Breaking a dative bond with mechanical forces

Bond breaking and forming are essential components of chemical reactions. Recently, the structure and formation of covalent bonds in single molecules have been studied by non-contact atomic force microscopy (AFM). Here, we report the details of a single dative bond breaking process using non-contact AFM. The dative bond between carbon monoxide and ferrous phthalocyanine was ruptured via mechanical forces applied by atomic force microscope tips; the process was quantitatively measured and characterized both experimentally and via quantum-based simulations. Our results show that the bond can be ruptured either by applying an attractive force of ~150 pN or by a repulsive force of ~220 pN with a significant contribution of shear forces, accompanied by changes of the spin state of the system. Our combined experimental and computational studies provide a deeper understanding of the chemical bond breaking process.

outside a spherical domain. We set the boundary sphere radius to 1100 pm. All atoms in the system are relaxed. The Fe-C bond length equals 168 pm in the final relaxed structure.

(2) CO-FePc and FePc complex on a Cu(111) substrate
Next, we model the CO-FePc complex on the copper substrate by placing the optimized CO-FePc complex on the surface. We model the substrate by a 4-layer 8x10 Cu(111) surface and place the CO-FePc (or FePc) complex at a bridge site. We employ an orthorhombic unit cell where a = 2042 pm, b = 2211 pm. We use a 2D slab boundary condition that assumes the system to be periodic along the x and y directions. We perform the calculations at the Γ point as the system is sufficiently large to obtain a reliable density from this point alone. We set the slab width to 2160 pm and fix the bottom 2 layers of the substrate during the relaxation. The Fe-C bond length increased from 168 pm to 175 pm in the final relaxed structure of CO-FePc. Furthermore, the distances between the center Fe atom and the middle of the two bridge Cu atoms decreased by ~ 30 pm upon CO removal.

(3) Probe tips with CO-FePc complex on a Cu(111) substrate
We model the interactions between different probe tips and the CO-FePc complex on the substrate by including the tips on top of the previously optimized geometries. Here, we still use a 2D slab boundary condition and set the slab width to 2670 pm. As for probe tip modeling, while some groups have modeled the probe tip as a combination of a metal cluster with an apex functionalized tip 7-9 , we obtain accurate images without including the metal cluster [10][11] despite the fact that the nominal tip apex radius is significantly larger than these theoretical models. We indeed find that including the Cu cluster has a negligible effect on the interaction energy as a function of tip-sample distance for both Cu tip (tests done on Cu2N and graphene) 12 and CO tip (tests done on benzene) 13 .
In agreement with our finding, a recent study on forces acting on a CO tip obtained reliable results by including only a single CO molecule 14 . In addition, we compute the tip-sample interaction energies for different tip conformations as a function of tip height, which is defined as the distance between the front atom of the tip and the average height of the FePc complex (excluding the decorated CO). For Cu tip, we tested Cu2 and Cu4 tips ( Supplementary Fig 2 a); for CO tip, we test CO, CuCO, Cu2CO and Cu4CO ( Supplementary Fig 2 b). In both cases, we do not see a significant variation in the interaction energy. Therefore, we confirm that our previous conclusion is still valid for the CO-FePc molecule.

(3.1) Cu tip
We model the Cu tip first because as there are less variables involved in terms of modelling it when compared to the CO tip. In the presence of the Cu tip, we relax the system again including a previously optimized Cu2 cluster on top of the complex. In our optimized model structure, Fe, C, O and two Cu atoms are lined vertically along the center axis of the molecule.

(3.2) CO tip
When modeling a CO-functionalized tip, we use a previously optimized Cu-CO cluster. A direct calculation of the rupture force is difficult as the position of the tip relative to the CO-FePc complex is unknown in the three-dimensional space and more than one solution is possible for a given rupture force. To estimate the forces, we first optimize the vertically aligned tip-samplesubstrate system with the tip above the center Fe atom. However, we find that varying the tip height in this vertically alighted geometry cannot rupture the dative bond. Next, we break the symmetry by displacing the tip horizontally by a small amount (~135 pm) from the equilibrium position and then adjust the tilting angles of the two COs so that the O-O distance (~250 pm) is kept constant. This allows for the existence of lateral forces. We then perform structural relaxation again. Once the new equilibrium structure is obtained, we compute the spatial distribution of the forces by manually displacing the CO tip to different sites while keeping all atomic positions fixed.
Note that, the O-O distance is no longer constant in the calculations of the force distribution. We expect the calculated forces to be overestimated as the tip moves further away from the equilibrium position owing to the fixed positions.
In order to ensure that our equilibrium structure is reliable, we perform additional structural relaxation calculations as the CO tip horizontally approaches the center of the sample molecule.
For simplicity, we exclude the substrate in our calculation as our objective is to obtain a general trend of the bending motion of the two COs. We illustrate this process at different tip-sample separation distances in Supplementary Fig 3. The relaxed atomic coordinates for all the conformations are given in Supplementary Data 1-6. These structures are in good agreement with previous studies [15][16] . As shown in Ref. [16], when the COs are close to each other, they bend due to repulsion while the general orientation of the two COs remains the same (parallel) as when they bend due to attraction.

Image Simulations
We employ a frozen density embedding theory (FDET) method for image simulations. Details about FDET and previous applications can be found in Ref [10][11][12][13]17]. We also apply a tip tilting correction 18 for the CO tip (Eq. 2). We compute the displacement of the tip in x and y directions, is the lateral spring constant of the CO tip. is an adjustable parameter which is set to be 0.80 N/m in the main text to achieve a better agreement with the experimental images.
Here, Supplementary Fig 4 shows

AFM Tip Scan Speed
For AFM measurement, the noise level can be adjusted by the scan speed of the tip. The longer the tip stays on one point, the lower the noise is. However, increasing the time of each point will also increase the drift, which will result in distortion of the image and inaccuracy of the data. The scan speed is about 20 ms -100 ms for each point, so the actual scan speed during our measurement is about 0.5 nm/s.