G. Barratt
Park
*ab,
Bastian C.
Krüger
a,
Sven
Meyer
a,
Alexander
Kandratsenka
b,
Alec M.
Wodtke
ab and
Tim
Schäfer
a
aUniversity of Goettingen, Institute for Physical Chemistry, Tammannstr. 6, 37077 Goettingen, Germany. E-mail: barratt.park@mpibpc.mpg.de
bMax Planck Institute for Biophysical Chemistry, Göttingen, Am Fassberg 11, 37077 Goettingen, Germany
First published on 12th July 2017
The conversion of translational to rotational motion often plays a major role in the trapping of small molecules at surfaces, a crucial first step for a wide variety chemical processes that occur at gas–surface interfaces. However, to date most quantum-state resolved surface scattering experiments have been performed on diatomic molecules, and little detailed information is available about how the structure of nonlinear polyatomic molecules influences the mechanisms for energy exchange with surfaces. In the current work, we employ a new rotationally resolved 1 + 1′ resonance-enhanced multiphoton ionization (REMPI) scheme to measure the rotational distribution in formaldehyde molecules directly scattered from the Au(111) surface at incidence kinetic energies in the range 0.3–1.2 eV. The results indicate a pronounced propensity to excite a-axis rotation (twirling) rather than b- or c-axis rotation (tumbling or cartwheeling), and are consistent with a rotational rainbow scattering model. Classical trajectory calculations suggest that the effect arises—to zeroth order—from the three-dimensional shape of the molecule (steric effects). Analysis suggests that the high degree of rotational excitation has a substantial influence on the trapping probability of formaldehyde at incidence translational energies above 0.5 eV.
The excitation of molecular degrees of freedom becomes increasingly important in the dissipation of incident kinetic energy during molecule/surface collisions as the number of atoms in the molecule is increased. In fact, rotational excitation has been invoked as a key component of the trapping mechanism in a number of polyatomic molecule–surface systems.4,5 However, to date, almost all experiments that probe quantum-state resolved rotational excitation at surfaces have been limited to diatomic or linear polyatomic26,27 molecules. The degree to which nonlinear polyatomic molecules are rotationally excited during collisions with surfaces remains an experimentally unexplored area. We are aware of only two previous surface scattering experiments that have probed the rotational distribution in a scattered nonlinear polyatomic molecule: CH4 from LiF(100)28 and NH3 from Au(111).25,29 The CH4 study, which was conducted at an incidence energy of 0.075 eV and an incidence angle of 60°, found no significant deviation from a thermal rotational distribution. On the other hand, the NH3 study, which was conducted at an incidence energy of 0.24 eV and an incidence angle of 45°, found a strong propensity for a rotationally cold NH3 beam to scatter elastically into low-J states. A propensity to excite low-K states (tumbling rather than twirling) was also observed. The results were interpreted in terms of a dynamical steering effect, which orients the symmetry axis of the NH3 molecule along the surface normal prior to collision.
In the current work, we report rotationally-resolved molecular beam scattering of formaldehyde from Au(111). We report an axis-specific rotational rainbow in the direct scattering channel. Unlike in the case of NH3, direct scatter of formaldehyde from Au(111) leads to a clear propensity for excitation of rotational states with a high degree of rotational energy about the symmetry axis. The results are interpreted with the aid of classical trajectory calculations. To our knowledge, the present work is the first report of rotationally resolved surface scattering of an asymmetric top molecule and the first report of a high-J rotational rainbow in a nonlinear molecule. The work demonstrates the ability to probe the highly structured steric effects that govern the interactions between polyatomic molecules and surfaces, and the results suggest that rotational excitation contributes to the trapping probability of formaldehyde on Au(111) at high incidence kinetic energies.
The incidence kinetic energy (Ei) of the incoming beam of formaldehyde was varied over the range 0.1–1.2 eV, by using different backing gas mixtures (see Table SI of the ESI†). The stagnation pressure behind the nozzle was also varied over the range 3–12 bar to achieve a 3–15 K rotational temperature (Trot) in the incoming molecular beam. Under these conditions, the incoming beams used in this study had no significant population in levels with Ka > 1 or J > 4.
