Dynamic Intermolecular Space for Reversible CO₂ Capture and Release

I.   INTRODUCTION

The massive anthropogenic CO₂ emission poses increasingly challenges to our life, leading to an urgent requirement to develop highly efficient, low cost, and low energy consumption carbon capture and storage (CCS) materials and technologies [1−4]. The design of new materials and the understanding of new mechanisms for CCS attract active research in environmental and material sciences [5−7]. The frontiers of CCS aim at high capacity and selectivity, reversible capture and release, and the catalytic activation for CO₂ transformation into value-added carbon-based materials. A series of porous materials, such as metal-organic frameworks (MOFs), covalent organic frameworks (COFs), porous organic polymers (POPs), porous carbon and zeolites, have been designed for the capture and separation of gases, benefiting from their tunable pore sizes, functional building units, large surface areas, and chemical stability [8−12]. A deep insight into how the nanopore structures interact with CO₂ gas requires direct real-space imaging at the molecular level, which, however, is challenging in such 3D crystalline or amorphous materials. To overcome such challenges, 2D materials such as self-assembled organic molecules on crystalline surfaces provide prototypical templates to interrogate the interaction of CO₂ molecules with organic structures. The surface science approaches [5], such as scanning tunneling microscopy (STM) [13−16] and atomic force microscopy (AFM) [17, 18], provide exceptional single- to sub-molecule resolution to directly interrogate the structure-property relationship in CO₂ capture processes.

The adsorption of CO₂ has been extensively studied on various surfaces [6, 7, 16, 19−24]. On metal surfaces, such as Pt, the adsorption of CO₂ molecules takes place at the terraces, steps, and defect sites with different adsorption energies at low temperature conditions [25]. On oxide surfaces, the defects of oxygen vacancies on TiO₂(110) [16] and SrTiO₃(001) [26], or the missing rows on reconstructed Cu(100)-O surface [27], act as effective sites for CO₂ adsorption. More intriguingly, the surface support MOFs with geometric topological diversity [28] provide promising templates for CO₂ capture, which can be optimized by design of functional groups and unsaturated coordination metal sites [29−33]. Among such materials, pseudo-halogen molecules such as isocyanides have received attention [34, 35], because the isocyanide groups not only provide electron lone pairs but also act as π-hole acceptors when they coordinate with metals [36].

The 1,4-phenylene diisocyanide (PDI) molecule, owing to its high symmetry and simple structure, has been used as a prototypical isocyanide [13−15, 37−40]. The self-assembled one-dimensional -[Au-PDI]_n- chains on Au(111) and Au(100) surfaces have exhibited high capability for CO₂ capture [13−15]. The self-catalyzed CO₂ adsorption turns on the attractive interchain interactions of the -[Au-PDI]_n- chains, which makes the initially dispersed chains gather into close packed bundles to stabilize the CO₂ molecules. Furthermore, the chemisorbed CO₂^δ− species with coordination to Au adatoms in-turn seed the physisorption of CO₂ molecules into highly-ordered two-dimensional islands. Based on these results, a more recent study by Custance et al. using functionalized probes with STM/AFM has revealed a chiral arrangement of CO₂ molecules in a windmill-like structure in the CO₂ islands [17]. These results mainly concern the structures of the physiosorbed and chemisorbed CO₂, and its interactions with PDI molecules and metal atoms.

Herein, we report how the templated PDI chain structures on Ag(110) can dynamically self-organize to facilitate CO₂ capture and release. Different from the interaction of the flat-lying PDI chains with Au adatoms on Au(111) and Au(100) [13, 14], the PDI molecules adsorb in upright geometry on Ag(110) with one-end isocyano functional group (-NC) bonding to surface Ag atom. The intermolecular steric interactions organize PDI molecules to form one-dimensional zigzag double chain structures along the [001] direction of Ag(110). The interchain space is defined by twice the Ag lattice distance along $\left[1\bar{1}0\right]$ direction (2${\alpha }_{\left[1\bar{1}0\right]}$). With different amount of CO₂ adsorption, the interchain space can be expanded to 3${\alpha }_{\left[1\bar{1}0\right]}$, 4${\alpha }_{\left[1\bar{1}0\right]}$ and 5${\alpha }_{\left[1\bar{1}0\right]}$, where the weak interchain attraction and the intermolecular interactions stabilize the CO₂ molecules. After the release of CO₂, the interchain space of PDI double chain structure is recovered to its original 2${\alpha }_{\left[1\bar{1}0\right]}$ width. Such a dynamic, flexible and self-adapting transformations of the organic structures on metal surface for CO₂ capture and release could provide new insights for the design of advanced materials in two-dimensional systems for gas capture.

