Imaging covalent bond formation by H atom scattering from graphene

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Science  26 Apr 2019:
Vol. 364, Issue 6438, pp. 379-382
DOI: 10.1126/science.aaw6378

Atom scattering reveals bond formation

When molecules collide, they can form an addition complex in which new chemical bonds can form. However, if energy does not flow out of this complex and into the rest of the molecule, the new bond will usually simply dissociate. Jiang et al. observed the scattering of hydrogen atoms from graphene and interpreted their results with a first-principles potential energy surface and a dynamical simulation (see the Perspective by Hornekaer). At near-normal incidence, these experiments probe transient carbon-hydrogen bond formation when the hydrogen atoms collide with the centers of the six-atom carbon rings. Rapid intramolecular vibrational relaxation results from orbital rehybridization and structural deformations that occur during bond formation.

Science, this issue p. 379; see also p. 331


Viewing the atomic-scale motion and energy dissipation pathways involved in forming a covalent bond is a longstanding challenge for chemistry. We performed scattering experiments of H atoms from graphene and observed a bimodal translational energy loss distribution. Using accurate first-principles dynamics simulations, we show that the quasi-elastic channel involves scattering through the physisorption well where collision sites are near the centers of the six-membered C-rings. The second channel results from transient C–H bond formation, where H atoms lose 1 to 2 electron volts of energy within a 10-femtosecond interaction time. This remarkably rapid form of intramolecular vibrational relaxation results from the C atom’s rehybridization during bond formation and is responsible for an unexpectedly high sticking probability of H on graphene.

When a free-radical collides with an unsaturated molecule, electronic rehybridization may lead to formation of an addition complex with a great deal of energy initially localized in the newly formed chemical bond. The addition complex is intrinsically unstable and may redissociate; however, energy flow from the reactive site to the rest of the molecule can delay this, allowing for isomerization, dissociation of other bonds, or stabilizing collisions. Naturally, there has been great interest to observe such energy flow in an addition complex, called intramolecular vibrational redistribution (IVR). In the classic work of Rabinovitch and Rynbrandt, IVR within an addition complex was indirectly detected in the following reaction (1).

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After 1CD2 addition, energy is initially localized in only a part of the molecule (indicated with an asterisk). Before IVR is complete, one expects dissociation to produce excess (I), otherwise similar amounts of (I) and (II) would form. By varying the pressure of an inert buffer gas and observing the branching between (I) and (II), the rate of energy flow could be determined. At the highest buffer gas pressures used, CF2 elimination occurred faster than ~1 ps after formation of the addition complex. (At longer times, the buffer gas quenched the energetic addition complex.) Under these conditions, excess (I) resulted. When longer times for reaction were allowed at lower buffer gas pressures, equal amounts of (I) and (II) were formed. This work remains some of the strongest evidence that IVR proceeds in an addition complex within a few picoseconds (1).

Since then, IVR experiments with ultrafast pump-probe spectroscopy proliferated, in which short laser pulses were used to excite specific vibrational motions in stable molecules and probe the rate of energy flow to other degrees of freedom (2). High-resolution spectroscopy also helped identify the pathways of energy flow out of initially highly excited C–H stretching motion (3). This large body of work (4, 5) confirmed that IVR proceeds on a picosecond time scale through a hierarchy of intramolecular processes involving gateway states (6) and bottlenecks (7). Unfortunately, these spectroscopy experiments cannot tell us about the bond formation process necessary to produce the addition complex.

Scattering experiments can directly probe collision complexes (8) and even reaction resonances whose lifetimes are only a few femtoseconds (9, 10). In these studies, researchers produce a beam of the incident free radicals with well-defined speed and direction. The speed and angular distributions produced by the scattering are then analyzed with first principles simulations. Scattering experiments and molecular dynamics simulations have also been used to develop an atomic-level understanding of energy transfer, accommodation, and reactions during collisions between gases and model organic surfaces (11). Scattering free radicals from surfaces allows collision alignment and removes the influence of impact angular momentum, further improving the fruitful interplay between experiment and theory (12, 13). To date, however, scattering studies have never directly probed the direct interplay between chemical bond formation and vibrational energy relaxation dynamics.

H atom chemisorption to graphene is relevant to hydrogen storage (14), the catalytic production of molecular hydrogen in the interstellar medium (15), and two-dimensional (2D) semiconductor materials because hydrogenation of graphene can induce a bandgap (16). For the purposes of this study, H adsorption to graphene exhibits the most important features associated with formation of an addition complex—namely, rehybridization during bond formation.

