Quantum tunneling in real space: Tautomerization of single porphycene molecules on the (111) surface of Cu, Ag, and Au

Quantum tunneling of H atoms (or protons) was recognized already at the dawn of quantum chemistry¹ and found to play a significant role in important chemical and biological reactions.^2–4 Coherent tunneling in H-bond rearrangement and H-atom transfer reactions has been studied extensively by means of high-resolution rotational–vibrational and electronic spectroscopies in which tunneling is manifested as splitting of rotational/vibrational levels.^5,6 Intramolecular H-atom transfer reactions, the so-called tautomerization, in organic molecules have served as an important model for studying hydrogen dynamics.⁷ For instance, tautomerization of malonaldehyde^8–13 and tropolone^14–20 has been intensely investigated by spectroscopic experiments and quantum chemical calculations. These studies revealed that relatively heavy atoms (e.g., carbon or oxygen) in the molecular frame also contribute to the tunneling process.

Recently, low-temperature scanning tunneling microscopy (STM) has been used to observe directly single-molecule tautomerization in porphyrin and phthalocyanine derivatives on surfaces.^21–25 Particularly, porphycene, the first synthesized structural isomer of porphyrin,²⁶ has emerged as a fascinating model of intramolecular H bonding and a double H-atom transfer.^27,28 Due to the strong H bonds in the molecular cavity,²⁹ the energy barrier of tautomerization in porphycene is relatively small, leading to a fast tautomerization rate^30,31 and a considerable contribution of hydrogen tunneling.^32–34 Recently, we have demonstrated that tautomerization in a single porphycene molecule can be induced by various stimuli, namely heat, electrons, light, and chemical force.^35–39 These studies not only revealed the microscopic reaction mechanisms but also highlighted that adsorption of porphycene on a surface results in additional complexities in the tautomerization dynamics, caused by the interaction between the molecule and the surface as well as symmetry lowering due to the adsorption. Moreover, low-temperature STM has also been used to probe directly tunneling dynamics of H-atom diffusion,⁴⁰ H-bond rearrangement in small water clusters,^41,42 and tautomerization,⁴³ and the zero-point energy contribution in the H bond.^44,45 Interestingly, tunneling of heavy atoms or molecules was also observed for Cu,⁴⁶ Co,⁴⁷ and CO⁴⁸ on a Cu(111) surface at cryogenic temperatures. One of the unique capabilities of a low-temperature STM is to manipulate the potential landscape of adsorbate reactions by modifying a local environment of the molecule,^36,37 which enables us to control precisely tunneling dynamics.^42,43 Another, yet almost unknown, influence on the hydrogen tunneling results from the surface. Here we present a study on the tunneling dynamics of tautomerization in single porphycene molecules on different noble metals, namely Cu(111), Ag(111), and Au(111), by a combination of STM experiments and DFT calculations.

All experiments were performed in an ultra-high vacuum chamber (base pressure of 10⁻¹⁰ mbar), equipped with a low-temperature STM (modified Omicron instrument with Nanonis Electronics). All STM images were acquired in the constant-current mode. The bias voltage was applied to either the tip (V_t) or sample (V_s), and all voltages are indicated as the sample bias V_s (=−V_t). The Cu(111), Ag(111), and Au(111) surfaces were cleaned by repeated cycles of argon ion sputtering and annealing. The STM tip was made from a W or PtIr wire and optimized in situ by applying a voltage pulse and poking the tip apex into the surface in a controlled manner. Porphycene molecules were deposited onto the surface at room temperature from a Knudsen cell (at 450–500 K).

