section 〈σ〉 for the total collision-induced self-relaxation from a particular rovibrational state (V, J, K).47 For example, we determine 1010 k ) 9.9 ( 0.3 cm3 molecule-1 s-1 and 〈σ〉 ) 1.42 ( 0.05 nm2 for the J ) 12 parent state,32,33 which is consistent with comparable measurements previously reported for other J-states of the (1 0 3 0 0)0 manifold of C2H2.39,47 Figures 8 and 9 (together with Figure 3 of ref 28) are representative of an extensive body of IR-UV DR kinetic results that can be satisfactorily simulated by a phenomenological master-equation model.32 Such an approach84 has previously been adopted in our treatments of collision-induced state-tostate rovibrational energy-transfer kinetics in D2CO26,27 and in the (νCC + 3νCH) manifold of C2H2.36 The above-mentioned body of IR-UV DR kinetic results curves was assembled from four sets of experimental data, each with the IR pump tuned successively to prepare the (1 0 3 0 0)0 J ) 1-19 levels. In the first three of these (sets A-C), the UV probe was tuned to 299 nm wavelengths characteristic of the (1 0 3 0 0)0 J ) 1, 12, and 17 levels, respectively. In the fourth (set D), the UV probe was set off-resonance from any discrete IR-UV DR feature so that it sampled the kinetics of the accompanying CIQCB bath.30,32 Figure 8 above corresponds to set C, while Figure 3 of ref 28 corresponds to set A. All such kinetic data were carefully standardized and signal-averaged prior to being fitted to the kinetic master-equation model.32 The model itself32,33 comprises a set of rate equations, expressed in the form of population vectors and rate-constant matrices.26,27,36,84 The aim of such detailed modeling is to

Figure 9. Averaged IR-UV DR kinetic curves for the “parent” features for (1 0 3 0 0)0 rovibrational levels with J ) 12 (lower trace) and J ) 17 (upper trace), with the UV probe wavelength set, respectively, at 299.452 and 298.973 nm in the Α ˜ -Χ ˜ 101 313 510 rovibronic band. The C2H2 sample pressure P is 0.20 Torr.

determine a set of microscopic state-to-state rate constants that adequately reproduces the observed rovibrational energy-transfer kinetics. In this way, it is possible to characterize the gateway roles of the J ) 12 and J ) 18 (main and perturber) rovibrational levels of the (1 0 3 0 0)0 submanifold and to make a qualitative representation of CIQCB bath effects30,32 (i.e., in terms of a quasi-continuous manifold of rovibrational bath states). Details of this model will be published in later papers of this series.33 In the meantime, Figure 10 compares observed (O) and modeled (-) IR-UV DR kinetic curves from set C, for even∆J RET from (1 0 3 0 0)0 J-states prepared by the IR pump, with the 298.973 nm UV probe monitoring the (1 0 3 0 0)0 J ) 17 doublet, as in Figure 8 and the upper half of Figure 9. The phenomenological master-equation model32,33 treats a total of 80 kinetic curves for rovibrational states prepared by the IR pump (with the UV probe monitoring 20 curves each for J ) 1, J ) 12, and J ) 17 and a further 20 curves for the offresonance CIQCB bath). A single set of 14 exponential-gaplaw36 fitting parameters (7 for RET and 7 for V-V transfer) is adjusted iteratively to optimize the overall quality of fit to the full range of 80 kinetic curves. An additional optional allowance is made for the J ) 18 (main and perturber) levels to serve as a gateway for population transfer to the CIQCB bath.30,32

8340 J. Phys. Chem. B, Vol. 109, No. 17, 2005

Payne et al.

Figure 10. Quality of fit of a phenomenological master-equation model (solid line) to IR-UV DR kinetic results (open circles) for C2H2 (P ) 0.20 Torr), with the 298.973 nm UV probe wavelength set to monitor both levels of the (1 0 3 0 0)0 J ) 17 doublet as in Figures 8 and 9.

