Metallic bonds remain one of the most important and least understood of the chemical bonds. In this study, we generated Re 2 molecules in which the Re–Re core is unsupported by ligands. Real-time imaging of the atomic-scale dynamics of Re 2 adsorbed on a graphitic lattice allows direct measurement of Re–Re bond lengths for individual molecules that changes in discrete steps correlating with bond order from one to four. Direct imaging of the Re–Re bond breaking process reveals a new bonding state with the bond order less than one and a high-amplitude vibrational stretch, preceding the bond dissociation. The methodology, based on aberration-corrected transmission electron microscopy imaging, is shown to be a powerful analytical tool for the investigation of dynamics of metallic bonding at the atomic level.

In this work, we create dirhenium molecules with unsupported Re–Re bonds using single-walled carbon nanotubes (SWNTs) as a nano–test tube while simultaneously imaging their structure and dynamics on the level of the single atom in real time using state-of-the-art chromatic and spherical aberration–corrected (C C /C S -corrected) SALVE (Sub Angstrom Low-Voltage Electron Microscopy) transmission electron microscopy (TEM) ( 14 , 15 ). Moving freely at room temperature along the SWNT, the Re 2 molecules have been shown to switch bond order between one, two, and four, and we could follow the process of dissociation and reformation of intermetallic bonds in individual Re 2 molecules.

Bonding between metal atoms is of fundamental importance to many areas of science and technology, including catalysis and magnetism ( 1 ), and since the discovery of the Re–Re quadruple bond in [Re 2 X 8 ] 2− in 1964 ( 2 , 3 ), the global effort in understanding the nature of the metal–metal (M–M) bond has been growing strongly ( 1 ). The key challenge is to establish the bond order of M–M, which can vary from one to five and determines fundamental physical and chemical properties ( 1 ). Spectroscopy methods such as nuclear magnetic resonance, infrared spectroscopy, ultraviolet-visible spectroscopy, and x-ray diffraction are typically used ( 4 – 6 ). The latter is particularly important, as it allows measurement of the M–M bond length, which is inversely proportional to the bond order. However, unlike bonds between nonmetallic elements, M–M bonds are very sensitive to ligands around the metals ( 7 , 8 ), creating the uncertainty whether the bond length and bond order reflect on the fundamental chemistry of the metals atoms or result from the effects of ligands, packing of molecules in the crystal or other external factors not related to the intrinsic M–M bonding. Encouraged by theoretical calculations predicting stable unsupported M–M bonds ( 9 , 10 ), the existence of homonuclear intermetallic bonds has been experimentally demonstrated in the noble gas matrices under cryogenic conditions ( 11 , 12 ), and more recently, the excited-state heteronuclear alkali metal diatomic molecule has been successfully obtained by combining two atoms with optical tweezers ( 13 ).

( A ) Time-series AC-HRTEM images (80 kV) (unprocessed data) of the first stage of movie S2 acquired by the SALVE TEM. At this stage, the dirhenium molecule moves at a defect site on the SWNT, climbs out from the defect, and then slides into the vdW gap between two parallel SWNTs. The corrected Re–Re bond length of each frame is presented; error is ±0.010 nm. ( B ) Selected frames with adjusted high contrast from movie S2 for analyzing the atomically precise position of the dirhenium molecule when it is drifting along the outer surface of host SWNT. The position of the Re atoms are indicated by yellow arrows. The AC-HRTEM images are partially covered by the model of an SWNT with chirality of (10, 10). The simulated structure shows the position of dirhenium molecule in the frame of 82 s. ( C ) Corrected bond length changing of the right dirhenium molecule in movie S1 (Titan Re 2 A); error is ±0.015 nm. ( D ) Corrected bond length of the dirhenium molecule drifting along the outer wall of SWNT in movie S2 (SALVE Re 2 ); error is ±0.010 nm. ( E ) The histogram shows the count frequencies of the different bond lengths of Titan Re 2 A (0 to 553 s).

( A ) Schematic illustration of the preparation of dirhenium molecule confined in SWNT by eliminating CO groups from Re 2 (CO) 10 precursor. Three dirhenium molecules in two SWNTs can be observed in the AC-HRTEM images [two dirhenium molecules imaged at 80 kV with Cs-corrected (top image) and one dirhenium molecule Cc/Cs-corrected (bottom two images) TEM, unprocessed data]. ( B ) Time-series AC-HRTEM images (80 kV) from movie S1 acquired by Titan C S -corrected TEM showing the characteristic states of the dirhenium molecule changing under e − -beam irradiation. This dirhenium molecule is the right one in the SWNT of the top AC-HRTEM image in (A) named “Titan Re 2 A.” The corrected Re–Re bond length of each frame is presented; error is ±0.015 nm. N/A is the standing state with unknown bond length.