The incoming beam was scattered at near-normal incidence angle from a Au(111) crystal (Mateck). Before each experiment, the Au(111) crystal is cleaned by sputtering with an Ar-ion gun (LK Technologies NGI3000) and annealed for 20 minutes at 900 K. Surface cleanliness is verified by Auger electron spectroscopy (Staib Instruments, Inc. ESA-150). The temperature (Ts) of the Au(111) crystal was monitored by a thermocouple (K type), and could be cooled by liquid nitrogen or heated resistively to achieve temperatures in the range 100–1000 K.
The rotational distribution in the vibronic ground state was monitored in the incoming and scattered molecular beam via a 1 + 1′ REMPI scheme, which we recently reported.32 Briefly, the frequency-doubled output of a pulsed dye laser (Sirah Cobra Stretch SL, operating with LDS 698 or 722 dye), pumped at 10 Hz by a Nd:YAG laser (Continuum Powerlite 8010), was scanned across the rotationally resolved à 1A2 ← 1A1 (410) transition at 353 nm. (We use the notation to denote the number of quanta of out-of-plane wagging vibration ν4 in the upper (v4′) and lower (v4′′) electronic state, respectively.) The pulse energy was typically 5–7 mJ and the beam was collimated to a diameter of ∼3 mm. A small portion of the dye laser fundamental was coupled into a high-precision wavemeter (HighFinesse, WS7) for frequency calibration, to an accuracy of ±0.02 cm−1.31 Variation in the laser intensity over the scan was monitored by recording the shot-by-shot pulse energy behind the chamber. After a delay of 20 ns, molecules were ionized from the à state by a single vacuum ultraviolet (VUV) photon at 157 nm, obtained from a molecular F2 laser (GAM EX350). The VUV beam (2–8 mJ pulse energy) was counter-propagated relative to the dye laser beam and was focused into the interaction region by a f = 58.1 cm CaF2 lens. The experiment is operated in a regime where the signal is linear with respect to both laser pulses, and the relative integrated ion intensities are directly proportional to the à ← absorption cross section to within ∼20% uncertainty.32 Molecular cations were collected by a set of ion optics and detected on a 2-stage microchannel plate assembly (Hamamatsu F1552) in chevron configuration.
At Ei = 0.1 eV, the scattering is dominated by a trapping/desorption mechanism in which molecules physisorb to the surface before undergoing thermal desorption. At higher incidence energies (Ei = 0.3–1.2 eV), we observe distinct channels for trapping/desorption and direct (single-impact) scattering. These channels have been characterized in detail in ref. 30. At incidence energies between 0.33–0.39 eV we probe the scattered molecules at a distance of 9 mm from the surface, 3 mm above the incoming beam. This allows us to capture a narrow range of near-specular scattering angles, in which the direct scatter channel dominates. At incidence energies greater than 0.39 eV the direct scatter channel dominates over a wider range of scattering angle. At high Ei, the direct scattering channel can also be resolved from the trapping/desorption channel and from the incoming beam via ion time-of-flight (TOF) to the detector.30 The scattering products in the Ei = 0.48–1.2 eV range were thus monitored 3 mm from the surface, such that a wide range of scattering angles is probed. No significant variation of rotational distribution was found over the range of distances and angles probed in our experiment.
Fig. 1 The 1 + 1′ REMPI spectrum of the à ← (410) band of formaldehyde molecules, scattered from a Au(111) surface at Ts = 300 K, is shown as a function of incidence kinetic energy, Ei (red, upward directed peaks). Shown for comparison are the best-fit simulated spectra obtained using the a-axis Rainbow model (eqn (1)), which will be introduced in Section III B.2. The locations of prominent R-bandheads are labeled at the top of the figure. |
Fig. 2 compares the observed 1 + 1′ REMPI spectrum in this region—obtained from molecules scattered at an incidence kinetic energy of 1.21 eV—with the spectrum simulated from the best-fit Boltzmann temperature (Trot = 1082 K). Also shown at the bottom of Fig. 2 is a spectrum simulated using a different model for the population distribution, which we will introduce in Section III B2. The intensities obtained from the Boltzmann distribution are in very good agreement with experiment for the rR5 bandhead at 28393 cm−1 (integrated intensity agrees to within 3%). However, the relative intensity of the prominent rR7 bandhead at 28411 cm−1 and the rR9 origin at 28424 cm−1 are underestimated by the Boltzmann fit by a factor of 1.73 and 2.17, respectively. At higher Ka′′, the discrepancy becomes worse. The intense features in the observed spectrum at 28429–28435 cm−1—which arise primarily from the prominent rR11 progression, as well as from the origins of the rR12–14 progressions—are underestimated by the Boltzmann fit by an integrated factor of 3.4. We can be quite confident about the assignments in this region because the bandheads curve around to the red after Ka′′ = 13, so that this region is relatively sparse and can only contain lines from the rR10–15 progressions. In order to reproduce the experimentally observed relative intensities in this region, it is necessary to use a Boltzmann rotational temperature of >3000 K. However, the simulated band shape at this temperature exhibits wide overall disagreement with the rest of the observed spectrum. The enhanced intensity in the high-Ka′′ bandhead region (relative to that predicted for a Boltzmann distribution) is reproducible across a wide range of incidence kinetic energies and increases monotonically with Ei.
