## Introduction

The extent to which trapped, encapsulated, or otherwise confined atoms and molecules are influenced by changes in the external electrostatic environment is a fascinating problem. Endohedral fullerenes1,2,3 are an especially important molecular class from this perspective, with their properties exploited in areas as diverse as nanoelectronic components4,5, qubit candidates6, and ‘tracer’ species or contrast agents7,8. Of particular interest is the proposal that C60 acts as a Faraday cage9,10,11,12,13, screening out electrostatic fields from its interior, and allowing near-complete decoupling of the encapsulated species from the outside world. The extent of electrostatic decoupling remains, however, very much an open question.

‘Molecular surgery’14 has provided exciting new opportunities to study much larger fullerene-encapsulated species than previously possible. One of the most well-studied examples is H2O@C6014,15,16,17, in which the encapsulated water molecule is free of any hydrogen-bonded partner. Ortho-para nuclear spin conversion has been observed in H2O@C60 by nuclear magnetic resonance18,19,20, infra-red spectroscopy16,18, and pulsed terahertz spectroscopy17. Remarkably, ortho-para conversion has also been detected in this system by temperature-dependent capacitance measurements of bulk H2O@C60 crystals21, strongly suggesting that, despite the shielding offered by the surrounding fullerene cage, the encapsulated water molecule can have a significant influence on the external environment. HF@C60 has more recently been synthesized22 and provides a key comparative system to that of H2O@C60, not least because of the strong similarity in the dipole moments of free H2O and HF.

Hampered by the absence of clear experimental evidence, there has been considerable debate about the extent to which H2O interacts with the C60 cage4,23,24,25. Calculations of charge transfer result in a wide range of values26. Although some simulations suggest that the water molecule in H2O@C60 is electrostatically isolated24, other reports suggest that the position and orientation of the encapsulated H2O can be tuned via electric, magnetic, or photon excitation4, mechanical force27, or static (or dynamic) fields28.

Here we provide direct experimental measurement of the location of two separate encapsulated molecules, H2O and HF, each caged within buckminsterfullerene, C60, as illustrated in Fig. 1a. Through single-molecule scanning tunnelling microscopy, non-contact atomic force microscopy (ncAFM), and valence band photoemission, we show that the frontier orbital structure of the C60 molecule is unaffected by the presence of water inside the cage. Using the normal incidence X-ray standing wave (NIXSW) technique for the H2O@C60 : Ag(111) system, we determine the intra-cage location of both H2O and HF. The measured heights of the H2O and HF molecules above the Ag(111) surface are in good agreement with dispersion-corrected density functional theory (DFT) and molecular dynamics (MD) calculations, confirming the lack of chemical interaction of the encapsulated molecules with the surrounding carbon cage, yet revealing the strong influence of an adsorption-induced intra-fullerene electric field.

## Results

### C60 as a Faraday cage?

The local density of states of H2O@C60 was probed using scanning tunnelling microscopy (STM) measurements of a 70 : 30 mixture of empty and water-filled cages, deposited as a submonolayer on Cu(111). Analysis of C60 (sub)monolayers prepared at room temperature is complicated by the well-studied underlying surface reconstruction induced by fullerene adsorption29. Detailed low-energy electron diffraction (LEED) studies by a number of groups have provided compelling evidence that fullerene-induced vacancy reconstruction is prevalent on Cu(111) and Ag(111) surfaces30,31,32, with STM reports suggesting a mixed picture of ‘bright’ and ‘dark’ molecules33,34. To confirm the presence of surface reconstruction, we compared STM measurements with constant height ncAFM imaging (Fig. 1b, c), which clearly reveals that the mixture of ‘bright’ and ‘dark’ features in Fig. 1b is indeed due to the variation of the geometric height of the adsorbed molecules. This most likely arises from a combination of atom-top and vacancy adsorption sites; the brightness variations observed in the STM image of Fig. 1b are unrelated to water encapsulation (see Supplementary Information and Supplementary Fig. S1).

Despite STM’s exceptional sensitivity to minor changes in electronic structure, we found no difference between the appearance of empty and filled C60 molecules. This observation was confirmed across a wide range of different imaging parameters (Supplementary Fig. S1), strongly suggesting that the frontier orbitals of the fullerene are unperturbed by the presence of H2O. Similarly, ncAFM measurements, including force–distance analysis designed to compress individual fullerene cages, revealed no discernible differences (Supplementary Fig. S3) above the noise floor of our measurements. These observations were further confirmed using valence band X-ray photoemission spectroscopy (VB-XPS) at the Diamond Light Source (Beamline I09) collected at a photon energy of 110 eV. VB-XPS of a bulk film of 95% pure H2O@C60 (thick enough to completely attenuate the Ag 3d core-level photoelectron peaks from the substrate) was indistinguishable from that of C60 within the limits of the natural, and substantial, linewidth broadening. There is no discernable difference between the spectrum shown in Fig. 1d and that of empty C60, acquired at the same photon energy (see, in particular, ref. 35). The lack of an oxygen contribution to the highest occupied molecular orbital (HOMO) and HOMO + 1 features was also verified via resonant photoemission at the O K-edge (see Supplementary Information and Supplementary Fig. S2).