Dirhenium molecules are generated from Re 2 (CO) 10 compound inserted into SWNTs, followed by thermal or e − -beam–induced elimination of CO ligands ( Fig. 1A ). The dissociation of Re 2 (CO) 10 molecules and the removal of CO ligands is confirmed by Fourier transform infrared spectroscopy (FTIR) measurements (fig. S1). If several precursor molecules Re 2 (CO) 10 are agglomerated in the nanotube, they form a metal nanocluster with several Re atoms under these conditions ( 16 , 17 ); in the case of a single isolated molecule, Re 2 (CO) 10 ligand elimination yields a well-defined Re 2 molecule as observed by aberration-corrected high-resolution TEM (AC-HRTEM) (three typical images of Re 2 are shown in Fig. 1A ). Two individual dirhenium molecules can be observed in the same SWNT in the top AC-HRTEM image of Fig. 1A . Monitoring an individual Re 2 by time-series 80-kV AC-HRTEM imaging ( Fig. 1B ) shows that the two Re atoms are bonded to each other within the dirhenium molecule, as Re 2 moves as a whole in the cavity of SWNT, which differs notably from the dynamics of individual heavy atoms in graphitic structures that move by hopping from one vacancy defect in the carbon lattice to another under e-beam irradiation ( 18 – 21 ). The Re–Re bond ensures that the movement of both atoms is correlated, and the dirhenium molecule takes positions in the SWNT, consistent with small number of possible orientations: (i) chemisorbed standing (20 s), (ii) chemisorbed lying (0 s), and (iii) successive chemisorbed standing and lying configurations during the exposure time (26 s) ( Fig. 1B ). The same Re 2 molecule is able to change its position and orientation over the duration of the experiment. This process is stimulated by the e − -beam serving as both a source of energy and the imaging probe, as the kinetic energy of the incident electrons is transferred to the Re atoms (directly ~1.0 eV and via carbon atom ~14.7 eV). As the positions of the rhenium atoms are monitored continually during the exposure time of each frame (1 s), the motion of Re 2 switching from one orientation to another can be captured within a single frame and analyzed (see Fig. 2 ). For example, it is possible to discern that the change in the bonding orientation that takes place during the 26th second corresponds to a change from the initial standing orientation lasting 0.29 s into the lying orientation lasting 0.71 s in the 1.0 s frame (fig. S2).

DISCUSSION

There is a well-known strong inverse correlation between the M–M bond length and bond order (3). The Re–Re single σ bond length in Re 2 (CO) 10 is 0.304 nm for the free molecule and 0.302 nm in the crystal (22). However, in our experiments, after the CO ligands have been removed, the Re–Re bond measures 0.220 nm (± 0.015 nm) at the initial state (0 s; Fig. 1B), indicating that the bond order is close to four, as it agrees well with the length of a quadruple Re–Re bond in [Re 2 X 8 ]2− of 0.224 nm (2). Our density functional theory (DFT) calculations for Re 2 match well with the experimentally observed distances, predicting Re–Re bond lengths of 0.21 nm for a free (nonbonded) Re 2 and approximately 0.22 nm for the dirhenium molecule bound to the SWNT wall by the stable standing orientation. Because the SWNTs are cylindrical surfaces, all the bond lengths quoted in this work are corrected from the directly measured projected distance using the method described in fig. S3. Statistical analysis of Re–Re bond lengths in 226 frames from 0 to 553 s (Fig. 2C) shows three major values of the length of 0.22, 0.25, and 0.30 nm, occurring with 44, 24, and 11% probability (Fig. 2E). The nonrandom, discrete values assumed by the Re–Re bond are likely to be correlated with the quadruple bond, double bond, and single bond, respectively, which were previously reported from bulk measurements on various complexes containing a Re 2 core (3, 22). In additional 18% of the cases, the bond length cannot be measured as marked “N/A,” as the “standing” state is aligned with the direction of the electron beam. Being limited by the spatial resolution of only spherical AC-TEM, the atomic structure of the SWNT and hence the precise position of the Re atoms with respect to the carbon lattice remain unresolved.

