Factors controlling the competition among rotational and vibrational energy transfer channels in glyoxal

Abstract

The state-to-state transfer of rotational and vibrational energy has been studied for S₁ glyoxal (CHOCHO) in collisions with D₂, N₂, CO and C₂H₄ using crossed molecular beams. A laser is used to pump glyoxal seeded in He to its S₁ zero point level with zero angular momentum about its top axis (K′ = 0). The inelastic scattering to each of at least 26 S₁ glyoxal rotational and rovibrational levels is monitored by dispersed S₁–S₀ fluorescence. Various collision partners are chosen to investigate the relative influences of reduced mass and the collision pair interaction potential on the competition among the energy transfer channels. When the data are combined with that obtained previously from other collision partners whose masses range from 2 to 84 amu, it is seen that the channel competition is controlled primarily by the kinematics of the collisional interaction. Variations in the intermolecular potential play strictly a secondary role.

Vibrational and rotational energy transfer during molecular collisions is a venerable subject whose study may be traced back to nearly the beginning of this century (ref. 1; note that in this reference the history is traced to the 1911 papers by J. Franck and R. W. Wood). Its durability is testament to its fundamental role in chemical reactivity as well as to its experimental challenges. For example, consider a molecule with 10 vibrational modes in some initial vibrational state that is in collision with the simplest of partners, He. We may ask a most basic question. What is the probability of populating each of the neighboring vibrational levels in a single collision? The answers to this seemingly elementary enquiry began to emerge only within the last two decades, and they are still limited to only a few molecules, mostly aromatics (2, 3).

More recently, a new level of detail has been added to the question. Suppose we are able to select a narrow distribution of initial rotational states within a vibrational state. Now rotational as well as vibrational resolution enters the study.

Experiments with rotational resolution are made possible by the use of crossed molecular beams (4, 5). In this paper, we discuss collisional energy transfer involving glyoxal (CHOCHO), a 12-mode molecule that has been under study for some time. Crossed molecular beams coupled with S₁–S₀ laser pumping and a dispersed fluorescence probe are used to observe state-to-state rotational and rovibrational inelastic scattering in the S₁ excited electronic state (6–10). The state resolution is sufficient to see the competition between many rotational and rovibrational channels.

In the present study, we focus on an exploration of the relative importance of factors that influence this channel competition. Specifically, we have chosen sets of collision partners that allow comparison of the effects due to changes in the intermolecular potential energy surface with the kinematic effects associated with the reduced mass of the collision pair. The comparisons are made by examining the inelastic scattering of glyoxal with H₂ vs. D₂ where only the mass changes, with D₂ vs. He where only the intermolecular potential changes, and with the trio of partners CO, N₂ and C₂H₄ where substantial differences in the intermolecular potential occur among partners of the same mass.

Preliminary experiments with the light pairs H₂ vs. D₂ and D₂ vs. He as well as with a pair of heavy partners Kr vs. C₆H₁₂ (cyclohexane), both 84 amu, have been carried out at a fluorescence resolution (10 cm⁻¹) where the individual rotational channels could not be seen (10). Those initial efforts suggested that the state-to-state channel competition is largely controlled by the kinematic effects. Now we not only extend the explorations to new collision partners, but we use a fluorescence resolution (2 cm⁻¹) that reveals individual rotational channels. As a result, the new data provide a far more definitive view of the collisional energy transfer competition.

The energy level diagrams in Fig. 1 show the unusually good opportunity provided by the glyoxal molecule to explore collisional energy transfer. The vibrational level diagram contains all glyoxal levels constructed from its 12 modes up to about 1,200 cm⁻¹ in the S₁ state. With tuned S₁–S₀ laser pumping of glyoxal molecules seeded in the beam, we can select the initial vibrational level of those S₁ glyoxal molecules that will undergo inelastic scattering with a 90° secondary beam. Experiments using the collision partner He have already been reported for each of the initial levels shown in bold in Fig. 1 (8, 9). They include the zero point level, both in-plane and out-of-plane fundamentals and an overtone of the CHOCHO torsion, ν₇.