Fig. 2 The high-Ka′′ bandhead region of the REMPI spectrum of the à ← (410) band of formaldehyde molecules, directly scattered from a Au(111) surface at Ts = 300 K and Ei = 1.21 eV is shown (top spectrum, red, upward directed peaks). Shown for comparison are the best-fit simulated spectra obtained from a Boltzmann model (middle spectrum, green, downward directed peaks) and from the a-axis rainbow model (eqn (1)), which will be introduced in Section III B2. The rR5–15 branch transitions are labeled. |
The low-frequency tail of the band below 28200 cm−1, which contains intensity primarily from branches, is another relatively sparse region that permits a detailed line-by-line analysis of the relative intensities. In Fig. 3, the observed spectrum in this region obtained from a scattered beam (Ei = 1.21 eV) is compared with the simulated spectrum from the best-fit Boltzmann distribution. Again, a simulation from a second model, which we will introduce in Section III B2, is also included in the figure. The observed spectrum contains prominent progressions that can be assigned to the pP9 and pP11 branches, labeled in the figure. However, the Boltzmann fit moderately underestimates the contribution of pP9 lines—particularly at low J′′—and grossly underestimates the contribution of pP11. For example, the spectrum displays significantly more intensity than the Boltzmann fit at 28110.6 cm−1 where the pP9(9) line is predicted. The features observed at 28076.0 cm−1 and 28100.1 cm−1 are significantly blue-shifted (by 0.25 and 0.1 cm−1, respectively) in the Boltzmann simulation, which is consistent with missing intensity from the pP9(15) and pP9(11) lines. Finally, the relative intensity of the features assignable to pP11(11–16) is strikingly absent from the Boltzmann fit.
Fig. 3 A portion of the pP region of the REMPI spectrum of the à ← (410) band of formaldehyde molecules, directly scattered from a Au(111) surface at Ts = 300 K and Ei = 1.21 eV is shown (top spectrum, red, upward directed peaks). Shown for comparison are the best-fit simulated spectra obtained from a Boltzmann model (middle spectrum, green, downward directed peaks) and from the a-axis rainbow model (eqn (1)), which will be introduced in Section III B2. Selected branches and transitions are labeled. |
There are other features that appear with high relative intensity in the Boltzmann fit, but are not observed in the spectrum. Among the most prominent of these features are the lines arising from pP1(32–38), which are labeled in Fig. 3. The intensity of the features that contain contributions from pP1(33–35) at 28082.1, 28092.6, and 28102.8 cm−1 are notably stronger in the Boltzmann fit than in the observed spectrum. Also, the Boltzmann fit predicts intensity at 28049.7 cm−1 and 28101.3 cm−1 that arises from the pP1(38) and p,pP3,30(33) lines, respectively, whereas there is almost no intensity in the observed spectrum at these frequencies.
The analysis presented in Section III B1 suggests that the rotational population distribution in the scattered molecular beam deviates from a thermal distribution in a way that favors “twirling” motion with Ka in the range 7–13, over “tumbling/cartwheeling” motion with the same amount of energy. Deviations from a Boltzmann rotational distribution appear quite commonly in experiments on direct scattering of diatomic molecules from surfaces.2,9,17 Such effects are orientation dependent12–16,35 and can often be interpreted in terms of a “rotational rainbow” effect, in which dependence of the potential energy surface on molecular orientation gives rise to one or more singularities in the classical distribution of angular momentum in the scattering product.