The fact that STM, ncAFM, and photoemission spectroscopy (including resonant photoemission) are each unable to distinguish between filled and empty C60 strongly suggests that neither electronic structure, the stiffness of the cage, nor the dielectric properties of the fullerene are appreciably affected by the presence of H2O (somewhat at odds with other findings21.) This seems to point towards a substantial screening of the encapsulate by the surrounding fullerene cage.

### Locating trapped molecules with NIXSW

Given the inability of scanning probes and photoemission to distinguish between filled and empty fullerene cages, we turned to the NIXSW technique36,37,38, illustrated in Fig. 2a, to determine the intra-cage position of each encapsulated molecule. The location of H2O was probed via the O 1s core-level photoelectron peak excited at the Ag{111} Bragg energy, whereas HF was located using F 1s photoemission. Figure 2a, b show the O 1s and F 1s photoemission peaks acquired with a photon energy of 700 and 900 eV, respectively (the lower photon energies, as compared to that used for the NIXSW measurements (hν = 2637 eV at 20 K), were chosen to enhance the photoabsorption cross-section for high-resolution photoemission measurements).

Ag(111) was chosen as a substrate for these synchrotron-based measurements, in order to exploit the well-defined (2$$\sqrt{3}$$ × 2$$\sqrt{3}$$)R30° molecular superlattice that forms on the silver surface30,39. Results were collected at temperatures ranging from 20 K up to 200 K, with particular care taken to limit the degree of both extrinsic water adsorption at low temperatures and beam damage (see Supplementary Information).

NIXSW results collected at 20 K for H2O@C60 and HF@C60 are shown in Fig. 2d, e, respectively (see also Supplementary Figs. S4S6 in the Supplementary Information file). The LEED patterns shown in the insets confirm the (2$$\sqrt{3}$$ × 2$$\sqrt{3}$$)R30° ordering of the molecular (sub)monolayer for both samples. The H2O@C60 XSW data averaged across the entire temperature range (see Supplementary Fig. S6) are best fit using a coherent position, Pc, of 0.36 ± 0.01 and a coherent fraction, Fc, of 0.72 ± 0.06 (see ref. 36 for a detailed explanation of the coherent position and coherent fraction parameters). These measurements translate to an oxygen atom position, z111(O), of 5.57 ± 0.03 Å above the Ag(111) surface. In comparison, and when again averaged across all temperatures, HF@C60 results in a coherent position, Pc, of 0.40 ± 0.05 and a coherent fraction, Fc, of 0.62 ± 0.07, placing the fluorine atom at a position, z111(F) = 5.7 ± 0.1 Å above the Ag(111) surface. The uncertainties in z111 in each case are an upper limit, determined from repeated measurements across different temperatures and sample preparations. Our NIXSW measurements show that the H2O and HF molecules are close to the centre of their respective fullerene enclosures.

### DFT and MD simulations

The results of the NIXSW measurements were compared to DFT calculations carried out within the Vienna ab initio simulation package (VASP)40 framework, using DFT-D341 to account for dispersion forces. Calculations for a single C60 molecule were checked against a DFT-D3 simulation of the (2$$\sqrt{3}$$ × 2$$\sqrt{3}$$)R30° cell (Supplementary Fig. S10), where the adsorption heights were found to be almost identical. The remaining discussion therefore focusses on a single fullerene either adsorbed on an atom-top site or above a single-atom vacancy30, both with a hexagonal face of the C60 cage aligned parallel to the surface.

Models of the DFT-D3-calculated geometries for H2O@C60 in the vacancy and atom-top arrangements are shown in Fig. 3a, b (see Supplementary Fig. S11 for HF@C60). A key observation is that, on adsorption, there are significant offsets in the position of the internal molecule relative to the centre of the C60 cage. For H2O@C60 and HF@C60 adsorbed in the vacancy site, the bottom layer of the C60 cage is calculated to be 1.89 Å above the surface Ag layer, resulting in a centre cage position of 5.17 Å. This is compared to an oxygen position of 5.03 Å and a fluorine position of 5.24 Å, i.e., the oxygen atom is located 0.14 Å closer to the surface, whereas for HF the fluorine is located 0.07 Å away from the surface. It is noteworthy that a detailed calculation of the potential energy surface of the frozen HF molecule inside the fixed C60 cage has also been reported42 using the DF-MP2 method43.