The geometric structures and the minimum energy paths (MEPs) of the adsorbed porphycene molecule on the Cu(111) and Ag(111) surfaces were obtained from van der Waals corrected DFT calculations using FHI-aims⁴⁹ and the Vienna ab initio simulation program (VASP).⁵⁰ In the VASP calculations, the electron–ion core interactions and the exchange–correlation effects were treated using the Projector Augmented Wave (PAW) method⁵¹ and the optB86b and vdW-DF-cx versions of the van der Waals density functional,^52–55 respectively. The Cu(111) surfaces were represented in a super-cell by a four-layer slab with a (6 × 6) surface unit cell with a 20 Å vacuum region and by using 3 × 3 × 1 k-grids. In the simulations performed with FHI-aims, we used the PBE functional augmented with van der Waals interactions tailored for surface adsorption (PBE+vdW^surf)⁵⁶ (unless specified otherwise), where we ignored the vdW contribution for pairs of metallic atoms, used tight settings for numerical grids and basis sets, a 6 × 6 surface including 4 metallic layers, a vacuum separation of 60 Å, and a k-grid of 12 × 12 × 1 for Cu(111) and 14 × 14 × 1 for Ag(111). In all calculations, we have employed a dipole correction in order to optimally decouple periodic images.⁵⁷ The MEPs were computed with the nudged elastic band method and the string method.^58,59 STM images were simulated considering a 0.2 eV window below the Fermi level with the Tersoff-Hamann model.^60,61

Figures 1(a) and 1(b) show an STM image of a single porphycene molecule on Cu(111) at 5 K in the trans and cis configurations, respectively. The surface lattice underneath the molecule (white grid lines) is determined from atomic-resolution images using the point contact method with a Cu adatom^47,62 (see the supplementary material, Fig. S1). The trans configuration is the thermodynamically stable form, whereas the cis configuration occurs as a meta-stable form.^37,38 A trans porphycene can be converted to the cis configuration in an unidirectional fashion either by injecting tunneling electrons from the STM³⁷ or photo-excitation,³⁸ whereas the backward cis → trans tautomerization can be induced by heating the surface and all cis molecules are converted to the trans configuration above ∼35 K. Although the cis ↔ cis tautomerization also occurs (cf. Fig. 3), no trans ↔ trans conversion was observed. The STM images [Figs. 1(a) and 1(b)] suggest a slight migration of porphycene upon the trans → cis tautomerization (see also the supplementary material, Fig. S2), which is estimated to be 0.7(±0.3) Å along the high-symmetry axis, e.g., the [110] direction, of Cu(111). Figures 1(c)–1(h) display the simulated STM images and the optimized structures on Cu(111). We have performed an exhaustive grid search of possible geometries of the trans and cis tautomers on Cu(111), by translating the center of mass and rotating the structures. Since porphycene can adopt distorted geometries on the surface, we found several minima that differ by slight rotations and buckling of the molecule, which differ by up to 0.1 eV in energy. In the following, we discuss only the lowest-energy structures. The optimized structures [Figs. 1(e) and 1(f)] reveal that the trans and cis porphycene adsorb on a different site with a relative displacement of about 0.7 Å, which is in good agreement with the migration distance observed in the experiment [Figs. 1(a) and 1(b)]. We discuss the adsorption site in terms of the character of the hollow or bridge site closest to the center of mass of the molecule. The theoretical STM images in Figs. 1(c) and 1(d) show remarkable agreement with the experiments. The calculated structures show a deformation of the macrocycle of porphycene [Figs. 1(g) and 1(h)], which is planar in the gas phase. The distortion can be attributed to the stronger interaction of the imine N atoms with the surface Cu atoms underneath. The simulated charge density differences (Fig. 2) indicate that the density rearrangement between the imine N atoms and the surface Cu atoms is larger than that for the amine groups. This deformation of the macrocycle leads to weakening of the inner H bonds, which is manifested as a significant blue-shift of the calculated harmonic frequencies of the symmetric and anti-symmetric N–H stretches compared to the gas-phase (Table I). Additionally, a Hirshfeld analysis⁶³ indicates that both tautomers of porphycene on Cu(111) are negatively charged with about 0.5e. This charging is in line with the experimental observation that porphycene does not aggregate spontaneously on the surface and no island formation occurs at low coverage.³⁷ 