Shown in Fig. 1 is a 2D cut through a high-dimensional potential energy surface (PES) developed in this work. Here, embedded mean-field theory (EMFT) electronic structure data (1719) is fitted with a reactive empirical bond order (REBO) function (20). Details of the PES are provided in the supplementary materials. H approach to graphene leads to chemical bond formation coincident with sp2 to sp3 rehybridization of a C atom. This is reflected in the binding well being displaced along the CZ coordinate. The structural distortion induced by the electronic rehybridization gives rise to a barrier; if the H cannot overcome this barrier, the H atom will be reflected (Fig. 1, blue trajectory) without inducing rehybridization. Alternatively, it may pass over the barrier, induce rehybridization, and become trapped (Fig. 1, gold trajectory) or scatter back to the gas phase (Fig. 1, black trajectory).

Fig. 1 Rehybridization in the formation of a C–H bond in collisions of an H atom at a graphene surface.

HZ and CZ are the distances of the H and C atoms from the graphene plane. Three trajectories are shown for H atoms with 1.92 eV incidence energy.

Here, we report H atom scattering experiments with graphene surfaces near zero coverage, which removes well-known ambiguities (21) associated with the energy and coverage dependence of C–H bond formation (22). H atom scattering distributions resolve themselves into a quasi-elastic and a strongly inelastic channel, determined by whether the barrier to chemical bond formation is overcome. The observed inelastic energy transfer distributions contain information about the rate of energy flow out of the newly formed C–H bond. By comparing with molecular dynamics simulations carried out with a full-dimensional PES fit to electronic structure data from an accurate quantum embedding theory (17), we reveal an energy loss mechanism able to remove electron volts of energy from the H atom within the ~10 fs of a single-bounce collision. This surprisingly efficient energy flow out of a newly formed chemical bond leads to unexpectedly high sticking probabilities of H on graphene. We show that it is a result of electronic rehybridization typical of bond formation leading to a covalently bound addition complex.

Experimental scattering distributions, P(ES; ϑS), are shown in Fig. 2, A to C, for collisions of H with graphene grown on a Pt(111) substrate. The incidence energy was 1.92 eV. Pt was chosen because it interacts weakly with graphene (23). Two scattering channels appear with narrow angular distributions peaking close to the specular angle typical of direct “single-bounce” scattering. The quasi-elastic (ES/EI ~ 1) “fast” channel dominates for large incidence angles, ϑI, and gives way to a highly inelastic (ES/EI ~ 0.5) “slow” channel at small ϑI. First principles simulations (Fig. 2, D to F) agree well with experiment, and by analyzing trajectories (Fig. 2G) we found that the slow channel results from trajectories forming a transient C–H bond, whereas the fast channel arises from trajectories that failed to pass over the barrier to bond formation. As ϑI decreases, H atoms more easily cross the barrier, causing the slow channel to grow in importance. This is further evidence for formation of a transient C–H bond that is most favorably oriented at 90° to the graphene plane and therefore formed efficiently with normal kinetic energy. The total scattering signal drops in both experiment and simulation as ϑI decreases. This is partly a result of enhanced scattering out of the plane of detection in the slow channel (supplementary materials, materials and methods S3, and fig. S7). It is also due to enhanced H atom sticking to the graphene surface.

Fig. 2

Bimodal scattering distributions arising from H collisions with graphene. (A to C) Measured H atom scattering energy, ES, and angular, ϑS, distributions with EI = 1.92 eV. Results for three incidence angles, ϑI, are shown. Thus, the normal component of incidence energy, En, varies from 0.5 to 1.4 eV. ϑS = 0 indicates the surface normal direction. Red ticks indicate the specular scattering angles. All observed scattering occurs within 2.8° of the plane defined by incident H atom beam and the surface normal. (D to F) Corresponding simulated scattering distributions, each shifted by ~10° in incidence angles. This shift is discussed in the supplementary materials, materials and methods S5. Each distribution is multiplied by the indicated red number to use the same color bar. Each image represents 1 million trajectories. (G) Analysis of theoretically calculated trajectories for EI = 1.92 eV and ϑI = 35°. Single-bounce trajectories are shown as red and black. Those in black do not cross the barrier to chemical bond formation. A small number of multibounce collisions (blue) are also seen. The simulations include a modeled treatment of the graphene interactions with Pt (supplementary materials, materials and methods S2).

The experimentally derived sticking probabilities, which increase with the normal component of incidence energy, are shown in Fig. 3. We lowered EI to 0.99 eV, where sticking is the fate of all H atoms that cross the barrier to C–H bond formation (supplementary materials, materials and methods S4, and figs. S10 and S11). Under these conditions, only the quasi-elastic channel remains, for which out-of-detection-plane scattering is more easily accounted for, and measured survival probabilities lead directly to reliable sticking probabilities. Theoretical simulations of sticking (Fig. 3, black symbols) are in excellent agreement with experiment; both show efficient sticking even at high incidence energies and an adsorption threshold at En ~ 0.4 eV reflecting the influence of the barrier to chemisorption.