Figure 1.

A vibrational energy level diagram (Left) of S₁ glyoxal with a rotational diagram (Right) showing the K = J rotational energy levels that may be observed in inelastic scattering from the 0⁰, K′ = 0 state of S₁ glyoxal. The bold levels are those so far pumped in published glyoxal experiments. The arrows show the principal vibrationally inelastic scattering channels from each initial level. Energies in cm⁻¹ of glyoxal fundamentals are given in parentheses. Glyoxal is planar and almost a symmetric top with the top “a” axis passing near the oxygen atoms (Inset).

Examination of vibrational structure in the S₁–S₀ fluorescence from those molecules that have undergone inelastic scattering with He reveals all of the vibrational destination states that have been significantly populated by the single-collision energy transfer. The arrows on the level diagram (Fig. 1) show the surprisingly high selectivity that occurs among the many levels accessible by the center of mass collision energy E_c.m. = 770 cm⁻¹. The cross sections for a Δν = ±1 transition in the lowest frequency mode, the CHOCHO torsion ν′₇ = 233 cm⁻¹, exceed those for other channels by at least an order of magnitude. In fact, strong bias to small quantum changes in the lowest frequency modes is the hallmark of single-collisional vibrational energy transfer in aromatic molecules (2, 3). The high channel selectivity occurring in glyoxal is an extreme expression of this characteristic.

When glyoxal is entrained in a cold (35 K) supersonic expansion of He, it is possible to select by laser pumping not only the initial vibrational state, but also to gain control over the rotational state. Glyoxal is almost a symmetric top (κ = −0.99), and accordingly its rotational states are each defined by the pair of quantum numbers J and K. J is related to the total rotational angular momentum and K is related to the angular momentum about the so-called top axis, specifically the “a” axis in Fig. 1. Laser pumping excites a narrow distribution of these rotational states where all states have K′ = 0 with J′ ≳ 10. While single rotational state pumping is not obtained, high rotational selection occurs in the sense that all excited molecules are prepared with zero angular momentum about the “a” top axis.

The spectroscopic characteristics of glyoxal S₁–S₀ fluorescence allow us to monitor the K′ identity of the new states populated by the collisional energy transfer. Even though the accompanying J′ changes cannot be resolved, the ability to follow the collisional excitation of angular momentum about the “a” axis adds an important component of state-to-state rotational information to the energy transfer study. From the 0⁰K⁰ starting point, rotationally inelastic scattering populates states with higher K′ within the zero point vibrational level. In competition, rovibrationally inelastic scattering also populates new rotational states within the 7¹ vibrational level.

Fig. 1 Right shows the K′ rotational levels associated with the zero point level 0⁰ and with the 7¹ level. Most can be resolved in the S₁–S₀ fluorescence from the inelastically scattered glyoxal molecules. These two dozen levels constitute the array of rotational and rovibrational channels available for quantitative energy transfer measurements. It is the competition among these levels that is under study. How does it respond to changes in the collision partner (rare gases, diatomic, or small polyatomic molecules), and what aspects of the collision interaction have dominant influence on the competition?

MATERIALS AND METHODS

A full description of the experimental approach is given elsewhere (7, 9, 11). The basic elements are molecular beams intersecting at 90° as shown in Fig. 2. The primary beam contains glyoxal seeded at a few mol percent in a He carrier, while the secondary target beam is an expansion of the pure collision partner. A laser incident on the intersection volume (approximately a 5-mm cube) pumps glyoxal to the S₁ level 0⁰, K′ = 0 by absorption within the K′ = 0 ← K" = 1 rotational sub-bandhead of the S₁–S₀ 0₀⁰ band near 455.0 nm. Roughly 20% of these excited molecules undergo inelastic scattering by collision with molecules or atoms in the target beam. At least 94% of the scattered glyoxal molecules encounter only one inelastic collision.

Figure 2.