Overall, experimental and theoretical results appear to be consistent within the expected error bars of around 10 meV in calculated energy differences. With the functionals used, we find the trans isomer to be isoenergetic or slightly lower in energy than the cis tautomer (Table II). Recently, Novko et al. showed that the treatment of dispersion interactions and the choice of exchange–correlation functionals could play a role to determine the relative stability between the trans and cis configurations of porphycene on Cu(111).^64,65 However, they did not take into account the migration of porphycene upon the tautomerization as described above. Our calculations show that placing a trans tautomer on the hollow (hcp) site (the preferred site for the cis tautomer) results in a spontaneous migration (barrierless) from the hollow site to the bridge site [Fig. 1(e)] when relaxation is allowed. For the cis ↔ cis tautomerization, we also find that porphycene moves from the hcp to the fcc site spontaneously, thus this process is also barrierless.

Figures 3(a) and 3(b) show STM images of a cis porphycene before and after one cis → cis tautomerization event. The tautomerization can be induced either by injecting energetic electrons from the STM³⁷ or photo-irradiation.³⁸ Additionally, we find that the cis ↔ cis tautomerization also occurs spontaneously even at 5 K, although the rate is much smaller than that of the STM- or photo-induced processes. By comparing the position of porphycene relative to the Cu adatom nearby, it is revealed that porphycene moves upon the tautomerization. The migration direction is governed by the molecular orientation; it takes place along one of the high-symmetry axes of Cu(111) which follows the long axis of porphycene, and no rotation of porphycene was observed. The calculated structure provides atomistic insight into the migration. As discussed above, the imine N atoms in the cis porphycene are strongly bound to the surface Cu atoms underneath [Figs. 2(c) and 2(d)]. The translation of the molecule by $∼1.4(≈a022)$ (along the [110] axis) makes it possible for the newly formed imine N atoms to resume a similar bonding geometry with the Cu atoms. It should also be noted that the translation results in a change of the adsorption position of porphycene, i.e., between the hcp and fcc sites of Cu(111). Porphycene at the hcp site is only 7 meV more stable than at the fcc site (Table II) in our calculations, including zero-point energies (ZPEs). In experiment we were not able to discriminate between the porphycene molecules at the fcc or hcp site in the STM image. However, a possible difference resulting from the fcc or hcp site is observed in the tautomerization rate (as discussed below), which indicates that the calculated energy difference between the cis tautomers on the fcc and hcp sites may be real. Our calculations also find that the trans–trans tautomerization without any translational motion of the molecule results in an increase of the total energy by more than 0.15 eV with respect to the optimized geometry; thus, the process should occur via the cis configuration.

