Chirality control of a single carbene molecule by tip-induced van der Waals interactions

Non-covalent interactions such as van der Waals interactions and hydrogen bonds are crucial for the chiral induction and control of molecules, but it remains difficult to study them at the single-molecule level. Here, we report a carbene molecule on a copper surface as a prototype of an anchored molecule with a facile chirality change. We examine the influence of the attractive van der Waals interactions on the chirality change by regulating the tip-molecule distance, resulting in an excess of a carbene enantiomer. Our model study provides insight into the change of molecular chirality controlled by van der Waals interactions, which is fundamental for understanding the mechanisms of chiral induction and amplification.


Supplementary Discussion 1. Chirality change of DPC in gas phase
The diphenylcarbene (DPC) is helically chiral in gas phase. It exists as two enantiomeric states M and P. The two phenyl rings are rotated by a dihedral angle of ± 46° (labels 1, 2, 3, 4 of M and P, Supplementary Fig. 1a) to reduce steric hindrance. 3 To estimate the energy barrier of the chirality change, we calculate the potential energy by altering the dihedral angle of the DPC molecule in steps of 1° ( Supplementary Fig. 1b).
The calculated energy barrier to change the chirality of DPC by rotating its C−C−C bonds is 72 meV, going through a transition state (TS) where its two phenyl rings are coplanar ( Supplementary Fig. 1b). The calculated chirality change in gas phase with a low energy barrier corroborates the flexible nature of the C−C−C bonds of DPC.

Supplementary Discussion 2. DPC enantiomers in different orientations.
In the main text, we show DPC enantiomers in two of their six orientations (Fig. 2c,d).
Here, we display DPC enantiomers in their six orientations ( Supplementary Fig. 2). The R-type and L-type enantiomers are rotated with respect to the <112> directions of the surface by angles of ± (16 ± 2)°, respectively.

Supplementary Discussion 3. Immobile center during the chirality change of DPC
As discussed in the main text, the carbene center serves as an anchoring site on Cu(111). This leads to an immobile center during the chirality change of the DPC molecule.
To determine this center, we plot the vertical bisectors (lines I and II, Supplementary Fig.   3a,b) of the main axes of the DPC molecules (solid lines, Supplementary Fig. 3a,b). The intersection of the two vertical bisectors determines the immobile center, i.e., the carbene center (grey spheres in Supplementary Fig. 3c,d). It should be pointed out that the bisection is based on the projection of the DPC molecules on Cu(111), which might introduce a small deviation in identifying the positions of the carbene center. Nevertheless, it corroborates the assignment in the main text that the carbene centers are situated at the sides of the depressions (Fig. 2c,d).

Supplementary Discussion 4. Schematics of chirality change of DPC on Cu(111)
In the main text, we flip the chirality of DPC by IET manipulation in pairs of Rn⟷Ln (n = 1, 2, and 3, Fig. 2b and Supplementary Fig. 2). The calculations reveal that the higher phenyl ring (1) of DPC absorbs close to a bridge site of Cu(111) (Supplementary Fig.   4a,b), but the lower phenyl ring (2) to a hollow site ( Supplementary Fig. 4c,d). The different adsorption sites lead to different ring-surface interactions and thereby different heights (ℎ ! and ℎ " ) of the two rings with respect to the surface. Thus, the molecule is In Fig. 3c of the main text, the electron yield vs. voltage was fitted separately in three voltage ranges by two-level Boltzmann functions where low and high are the low and high yield levels in the corresponding voltage ranges, is the apparent first-order constant, and !/" is the voltage required to reach half the yield between low and high . Here, we demonstrate the fitting procedure in the range between 140 mV and 200 mV. As shown in Supplementary Fig. 6, the fitting curve

Supplementary Discussion 8. Energy barrier of chirality change of DPC on Cu(111)
As discussed in the main text, the yield changes at three threshold voltages of (64 ± 2) mV (I), (125 ± 2) mV (II), and (161± 1) mV (III) (Fig. 3c). These values fit nicely to the infrared spectra of DPC in rare gas matrices, with one skeletal vibrational mode at 62 meV and two C-H deformation modes at 126 meV and 172 meV. 4 Power law fittings #! ∝ * give ≈ 1 (Fig. 3d), indicating a single tunneling electron being sufficient to excite the vibrational mode above the energy barrier of the chirality change ( Supplementary Fig. 8). We thus propose that the energy barrier of the chirality change of DPC on Cu(111) is below the lowest threshold energy at (64 ± 2) meV (I).