II.   EXPERIMENTAL AND COMPUTATIONAL METHODS

A   Sample preparation and STM experiments

The STM measurements are performed in an Omicron LT-STM system under ultrahigh vacuum at about 7×10⁻¹¹ mbar pressure. The Ag(110) samples are cleaned by several cycles of Ar⁺-ion sputtering and annealing at ~700 K. The STM tip is an electrochemically etched polycrystalline tungsten tip. All the images are obtained with constant current mode at ~80 K and the bias being the sample bias. The PDI molecules are dosed as described in previous studies [13−15]. CO₂ molecules are dosed to sample surface through a dedicated tube from a leak valve into the STM sample stage at ~80 K [16].

B   Theoretical calculations

Plane-wave pseudopotential density functional theory (DFT) calculations were performed using the Vienna ab initio simulation package (VASP) code [41−43] to simulate CO₂ capture in self-assembled PDI molecular chains on the Ag(110) surface. The geometry optimization and electronic structure calculations utilized the Perdew−Burke−Ernzerhof (PBE) functional with generalized gradient approximation (GGA) [44]. The core electrons are modeled using the projector-augmented wave method [45]. Structural relaxation employed a conjugate gradient scheme without symmetry restrictions until the maximum force on each atom was below 0.02 eV/Å. The periodically repeated slabs were separated by 20 Å vacuum gaps, and the energy cutoff was set to 500 eV. For all the models explored, the chosen k-grids have been validated by the convergence test. In the DFT simulation, the Ag(110) surface slab contains four Ag layers, where the lowest two are fixed to the bulk structure, while the upper two are relaxed together with the PDI and CO₂ complex. The average adsorption energy of CO₂ molecules in PDI groove is calculated as follows:

where $E\left({\rm{PDI}}_{\rm{Ag}}\right)$ and $E\left({{\rm{CO}}_{2}@\rm{PDI}}_{\rm{Ag}}\right)$ are the energy of PDI groove before and after CO₂ capture, respectively, and $E\left({\rm{CO}}_{2}\right)$ is the total energy of a single CO₂ molecule.

III.   RESULTS AND DISCUSSION

A   Formation of 1D chain structures of PDI molecules at Ag(110) surface

The self-assembly of PDI molecules has been studied at various noble metal substrates, such as Au(111), Au(100), and Ag(111) [13−15]. The self-assembly process is initiated by the interaction of -NC group of PDI with metal atoms, and guided by the substrate symmetries. The temperature is a key further parameter that governs the self-assembled structures. For example, at Ag(111) surface, PDI molecules form a close-packed $\sqrt{7}\times 2\sqrt{7}$ structure in upright-standing configuration bonding to substrate Ag atoms at ~150 K; by contrast, PDI molecules adsorb in flat-lying configuration bonding to surface Ag adatoms constructing a 2D honeycomb lattice at ~200 K [15]. At Ag(110) surface, we find that at the low temperature of ~5 K (liquid helium cooling), the PDI molecules adsorb mostly in the flat-lying configuration across the Ag trough (FIG. S1 in Supplementary materials, SM); at higher temperature of ~250–300 K, molecular clusters form with complicated configurations (FIG. S2 in SM). Of key interest to the present study, however, at a modest temperature range of ~80–250 K, the PDI molecules adsorb in upright-standing configuration, self-assembling into 1D chains. The highly-ordered chain structures of PDI at Ag(110) are the main focus of this study (FIG. 1).