A schematic of the experimental geometry showing a pulsed skimmed beam of glyoxal seeded in a He carrier gas intersecting a pulsed beam of pure target gas such as D₂ or CO. A laser irradiating the collision volume pumps glyoxal to its S₁ zero point level with rotational selection. Two fluorescence collection systems are used. One directs fluorescence to a monochromator that produces an S₁–S₀ fluorescence spectrum with vibrational and rotational resolution. The second monitors total fluorescence and is used to normalize the dispersed fluorescence signal for fluctuations in laser intensity.

The states populated by inelastic scattering are detected by the vibrational and rotational structure in the S₁–S₀ glyoxal fluorescence. A trick based on the pulsed nature of the beam expansion allows isolation of the fluorescence from only those molecules that have undergone inelastic scattering. To do this, the target beam is present on only alternate laser pulses so that the computer storage of the fluorescence signal allows two interleaved spectra to be acquired. One is with both beams, whereas the other is from glyoxal without scattering. The difference spectrum obtained by subtraction isolates the fluorescence contribution of glyoxal in the new S₁ states populated by the inelastic scattering.

A great advantage of dispersed fluorescence detection is that all dominant energy transfer channels that populate new K′ states can be monitored simultaneously whereas most other detection schemes follow only one channel at a time. The major experimental challenge of these experiments is to obtain sufficient fluorescence signal for quantitative measurement. The issue is discussed elsewhere (11).

The key aspect of data analysis involves extracting relative cross sections for the state-to-state inelastic scattering from the dispersed fluorescence (9). We acquire a set of cross sections that defines the competition among inelastic channels by computer simulation of the spectrum. So much is known about the spectroscopic and photophysical characteristics of glyoxal that the simulation requires adjustment of only two parameters for a close fit to the experimental spectrum. We first guess a final distribution of J′ states to match the width of the individual K′ state sub-bandheads. Unfortunately, the sub-bandhead widths are not very sensitive to reasonable variations among our guesses, so that little information emerges about excitation of overall molecular rotation. The most important parameter is the relative populations of the K′ states reached by the inelastic scattering. By adjusting these populations, the simulated amplitudes of the K′ sub-bandheads can be brought into close correspondence with those in the experimental spectrum. Because the inelastic scattering is dominated by molecules that have undergone only a single collision, the relative populations are also the relative cross sections for state-to-state energy transfer that we seek.

RESULTS

We present new fluorescence spectra from S₁ glyoxal molecules that have been pumped to the initial level 0⁰, K′ = 0 and subsequently experience a single collision with D₂, N₂, CO, or C₂H₄. Spectra from earlier work involving H₂ and He are included for comparison. [Spectra from other initial levels and with other collision partners have been shown elsewhere (6–10)].

Fig. 3 displays a typical S₁–S₀ fluorescence spectrum from S₁ glyoxal molecules that have undergone inelastic scattering from a D₂ target gas. The segment includes the 0₀⁰ band and much of the 7₁¹ band. It is obtained at a spectral resolution of 2 cm⁻¹ where the K′ sub-bandheads can be clearly seen. Emission in the 0₀⁰ band comes from molecules that have undergone pure rotationally inelastic scattering to the K′ levels shown in Fig. 1. One can see emission from K′ = 3, 4 … as marked in Fig. 3. In a similar manner, emission in the 7₁¹ band (with less clearly displayed sub-bandheads) corresponds to states populated by rovibrational inelastic scattering reaching members of the K′ stack built on the 7¹ level shown in Fig. 1. Fluorescence from vibrational levels other than 0⁰ and 7¹ is too weak to observe. This result shows that the cross section for vibrationally inelastic scattering with Δν′ = +1 exceeds that for exciting any other mode (or combination of modes) by at least an order of magnitude. Levels up to about 770 cm⁻¹ are energetically accessible.

Figure 3.