Supplementary Discussion 9. Estimation of z-offset
The observation of vacuum tunneling was established by the exponential dependence of the tunneling current on the width of the tunneling gap. 5 Based on this, we use an I-z curve to estimate the z-offset of the STM tip with respect to the initial setpoint at a tunneling resistance of 2 GΩ. A low voltage of 10 mV is applied during approach to avoid the chirality change of the DPC molecule. As expected, the tunneling current decays exponentially as a function of the z-offset (Supplementary Fig. 9). Based on the I-z curve, we calculate the z -offset of the STM tip from the corresponding tunneling parameters.

Supplementary Discussion 10. Derivation of potential well depths from I-t trace
In Fig. 4 of the main text, we show the change of DPC between its two enantiomers with the I-t trace, the occupations in time, the normalized occupations, and potential well depths. Here, we exemplify at one data set (z-offsets of 0.14 nm, Fig. 4e-h) how to derive the potential well depths from the I-t trace via the occupations in time and the normalized occupations ( Supplementary Fig. 10).
Step I: The occupations in time, Occ H and Occ L , are derived from a histogram of the I-t trace, displaying two well-separated maxima at the current values H and L . Their relative areas yield the percentages Occ H and Occ L during which the molecule is either in its high state (H) or its low state (L).
Step II: The occupations in time must be normalized to occupations per electron because, given the same time interval, there are more electrons flowing through the molecule for a higher current value than a lower one. Thus, more switching events will be generated per time interval for a higher current value than a lower one. To compensate for this effect, we define a normalized occupation probability where i with i = H or L represent the high-current (H) and low-current (L) states. They reflect the probabilities per electron for the molecule staying in the H or L states.
Step III: The molecule switching between the two states is considered as a classic system following the Boltzmann distribution. Thus, the energy difference is extracted based on the Boltzmann distribution -.

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where ∆ = H − L is the energy difference between the two minima of the double-well potential with depths of H and L , k is the Boltzmann constant, and is the surface temperature. For the example in Supplementary Fig. 10, ∆ = 0.5 meV is calculated from H ∶ L = 74.2% : 25.8% at = 5.1 K.

Supplementary Discussion 11. Tip-induced enantiomeric excess
In the main text, we present the asymmetric distribution of DPC between its two enantiomers induced by an STM tip apex (tip #1). The normalized occupation H increases monotonously with decreasing tip-molecule distance (Fig. 4). Here, we show another example recorded by another STM tip apex (tip #2). Likewise, the molecule prefers to stay more and more in the high current state with decreasing tip-molecule distance (see I-t traces in Supplementary Figure 11a

Supplementary Discussion 12. Influence of tip field on normalized occupation PH
In the main text (Fig. 4), we demonstrate that the ratio of H ∶ L is largely altered by the tip-molecule distance. Here, we modulate the electric field at a fixed tip-molecule distance (z-offset of 0.08 nm) for excluding other causes than the vdW interactions for the alteration. Increasing the voltage by a factor of four influences the normalized occupation H only marginally ( Supplementary Fig. 12). It excludes that the electric field induces the asymmetric distribution of DPC between its two enantiomers at closer tipmolecule distances.

Supplementary Discussion 13. Manipulating DPC by tip-induced interactions only
In the main text, we used inelastic electrons and tip-induced vdW interactions to mimic a chiral induction in a molecular assembly, where the chirality of the DPC molecule was reversibly switched in a well-controlled fashion without any unintended side processes (Fig. 1a). Here, we demonstrate the chirality change of DPC driven by tip-induced interactions only (Supplementary Fig. 13). However, this change demands stronger tipsample interactions that not only change the chirality of the molecule but also induce unintended side-processes, such as rotation ( Supplementary Fig. 13a to 13e) and translation ( Supplementary Fig. 13g to 13i). Because more than one process is induced by the manipulation, the frequency shift (∆ ) curves are often undefined. For instance, many ∆ curves do not follow the excepted Lennard-Jones potential but are dominated by sudden jumps. Nevertheless, we present a relatively well-defined ∆ curve which is altered by only one change to the molecule in the repulsive interaction regime (red arrow, Supplementary Fig. 13f). However, such changes have also been observed in the attractive interaction regime. Overall, these side processes undermine characterizing the influence of tip-induced interactions on the chirality change of the molecule by dynamic AFM.