We find that the oxygen atom is located at 5.03 Å or 5.43 Å above the surface Ag(111) layer for the vacancy and atom-top structures, respectively—values that are both significantly different from that determined via the NIXSW measurements, i.e., 5.57 ± 0.03 Å. A similar discrepancy between experiment and DFT calculations is observed for the HF@C60 data: e.g., DFT calculations (VASP) for the relaxed vacancy model predict a separation between the fluorine atom and the uppermost Ag(111) layer of 5.24 Å, as compared to the NIXSW measurement of 5.7 ± 0.1 Å.

Calculated rotational energy barriers44 for water in H2O@C60 are of the order of 8 meV—the encapsulated molecule is extremely mobile. We similarly found that MD simulations (for T = 180 K, and within the CP2K-DFT-D3 framework45) revealed significant internal rotational motion. Figure 4a, b show plots of the internal molecular height and angle respectively, resulting in an average height increase of 0.3 Å relative to the ground state DFT calculation. This means that the average height is therefore 5.33 Å and 5.73 Å for the H2O molecule in the vacancy and atop structures, respectively (as discussed in the Supplementary Information, temperature-dependent NIXSW measurements showed little variation in the 20–200 K range. See Supplementary Fig. S6).

### Probing the intermolecular potential

The contribution of disorder notwithstanding, the theoretically predicted intra-cage positions of the encapsulated H2O and HF are due to charge redistribution from chemisorption of the C60 molecule on Ag(111)46,47,48, producing an intra-cage electric field with which the internal molecules interact (Fig. 3c inset). Good experimental evidence for the inhomogeneous electric field in H2O@C60 comes from O 1s photoelectron spectra. For a bulk endofullerene film, the O 1s peak associated with the encapsulated water has a Gaussian full width at half maximum (FWHM) of 0.7 eV, whereas for the chemisorbed monolayer the Gaussian width (under the same analyser operating conditions) increases almost 50% to 1.0 eV (compare Fig. 3c, d). The O 1s peak position, as referenced to the Ag 3d core level-binding energy, also shifts by ~200 meV. Given the lack of chemical interaction with the surrounding C60 cage, a plausible explanation for this 200 meV shift is that it arises from the difference in screening of the photogenerated core hole due to the modification of the intra-cage electrostatic environment.

Moreover, MD calculations semi-quantitatively explain the experimentally observed broadening of the O 1s photoemision peak and its shift to higher energies as compared to the bulk measurements. The O 1s core level shift (CLS) was approximately calculated49 as the energy required to excite the O 1s core electron for a sampling of different geometries of the H2O molecule inside the C60 cage obtained during the MD simulations (see Supplementary Information). We find that the FWHM value of the distribution of the O 1s CLSs for the adsorbed H2O@C60 is indeed larger than that for the gas-phase endofullerene, although the MD simulations produce a somewhat smaller increase in FWHM as compared to that seen in experiment (0.1 eV vs. 0.3 eV.) Similarly, the O 1s binding energy determined via this calculation shifts towards higher energy, again in agreement with experiment, although the magnitude of the shift is overestimated as compared to the experimental value (0.20 eV vs. 0.46 eV). Considering the approximate character of the method used for the calculation49, we would not expect full quantitative agreement. The fact that the calculation reproduces both the direction of the shift in binding energy and the increase in broadening of the core-level peak seen in the experiment provides good qualitative support for the presence and influence of the intra-cage electric field.

As noted above, C60 adsorption on metal (111) substrates is a surprisingly complex problem, being highly surface dependent29, and, as shown in Fig. 1c, is often associated with a significant inhomogeneity in molecular adsorption height. The majority of STM studies indicate a mixed picture33,34 of both ‘bright’ and ‘dark’ fullerenes (similar to those in Fig. 1b), where variations in brightness arise from a combination of atom-top and vacancy sites. In an influential piece of work, Li et al.30 suggested that C60 molecules on Ag(111) situate in vacancy sites, evidenced by a compelling combined LEED and DFT study. In a follow-up report32, the same authors extended this model and determined that the (2$$\sqrt{3}$$ × 2$$\sqrt{3}$$)R30° structure in fact comprised a mixture of C60 fullerenes on vacancy and atom-top sites. Indeed, our own LEED I(V) modelling (see Supplementary Fig. S9 and associated discussion) using the DFT coordinates from Fig. 3, suggests that a mixture of the two adsorption sites is also highly likely in our system, giving rise to an appreciable amount of static disorder in the positions of the encapsulated molecules with respect to the Ag(111) substrate and significantly complicating the XSW analysis.

