Collision geometry is central to reaction dynamics. An important variable in collision geometry is the miss-distance between molecules, known as the “impact parameter.” This is averaged in gas-phase molecular beam studies. By aligning molecules on a surface prior to electron-induced dissociation, we select impact parameters in subsequent inelastic collisions. Surface-collimated “projectile” molecules, difluorocarbene (CF 2 ), were aimed at stationary “target” molecules characterized by scanning tunneling microscopy (STM), with the observed scattering interpreted by computational molecular dynamics. Selection of impact parameters showed that head-on collisions favored bimolecular reaction, whereas glancing collisions led only to momentum transfer. These collimated projectiles could be aimed at the wide variety of adsorbed targets identifiable by STM, with the selected impact parameter assisting in the identification of the collision geometry required for reaction.

Here, the accelerated reagent projectile, difluorocarbene (CF 2 ), comes from electron-induced dissociation of chemisorbed trifluoromethyl (CF 3 ) on Cu(110) at 4.6 K. Crucially, CF 2 retains excess energy while being collimated at the surface by successive bonding to the atoms of the underlying copper row. This recoiling “hot” CF 2 can then collide at selected impact parameters with a cold chemisorbed target CF 2 or I atom, whose position and geometry have been established by scanning tunneling microscopy (STM). Our findings are that for a zero impact parameter and sufficient collision energy the bimolecular reaction CF 2 + CF 2 = C 2 F 4 occurs, whereas for greater impact parameters, the collision geometry precludes reaction.

Valuable information concerning this parameter has previously been obtained, a posteriori, from measurement of the magnitude and planarity of the rotational motion in gaseous reaction products ( 6 ). Impact parameter has been restricted in reactive events by photoinduced or electron-induced reaction within van der Waals complexes ( 7 ) or in surface-aligned reaction (SAR) ( 8 – 16 ) and time-resolved SAR ( 9 , 17 ). In these cases, the impact parameter is set by the relative alignment of the adjacent molecules, constituting the donor and acceptor of a recoiling radical that stems from bond breaking in the donor molecule. However, retention of collision energy and direction in this recoiling radical requires that the donor molecule be placed in close proximity to the acceptor, precluding variation in impact parameter. The ability to vary the impact parameter has awaited the development of a means to accelerate an adsorbed reagent over long distances in a selected direction, but with differing collision impact parameters toward the molecule under attack.

Molecular motion in the course of bimolecular chemical reactions depends on collision energy and collision geometry ( 1 – 3 ). Measurement of impact parameter, an important variable in collision geometry, poses a long-standing problem since the incoming species, in general, randomly misses the target’s center of mass. In an insightful analysis of reaction pathways, Herschbach et al. characterized the task of measuring the impact parameter as the pursuit of the “forbidden fruit” of reaction dynamics ( 4 , 5 ). Here, we undo the averaging for surface reaction by aiming an incoming “projectile” molecule with subatomic precision at the “target” molecule, by the novel means of using the rows of substrate atoms as a collimator for the projectile. The importance of the impact parameter is evident even for the case of billiards, where a head-on collision leads to a very different outcome from a glancing one.

RESULTS AND DISCUSSION

The products of the electron-induced dissociation of CF 3 are chemisorbed CF 2 found at distances ranging as far as 50 Å from the CF 3 along the [ ] direction (see Fig. 1, A and B); the second product of dissociation is a F atom, which recoils only one lattice space. This short recoil of the F atom, as opposed to the long recoil of CF 2 , is attributable to the strong binding of F to the surface, computed to be 5.0 eV, as compared to that of CF 2 , computed as 1.9 eV. The CF 2 is found to be sharply collimated to a single Cu row, with a measured spread of only ±1° (Fig. 1B). This directionality is present in all the 336 of the CF 2 recoil events examined. Density functional theory (DFT) calculations of the adsorbed CF 3 shows a bond extension of 0.07 Å for the C–F bond along the [ ]; this is consistent with weakening of the C–F bond that is found to break.