Figure 4(a) shows the current dependence of the cis ↔ cis tautomerization rate obtained at different bias voltages. At 170 mV, tunneling electrons trigger the reaction through vibrational excitation via an inelastic electron tunneling process.³⁷ The rate increases linearly with increasing current, indicating that the reaction proceeds via a single-electron process. Additionally, a possible difference between the cis(hcp) → cis(fcc) and cis(fcc) → cis(hcp) tautomerization is observed. The upward and downward triangles in Fig. 4(a) represent the rate determined for odd- and even-numbered cis → cis tautomerization events, respectively. With this analysis, a possible difference in the tautomerization rate from the hcp to fcc site and vice versa may appear since every cis → cis tautomerization event changes the adsorption site. We find, in this experiment, a higher tautomerization rate for the even-numbered events than that for the odd-numbered ones. According to the calculations, the cis configuration at the hcp site is slightly more favorable than that at the fcc site. Therefore, the even-numbered events may be assigned to the cis(fcc) → cis(hcp) transition. On the other hand, the rate obtained at a bias voltage of −50 mV shows only a rather weak dependence on the current [Fig. 4(a)], indicating that the tautomerization is not induced by the tunneling electron and besides the influence of an electric field and tip–molecule interactions also plays a minor role. The tautomerization rate is also not significantly affected at a voltage of −10 mV. Note that the tautomerization rate shows a similar dependence at both bias polarities.^37,38 Because tautomerization occurs much less frequently at −50 mV, we obtained the rate by monitoring approximately 100 molecules in the consecutive STM images and sampling all the events (see the supplementary material). Hence, a possible difference in the tautomerization rate between the cis(fcc) and cis(hcp) molecules was not considered. This procedure provides the average rate between the cis(fcc) → cis(hcp) and the opposite processes. Importantly, the tautomerization rate at −50 mV shows a rather weak dependence on the temperature below ∼23 K [Fig. 4(b)], indicating that the process is governed by quantum tunneling. Note that the tautomerization rate appears to be significantly affected by the tip conditions. For instance, the use of a different tip or strong in situ tip forming procedure such as application of a voltage pulse and controlled indentation of the tip into the surface results in variation of the rate [data obtained with different tip conditions at 5 K are shown in Fig. 4(b)]. As we have demonstrated recently, the interaction between an STM tip and porphycene can modify the potential energy surface of the tautomerization.³⁹ Such a modification of potential energy surface may have a crucial impact particularly on the tunneling process. However, the lack of detailed knowledge of the tip apex structure hampers further quantitative description. A similar tip-to-tip variation was also observed for the cis ↔ cis tautomerization via tunneling on Ag(110).⁴³ The different behavior below and above ∼23 K could be traced to a different H-atom transfer mechanism. For example, our DFT calculations find that a translational mode of the molecule starts being thermally excited at around 25 K, which would add a thermally activated contribution to tautomerization. However, the cis → trans conversion does depend on temperature even below 23 K, indicating a different mechanism, likely through thermally assisted tunneling.

It is evident that the cis ↔ cis tautomerization is coupled with the translational coordinate of porphycene along the surface (cf. Fig. 3). Additionally, the tautomerization can occur either in a stepwise or concerted fashion. In the former case, individual H atoms move separately and the reaction proceeds through a trans configuration. In the latter case, the H atoms are transferred collectively. Figure 5 displays the two-dimensional potential energy surface calculated for the stepwise cis ↔ cis tautomerization, where the vertical and horizontal axes correspond to the coordinate of the translational motion of the molecule and the H-atom transfer, respectively. We only calculated the points marked with a cross in Fig. 5 and the others were obtained by an interpolation with cubic splines so that Fig. 5 should be taken as a qualitative representation of the potential energy surface. These energies do not include any ZPEs. We find that at this level, the stepwise pathway is energetically more favorable than the concerted one, with barriers along the minimum energy path of 76 meV for cis–trans and 135 meV for cis–cis (PBE+vdW^surf). The potential energy surface also reveals that the double H-atom transfer without migration of the molecule (path along the black arrow in Fig. 5) is not feasible because of a large activation barrier (369 meV). The trans configuration along the MEP is the same as the optimized structure in Fig. 1(e). However, in experiment, the trans configuration was not observed as a transient state during the cis ↔ cis tautomerization, and in addition, the cis → trans conversion rate is much smaller below about 23 K [Fig. 4(b)] and not observed at 5 K. The experimental results indicate that the cis ↔ cis tautomerization is governed by tunneling at low temperatures. However, a full evaluation of this path including ZPE and tunneling, e.g., with path-integral molecular dynamics simulation, is beyond the scope of this work.

The tautomerization rate via tunneling is largely reduced for porphycene on the Cu(111) surface compared to the isolated molecule, e.g., 6 × 10¹¹ Hz for the trans ↔ trans tautomerization determined from the tunneling splitting of 4.4 cm⁻¹ in the vibronic levels of the ground state.³³ This reduction of the rate can be explained by the increase of the tautomerization barrier compared to the isolated porphycene in inert media (estimated to be ∼23 meV³⁰). Additionally, the translational motion of porphycene during tautomerization on the surface leads not only to an increase of the path length and barrier but also to participation of other relatively heavy atoms (C and N atoms) in the reaction, giving rise to a further reduction of the tunneling rate.