This model has proved to be a difficult undertaking, particularly in view of the fact that the rovibrational identity and LIF cross sections of destination states outside the (1 0 3 0 0)0 submanifold were unknown. However, a remarkably good global fit to the observed kinetic data has been obtained with a minimal number of physically realistic fitting parameters as will be reported in a future paper.33 It is apparent from Figure 10 that our phenomenological model can yield a satisfactory fit to the observed IR-UV DR results for set C (J ) 17 probed), despite their evident complexity. Nevertheless, kinetic curves for virtually all prepared J-states (apart from J ) 19) are observed to decay more rapidly than the model prediction, although the population amplitudes are generally well reproduced; this is taken to indicate that, like J ) 12 and J ) 18 (main and perturber), the J ) 17 doublet acts as a gateway for population transfer to the CIQCB bath that still needs to be taken into account. As will be reported elsewhere,33 the quality of fit obtained for sets A

and B (J ) 1 and J ) 12 probed, respectively)32 is superior to that depicted in Figure 10 for set C (J ) 17 probed). Likewise, the model provides an adequate fit to the rovibrational kinetics of the CIQCB bath states (as in set D), observed with an off-resonance UV probe wavelength. Such collision-induced transfer to the CIQCB bath appears to be ubiquitous in the 4νCH manifold of C2H230 and is now believed to account largely for the odd-∆J RET satellite structure of IR-UV DR spectra such as those in Figures 1b and 7b or in Figure 1c of ref 30. V. Concluding Discussion This paper and its predecessors28-30,32 are concerned with the extent to which intramolecular perturbations (e.g., anharmonic, l-resonance, and/or Coriolis coupling) within the 12 700 cm-1 4νCH manifold of C2H2 may influence collision-induced state-to-state rovibrational energy-transfer processes, detected by time-resolved, LIF-detected IR-UV DR spectroscopy. The present 4νCH manifold investigations follow through from our

Rovibrational Energy Transfer in Acetylene previous studies of the 11 600 cm-1 (νCC + 3νCH) manifold of C2H234-37 and a variety of other LIF-detected IR-UV DR experiments on C2H2 and its isotopomers.9,10,38-49,67,69-71,74 Many of these experiments reveal aspects of the role of intramolecular perturbations in terms of either spectroscopy or collision-induced energy transfer, complementing what is known on the basis of other spectroscopic measurements.31,50-55,57,58,60-66,68-71,75-79 The ostensibly simple, linear, nondipolar, tetratomic, centrosymmetric structure of C2H2 makes it amenable to investigations of supposed “symmetry-breaking” processes (e.g., odd-∆J RET and apparent interchange of a and s or ortho and para nuclearspin modifications) that are masked by their allowed counterparts in molecules of lower symmetry and/or more complicated structure.28-30,34-37 Moreover, C2H2 has a long and illustrious history of defying expectations that its spectroscopic, structural, or dynamical behavior should be simple; particular instances of its remarkable complexity include the classic bent/linear character of its primary Α ˜ -Χ ˜ electronic transition,82,83,85 its photochemical isomerization to vinylidene,72,86 and its complicated but well-characterized rovibrational spectra.55,56 In this paper, we have directly examined possible links between intramolecular perturbations and anomalous collisioninduced rovibrational energy transfer within the 4νCH manifold of C2H2, by measuring time-resolved, LIF-detected IR-UV DR spectra with the IR pump preparing either of the (1 0 3 0 0)0 J ) 17 and J ) 18 levels. These are known to appear as locally perturbed doublets in IR-absorption spectra57,58,73,75 (see also Figure 2), in IR-UV DR spectra28-30,32,74,76 (see also Figures 1b, 5, 6, 7, and 8), and in vibrationally mediated photodissociation action spectra.71 The same levels also have anomalously large collision-induced lineshifts75,78 and photodissociation cross sections.71 We have taken advantage of a recently published assignment58 of the local perturbation that causes doublet splitting of the J ) 17 and J ) 18 levels, in terms of a crossing between the Coriolis-coupled zero-order levels of the IR-bright, UV-dark (1 0 3 0 0)0 Σ+ u submanifold and of the IR-dark, UVbright (0 5 0 4 1)1 Πu submanifold. In the case of the main and perturber (1 0 3 0 0)0 J ) 18 rovibrational levels, relative efficiencies for several dynamical processes (UV-brightness, collision-induced RET and V-V transfer, and vibrationally mediated photodissociation) are significantly different from relative doublet intensities observed in IR-absorption spectra57,58,73,75 (see also Figure 2). Figure 5 indicates that the two (1 0 3 0 0)0 J ) 18 eigenstates have virtually indistinguishable UV-scanned IR-UV DR spectra, despite their 0.33 cm-1 energy separation. It has therefore not been feasible to measure