Fig. 1 Generation of CF 2 projectile from the electron-induced dissociation of CF 3 . (A) STM images showing the initial and final states of CF 3 dissociation. The tip was placed above the CF 3 (white cross) to induce dissociation. The white arrow indicates the recoil direction of the CF 2 . (B) Distance distribution of CF 2 (red squares) and F atom (green squares) along the [ ] direction (x axis) and the [001] direction (y axis; 1 unit cell = 3.61 Å). (C) CF 2 rotation in CF 2 ratcheting. (D) CF 2 translation in CF 2 ratcheting. (E) Alternating kinetic energy of F and C atoms in the ratcheting CF 2 , obtained from the trajectory in fig. S1 and movie S1.

Molecular dynamics (MD) calculations using the “Impulsive Two-State” (I2S) model (18–20) account for the observed long-range recoil of the chemisorbed CF 2 product (see Supplementary Text). These dynamics (fig. S1) led to a calculated CF 2 travel distance of 21.6 Å, comparable with the observed recoil that averaged 19.7 ± 8.0 Å. The recoil calculated in the I2S model was due to the C–F repulsion in the anionic state of CF 3 . Upon returning to the ground state, the CF 2 and the F atom recoil in opposite directions.

The sustained long-range motion of the chemisorbed CF 2 , initiated by the repulsion described above, took place through multiple alternating motions resembling a ratchet. This “ratcheting” (see Fig. 1, C and D) comprised frustrated rotation followed by frustrated translation, the latter producing the largest center-of-mass displacement along the copper row. Efficient rotation-translation coupling has previously been proposed in theoretical studies of migration dynamics (21) and in laser-induced CO migration (22, 23).

The CF 2 ratcheting is shown in Fig. 1 (C and D) and movie S1. The dynamics of the alternating motion involve CF 2 partial rotation, which displaces its C atom by 2.55 Å from a Cu atom toward the adjacent Cu atom of the same row (see Fig. 1C). The breaking of the old C–Cu bond causes the Cu atom left behind by the CF 2 to rise as much as 0.4 Å. This resembles the “walking” of a divalent C atom of CH 2 migrating by alternate bonding to Cu atoms of a pair of rows (20). Here, it is due to successive binding of the sp3-hybridized C atom to adjacent Cu atoms of a single row.

Following partial rotation, the singly bound CF 2 -Cu behaves as if sp2-hybridized, with a p orbital inducing the tilt of the CF 2 plane that propels the F atoms forward. Since the F atoms are at the center of mass of CF 2 , the resulting motion resembles frustrated translation (Fig. 1D). The ratcheting is seen in Fig. 1E to embody the alternating motion of the C and the F atoms, carrying the chemisorbed CF 2 along the single Cu row. Facile energy transfer between rotation and translation permits these motions to dominate energy dissipation to the surface (fig. S2). Thereafter, the CF 2 retains sufficient energy to have reactive or other inelastic encounters of a known impact parameter.

We have studied encounters between the CF 2 projectile and a stationary target, chemisorbed CF 2 , and, later in the text, chemisorbed I atom. Since the CF 2 projectile recoil is collimated along [ ], the perpendicular distance along [001] becomes the collision impact parameter (b). The distance along [ ], denoted as d, governs the collision energy since the CF 2 cools as it travels (Fig. 1E and fig. S2). The lower the value of d, the higher the projectile energy in a subsequent collision (see fig. S2).

The principal finding of this work is that association reaction between the CF 2 projectile and the CF 2 target occurs at zero impact parameter, b = 0, but not at b ≥ 3.61 Å, at comparable d values and hence comparable collision energies. We obtain the contrasting impact parameters by having the projectile and target on the same row for b = 0 or on adjacent Cu rows for b = 3.61 Å (see Fig. 2). For b = 0, experimentally, the CF 2 projectile collides with the CF 2 target to produce a bright oval feature on the surface. This new feature is confirmed to be a single molecule by its intact electron-induced diffusion. The feature is identified as chemisorbed C 2 F 4 by STM simulation (see fig. S3). The formation of C 2 F 4 is due to the association reaction between projectile and target in 29 cases out of 34 of zero impact parameter collision, CF 2 + CF 2 .

Fig. 2 Effects of different impact parameters, b, on CF 2 + CF 2 collision. (A) STM images and schematics showing the initial and final states of b = 0 collision. (B) Same data for b = 3.61 Å collision. In both panels, the tip was placed above the CF 3 (white cross) to produce the CF 2 projectile. The black cross marks the initial position of the CF 2 target. In the final state for b = 3.61 Å, the dashed circles indicate the new positions of the CF 2 projectile and CF 2 target (white and black circles, respectively) after the collision.