A segment of dispersed S₁–S₀ fluorescence (2 cm⁻¹ resolution) from glyoxal molecules initially pumped to the S₁ level 7⁰, K′ = 0 that are inelastically scattered by collision with D₂. Open circles show the experimental spectrum with three-point smoothing. The solid curve is the best fit obtained with a computer simulated spectrum. The labeling includes the K′ numbering of some sub-bandheads within the 0₀⁰ band (centered at 21,970 cm⁻¹) or the 7₁¹ band (origin is near 22,050 cm⁻¹). Regions dominated by S₁ emission from states reached by pure rotationally inelastic scattering or by rovibrationally inelastic scattering are marked. Emission from 22,020 cm⁻¹ to lower energies is also shown with 5 times enlargement and upward displacement for clarity. The hole in the 0₀⁰ band in this difference spectrum occurs where the population of the initially pumped state is depleted by the inelastic scattering.

A display is given in Fig. 4 of similar segments of the experimental spectra obtained with H₂ and He target beams. The D₂ spectrum of Fig. 3 is overlaid on each for comparison. These spectra are all displayed with three-point smoothing. The center-of-mass collision energies E_c.m. are 80 meV (650 cm⁻¹) for H₂ and 95 meV (770 cm⁻¹) for D₂ and He as calculated from the beam expansion conditions.

Figure 4.

A segment of the experimental fluorescence spectra (2 cm⁻¹ resolution) as in Fig. 3, but from collisions with H₂, D₂, or He. The D₂ spectrum is that of Fig. 3, but displayed with a continuous trace generated by three-point smoothing of the individual data points. The H₂ and He spectra are similarly displayed, but taken from work published earlier (9).

Fig. 5 shows the inelastic scattering spectra for glyoxal in collisions with N₂, CO, and C₂H₄. The comparisons are pairwise with N₂ vs. CO and N₂ vs. C₂H₄, because an overlay of all three spectra is too congested to be useful. The calculated center-of-mass collision energy is approximately 210 meV (1,700 cm⁻¹) for all three collision partners.

Figure 5.

Experimental glyoxal fluorescence spectra as in Fig. 4, but for the collision partners N₂, CO, and C₂H₄.

DISCUSSION

Fluorescence spectra such as those shown in Figs. 3, 4, and 5 from S₁ glyoxal molecules that have undergone rotationally or rovibrationally inelastic scattering constitute the experimental basis of our study. Those spectra contain intensity from each level involved in the competition among the inelastic scattering channels shown in Fig. 1. On account of the fortuitous occurrence of ^rR rotational sub-bandheads, the relative populations of most destination levels may be gauged qualitatively from the amplitudes of the sub-bandheads. Because populations are directly proportional to the relative inelastic scattering cross sections, we may use the fluorescence spectra as assigned in Fig. 3 to give directly a qualitative answer to our exploration. Comparisons of the fluorescence spectra can reveal the extent to which the state-to-state channel competition is driven by changes in the intermolecular potential energy surface as opposed to kinematic effects embodied in the reduced mass of the collision pair.

Consider first the light gases H₂, D₂, and He. The inelastic scattering spectra from the interaction of S₁ glyoxal with each gas are compared in Fig. 4. The superposition of H₂ and D₂ spectra is a marked contrast to that of D₂ vs. He. The D₂ and He spectra are a matched pair whereas the H₂ and D₂ spectra differ. The H₂ vs. D₂ discrepancies are particularly evident near the 22,050 cm⁻¹ region where emission from states populated by pure rotational inelastic scattering overlaps a region of congested emission that comes from the rovibrational states (the ^pP sub-bands of the 7₁¹ emission band). The D₂ and He spectra match within the reproducibility of separate He experiments. In contrast, the mismatches between the H₂ and D₂ spectra are well beyond experimental scatter.

The three 28 amu scattering gases N₂, CO, and C₂H₄ also produce a matched set of S₁ glyoxal inelastic scattering spectra. The comparisons in Fig. 5 show the degree to which the emission intensities from the various destination states correspond. Some of the differences are reproducible, but they are small relative to the mismatch that occurs when one of these spectra is compared with that from a target gas of a substantially different mass.