Figure  1.  Formation of 1D chain structures of PDI molecules at Ag(110) surface. (a–d) STM images of PDI molecules with a coverage of ~0.05 ML (a), ~0.15 ML (b), ~0.5 ML (c), and ~0.8 ML (d). The inset of (a) shows the atomically resolved image of Ag(110) lattice, which was smoothed to get higher contrast. (e, f) STM images obtained by continuous scanning in a same area. The white arrows show the moving of PDI molecules from a single chain to form a double chain. (g, h) Line profiles obtained along the positions marked by the green and blue lines, respectively. The red bracket in (h) indicates the four PDI molecules which have merged into a double chain. (i, j) DFT simulated structure of a PDI double chain and its orbital contour. (k) STM image of PDI double chains obtained with a special tip. In the middle chain, the blue ellipses indicating the orientation of PDI molecular plain in the double chain. All the STM images were obtained at 80 K with scanning bias voltage of –1.0 V, except the one in (k) with –1.6 V. Setpoint: 100 pA in (a–d, k) and 20 pA in (e, f).

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Gradually depositing PDI molecules onto Ag(110) surface enables us to monitor how the chain structures form (FIG. 1(a–d)). At the low coverage of ~ 0.05 monolayer (ML), a few short chains can be seen in the STM image along the [001] direction of Ag(110), in which each bright spot represents a single PDI molecule (FIG. 1(a)). Some scratches are also observed, which could be assigned to the fast migration of individual PDI molecules. By increasing the coverage to ~0.15 ML, double chains of PDI molecules appear at the surface with a zigzag arrangement (FIG. 1(b)). Intriguingly, well-ordered double chains dominate at the coverage to ~0.5 ML (FIG. 1(c)). As compared to the short single chains, these double chains are strictly aligned along [001] direction and have lengths that can extend over the whole terrace. Further increasing the coverage to ~0.8 ML, PDI molecules can occupy the space among the adjacent chains, leading to the formation of closely-packed molecular islands (FIG. 1(d)). We focus further discussion to 0.4–0.6 ML coverage that best illustrates the interactions of double chain structures with CO₂ molecules.

The changeover from FIG. 1(b) to FIG. 1(c) indicates the single chains are less stable with respect to double chains, favoring molecular migration to organize into double chains. A set of in situ STM images directly record such transformations (FIG. 1(e, f)): four PDI molecules in a single chain diffuse over several sites to combine with another single chain as indicated by the white arrows, forming a double chain. FIG. 1(g) shows the line profiles obtained along both the single chain (blue curve) and the double chain (green curve) in FIG. 1(e), which indicate the double chain has a slightly brighter contrast than single chain in the STM topographic images. After the transformation in FIG. 1(f), the corresponding line profiles are plotted in FIG. 1(h). It can be seen that the blue curve in FIG. 1(h) becomes higher at the double chain sites as indicated by the red bracket. Nevertheless, it is noted that the heights of PDI molecules in both single chains and double chains are much higher than the flat-lying configuration of an individual PDI molecule (FIG. S1 in SM), indicating the PDI are adsorbed in an upright configuration. The line profile analysis also gives a period of ~0.82 nm between the PDI molecules at one side along [001] direction (i.e., 2${\alpha }_{\left[001\right]}$) and the interchain separation of 2${\alpha }_{\left[1\bar{1}0\right]}$, providing a good reference for DFT optimization of the adsorption structures.

DFT calculation are conducted to get the adsorption energies and geometries for the PDI molecules in the single chain and the double chain. The results show the average adsorption energy of each PDI molecule in single chain drops by 0.02 eV after merging into double chain, suggesting a stronger interchain interaction to stabilize the double chain configuration. For individual molecules in the double chain, the calculated average adsorption energy is −0.42 eV and the charge density difference map indicates apparent charge transfer between the isocyanide group of PDI and the substrate Ag atom (FIG. S3 in SM), suggesting a modest chemisorption of PDI on Ag substrate. A small diffusion barrier of ~0.07 eV is also revealed for PDI molecules to move along the [$1 \bar{1}0$] direction (perpendicular to the chain direction, FIG. S4 in SM), which rationalizes the migration of a single chain to form a double chain. The optimized double chain geometry includes the zigzag arrangement of PDI molecules in a cross-herringbone shape. Specifically, the top view in FIG. 1(i, j) indicates the molecular plane has an angle of ~45° with respect to the [$1\bar{1}0$] direction, and the molecular planes are mirror-symmetric in the two sides of the double chain. Although in most cases, individual PDI molecules are imaged as round spots in STM topographic images, under some special tip conditions, such ~45° cross-herringbone arrangement can be imaged. One example can be found in FIG. 1(k), where the upper and lower fragments of the middle chain have opposite herringbone arrangements, and the PDI molecules exhibit shell-like shape as indicated by the ellipses. The shell-like shape of individual PDI molecules can be related to its p orbitals that distributes in the molecular plane (FIG. 1(j, k)).