With the help of the C C /C S -corrected SALVE TEM, the e−-beam–stimulated dynamics of dirhenium molecule are recorded with a much higher spatial resolution, as shown in movie S2. A Re 2 molecule can be observed standing at defective sites on the top SWNT of two parallel SWNTs at the initial state (0 s; Fig. 2A shows the first stage of movie S2 from 0 to 87 s). A van der Waals (vdW) gap of 0.3 nm is formed by the two parallel SWNTs with different chirality. In the first 50 s, Re 2 shows similar behavior to the Re 2 in Fig. 1B, switching between multiple different orientations at the defective site. An intact SWNT is impermeable to almost all atoms and ions except H+ (23). However, a vacancy defect on the SWNT could provide a channel for atoms to penetrate. At 50 s, one Re atom of the dirhenium molecule goes across the upper wall of the host SWNT from the defective site. In the following 20 s, the whole dirhenium molecule climbs out and starts drifting along the outer surface of the host SWNT, driven by stronger bonding of the metal with defect from outside, as was predicted by dynamic simulations (24). From 72 to 85 s, the dirhenium molecule drifts along the outer surface of the host SWNT and then slides into the one-dimensional vdW gap, as indicated by yellow arrows (Fig. 2B). The simulated structure in the right of Fig. 2B shows an atomic structure of the lying orientation of dirhenium molecule in the AC-HRTEM image of 82 s with a Re–Re bond length of 0.22 nm. Figure 2D only shows the bond length changing of the dirhenium molecule when it is drifting along the outer wall before it slides into the vdW gap (72 to 85 s), because the real bond length of Re 2 moving and rotating at the defect site is immeasurable. According to the analysis of the bond length distribution measured over time for the dirhenium molecules (Fig. 2, C to E), the lying orientation with corrected Re–Re bond length of 0.22 nm and the standing orientation with immeasurable bond length are the most common bond structures observed in these two time series, although bond lengths of 0.25 and 0.30 nm are also observed. The measured metallic bond length changes in discrete steps, indicating the existence of single and double Re–Re bonds (Fig. 2C).

The vdW gap between the two parallel SWNTs in the initial state of the second stage (89 s in Fig. 3A) is approximately 0.32 nm (± 0.010 nm), consistent with the theoretical prediction by Lennard-Jones model (25). This vdW gap confines Re 2 and provides a one-dimensional channel in the vacuum, limiting Re 2 translation and rotation. In the first 7 s (87 to 94 s) after the dirhenium molecule moves into the vdW gap, the contrast of the Re atoms shows unusual symmetrically elongated features, indicating that the Re atoms are delocalized on the time frame of a single exposure (0.5 s), which may be caused by oscillations along the Re–Re bond, described as a stretch vibration (Fig. 3B). The center distance of the elongated spots is 0.36 nm, which is slightly longer than the Re–Re single bond (around 0.30 nm) in compounds (21), while the amplitude of the oscillation of Re atoms is ±0.04 nm. After oscillating for 7 s, Re 2 breaks into two unbound Re atoms with a distance of 0.58 nm (94 s in Fig. 3A and the second column in Fig. 3B). After the separation, the contrast of two Re atoms is no longer elongated and becomes near round. This observation indicates that once the Re–Re bond length exceeds that of a single bond, the molecule may exist in an excited state manifested in a large amplitude of vibrations, and that beyond this critical point, the bond breaks and the two metal atoms separate. In our experiments, Re 2 trapped in the one-dimensional vdW gap acts like a harmonic oscillator, pumped with the kinetic energy transferred from the 80-keV electrons to the Re atom, until it is large enough to overcome the barrier of Re–Re bond dissociation (at 94 s in Fig. 3A). The two Re atoms move freely in the one-dimensional vdW gap until they collide and recombine into Re 2 at 97 s. The bond distance of the reformed Re 2 reduces from 0.30 (97 s) to 0.23 nm (132 s). The contrast of two Re atoms in the frame of 132 s are near round with a distance of 0.23 nm, indicating that the two Re atoms are bound again by a quadruple bond. This reformed dirhenium molecule shows the same properties as before, moving between different orientations in the one-dimensional vdW gap in the following 34 s, similar to the behavior inside and on the SWNT. In addition, the free Re atom is chemically active toward SWNT, as shown in our previous work (26), and interacts with the upper SWNT restructuring the carbon lattice at 97 s. At 200 s, Re 2 dissociates again and recombines at 212 s. This dirhenium molecule moves in the vdW gap in the following 181 s and merges into the large Re cluster in the lower SWNT as shown in movie S2.

Fig. 3 Atomic-scale dynamics of Re–Re bond dissociation. (A) Time-series AC-HRTEM images (80 kV) (unprocessed data) of the second stage of movie S2 acquired by the SALVE TEM. At this stage, the dirhenium molecule confined in the vdW gap shows various dynamic processes. The metallic bonds between two Re atoms break and rebind twice. The dirhenium molecule also stands and lies down in the gap. (B) In the first row, false-color images of the red dashed line framed areas in the AC-HRTEM images of 89, 94, and 132 s in (A). The second row shows the intensity profiles of the corresponding black dashed line in the false-color images of the same column. The distances between two Re atoms are measured with an error of ±0.010 nm. The third row shows the possible state of the two Re atoms in each image of the first row.