Lower resolution fluorescence scattering spectra obtained in a preliminarily study (10) with two 84 amu collision partners, Kr and C₆H₁₂, also occur as a matched pair. While the individual K states were not resolved, it is clear that the general rotational scaling and particularly the rotational vs. vibrational competition are similar for Kr and C₆H₁₂. The result is consistent with the higher resolution comparisons among 28 amu and among 4 amu target gases. As an ensemble, the spectra provide evidence that dominant control of the competition among the rotational and rovibrational channels is derived from kinematic effects associated with the reduced mass of the collision pair. Details of the intermolecular potential energy surface, with some rather bold differences among the 28 amu gases CO, N₂, and C₂H₄, appear to play strictly a secondary role.

The experiment is not informative about which aspects of the kinematics are most important. Consider, for example, the center of mass collision energy, E_c.m., the relative velocity and the collision momentum of the H₂ vs. D₂ collision partners. In our experiments, H₂ and D₂ have approximately the same collision energy (E_c.m. = 80 vs. 93 meV), and for equal E_c.m., the relative velocity, ν_rel, of the glyoxal + H₂ pair exceeds that of glyoxal + D₂ by a factor of ≈. In contrast, the collisional momentum, mν_rel, of the glyoxal + D₂ pair is the greater, again by approximately a factor of . To achieve equal ν_rel, the collision energies of the D₂ vs. H₂ systems must be nearly in the ratio of 2:1. For equal collision momenta, the E_cm ratio must be the inverse, with E_cm (H₂) exceeding that for D₂ by approximately a factor of 2.

While the experimental explorations are yet to be done, one expects that the collisional momentum is the key kinematic factor of this inelastic scattering. The collisions are impulsive rather than adiabatic for all collision partners, so that the relatively slow torsional vibration and certainly the rotational motion of glyoxal is frozen during the time of a collisional encounter. (For an assumed 1-Å interaction distance in the glyoxal + He system, τ_collision ≈ 35 fs compared with a ν′₇ vibrational period τ_vib ≈ 140 fs and a rotational period τ_rot ≈ 17,000 fs.) At our high collision energies, repulsive potential interactions surely dominate the collision encounter. For such a case, the collision outcome should not be particularly sensitive to the range of the repulsive interaction. Instead, the energy transfer may be expected to be controlled by impulsive momentum transfer, and the lighter gas behavior should approach that of the heavier collision partner when the light gas E_cm is increased. By this view, we should see that the outcome of H₂ and D₂ (or He) collisions becomes similar when the H₂ E_cm is doubled to approximately 180 meV.

The subsidiary role of the interaction potential in determining the collision outcome is a central feature of the theory most generally used for polyatomic vibrational energy transfer, the so-called SSH-T theory (12–14). It is based on a relatively simple model involving impulsive collisions with the repulsive wall of an interaction potential that is isotropic and without an attractive well. The potentials of different collision partners differ only by the steepness of the repulsive wall. This parameter has a highly limited range over a variety of collision partners and, consequently, the predicted vibrational energy transfer differences among collision partners arise primarily from mass effects. Of course, a potential must be anisotropic to accommodate rotational energy transfer, so that the SSH-T model is not readily extended to treat the competition among both rotational and rovibrational energy transfer channels.

Fully quantal, three-dimensional inelastic scattering predictions (15–19) are available for some of the results of the present study, specifically the scattering by H₂ and He. A comparison of our H₂ and He cross sections with the theoretical predictions has been shown elsewhere (9). The quality of the theoretical fit is high, with mismatches not generally exceeding the 20-30% experimental error bars. Most importantly, the predictions reproduce accurately the big difference that occurs in the rotational vs. rovibrational competition with the collision partners H₂ and D₂.

An informative point concerning the role of the intermolecular potential is implicit in these calculations. The good fit between theory and experiment was obtained with identical intermolecular potentials for both He and H₂. Furthermore, the potential used to fit these S₁ electronic state experiments is calculated from atom–atom pair potentials derived from the interaction of He with ground electronic state (S₀) formaldehyde (16). Even deliberate changes to make the potential more repulsive or more attractive had only limited effect on the predicted cross sections (16). The competition among the main channels in the glyoxal + H₂ scattering was hardly changed. The greatest sensitivity occurs in the channels of low probability, at or below our detection limits, where these alterations in the potential changed cross sections by factors of two or three. Such good results with such approximate potentials drives home the message of the experiments. Kinematics rather than details of the potential are primarily responsible for establishing the energy transfer channel competition.