collision-induced ∆J ) 0 energy transfer between them and to test how that is affected by the intramolecular perturbations. Following conventional expectations,3-6,24 it might be presumed that collision-induced energy transfer between two such strongly coupled rovibrational eigenstates will “invariably”6 be highly efficient. However, that is by no means certain, given our contrary experience7-9 in the classic case of Fermi resonance87 between the (1 00 0, 0 20 0)I and (1 00 0, 0 20 0)II vibrational manifolds of CO2,88 where destructive interference between relatively uncongested quantummechanical channels are predicted7-9 to yield an unexpectedly low energy-transfer efficiency, consistent with experiment.23 A similar destructive interference is predicted7,9 in the case of V-V transfer between the Fermi-coupled “ν1” and “2ν2” manifolds of OCS, contrary to original experimental interpretation.89 IRscanned IR-UV DR spectra in Figures 6 and 7 for the (1 0 3 0 0)0 J ) 17 doublet, with its smaller splitting (0.08 cm-1,

J. Phys. Chem. B, Vol. 109, No. 17, 2005 8341 unresolved in most of our experiments), show that even-∆J RET is insensitive to the UV probe wavelength (∼299 or ∼323 nm) used to monitor collision-induced energy transfer, whereas odd∆J RET is more prominent with the UV probe at ∼299 than at ∼323 nm, where it is largely attributable to energy transfer into a manifold (as yet poorly defined) of CIQCB bath states.32 Such interpretations are confirmed by recording IR-UV DR kinetic curves (as in Figures 8 and 9) and satisfactorily fitting them (as in Figure 10) to a phenomenological kinetic master-equation model.32,33 Details of this model will be presented in future publications33 as will further IR-UV DR studies of the (1 0 3 0 0)0 J ) 12 gateway state28-30,32 and of CIQCB effects.30,32 In the meantime, it has been proposed in this paper that the locally perturbed (1 0 3 0 0)0 J ) 17 and J ) 18 rovibrational levels appear to play additional gateway roles between the CIQCB bath and/or other discrete rovibrational levels that are IR-dark. Whatever the efficiency of collision-induced energy transfer to or from perturbed rovibrational eigenstates of C2H2 such as J ) 12, J ) 17, and J ) 18 levels of the (1 0 3 0 0)0 submanifold, it is clear that rotational-state resolution, as available in the LIF-detected IR-UV DR method, is essential in tracking the finer details of the dynamical processes that are inclined to vary markedly from one J-state to the next. We have attained this level of detail in various rovibrational levels (V, J, K) of a “not-so-big” polyatomic molecule excited to vibrational manifolds with term energies Gv of ∼11 600 cm-1 (νCC + 3νCH)34-37 and ∼12 700 cm-1 (4νCH);28-30,32 these manifolds are not sufficiently energetic to be chemically significant72,86 but are nevertheless highly congested (estimated62 to be at least 10 vibrational states per cm-1) and affected by widespread global and local perturbations. “The dawn of the quantum state resolved era,” as heralded by Weston and Flynn12 in the context of molecular relaxation at chemically significant vibrational energies, has shed much light on energy-transfer dynamics in high-vibrational states of small molecules (such as C2H2 )28-30,32,34-37,38-43,64-72 and in larger molecules (as surveyed very selectively in section I above).10,12-22 A longstanding but still topical question concerns what was once termed90 a “zone of ignorance” separating the dynamical behavior of small and large molecules, with a tendency10,12-14,16,18-20 to treat them respectively in terms of two distinct dynamical descriptions. This approach is natural, in view of the apparent contrasts between experimental observables and modeling capabilities that have typically been available for each of these two perceived classes of molecules. However, it may eventually prove as inappropriate as sharp distinctions between chemistry and biology in the current era of molecular biology or between organic and inorganic chemistry since the synthesis of urea by Wo¨hler91 (or of acetic acid by Kolbe)92 discredited the vitalism concept.93 It seems logical (albeit reductionist)94 to expect that there are no substantial fundamental differences between the underlying physics of small molecules (amenable to relatively detailed characterization) and of larger molecules (although relatively complicated and statistically averaged). This viewpoint implies that apparently anomalous quantum-state-resolved dynamical properties of molecules as small as C2H2 (e.g., as reported in this paper) may eventually prove to be mechanistically relevant to the energetics and reactivity of some larger molecules,13 even if it is more difficult (or unnecessary) to resolve and characterize such effects as molecular size increases. Acknowledgment. Financial support from the Australian Research Council (ARC) is gratefully acknowledged, including the award of an ARC Postdoctoral Fellowship to A.P.M.