Porphycene was also investigated on a Ag(111) surface. The STM appearance and adsorption geometries are similar to those on Cu(111) [Fig. 6(a)]. However, tautomerization between the trans and cis configurations also occurs spontaneously even at 5 K as well as the cis ↔ cis tautomerization with the latter being much more frequent. The resident time of the trans tautomer is significantly longer than of the cis tautomer. Therefore, the former appears to be the thermodynamically stable form. Although a direct trans ↔ trans conversion event was rarely observed, we note that this might be attributed to the limited time resolution of the STM and the process could actually happen via the cis configuration. The displacement of porphycene is also observed in these tautomerizations (supplementary material, Fig. S4). The cis ↔ cis tautomerization rate on Ag(111) is obtained to be about 0.01 Hz at 5 K and does not depend on the tunneling current [Fig. 6(b)], suggesting that the process is governed by tunneling. It should be noted that the rate may be affected by tip conditions. The tautomerization rate on Ag(111) is about two orders of magnitude higher than on Cu(111). This suggests a smaller tautomerization barrier due to the weaker interaction of porphycene with the Ag(111) surface. Our calculations reveal that the trans and cis configurations on Ag(111) are essentially isoenergetic, with the trans configuration being only 4 meV more stable than cis (Table III). However, the translation from hcp to bridge site in the cis–trans tautomerization and from hcp to fcc site in the cis–cis tautomerization, observed for porphycene on Cu(111), does not happen spontaneously on Ag(111) due to a very low barrier in our calculation. Table IV summarizes the porphycene–surface distance, buckling of the molecule, and calculated binding energies taking as a reference the molecule in the gas-phase. The buckling of the cis porphycene is smaller on Ag(111) than Cu(111) due to a weaker interaction of the molecule with the surface atoms, which is also reflected in the larger molecule–surface distance on Ag(111). Additionally, the calculations indicate a significantly smaller charge density rearrangement of porphycene on Ag(111) [Figs. 6(e) and 6(f)] as compared to Cu(111) (Fig. 2), corroborating the relatively weak interaction of the molecule with Ag(111). Therefore, the potential energy surface of tautomerizations on Ag(111) is expected to be less corrugated than that on Cu(111), which rationalizes the much higher tautomerization rates observed in the experiment on Ag(111) than on Cu(111).

Porphycene was also investigated on the Au(111) surface where the molecules rapidly diffuse even at 5 K and under very low voltage and current conditions, like V_s = 10 mV, I_t = 1 pA. This rapid diffusion suggests a weaker interaction of porphycene with the Au(111) surface compared to Cu(111) and Ag(111). However, stationary molecules can be found at elbow sites of the herringbone reconstruction of Au(111) [Fig. 7(a)]. Unlike for porphycene on Cu(111) and Ag(111), the trans and cis tautomers are indistinguishable in the STM image [Fig. 7(b)] and no evidence of a possible tautomerization was observed. The hopping and rotation of porphycene at the elbow site can be induced when the bias voltage is increased [Figs. 7(c)–7(h)]. However, the STM appearance does not change significantly upon hopping and rotation. The absence of any discernible trans or cis configuration suggests that either the tautomerization rate is much faster than the time-resolution of the STM (hundreds of microseconds) or the molecular orbitals of trans and cis cannot be distinguished. Our DFT calculations reveal that the frontier orbitals of trans and cis tautomers in the gas-phase appear to be similar (see the supplementary material, Fig. S5), and the weak interaction between the molecule and Au(111) is close to the gas-phase limit, making these tautomers indistinguishable in the STM image.