As described elsewhere (9), computer simulation of the inelastic scattering spectra can be used to extract relative cross sections for the channel competition. The cross sections derived from the present study for the collision partner D₂ are shown in Fig. 6, where they are plotted against ΔE, the (T → V, R) energy exchange in the transfer. The cross sections obtained earlier (9) for glyoxal collisions with H₂ and He are included for comparison.

Figure 6.

The relative cross sections plotted against the energy transfer ΔE (T → V, R) for inelastic scattering from S₁ glyoxal (0⁰, K′ = 0) by He (filled symbols) and D₂ (open symbols). The circles and squares are the rotational and rovibrational relative cross sections, respectively.

The D₂ relative cross sections match those for He to within their respective error bars, whereas cross sections for H₂ are distinctive. In particular, the expected discontinuity between the rotational and rovibrational sets of cross sections that occurs for He and D₂ is not seen for H₂, whose rotational and rovibrational sets of cross sections merge smoothly. In fact, the overlap of these H₂ sets with nearly the same scaling against ΔE is highly unusual and seemingly provocative. No physical rationale emerges from the quantal inelastic scattering calculation even though they reproduce the data. The phenomenon is probably a kinematic accident of our collisional parameters.

While all cross sections for a given collision partner are in the same arbitrary units, the data give no information about the absolute cross sections. The inelastic scattering calculations predict that they are large, with, for example, the rotational cross section for 0⁰, K′ = 0 → 0⁰, K′ = 3 scattering by H₂ predicted (16) to be about 3 Ų and the 0⁰K′ = 0 → 7¹K′ = 3 rovibrational cross section about 0.8 Ų, both for E_c.m. = 80 meV. The hard sphere cross section (20) for glyoxal + H₂ is about 25 Ų (derived from collision radii of 2.0 and 0.75 Å, respectively). The total rotational cross section for glyoxal + H₂ at 80 meV obtained by summing over all rotational channels is predicted (16) to be σ_rot = 22 Ų, compared with that for total rovibrational scattering, σ_rovib = 0.90 Ų.

CONCLUSIONS

Crossed molecular beams combined with laser pumping of selected initial rovibrational states and dispersed fluorescence for detection of inelastic scattering opens a detailed view of the competition among rotational and vibrational energy transfer channels in the six-atom molecule glyoxal. High selectivity occurs among the vibrational channels for every target gas used so far. The only vibrational channels with cross sections large enough to see are those in which the lowest frequency mode, the CHOCHO torsion ν′₇ = 233 cm⁻¹ undergoes Δν = ±1 quantum changes. The transfer cross sections for other likely vibrational channels such as neighboring levels are too small to be observed. This selectivity is an extreme case of the propensity for small quantum changes in low frequency modes that dominates vibrational energy transfer in aromatic molecules.

The cold (35 K) supersonic glyoxal beam allows study of an initial vibrational state with selected rotational excitation. The present study concerns the S₁ zero point level with zero angular momentum about the symmetric top axis. Both rotationally and rovibrationally inelastic scattering may be followed as collisions excite angular momentum about this axis. The approximately two dozen rotational and rovibrational destination levels constitute a rich array of energy transfer channels that may be followed quantitatively.

The competition among these channels has been studied for collision partners whose mass ranges from 2 amu (H₂) to 28 amu (N₂, CO, and ethylene). The competition is almost identical for partners with the same mass, even though the interaction potentials differ substantially. Comparisons among H₂ vs. D₂ vs. He and among N₂ vs. CO vs. C₂H₄ clearly show that the interaction potential plays only a secondary role in the channel competition. Other less well-defined studies suggest that this situation persists even for heavier and more disparate collision partners—e.g., Kr and cyclohexane (84 amu) (10). Some aspect of the collisional kinematics, yet to be identified, has by far the dominant influence on the relative sizes of the inelastic scattering cross sections. This somewhat surprising aspect of the rotational and rovibrational energy transfer has been partially corroborated by the theoretical treatments of others.