8342 J. Phys. Chem. B, Vol. 109, No. 17, 2005 References and Notes (1) Moore, C. B. AdV. Chem. Phys. 1973, 23, 41. (2) Weitz, E.; Flynn, G. Annu. ReV. Phys. Chem. 1974, 25, 275. (3) Yardley, J. T. Introduction to Molecular Energy Transfer; Academic Press: New York, 1980. (4) Flynn, G. W. Acc. Chem. Res. 1981, 14, 334. (5) Weitz, E.; Flynn, G. AdV. Chem. Phys. 1981, 47, 185. (6) Bondybey, V. E. Annu. ReV. Phys. Chem. 1984, 35, 591. (7) Orr, B. J.; Smith, I. W. M. J. Phys. Chem. 1987, 91, 6106. (8) Orr, B. J. Chem. Phys. 1995, 190, 261. (9) Orr, B. J. In AdVances in Chemical Kinetics and Dynamicss Vibrational Energy Transfer InVolVing Large and Small Molecules; Barker, J. R., Ed.; JAI Press: Greenwich, CT, 1995; Vol. 2A, p 21. (10) Flynn, G. W.; Parmenter, C. S.; Wodtke, A. M. J. Phys. Chem. 1996, 100, 12817. (11) (a) Oref, I.; Tardy, D. C. Chem. ReV. 1990, 77, 1407. (b) Gilbert, R. G.; Smith, S. C. Theory of Unimolecular and Recombination Reactions; Blackwell Scientific: Oxford, U. K., 1990. (c) Gilbert, R. G. Int. ReV. Phys. Chem. 1991, 10, 319. (d) Baer, T.; Hase, W. L. Unimolecular Reaction Dynamics. Theory and Experiments; Oxford University Press: New York, 1996. (12) Weston, R. E.; Flynn, G. W. Annu. ReV. Phys. Chem. 1992, 43, 559. (13) Barker, J. R.; Yoder, L. M.; King, K. D. J. Phys. Chem. A 2001, 105, 796. (14) Quack, M. Annu. ReV. Phys. Chem. 1990, 41, 839. (15) (a) Lehmann, K. K.; Scoles, G.; Pate, B. H. Annu. ReV. Phys. Chem. 1994, 45, 241. (b) Keske, J.; McWhorter, D. A.; Pate, B. H. Int. ReV. Phys. Chem. 2000, 19, 363. (c) Keske, J. C.; Pate, B. H. Annu. ReV. Phys. Chem. 2000, 51, 323. (16) Nesbitt, D. J.; Field, R. W. J. Phys. Chem. 1996, 100, 12735; Silva, M.; Jongma, R.; Field, R. W.; Wodtke, A. M. Annu. ReV. Phys. Chem. 2001, 52, 811. (17) (a) Yoo, H. S.; DeWitt, M. J.; Pate, B. H. J. Phys. Chem. A 2004, 108, 1348. (b) Yoo, H. S.; DeWitt, M. J.; Pate, B. H. J. Phys. Chem. A 2004, 108, 1365. (c) Yoo, H. S.; McWhorter, D. A.; Pate, B. H. J. Phys. Chem. A 2004, 108, 1380. (18) Krajnovich, D. J.; Catlett, D. L., Jr.; Parmenter, C. S. Chem. ReV. 1987, 87, 237. (19) (a) Waclawik, E. R.; Lawrance, W. D. J. Chem. Phys. 1995, 102, 780. (b) Waclawik, E. R.; Lawrance, W. D. J. Phys. Chem. A 2003, 107, 10507. (c) Waclawik, E. R.; Lawrance, W. D. J. Phys. Chem. A 