B   CO₂ adsorption in the groove of PDI double chains

The upright-standing double chain configuration constructs a natural groove for potential adsorption of CO₂ molecules. The inter-groove space has a width of 2${\alpha }_{\left[1\bar{1}0\right]}$ and a height of the PDI molecular length. We next conduct in situ experiments by dosing CO₂ gas molecules at a sample temperature of 80 K. FIG. 2 (a) and (b) are the same area STM images obtained before and after CO₂ dosing to PDI double chains pre-adsorbed on Ag(110) surface. As a consequence of CO₂ adsorption, some of the double chains are obviously broadened as labeled by the rectangles in FIG. 2(a, b). In the groove of the broadened double chains, a bright contrast appears, which could be assigned to intercalated CO₂ molecules. Line profiles across the chains along the positions of 1 and 2 in FIG. 2(a, b) are plotted in FIG. 2(c). At the position 1, the orange curve indicates PDI row at one side has been pushed out by one ${\alpha }_{\left[1\bar{1}0\right]}$ distance, expanding the width of the groove from 2${\alpha }_{\left[1\bar{1}0\right]}$ to 3${\alpha }_{\left[1\bar{1}0\right]}$. At the position 2, the orange curve indicates PDI rows at both sides have been pushed out, expanding the interchain space to 4${\alpha }_{\left[1\bar{1}0\right]}$ after CO₂ adsorption. These changes indicate that the self-adjustable interchain space of the PDI double chain can facilitate higher density CO₂ adsorption. By contrast, no CO₂ adsorption is observed at the dispersed PDI molecules or single chains.

Figure  2.  CO₂ adsorption in the groove of PDI double chains. (a, b) STM images of the same area before and after dosing CO₂ to the sample surface. The yellow dash frames show the double chains, which are expanded after CO₂ adsorption, with the space changing from 2${\alpha }_{\left[1\bar{1}0\right]}$ to 3${\alpha }_{\left[1\bar{1}0\right]}$ and 4${\alpha }_{\left[1\bar{1}0\right]}$. Images were obtained with −1.0 V, 100 pA. (c) Line profiles obtained in (a) and (b) along the labeled positions 1 and 2. The green arrows indicate the expanded sites. (d, e) In situ STM images of another area before and after introducing CO₂ to the sample surface. Images were obtained with −1.0 V, 20 pA. The blue rectangles mark the areas which are enlarged in (f, g), respectively. The blue arrows in (f) indicate the movement of PDI molecules when capturing CO₂. The red arrows indicate the contrast of CO₂ molecules. (h, i) The sketched models for PDI and CO₂ molecules in (f, g).

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In addition to the above structural changes to individual double chains, more fruitful transformations are observed among the double chains upon CO₂ adsorption. FIG. 2(d) shows a surface with the double chain coverage of ~0.6 ML, where the dark contrast regions indicate the interchain spaces. After a large amount of CO₂ dosing towards a saturate adsorption, most of the dark contrast regions are occupied by the CO₂ molecules, except the larger interchain spaces with width ≥6${\alpha }_{\left[1\bar{1}0\right]}$, as can be seen in FIG. 2(e). A close look into the images at the amplified regions (marked by the blue rectangles) gives more detailed structural transformations in FIG. 2(f, g), which are further sketched in FIG. 2(h, i): three double chains with separations of 5${\alpha }_{\left[1\bar{1}0\right]}$ or 6${\alpha }_{\left[1\bar{1}0\right]}$ are shown in the original surface; after CO₂ dosing, part of the right side PDI molecules in the middle chain shift to right by 2${\alpha }_{\left[1\bar{1}0\right]}$ as indicated by the blue arrows, forming two adjacent interchain spaces with a width of 4${\alpha }_{\left[1\bar{1}0\right]}$. Clearly, CO₂ molecules fully fill up the interchain spaces with the width of 4${\alpha }_{\left[1\bar{1}0\right]}$ and 5${\alpha }_{\left[1\bar{1}0\right]}$, but not the space of 6${\alpha }_{\left[1\bar{1}0\right]}$, implying the interchain attractions at ≥6${\alpha }_{\left[1\bar{1}0\right]}$ distance might be too weak to stabilize CO₂ molecules.