DFT calculations have been carried out to elucidate the stable configurations and electronic structure of Re 2 bonded to SWNT (Fig. 4). As discussed in Materials and Methods, a search of possible stable bonding configurations inside the SWNT revealed only the presence of a single standing mode with a Re–Re bond length of 0.22 nm, in which Re 2 bonds in an η6-mode to all six carbon atoms of a single hexagon with a “4 + 2” asymmetry introduced by the curvature of the nanotube wall. The binding energy of this configuration is −165 kJ/mol (−1.71 eV), relative to the separated dirhenium molecule and SWNT. On the outside of the nanotube, the η6-standing configuration is again found to be the lowest energy orientation, but the change in curvature introduces several stable lying configurations, which are local minima at higher energy, geometrically and energetically similar to one another (fig. S7).

Fig. 4 Interactions of Re 2 with carbon nanotube. (A) Comparison of the spatial extent of the Re 2 HOMO (SOMO) viewed end-on and side-on; the overlap with electron density of the SWNT LUMO sufficient for bonding is only achieved when Re 2 approaches the nanotube wall in the end-on orientation. (B) Side-on and end-on views of the HOMO (SOMO) of the bound configuration, showing the contraction of the (blue) orbital lobes that maximizes bonding overlap (in the end-on view, some carbon atoms have been removed and the electron density isovalue has been increased to aid visualization). (C) Illustration of the dynamics of the dirhenium molecule in the SWNT, with the associated calculated energies relative to the separated molecule and SWNT (left), and front and side views of each state.

To understand the bonding configurations observed, it is instructive to examine the spatial extent of the molecular orbitals involved in the bonding. The atomic Re orbitals and the occupied and low-lying unoccupied orbitals of Re 2 are presented in fig. S4, and the electronic structure of the dirhenium molecule is discussed in more detail in the Supplementary Materials. The highest occupied molecular orbital (HOMO) [singly occupied molecular orbital (SOMO)] of the bound species in the standing configuration corresponds to the HOMO (SOMO) of the isolated Re 2 , but with contraction of the orbital lobes that are perpendicular to the nanotube axis (Fig. 4B). This maximizes the overlap with the two carbon atoms that are closer to the dirhenium due to the curvature-induced 4 + 2 asymmetry (shown in blue in Fig. 4A). The “end-on” standing η6-bonding is more stable than “side-on” lying bonding, as this provides a better orbital overlap between the Re 2 HOMO and the SWNT LUMO, in terms of size, shape, and ease of the above orbital contraction. On the outside of the SWNT, the rhenium dimer encounters the convex curvature of the nanotube, and two carbon atoms lie further from the dimer than the other four. The orbital contraction is therefore less pronounced, and the larger orbital lobes presented by the side-on orientation of dirhenium are able to take part in stable bonding with the nanotube wall. Note that the curvature of the SWNT wall is, in turn, affected by the dirhenium molecule, exhibiting a slight flattening of the wall in the region of the bonding, as can be seen in the side views in Fig. 4C. Our calculations predict the presence of standing configurations inside the nanotube; the presence of stable lying configurations could be caused by the different curvature of SWNTs with different diameters. As the bonding modes available to Re 2 seem to be largely influenced by the curvature of the SWNT wall, it is reasonable to assume that the wider nanotube with a smaller degree of curvature imposes less of a restriction on the possible bonding modes and behaves more similarly to the outside of the tube. In addition, the presence of defects and deformations in the SWNT under electron irradiation were not considered in our simulations but may affect the bonding between dirhenium and the SWNT.

Using our experimental observations in conjunction with the theoretical modeling, Fig. 4C illustrates a plausible energy profile for the movement of Re 2 along the nanotube. We propose that, upon elimination of the CO ligands from the precursor molecule, Re 2 bonds to the interior of the SWNT wall, a process we predict to be strongly thermodynamically (−165 kJ/mol binding energy) and kinetically (no energy barrier) favorable. On the order of seconds in our conditions, the electron beam transfers energy to excite Re 2 , from which the molecule can relax into adjacent energy minima (Fig. 4C). The absence of any local minima in which Re 2 exists inside the SWNT without being bonded to the walls explains the observed stepwise motion of the dirhenium molecule under electron irradiation, as these would result in a more long-range migration process.