To provide insight into whether the experimental NIXSW data are consistent with the mixed adsorption model, we explored the parameter space via an Argand diagram analysis. In this approach, the experimental values for Fc(T) and Pc(T) are plotted as a vector, as shown in Fig. 4c. We decompose the experimental vector into two components, which we label 0 and 1, assigned to the vacancy and atom-top adsorption sites, respectively. The vector combinations are then varied and recombined into a resultant (see Supplementary Information and Supplementary Figs. S7 and S8 for details), to represent different ratios of on-top and vacancy sites within the mixed film. A key difficulty in interpreting the NIXSW data in this way is that the underpinning equations are essentially under-determined and can therefore not be used to extract unique values of coherent fraction and coherent position. Despite this, the Argand analysis (summarized in Fig. 4c and detailed at length in the Supplementary Information file) illustrates that the NIXSW data are broadly consistent with a mixture of on-top and vacancy adsorption sites, suggesting that the measured oxygen position of z111(O), i.e., 5.57 ± 0.03 Å, can be interpreted as a combination of the two calculated positions of 5.33 Å and 5.73 Å for the H2O molecule in the vacancy and atop structures, respectively.

## Conclusions

In conclusion, our results address long-standing questions regarding the extent to which fullerene-encapsulated molecules, in particular H2O, are electrostatically screened and decoupled from their external environment. Although both H2O and HF contribute no discernable electronic state density to the frontier molecular orbitals of their surrounding C60—in other words, there is a distinct lack of orbital mixing and hybridization—adsorption on a metal surface (in this case, Ag(111)) causes a strong modification of the electrostatic potential within the cage. This in turn modifies the position of the encapsulated molecule as compared to that adopted in the gas-phase endofullerene4. Direct determination of the position of the intra-cage molecule is, however, very much complicated by the bonding geometry of the parent fullerene; a naive interpretation of the XSW data by itself fails to capture the many subtle contributions to the intra-cage energy balance and dynamics. Instead, the results of a comprehensive series of DFT, MD, and XSW analyses of the position of the encapsulated H2O and HF molecule can only be reconciled by taking into account both dynamic and static disorder in the position of the molecular encapsulate.

## Methods

### Scanning probe microscopy

Measurements were collected on a Createc GmbH LT STM-AFM system controlled by Nanonis electronics. Endohedral fullerenes were deposited via standard thermal sublimation under ultrahigh vacuum conditions (better than 1 × 10−10 mbar). For all scanning probe microscopy (SPM) measurements, we used a mixed monolayer film of C60 : H2O@C60 (in a 70 : 30 ratio) on a clean sputter-annealed Cu(111) surface. For reconstructed samples, the Cu(111) crystal was held at room temperature. A commercial qPlus sensor (Createc GmbH) with a separate tunnel current wire was used for both the STM and NC-AFM experiments (f0 ~ 20 kHz; Q ~ 30,000 at 5 K; nominal spring constant 1800 N m−1).

### Synchrotron XPS and NIXSW

Measurements were collected at beamline I09, Diamond Light Source. I09 is equipped with both a hard X-ray undulator, which was used for our XSW measurements at the Ag(111) Bragg energy of 2.63 keV, and a soft X-ray undulator, used for the acquisition of high-resolution C 1s, O 1s, F 1s, and valence band spectra. All synchrotron data were collected on an Ag(111) crystal prepared by standard sputter-annealing methods, after which 95% pure samples of H2O@C60 or HF@C60 were deposited via thermal sublimation. Considerable care was taken to reduce beam damage by detuning the beam and continuously moving across the crystal (see Section I.1 of the Supplementary Information for more detail.)

### DFT and MD calculations

Our relaxation calculations were based on DFT and were carried out using two ab initio codes: (i) the VASP50 that uses plane waves basis set and norm-conserving pseudopotentials, and (ii) the CP2K Quickstep package45, which employs hybrid Gaussian and plane-wave orbitals with a triple-zeta Gaussian molecularly optimized basis51, and Goedecker–Teter–Hutter pseudopotentials52. In both sets of calculations the Perde–Burke–Ernzerhof exchange-correlation density functional53 was used and the dispersion interactions were added via the Grimme DFT-D3 method54. The geometry optimization was considered complete when the forces on atoms were better than 0.01 eV Å. The Ag(111) surface was constructed using a slab model consisting of four atomic layers, where the atoms in the bottom two layers were kept fixed throughout all calculations. DFT simulations using VASP are regarded as being of higher precision due to the better approximation to a complete basis set that is possible with the inclusion of larger numbers of plane waves. As MD simulations were, however, only possible using CP2K due to high computational cost, we have also provided in Supplementary Fig. S11 CP2K results for two geometries of HF@C60 for validation purposes. MD simulations used a time step of 0.5 fs. Statistical analysis started from the 600th step, i.e., 0.3 ps after the NVT heat bath was applied. The temperature for MD was 180 K.