For impact parameter b = 3.61 Å, with CF 2 projectile and target on adjacent rows, no C 2 F 4 adduct is observed in all five cases that showed inelastic encounters. These nonreactive cases involve a CF 2 projectile with recoil distance d as small as 1.3 Å, hence the highest achievable collision energy. As shown in Fig. 2B, the projectile travels along the [ ] Cu row, and following the inelastic encounter, the previously cold target moves in the same direction along its adjacent Cu row. It is noteworthy that collision between the CF 2 projectile and CF 2 target causes the target to recoil despite the large impact parameter of 3.61 Å, surmounting a computed 0.3-eV diffusion barrier. This long-range repulsion between the two CF 2 is to be expected, given the diameter of saturated fluorocarbons, for example, carbon tetrafluoride with a diameter of 4.7 Å, obtained from transport properties (24).

A qualitatively similar momentum transfer is observed for the CF 2 projectile colliding with a chemisorbed I atom at an impact parameter b = 1.80 Å (fig. S4). The inelastic collision between the CF 2 projectile and the I atom is observed to move the I atom one lattice spacing surmounting a diffusion energy barrier of 0.1 eV.

We further investigate reactive collisions between the CF 2 projectile and the CF 2 target with zero impact parameter to experimentally form C 2 F 4 for different projectile energies. This is done by examining the effect on the observed dynamics of varying the distance, d, between the CF 3 parent and the CF 2 target. As shown in Fig. 3, we examined a total of 34 cases. For small d, <11 Å, corresponding to higher projectile energies, all cases give forward scattering of the C 2 F 4 product, along the continuation of the direction of the projectile. For higher d, >11 Å, hence lower projectile energies, the majority of cases (66 %) gives backward scattering of C 2 F 4 . In addition, lower collision energy gives rise to a small number of abortive outcomes (19%) and to a minor percentage of forward-scattered product, C 2 F 4 (15%). The abortive outcome denotes a nonreactive event (fig. S5). The observation of forward scattering at increased collision energy and backward scattering at lowered collision energy, measurable here for the first time at a single impact parameter, conforms to the results from MD calculations at selected impact parameters described below.

Fig. 3 Effects of different initial projectile-target separation on zero–impact parameter CF 2 + CF 2 collision. The dashed line at ~11 Å demarcates the regime with 100% reaction probability (high CF 2 + CF 2 collision energy) from that with mixed outcomes (low collision energy). The stacked histogram plot uses a bin size of 2.55 Å (1 unit cell along the [ ] direction). Assocn means association.

We performed the MD calculations for b = 0 and b = 3.61 Å. The observation of reaction at b = 0 and no reaction at b = 3.61 Å is explained by the differing geometries in the CF 2 + CF 2 collisions at the two impact parameters. MD calculations for b = 3.61 Å show F–F repulsion between the projectile and the target, with no reaction. By contrast, calculations for b = 0 lead to association reaction due to C–C collision, as in Fig. 4. MD gives forward-scattered C 2 F 4 at a higher collision energy of 1.5 eV and backward-scattered C 2 F 4 at a lower collision energy of 1.2 eV. In the course of reaction, the two reagents are seen to rotate toward each other to form the C–C bond. At a low collision energy of 0.7 eV, insufficient projectile rotation prevented C–C bond formation.

Fig. 4 Computed dynamics for “direct” and “indirect” association reactions. (A) Trajectory for direct single-collision reaction giving the forward-scattered C 2 F 4 product at 1.5-eV collision energy. (B) Trajectory for indirect double-collision reaction giving the backward-scattered C 2 F 4 product at 1.2-eV collision energy. In both panels, the vertical dashed lines indicate the initial position of the CF 2 target. Here, a collision is said to occur when both CF 2 have reached their closest-approach distance of 2.55 Å, 1 unit cell along the [ ] direction (whether the first or the second collision).

The forward trajectory shows the projectile momentum transferred to the C 2 F 4 product, which retains its direction of travel (see Fig. 4A and movie S2). The forward-scattered C 2 F 4 is the product of a direct association with a single encounter between the CF 2 reagents, which overcome a computed barrier of 0.6 eV (shown in fig. S6).