Fig. 3 H atom sticking probabilities at graphene.

Experimentally derived (blue) and theoretically predicted (black) sticking probabilities for EI = 0.99 eV plotted against the normal component of the incidence energy (En). Theoretically predicted sticking probabilities for EI = 1.92 eV are shown in red. Theoretical simulations used a full dimensional EMFT-REBO PES that includes the influence of the Pt substrate with classical molecular dynamics (solid symbols) or ring polymer molecular dynamics (open symbols).

There have been many theoretical predictions of the height of the barrier to C–H bond formation on graphene (24, 25); up to now, no experimental validation has been possible. The fact that our dynamical simulations agree well with experimental sticking probabilities argues that the EMFT-REBO PES used here is accurate. The minimum energy path for C–H bond formation is shown in fig. S2, comparing the EMFT-REBO PES with several other calculations all for free standing graphene. Both the chemisorption well depth and the barrier height found on the EMFT-REBO PES compare well with values found with CCSD(T) (coupled-cluster with single and double and perturbative triple excitations) calculations of H addition to coronene (24).

The small deviations between experiment and simulation seen in Fig. 3 could be due to remaining errors in the PES; deficiencies in our treatment of the influence of Pt, which, for example, does not properly treat C–Pt bond formation; or the classical approximation for the nuclear motion. Ring polymer molecular dynamics (Fig. 3, open symbols) (26, 27) suggest that the net effect of nuclear quantum effects are modest under the conditions studied here, which is in agreement with previous analysis (28). We also show calculated sticking probability curves with and without the influence of the Pt substrate in fig. S6, suggesting also that the influence of Pt is small.

We present in Fig. 4 an analysis of trajectories to better understand the H atom translational energy loss and sticking mechanisms. Inelastic scattering is dominated by ultrashort single-bounce events (Fig. 4A). The distribution of times spent within the chemisorption well for the red and blue trajectories of Fig. 1G peaks at only ~10 fs; double-bounce collisions can also be seen clustered near 22 fs. Despite this, the H atom energy loss is large. Additional insight is provided with Fig. 4B, where the curves are averages over the subset of (60) trajectories for which the H atom collides on top of a C atom. The kinetic energy that is lost from the incoming H atom appears as increased kinetic and potential energy for graphene within 10 to 20 fs of the initial collision; the kinetic energy of that C atom directly involved in the collision hardly changes.

Fig. 4 The dynamical mechanism of energy transfer.

(A) The collision time correlation with H atom energy loss for trajectories that cross the barrier. The collision time is defined as the time spent with a C–H bond distance less than 1.4 Å. (B, C, and D) An average over 60 trajectories that collide on top of a C and pass over the barrier. A collision is labeled “on top” if at the point of closest approach, one C–H distance is smaller than 1.15 Å and three and only three C–H distances are between 1.6 and 2 Å. t = 0 is taken as the time of the H atom’s closest approach. The incidence conditions are identical to those of Fig. 2G. The yellow curve in (B) shows the H distance to surface, HZ; single-bounce collisions dominate. Also shown are the kinetic energy change of H atom (ΔKH, blue), the kinetic energy change of all C atoms (ΔKslab, purple), the kinetic energy of the C atom hit by the H atom (ΔKC, green), and the graphene deformation energy (ΔUdeform, gold). (C) and (D) show the kinetic energy appearing in different C shells. (E) The shell structure.

Instead, the neighbors of this C atom absorb the energy released by transient C–H bond formation. The graphene structure is shown in Fig. 4E and is defined in terms of shells. The 0th shell is the C atom struck by the H atom, and the first shell reflects the three nearest neighbors. Atoms in the first shell pick up kinetic energy first (Fig. 4, C and D). The creation of an electronically hybridized sp3 C center during transient C–H bond formation exerts strong in-plane forces between the 0th - and first-shell C atoms. Subsequent to in-plane excitation of first-shell atoms, the H atom induces the 0th-shell C atom to pucker out of the plane, only fully experiencing the attractions of a sp3-hybridized C–H bond once the puckering has occurred and as the H atom is leaving. The supplementary materials include an animation that shows the interaction energy throughout a typical trajectory, revealing that a bonding well is formed only at times > 0, where the H atom is recoiling back from the repulsive wall (movie S1). After departure of the H atom, the deposited energy flows outward from the region of impact at close to the in-plane speed of sound of graphene (supplementary materials, materials and methods S6, and fig. S16) (29).