In diatomic molecule experiments, the observed rotational rainbow population distribution often resembles a Boltzmann distribution with an added Gaussian term, centered at the rainbow energy.18,36 In formaldehyde, there are three distinct projections of the angular momentum onto the molecular body frame and the problem is more complicated. Based on the results of our analysis in Section III B1, we attempt a model that partitions the rotational energy into two parts: Ea (a-axis rotational energy) and Ebc (combined b- and c-axis rotational energy). We add a Gaussian contribution to the a-axis distribution function to obtain
Pi = Ngie−Ebc,i/kTbc(e−Ea,i/kTa + Se−(E0−Ea,i)2/σa2). | (1) |
Ea = AKa2 |
Ebc = Erot − AKa2, |
The spectrum was recorded several times at each Ei shown in Fig. 1, and each spectrum was fit individually to eqn (1). The average and standard deviation of the fit parameters obtained at each Ei are shown in Fig. 4(A–C) and are tabulated in Table SIII of the ESI.† Also shown in Fig. 4(D) is the percent improvement in the root mean square error (RMSE) that is obtained from the fit to eqn (1), relative to the RMSE obtained from a fit to a Boltzmann distribution. Shown in Fig. 4(E) is the expectation value of rotational energy, 〈Erot〉, obtained from the model at each incidence kinetic energy as well as the individual contributions, 〈Ea〉, and 〈Ebc〉. The best-fit spectrum obtained at each incidence energy is compared with the observed spectrum in Fig. 1, and the result obtained at Ei = 1.21 eV is included in Fig. 2 and 3.
Fig. 4 The best-fit parameters obtained by fitting the spectra of scattered molecules to eqn (1), with the constraints Tbc = Ta = T and σa = 850 cm−1, are shown as a function of incidence kinetic energy, Ei, in panels (A), (B) and (C). Panel (D) shows the average percent improvement, Ri, in the root mean square error of the fit, Rfit, relative to the RMSE obtained from a fit to a Boltzmann temperature, Rb. Ri = (1 − Rb/Rfit) × 100%. Panel (E) shows the expectation value, obtained from the fit model, for total rotational excitation, and for the components Ea and Ebc. |
Several trends are evident in the fit results. As Ei is increased, there is a slight trend towards higher T parameter (Fig. 4(A)), consistent with a general increase in both 〈Ea〉 and 〈Ebc〉. The average rotational energy obtained from the model for the scattered beam increases approximately linearly over the range Ei = 0.33–0.8 eV with a slope of 〈Erot〉 ≈ 0.24Ei, and appears to exhibit some degree of saturation above Ei = 0.8 eV (Fig. 4(E)). In addition, the a-axis rainbow model reveals an increasing propensity for energy to be channeled into a-axis rotation as Ei is increased. This trend is evident from the increasing ratio between 〈Ea〉 and 〈Ebc〉 (Fig. 4(E)) and leads to a linearly increasing trend in the best-fit amplitude, S, of the non-thermal Gaussian term, which has a near-zero intercept at Ei = 0 (Fig. 4(B)). The fitted values for E0 (Fig. 4(C)) indicate that the maximum in the non-thermal Gaussian contribution to the population distribution shifts from Ka ≈ 7 at Ei = 0.4 eV to Ka ≈ 10 at Ei = 1.2 eV.
A consequence of the increasing importance of the non-thermal contribution to the population distribution is that the failure of the Boltzmann model to reproduce the observed spectrum increases strikingly as Ei is increased. At low incidence kinetic energy (Ei < 0.4 eV), the observed spectrum is well reproduced by the Boltzmann fit, and the improvement of the fit error that is obtained by including the non-thermal Gaussian component of eqn (1) is negligible (Fig. 4(D)). However, at higher Ei, the Boltzmann fit fails to reproduce the spectral intensities (as shown in Fig. 2 and 3) and the improvement in the overall RMSE obtained by including the Gaussian term reaches almost 20% at Ei = 1.2 eV.