2003, 107, 10826. (20) Kable, S. H.; Knight, A. E. W. J. Phys. Chem. A 2003, 107, 10813. (21) (a) Mullin, A. S.; Park, J.; Chou, J. Z.; Flynn, G. W.; Weston, R. E. Chem. Phys. 1993, 175, 53. (b) Mullin, A. S.; Michaels, C. A.; Flynn, G. W. J. Chem. Phys. 1995, 102, 780. (c) Michaels, C. A.; Lin, Z.; Mullin, A. S.; Tapalian, H. C.; Flynn, G. W. J. Chem. Phys. 1997, 106, 7055. (d) Michaels, C. A.; Mullin, A. S.; Park, J.; Chou, J. Z.; Flynn, G. W. J. Chem. Phys. 1998, 108, 2744. (e) Sevy, E. T.; Muyskens, M. A.; Rubin, S. M.; Flynn, G. W.; Muckerman, J. T. J. Chem. Phys. 2000, 112, 5829. (f) Sevy, E. T.; Michaels, C. A.; Tapalian, H. C.; Flynn, G. W. J. Chem. Phys. 2000, 112, 5844. (22) (a) Higgins, C.; Ju, Q.; Seiser, N.; Kavita, K.; Flynn, G. W.; Chapman, S. J. Phys. Chem. A 2001, 105, 2858. (b) Seiser, N.; Kavita, K.; Flynn, G. W. J. Phys. Chem. A 2003, 107, 8191 (23) Dang, C.; Reid, J.; Garside, B. K. Appl. Phys. B 1983, 31, 163. (24) Sheorey, R. S.; Flynn, G. J. Chem. Phys. 1980, 72, 1175. (25) (a) Haub, J. G.; Orr, B. J. Chem. Phys. Lett. 1984, 107, 162. (b) Haub, J. G.; Orr, B. J. J. Chem. Phys. 1987, 86, 3380. (26) Orr, B. J. Int. ReV. Phys. Chem. 1990, 9, 67. (27) (a) Bewick, C. P.; Orr, B. J. J. Chem. Phys. 1990, 93, 8634. (b) Bewick, C. P.; Martins, J. F.; Orr, B. J. J. Chem. Phys. 1990, 93, 8643. (28) Payne, M. A.; Milce, A. P.; Frost, M. J.; Orr, B. J. J. Phys. Chem. A 2003, 107, 10759. (29) Payne, M. A.; Milce, A. P.; Frost, M. J.; Orr, B. J. Chem. Phys. Lett. 1997, 265, 244. (30) Payne, M. A.; Milce, A. P.; Frost, M. J.; Orr, B. J. Chem. Phys. Lett. 2000, 324, 48. (31) (a) Barnes, J. A.; Gough, T. E.; Stoer, M. Chem. Phys. Lett. 1995, 237, 437. (b) Barnes, J. A.; Gough, T. E.; Stoer, M. ReV. Sci. Instrum. 1999, 70, 3515. (c) Barnes, J. A.; Gough, T. E.; Stoer, M. J. Chem. Phys. 2001, 114, 4490. (32) Payne, M. A. Ph.D. Thesis; Macquarie University, Sydney, Australia, 1999. (33) Payne, M. A.; Milce, A. P.; Frost, M. J.; Orr, B. J. Unpublished work, including Z. Physik. Chemie 2005, 219, in press. (34) Milce, A. P.; Barth, H.-D.; Orr, B. J. J. Chem. Phys. 1994, 100, 2398. (35) Milce, A. P.; Orr, B. J. J. Chem. Phys. 1996, 104, 6423. (36) Milce, A. P.; Orr, B. J. J. Chem. Phys. 1997, 106, 3592. (37) Milce, A. P.; Orr, B. J. J. Chem. Phys. 2000, 112, 9319.