C   Configurations of CO₂ molecules in interchain spaces

The above experimental results show that during CO₂ adsorption in the groove of the double chain, the groove width can expand to 3${\alpha }_{\left[1\bar{1}0\right]}$, 4${\alpha }_{\left[1\bar{1}0\right]}$ and 5${\alpha }_{\left[1\bar{1}0\right]}$, as sketched in FIG. 3(a–d). Such a dynamic, flexible and self-adapting structural transformation enables the efficient and stable CO₂ capture. The gas phase CO₂ molecule has a kinetic diameter of 0.33 nm, requiring the change of the PDI interchain space to reach a suitable steric hindrance for its adsorption. In experiments, it is found that the 4${\alpha }_{\left[1\bar{1}0\right]}$ interchain space is the most preferred structure for CO₂ adsorption, the 5${\alpha }_{\left[1\bar{1}0\right]}$ interchain space has the maximum capacity for CO₂ adsorption, while the 3${\alpha }_{\left[1\bar{1}0\right]}$ space with CO₂ is only occasionally observed. Possible configurations of CO₂ molecules are simulated in FIG. 3(b–d). Moreover, some high-resolution STM images help to determine the CO₂ configurations in the expanded grooves of 4${\alpha }_{\left[1\bar{1}0\right]}$ and 5${\alpha }_{\left[1\bar{1}0\right]}$. As shown in FIG. 3(e), the contrast for individual CO₂ molecules could be recognized indistinctly, but point to possible double-row arrangement of CO₂ molecules in 5${\alpha }_{\left[1\bar{1}0\right]}$ PDI groove and single-row arrangement in 4${\alpha }_{\left[1\bar{1}0\right]}$ PDI groove (marked by red circles). More clearly in FIG. 3(f), individual CO₂ molecules can be recognized as small spots under some special tip condition, which connect with the edge side of the PDI molecular plane (marked by blue ellipses). In combination with the DFT simulation, we propose single CO₂ chain configuration in the 4${\alpha }_{\left[1\bar{1}0\right]}$ PDI groove (FIG. 3(c)) and double CO₂ chains configuration in the 5${\alpha }_{\left[1\bar{1}0\right]}$ PDI groove (FIG. 3(d)), resulting in the utilization efficiency of PDI molecules for CO₂ capture as 1 PDI/CO₂ and 0.5 PDI/CO₂, respectively.

Figure  3.  (a−d) DFT optimized configurations of pure PDI double chain and with CO₂ adsorption in its groove. After CO₂ adsorption, the width of the PDI double chain changes from 2${\alpha }_{\left[1\bar{1}0\right]}$ to 3${\alpha }_{\left[1\bar{1}0\right]}$, 4${\alpha }_{\left[1\bar{1}0\right]}$ and 5${\alpha }_{\left[1\bar{1}0\right]}$, where the CO₂ structures are different. (e, f) Representative high-resolution STM images, which show the possible arrangements of CO₂ molecules in the grooves with width of 4${\alpha }_{\left[1\bar{1}0\right]}$ and 5${\alpha }_{\left[1\bar{1}0\right]}$. Red circles in (e, f) mark the positions of CO₂, and the blue ellipses indicate the orientation of PDI molecules. STM image in (e) was obtained with −1.0 V, 20 pA and in (f) was obtained with −0.02 V, 2 pA. (g, h) The differential charge density plots of the configurations in (c, d), respectively. The contour value of charge density is 0.0025 e/ų.

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The charge density difference maps provide an insight into how the CO₂ molecules are captured by PDI molecules. In the 4${\alpha }_{\left[1\bar{1}0\right]}$ PDI groove, the linear O-C-O point to the PDI molecular plane (top view in FIG. 3(g)), connecting with the C–H bonds at the middle benzene ring (side view in FIG. 3(g)). The electron loss at the C−H bonds and electron gain at the O atom of one end of CO₂ molecule result in the electrostatic interaction that stabilize the adsorption. Similar charge redistribution can be also observed among PDI and CO₂ molecules in the 5${\alpha }_{\left[1\bar{1}0\right]}$ PDI groove (FIG. 3(h)). In simulations, it is noted that in the 5${\alpha }_{\left[1\bar{1}0\right]}$ PDI groove there are two sets of CO₂ molecules, and the CO₂ molecules that are closer to PDI molecules have larger charge redistribution. However, in experiments it is difficult to distinguish these two sets of CO₂ molecules. We therefore evaluate the average adsorption energies for each CO₂, which is −0.06 eV in 5${\alpha }_{\left[1\bar{1}0\right]}$ PDI groove and −0.04 eV in 4${\alpha }_{\left[1\bar{1}0\right]}$ PDI groove, respectively. These small adsorption energies suggest the CO₂ capture by PDI grooves on Ag(110) is still a physisorption process.