From a comparison of the observed spectra in Fig. 2 and 3 to the Boltzmann fit and the a-axis rainbow model fit, it is clear that the a-axis rainbow model provides significantly better agreement with experiment. The integrated intensities in the rR5, rR7, and rR9 bandheads obtained from the rainbow model all agree with experiment to within 16%, and the integrated intensity over the origins of the rR11–14 progressions (28429–28435 cm−1) agrees with experiment to within 4% (Fig. 2). The a-axis rainbow fit also correctly reproduces the observed relative intensities in the pP11(11–16) lines between 28000 and 28060, and includes features from the pP9 branch such as the intensity due to pP9(9) at 28110.6 cm−1 (Fig. 3). Unlike the Boltzmann fit, the a-axis rainbow fit does not place too much intensity in the pP1(33–38) lines or in the p,pP3,30(33) line (discussed in Section III B1). Furthermore, the a-axis rainbow fit correctly reproduces (to within 0.05 cm−1) the center frequencies of the observed features at 28076.0 cm−1 and 28100.1 cm−1, which are shifted relative to the Boltzmann fit due to contributions from pP9(15) and pP9(11).
In Fig. 5, the sum of the population in each Ka manifold (divided by the gns nuclear spin degeneracy) obtained from the fit to the a-axis rainbow model is plotted versus Ea = AKa2 as a function of Ei. At the lowest incidence energy, the population decreases approximately exponentially with Ea, as expected in a thermal distribution. As Ei is increased, a strong shoulder grows in at ∼0.12 eV, due to the increasing importance of the Gaussian term in eqn (1). The population in Ka = 0 is a factor of two below the trend because this manifold lacks the two-fold k = ±|Ka| degeneracy (i.e. there are no asymmetry doublets).
The trajectories were calculated at normal incidence angle and random incidence orientation, over a range of incidence kinetic energies (Ei = 0.33–1.2 eV). The surface was initially at rest and the molecule was initially at a distance of z0 = 10 Å from the surface with zero incident angular momentum. We integrated 10k trajectories for 2.4 ps at each Ei. For the L-J potential, any trajectory in which the molecule remained within 8 Å of the surface after 2.4 ps was labeled a “trapping” trajectory and was discarded. At Ei = 0.33 eV, 28% of trajectories were discarded on this basis. The proportion of “trapping” trajectories drops to 15% at Ei = 0.47 eV and to 2.1% at Ei = 1.2 eV. This trend moderately underestimates the observed trapping probability,30 which drops from 57% at Ei = 0.32 eV to 25% at Ei = 0.58 eV.
After exiting the surface potential, the rotational motion of the directly scattered asymmetric top molecules propagates according to Newton's equations of torque-free motion:
(2a) |
(2b) |
(2c) |
Fig. 6 shows the final average rotational energy about each internal axis of rotation, calculated from the two potentials as a function of Ei. The calculated values may be compared directly with the values from the experimental fits, shown in Fig. 4(E). Although the calculations overestimate the overall amount of rotational excitation, relative to the experimental fit, by a factor of ∼2, they nevertheless reproduce key qualitative features of the experimental observation. Most notably, regardless of whether an attractive potential is used, the calculation predicts that 〈Ea〉 excitation is greater than 〈Eb〉 or 〈Ec〉 excitation by an average factor of 2 〈Ea〉/(〈Eb〉 + 〈Ec〉) = 1.6 (L-J) or 1.3 (hs), compared to an experimental value of 1.5. When the purely repulsive hard sphere potential is used, rotational excitation increases linearly with Ei, but when the Lennard-Jones potential is used, the calculation also qualitatively reproduces the experimental observation that 〈Ea〉 exhibits some degree of saturation at higher Ei. These results suggest that the propensity to excite a-axis rotation is a simple consequence of the three-dimensional repulsive van der Waals shape of the formaldehyde molecule, whereas the saturation effect may be a signature of dynamical steering due to the orientation dependence of the attractive potential.
The top half of Fig. 7 shows the distribution of rotational energy about the internal axes of rotation calculated using the L-J potential with Ei = 1.2 eV. The Eb and Ec distributions can be approximated by an exponential decay. On the other hand, the Ea distribution exhibits a distinct non-exponential component, which gives rise to a broad feature between 0.15–0.4 eV. The calculated rotational distributions are in qualitative agreement with the distributions obtained from our fit model. Namely, the Eb and Ec distributions resemble an exponential Boltzmann population distribution whereas the Ea distribution resembles an exponential decay plus an added Gaussian component (see Fig. 5).