Payne et al. (38) Carrasquillo M., E.; Utz, A. L.; Crim, F. F. J. Chem. Phys. 1988, 88, 5976. (39) Utz, A. L.; Tobiason, J. D.; Carrasquillo M., E.; Fritz, M. D.; Crim, F. F. J. Chem. Phys. 1992, 97, 389. (40) Tobiason, J. D.; Utz, A. L.; Crim, F. F. J. Chem. Phys. 1992, 97, 7437. (41) Tobiason, J. D.; Utz, A. L.; Crim, F. F. J. Chem. Phys. 1994, 101, 1108. (42) Tobiason, J. D.; Fritz, M. D.; Crim, F. F. J. Chem. Phys. 1994, 101, 9642. (43) Utz, A. L.; Carrasquillo M., E.; Tobiason, J. D.; Crim, F. F. Chem. Phys. 1995, 190, 311. (44) Chadwick, B. L.; Orr, B. J. J. Chem. Phys. 1991, 95, 5476. (45) Frost, M. J.; Smith, I. W. M. Chem. Phys. Lett. 1992, 191, 574. (46) Frost, M. J. J. Chem. Phys. 1993, 98, 8572. (47) Chadwick, B. L.; Milce, A. P.; Orr, B. J. Can. J. Phys. 1994, 72, 939. (48) Frost, M. J.; Smith, I. W. M. J. Phys. Chem. 1995, 99, 1094. (49) (a) Henton, S.; Islam, M.; Smith, I. W. M. Chem. Phys. Lett. 1998, 291, 223. (b) Henton, S.; Islam, M.; Smith, I. W. M. J. Chem. Soc., Faraday Trans. 1998, 94, 3207. (c) Henton, S.; Islam, M.; Gatenby, S.; Smith, I. W. M. J. Chem. Soc., Faraday Trans. 1998, 94, 3219. (50) Chadwick, B. L.; King, D. A.; Berzins, L.; Orr, B. J. J. Chem. Phys. 1989, 91, 7994. (51) (a) Dopheide, R.; Gao, W. B.; Zacharias, H. Chem. Phys. Lett. 1991, 182, 21. (b) Dopheide, R.; Zacharias, H. J. Chem. Phys. 1993, 99, 4864. (52) Chadwick, B. L.; Orr, B. J. J. Chem. Phys. 1992, 97, 3007. (53) Chadwick, B. L.; Milce, A. P.; Orr, B. J. Chem. Phys. 1993, 175, 113. (54) (a) Rudert, A. M.; Martin, J.; Gao, W.-B.; Halpern, J. B.; Zacharias, H. J. Chem. Phys. 1999, 111, 9549. (b) Rudert, A. M.; Martin, J.; Gao, W.-B.; Zacharias, H.; Halpern, J. B. J. Chem. Phys. 2000, 112, 9749. (55) (a) Herman, M.; Lie´vin, J.; Vander Auwera, J.; Campargue, A. AdV. Chem. Phys. 1999, 108, 1. (b) Herman, M.; Campargue, A.; El Idrissi, M. I.; Vander Auwera, J. J. Phys. Chem. Ref. Data 2003, 32, 921. (c) Jacquemart, D.; Mandin, J.-Y.; Dana, V.; Claveau, C.; Vander Auwera, J.; Herman, M.; Rothman, L. S.; Regalia-Jarlot, L.; Barbe, A. J. Quant. Spectrosc. Radiat. Transfer 2003, 82, 363. (56) (a) Halonen, L.; Child, M. S.; Carter, S. Mol. Phys. 1982, 47, 1097. (b) Child, M. S.; Halonen, L. AdV. Chem. Phys. 1984, 57, 1. (57) Zhan, X.; Halonen, L. J. Mol. Spectrosc. 1993, 160, 464. (58) Hurtmans, D.; Kassi, S.; Depiesse, C.; Herman, M. Mol. Phys. 2002, 100, 3507. (59) Kellman, M.; Chen, G. J. Chem. Phys. 1991, 95, 8671. (60) (a) Abboutti Temsamani, M.; Herman, M. J. Chem. Phys. 1995, 102, 6371. (b) Abboutti Temsamani, M.; Herman, M. J. Chem. Phys. 1996, 105, 1355. (61) (a) Campargue, A.; Abboutti Temsamani, M.; Herman, M. Chem. Phys. Lett. 1995, 242, 101. (b) Campargue, A.; Abboutti Temsamani, M.; Herman, M. Mol. Phys. 1997, 90, 793. (c) Yang, S.