Single porphycene molecules were investigated on Cu(111), Ag(111), and Au(111) surfaces by using low-temperature STM. We find a correlation of the adsorption structure and tautomerization dynamics with the interaction strength between porphycene and the surfaces. On Cu(111) and Ag(111), the trans configuration is found to be the thermodynamically stable form, whereas the cis configuration occurs as the meta-stable form. On Cu(111), the cis ↔ cis tautomerization occurs spontaneously even at low bias voltages (<50 mV) and the tautomerization rate is temperature independent at low temperatures, indicating that the process is governed by quantum tunneling. However, on Ag(111), the cis ↔ cis tautomerization rate is much greater than on Cu(111) and trans ↔ cis tautomerization occurs spontaneously at 5 K, indicating smaller potential barriers for the tautomerization on Ag(111) than on Cu(111) because of the weaker porphycene–surface interaction. Additionally, it is also found that the tautomerization of porphycene on Cu(111) and Ag(111) occurs with a migration of the molecule along the surface. This indicates that the translational motion of porphycene couples with the tautomerization coordinate. The adsorption geometries of porphycene were obtained on the Cu(111) and Ag(111) surfaces by using van der Waals corrected DFT calculations. The calculated structures revealed that the porphycene macrocycle, which is planar in the gas phase, is deformed on both surfaces due to the interaction of the molecule with the surface atoms. This distortion is smaller on Ag(111) than on Cu(111), which points to a weaker interaction of porphycene with Ag(111) than with Cu(111), corroborated by smaller charge density rearrangement of the molecule on the former. The two-dimensional potential energy surface of the tautomerization was also examined on Cu(111). Our calculations predict that the translational motion of porphycene upon tautomerization and the calculated barriers for all tautomerization processes are too high to be overcome at cryogenic temperatures used in the experiment. Zero-point energy corrections to the minimum energy structures do not change the potential energy landscape. This observation, together with the experimental results, suggests that the tautomerization proceeds predominantly by tunneling. Indeed, in our current calculation that does not include nuclear quantum effects, we predict that the cis ↔ cis tautomerization would likely happen through a stepwise mechanism, which was not observed experimentally. The multidimensional nature of this tunneling process calls for a high-level theoretical treatment of the inclusion of tunneling in the reaction rates, which is a natural next step for this work. Finally, on the Au(111) surface, it is not possible to discern trans and cis tautomers by the STM images and thus no tautomerization rate could be extracted. This observation may suggest that the tautomerization rate is much faster than the time resolution of the STM or that due to the similarity of the frontier molecular orbitals of the trans and cis configurations in the gas-phase, these tautomers may become indistinguishable for the STM when the interaction with the surface is very weak.

See supplementary material for (1) adsorption geometry analysis of porphycene on Cu(111) using point contact imaging with a Cu adatom, (2) migration of porphycene upon trans → cis tautomerization on Cu(111), (3) analysis of the cis ↔ cis tautomerization rate on Cu(111) at V_s = 170 mV, (4) analysis of the cis ↔ cis tautomerization rate on Cu(111) at low voltages and temperatures, (5) analysis of the cis → trans and cis ↔ cis tautomerization rate on Cu(111) at elevated temperatures, (6) migration of porphycene upon tautomerization on Ag(111), (7) analysis of the cis ↔ cis tautomerization rate on Ag(111), and (8) images of HOMO and LUMO of trans and cis porphycene in the gas-phase. We also provide the geometries of the cis and trans isomers of porphycene on Cu(111) optimized with the PBE+vdW^surf functional used in this work.

T.K. acknowledges the support of Morino Foundation for Molecular Science. J.W. acknowledges the Polish National Science Centre Grant No. 2016/22/A/ST4/00029. Y.L. and M.R. acknowledge computer time from the Swiss National Supercomputing Centre (CSCS), under Project No. s719. M.P. acknowledges computer time allocated on ARCHER through the Materials Chemistry Consortium (EPSRC Grant No. EP/L000202), on Polaris through N8 HPC (EPSRC Grant No. EP/K000225/1) and on Chadwick at the University of Liverpool.