The classical trajectory calculation is not in complete quantitative agreement with the experimental fit model. The calculation overestimates the average overall rotational excitation, and the calculated non-Boltzmann hump in the Ea distribution is broader and extends to higher energy than that of the fit model. The trajectory calculation places the center of the hump at 0.30 eV whereas the fit model places the center at 0.12 eV. However, since the trajectory calculation uses only a crude empirical potential energy surface, it is unlikely to capture the orientation dependence of the potential accurately and complete quantitative agreement cannot be expected. Theoretical investigations involving a more sophisticated ab initio potential energy surface are merited, but are beyond the scope of the current work. Nevertheless, since the classical trajectories reproduce key qualitative features of the experiment, they provide clues as to the likely origin of these features.
The bottom half of Fig. 7 shows the components, Ea and (Eb + Ec)/2, of rotational energy, calculated as a function of the incident Euler angles, θi and ψi. In our chosen coordinate system, θi represents the polar angle between the molecular CO-bond symmetry axis and the surface normal, and ψi represents the angle between the surface normal and its orthogonal projection onto the CH2 plane. See cartoons in Fig. 7 for clarification. Normal angle scattering of a C2v molecule from a flat, structureless surface is totally symmetric in the molecule-fixed axis frame with respect to the third Euler angle, ϕ, which is omitted from the figure. The b- and c-axis projections of the rotational energy are maximally excited at incidence orientations where the CO axis is nearly (but not exactly) along the surface normal (θi ≈ 0 or π), and are minimally excited when the incident CO axis orientation is “flat-on” (θi ≈ π/2). At incidence angles near θi ≈ 0 (CH2 group oriented toward the surface), the prevalence of “multi-bounce” collisions, where the two hydrogen atoms strike the surface in rapid succession, give rise to complicated structure in all three components of Erot. Apart from a relatively narrow region near θi = π, the plot of (Eb + Ec)/2 versus incident orientation does not reveal any widespread regions over which the function exhibits a smooth maximum.
In contrast, Ea exhibits broad regions of incidence orientation space over which it is excited to approximately the same value. Most strikingly, when π/20 < ψi < π/4 or 3π/4 < ψi < 19π/20, excitation to Ea ≈ 0.3 eV is highly likely, regardless of the value of θi. The explanation is simple. A large degree of a-axis excitation results whenever one of the hydrogens strikes the surface at a skew angle of ψi, regardless of the polar angle θi between the CO axis and the surface normal. This occurs even at incident orientations in which the CH2 group is initially pointed away from the surface (θi < 0) due to “double-bounce” collisions in which the O and CH2 moieties strike the surface in rapid succession. Since this behavior arises over a wide swath of orientation space, excitation probability accumulates at Ea ≈ 0.3 eV over many trajectories and gives rise to the distinctly non-Boltzmann propensity for high Ka excitation which is observed. This explanation allows us to interpret the effect in terms of a sterically induced rotational rainbow scattering phenomenon. Because there is a wide region of orientation space over which the Jacobian ∂Ea/∂(ψi,θi) is approximately zero (and a long curve over which ∂Ea/∂ψi is rigorously zero), the classical probability distribution for Ea as a function of ψi contains singularities for excitation to the local extrema in Ea.
Another possible source of intensity error in our measurement arises from the fact that we have not performed exhaustive rotationally-resolved measurement of the speed distribution of scattered molecules. Therefore, our population estimates are based on scattered beam density measurements that have not been converted to flux, and are only valid in the limit Δv/〈v〉 ≪ 1 (i.e. when the velocity spread is small compared with the mean velocity.) Experimental limitations make it difficult to perform precise rotationally resolved time-of-flight measurements. However, we have made coarse speed measurements for a representative sample of rotational states differing in Erot and Ka. The results, which are detailed in Section SV of the ESI,† provide an upper limit for Δv/〈v〉 < 10% for the rotational state dependence of the average scattered velocity at Ei = 1.21 eV, which is far too small to account for deviation of the observed intensities from a Boltzmann model.
We have also investigated the effect of laser polarization, and we find no difference in relative intensities when the dye laser polarization is rotated from horizontal to vertical polarization. Orientation of the angular momentum due to the surface is likely scrambled due to nuclear hyperfine dephasing before the scattered molecules reach the detection region.