-F.; Biennier, L.; Campargue, A.; Abboutti Temsamani, M.; Herman, M. Mol. Phys. 1997, 90, 807. (62) (a) El Idrissi, M. I.; Lie´vin, J.; Campargue, A.; Herman, M. J. Chem. Phys. 1999, 110, 2074. (b) Zhilinskii, B.; El Idrissi, M. I.; Herman, M. J. Chem. Phys. 2000, 113, 7885. (c) El Idrissi, M. I.; Zhilinskii, B.; Gaspard, P.; Herman, M. Mol. Phys. 2003, 101, 595. (63) Abboutti Temsamani, M.; Herman, M.; Solina, S. A. B.; O’Brien, J. P.; Field, R. W. J. Chem. Phys. 1996, 105, 11357. (64) (a) Solina, S. A. B.; O’Brien, J. P.; Field, R. W.; Polik, W. F. Ber. Bunsen-Ges. Phys. Chem. 1995, 99, 555. (b) Solina, S. A. B.; O’Brien, J. P.; Field, R. W.; Polik, W. F. J. Phys. Chem. 1996, 100, 7797. (c) O’Brien, J. P.; Jacobson, M. P.; Sokol, J. J.; Coy, S. L.; Field, R. W. J. Chem. Phys. 1998, 108, 7100. (d) Jacobson, M. P.; O’Brien, J. P.; Silbey, R. J.; Field, R. W. J. Chem. Phys. 1998, 109, 121. (e) Jacobson, M. P.; O’Brien, J. P.; Field, R. W. J. Chem. Phys. 1998, 109, 3831. (65) (a) Jonas, D. M.; Solina, S. A. B.; Rajaram, B.; Silbey, R. J.; Field, R. W.; Yamanouchi, K.; Tsuchiya, S. J. Chem. Phys. 1993, 99, 7350. (b) Moss, D. B.; Duan, Z.; Jacobson, M. P.; O’Brien, J. P.; Field, R. W. J. Mol. Spectrosc. 2000, 199, 265. (66) Srivastava, H. K.; Conjusteau, A.; Mabuchi, H.; Lehmann, K. K.; Scoles, G.; Silva, M. L.; Field, R. W. J. Chem. Phys. 2000, 113, 7376. (67) Hoshina, K.; Iwasaki, A.; Yamanouchi, K.; Jacobson, M. P.; Field, R. W. J. Chem. Phys. 2001, 114, 7424. (68) (a) Jungner, P.; Halonen, L. J. Chem. Phys. 1997, 107, 1680. (b) Saarinen, M.; Permogorov, D.; Halonen, L. J. Chem. Phys. 1999, 110, 1424. (c) Metsala, M.; Yang, S.; Vaittinen, O.; Halonen, L. J. Chem. Phys. 2002, 117, 8686. (69) (a) Arusi-Parpar, T.; Schmid, R. P.; Li, R.-J.; Bar, I.; Rosenwaks, S. Chem. Phys. Lett. 1997, 268, 163. (b) Schmid, R. P.; Arusi-Parpar, T.; Li, R.-J.; Bar, I.; Rosenwaks, S. J. Chem. Phys. 1997, 107, 385. (c) ArusiParpar, T.; Schmid, R. P.; Ganot, Y.; Bar, I.; Rosenwaks, S. Chem. Phys. Lett. 1998, 287, 347. (d) Schmid, R. P.; Ganot, Y.; Bar, I.; Rosenwaks, S. J. Chem. Phys. 1998, 109, 8959. (d) Schmid, R. P.; Ganot, Y.; Bar, I.;

Rovibrational Energy Transfer in Acetylene Rosenwaks, S. Chem. Phys. Lett. 1998, 287, 347. (e) Schmid, R. P.; Ganot, Y.; Rosenwaks, S.; Bar, I. J. Mol. Struct. 1999, 480-481, 197. (f) Bar, I.; Rosenwaks, S. Int. ReV. Phys. Chem. 2001, 20, 711. (g) Ganot, Y.; Sheng, X.; Bar, I.; Rosenwaks, S. Chem. Phys. Lett. 2002, 361, 175. (h) Ganot, Y.; Golan, A.; Sheng, X.; Rosenwaks, S.; Bar, I. Phys. Chem. Chem. Phys. 2003, 5, 5399. (70) (a) Mizoguchi, M.; Yamakita, N.; Tsuchiya, S.; Iwasaki, A.; Hoshina, K.; Yamanouchi, K. J. Phys. Chem. A 2000, 104, 10212. (b) Yamakita, N.; Iwamoto, S.; Tsuchiya, S. J. Phys. Chem. A 2003, 107, 2597. (71) Sheng, X.; Ganot, Y.; Rosenwaks, S.; Bar, I. J. Chem. Phys. 2002, 117, 6511. (72) (a) Jacobson, M. P.; Field, R. W. J. Phys. Chem. A 2000, 104, 3073. (b) Loh, Z.