D   Release of CO₂ from PDI grooves

The weak physisorption of CO₂ in the PDI grooves makes us to consider how the reverse CO₂ release process occurs. The CO₂ capture is achieved by dosing CO₂ to the PDI sample at the low temperature of 80 K. We find that warming up the sample can cause the CO₂ release from the PDI grooves. FIG. 4(a) show the original surface with double PDI chain structures. After CO₂ dosing at 80 K, most of the double chain grooves are filled by CO₂ molecules, as shown by the green arrows in the expanded image in the inset of FIG. 4(b). After warming up the sample to ~150 K, apparently CO₂ molecules have mostly desorbed from the grooves (FIG. 4(c)). The desorption of CO₂ also causes the damage of part of PDI chain structures. Some disordered areas can be observed in FIG. 4(c). Apparently, CO₂ increases the PDI chain separation during the adsorption, and the desorption occurs at a temperature below the temperature when the cold PDI chain can be reorganized. It is found that slightly annealing the sample to ~200 K can recover the ordered PDI double chain structure as shown in FIG. 4(d, e) (Note, we have mentioned in FIG. S2 (SM), high temperature of ~250–300 K will change the chain structures to complicated clusters). These results show that not only the CO₂ capture and release are reversible, but also the PDI chain structures can be recovered by cyclical temperature control.

Figure  4.  Reversible adsorption and desorption of CO₂ by the PDI double chain structures. (a, b) STM images of PDI grooves before and after CO₂ dosing. (c) STM images after warming up the sample in (b) to ~150 K, which causes the CO₂ desorption from the grooves. Inset of (b) shows the captured CO₂ molecules in the grooves indicated by green arrows. (d, e) STM images of short PDI chain, which can be reshaped to long ordered double chain structures after heating to ~200 K.

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IV.   CONCLUSION

The self-assembly behavior of PDI molecules and their interaction with CO₂ on Ag(110) exhibit unique characteristics, which significantly differ from the behaviors observed on Au(111), Au(100) and Ag(111) surfaces [13−15]. The orthogonal lattice on Ag(110) makes natural confinement for the formation of straight double chain structures of PDI molecules along [001] direction, and the interchain width can be turned with ${\alpha }_{\left[1\bar{1}0\right]}$. The flexibility and mobility of PDI chain structures are actually reflected in porous crystal materials such as MOFs and COFs, where the “breathing effects” have been designed, with the interpore size or framework structure responding to the gas composition and partial pressure [46−48].

In summary, we have revealed a flexible and dynamic PDI chain structure on Ag(110) surface for self-adapted CO₂ capture and release. At 80 K, PDI molecules adsorb on Ag(110) with standing-up configuration and organize into long-range ordered zigzag double chain structures. In situ STM experiments reveal the CO₂ capture and release by the PDI double chain grooves, where the interchain width are self-adapted to 3${\alpha }_{\left[1\bar{1}0\right]}$, 4${\alpha }_{\left[1\bar{1}0\right]}$ and 5${\alpha }_{\left[1\bar{1}0\right]}$ with different amount of CO₂ molecules. DFT calculation proposes the possible CO₂ adsorption structures and charge transfer between CO₂ and PDI structures, suggesting a physisorption process of CO₂ in PDI grooves. The physisorption nature guarantees a controllable reverse process of CO₂ release by heating from 80 K to ~150 K. Our results could provide valuable single-molecule-level information for the design of molecular materials for highly efficient gas capture, storage and release.

Supplementary materials: Different adsorption configurations of PDI on Ag(110) at the low temperature of ~5 K, and at the high temperature of ~300 K; the charge difference map of upright standing PDI in the double chain structure on Ag(110); the calculated energy barrier for PDI migration along the [$1\bar{1}0$] direction are shown.