Fig. 8 In the top panel, the estimated trapping probability of formaldehyde on Au(111)30 is plotted as a function of incidence kinetic energy. Measured trapping probabilities from three other weakly bound molecular scattering systems with similar molecular and surface atom masses are shown for comparison. Data for ethane on Pt(111) (0.33 eV binding energy) is taken from ref. 46; NO on Au(111) (0.24 eV binding energy) is from ref. 47; and CO on Au(111) (0.18 eV binding energy48) is from ref. 49. The bottom panel shows the normalized rotational energy distribution that results from direct scatter of formaldehyde at Ei = 0.47 eV. Shown for comparison are the distribution that is obtained when the S parameter, describing the contribution of the a-axis rotational rainbow, is set to zero. Also shown is the distribution that is obtained from the direct scatter of NO from Au(111) at Ei = 0.63 eV, reported in ref. 45. The tails of the distribution with Erot ≥ 0.31 eV are shaded. This is the portion of the distribution with sufficient rotational excitation to give rise to rotationally mediated trapping, according to a simple model (see text). |
In classical trajectory simulations of ethane trapping on Pt(111) reported in ref. 4, the excitation of molecular rotation was found to play a decisive role in the trapping probability, especially for the highest normal incidence kinetic energy investigated (0.4 eV). In trajectories where the first bounce led to sufficient excitation of molecular rotation, the molecule became temporarily “rotationally trapped” in the surface potential. The average energy transferred to phonons during the first bounce was the similar in the “rotational trapping” and “single-bounce scattering” channels. In >90% of “rotationally trapped” trajectories, the initially stored rotational energy was dissipated to surface degrees of freedom during subsequent bounces, leading eventually to a relaxed trapping configuration. Thus, the degree of rotational excitation that occurred during the first bounce determined the eventual fate of the molecule (trapping or direct scattering) to within 10% uncertainty. In ref. 30, it was remarked that a similar mechanism might explain the trapping of formaldehyde on Au(111) at Ei = 0.58 eV.
We examine the feasibility of the “rotational trapping” mechanism by analysis of our experimentally measured rotational distribution. Assuming that the average phonon excitation during the first bounce is determined by a hard sphere collision model involving a single gold atom, a 30 amu formaldehyde molecule will lose 46% of its incident energy to phonon excitation.30 At Ei = 0.58 eV, an additional 0.31 eV of kinetic energy must therefore, on average, be dissipated in order for trapping to occur. If we make the (admittedly naive) assumption that there is no correlation between energy transfer to phonons and to molecular rotation, then the trapping probability that will result from rotational excitation mechanisms will be given approximately by the fraction of molecules with ≥0.31 eV of rotational excitation. In our fitted rotational distribution, shown in the bottom panel of Fig. 8, 9.8% of directly scattered formaldehyde molecules at Ei = 0.47 eV are excited to this energy. This is less than the observed trapping probability of 25% (at Ei = 0.58 eV), but is obtained at a slightly lower value of Ei and represents only the rotational energy distribution in the direct scatter channel (i.e., in molecules that do not trap). The semi-quantitative agreement is therefore a strong argument that rotation plays a major role in the trapping mechanism. On the other hand, in the ground state rotational distribution of NO molecules scattered from Au(111) at Ei = 0.60 eV (shown for comparison in Fig. 8) only 1.1% of molecules are excited to Erot ≥ 0.31 eV.45 This is consistent with the observation that the trapping probability in the NO on Au(111) system is an order of magnitude less than that of formaldehyde. Finally, we note that without the a-axis rainbow (i.e., with the S parameter of eqn (1) set to zero) the fraction of directly scattered formaldehyde molecules with ≥0.31 eV of rotational excitation is only 3.1% at Ei = 0.47 eV. (This distribution is also shown for comparison in Fig. 8) This underscores the importance of a-axis rotation to the high-energy tail of the rotational distribution and points to the likely contribution of this additional degree of rotational freedom (not present in diatomic molecules) to trapping at higher incidence kinetic energies.
Footnote |
† Electronic supplementary information (ESI) available: Backing gas mixtures, method for fitting the spectra, rotational distributions from the trapping-desorption channel, tabulation of parameters for the direct scatter rotational distributions, and rotational state dependence of the scattered beam velocity. See DOI: 10.1039/c7cp03922k |
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