-H.; Field, R. W. J. Chem. Phys. 2003, 118, 4037 (73) Smith, B. C.; Winn, J. S. J. Chem. Phys. 1991, 94, 4120. (74) Tobiason, J. D. Ph.D. Thesis; University of WisconsinsMadison, Madison, WI, 1992. (75) Herregodts, F.; Hurtmans, D.; Vander Auwera, J.; Herman, M. J. Chem. Phys. 1999, 111, 7961. (76) Baxter, G. W.; Payne, M. A.; Austin, B. D. W.; Halloway, C. A.; Haub, J. G.; He, Y.; Milce, A. P.; Nibler, J. W.; Orr, B. J. Appl. Phys. B 2000, 71, 651. (77) Georges, R.; Vandervorst, D.; Herman, M.; Hurtmans, D. J. Mol. Spectrosc. 1997, 185, 187. (78) Herregodts, F.; Hurtmans, D.; Vander Auwera, J.; Herman, M. Chem. Phys. Lett. 2000, 316, 460. (79) (a) Herregodts, F.; Hurtmans, D.; Vander Auwera, J.; Herman, M. J. Chem. Phys. 1999, 111, 7954. (b) Herregodts, F.; Kerrinckx, E.; Huet, T. R.; Vander Auwera, J. Mol. Phys. 2003, 101, 3427. (80) Tobiason, J. D.; Utz, A. L.; Crim, F. F. J. Chem. Phys. 1993, 99, 928.

J. Phys. Chem. B, Vol. 109, No. 17, 2005 8343 (81) Utz, A. L.; Tobiason, J. D.; Carrasquillo M., E.; Sanders, L. J.; Crim, F. F. J. Chem. Phys. 1993, 98, 2742. (82) Hougen, J T.; Watson, J. K. G. Can. J. Phys. 1965, 43, 298. (83) (a) Dixon, R. N.; Wright, N. G. Chem. Phys. Lett. 1985, 117, 280. (b) Huet, T. R.; Godefroid, M.; Herman, M. J. Mol. Spectrosc. 1990, 144, 32. (84) (a) Gordon, R. J. J. Chem. Phys. 1967, 46, 4399. (b) Steinfeld, J. I.; Houston, P. L. In Laser and Coherence Spectroscopy; Steinfeld, J. I., Ed.; Plenum: New York, 1978; Chapter 1, p 1. (c) Gordon, R. J. Comments At. Mol. Phys. 1988, 21, 123. (85) (a) Ingold, C. K.; King, G. W. J. Chem. Soc. 1953, 2702. (b) Innes, K. K. J. Chem. Phys. 1954, 22, 863. (86) Gallo, M. M.; Hamilton, T. P.; Schaefer, H. F. J. Am. Chem. Soc. 1990, 112, 8714. (87) Fermi, E. Z. Physik 1931, 71, 250. (88) Howard-Lock, H. E.; Stoicheff, B. P. J. Mol. Spectrosc. 1971, 37, 321. (89) Mandich, M. L.; Flynn, G. W. J. Chem. Phys. 1980, 73, 1265. (90) Docker, M. P.; Hodgson, A.; Simons, J. P. In AdVances in GasPhase Photochemistry and Kinetics: Molecular Photodissociation Dynamics; Ashfold, M. N. R., Baggott, J. E., Eds.; Royal Society of Chemistry: London, U. K., 1987; p 115. (91) Wo¨hler, F. Poggendorfs Ann. Phys. Chem. 1828, 12, 253. (92) Kolbe, H. Liebigs Ann. 1845, 54 145. (93) Wilkinson, I. EJIFCC 2003, 13, http://www.ifcc.org/ejifcc/vol13no4/ 130304003.htm (94) (a) Weinberg, S. Dreams of a Final Theory; Pantheon Books: New York, 1992; pp 51-64. (b) Hoffmann, R. The Same and Not the Same; Columbia University Press: New York, 1995; pp 18-21, 111-115.