The large inelasticity seen in the slow channel is peculiar to a network of covalently bound atoms, where C–H bond formation induces forces between multiple C atoms through a disruption of the delocalized covalent bonding network. This contrasts starkly with the interactions in the fast, quasi-elastic channel (supplementary materials, materials and methods S7). Here, the H atom interacts with graphene through van der Waals forces, which do not disturb the bonding between C atoms of the graphene. The most probable collision site giving rise to this kind of scattering is near the center of the six-membered C-ring, where chemical bond formation is least likely (fig. S18). Hence, the inelasticity in the fast channel follows the predictions of the hard cube model, in which the cube has the mass of 5 to 6 C atoms (fig. S17).

Next, we used our experimentally validated theoretical model to predict sticking under conditions in which sticking is difficult to measure. Theoretical simulations at EI = 1.92 eV show large sticking probabilities (Fig. 3, red symbols). Trapping is efficient, even for H atoms more than 2.5 eV above the potential energy minimum, more than three times the binding well depth. Both the experimental and simulated results presented in Fig. 3 contradict previous theoretical studies, which predicted much smaller sticking probabilities (supplementary materials, materials and methods S9, and fig. S19) (28, 3033). This contradiction reflects deficiencies in previous models arising from reduced dimensionality approximations as well as errors in the electronic energies produced by density functional theory at the generalized gradient approximation level. We conclude that because of the higher accuracy of the electronic energies made possible by the EMFT method and the ability to overcome reduced dimensionality approximations by use of a fitted REBO PES, the results presented here are the best present knowledge of the sticking probability of H on graphene grown on Pt.

This work also provides insights into the fundamental steps of IVR in a newly formed addition complex. For this analysis, we have also simulated IVR from a highly excited C–H bond to the graphene substrate, for an initially puckered sp3 hydrogenated graphene structure (supplementary materials, materials and methods S9). These calculations show that when all energy is initially placed in H kinetic or potential energy, relaxation takes place on two time scales, with quasi-exponential lifetimes of 0.5 and 3 to 4 ps, respectively. A vibrational relaxation time of 5 ps was previously reported for H on graphene (34, 35). These processes reflect the coupling between different vibrational degrees of freedom typical of an anharmonic interaction potential, and the time scales seen here are similar to previous reports about IVR on stable molecules. A particularly surprising aspect of this study is the discovery of a much faster energy loss mechanism requiring only 10 to 20 fs to remove 1 to 2 eV of energy from the newly formed C–H bond. This process proceeds on the time scale of the C network deformation induced by sp2-sp3 rehybridization. There is every reason to believe that this “rehybridization IVR” plays an important role in the recombination of many covalently bound free radicals forming addition complexes. In particular, we expect rehybridization IVR to be a strong effect when the structural reorganization associated with complex formation is large—implying the participation of many covalently bound atoms—and when the frequencies associated with the distortion are high, making the time scale of energy uptake short. In analogy to its important role in determining the sticking probability of H to graphene, rehybridization IVR is likely to be a determining factor in calculating the collisional formation probability for addition complexes.

Supplementary Materials

Materials and Methods

Figs. S1 to S20

Tables S1 and S2

References (3665)

Movie S1

References and Notes

Acknowledgments: We thank D. Auerbach and D. Schwarzer for helpful discussions. Funding: H.J., O.B., and A.M.W. acknowledge support the from the SFB1073 under project A04, from the Deutsche Forschungsgemeinschaft (DFG) and financial support from the Ministerium für Wissenschaft und Kultur (MWK) Niedersachsen, and the Volkswagenstiftung under grant INST 186/902-1 to build the experimental apparatus. A.M.W., M.K., and A.K. also acknowledge the Max Planck Society for the Advancement of Science. F.D. and T.F.M. acknowledge that this material is based on work performed by the Joint Center for Artificial Photosynthesis, a U.S. Department of Energy (DOE) Energy Innovation Hub, supported through the Office of Science of the DOE under award DE-SC0004993. T.F.M. and F.R.M. acknowledge joint support from the DOE (award DE-SC0019390). F.R.M. is grateful to the Engineering and Physical Sciences Research Council for funding (EP/M013111/1). Author contributions: H.J. carried out experiments, analyzed experimental data and contributed to the manuscript. M.K. participated in the MD and RPMD code development, fit the EMFT data to a REBO potential, carried out molecular dynamics calculations, and contributed to the manuscript. Y.D. assisted with experiments. F.D. contributed to the EMFT code, carried out the EMFT calculations, and contributed to the manuscript. F.R.M. contributed to the EMFT code. A.K. directed the molecular dynamics work, developed the MD code, and contributed to the manuscript. A.M.W. conceived the experiment and wrote the paper. T.F.M. directed the electronic structure work, contributed to the EMFT code, and contributed to the manuscript. O.B. built and commissioned the Rydberg tagging apparatus, conceived and supervised experimentation, and contributed to the manuscript. Competing interests: None declared. Data and materials availability: The PES is archived at There are no restrictions on materials used in this work. All data needed to evaluate the conclusions in the paper are present in the paper or the supplementary materials.
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