Correlation of Work Function and Conformation of C80 Endofullerenes on h‐BN/Ni(111)

Change of conformation or polarization of molecules is an expression of their functionality. If the two correlate, electric fields can change the conformation. In the case of endofullerene single‐molecule magnets the conformation is linked to an electric and a magnetic dipole moment, and therefore magnetoelectric effects are envisoned. The interface system of one monolayer Sc2TbN@C80 on hexagonal boron nitride (h‐BN) on Ni(111) has been studied. The molecular layer is hexagonally close packedbut incommensurate. With photoemission the polarization and the conformation of the molecules are addressed by the work function and angular intensity distributions. Valence band photoemission (ARPES) shows a temperature‐induced energy shift of the C80 molecular orbitals that is parallel to a change in work function of 0.25 eV without charging the molecules. ARPES indicates a modification in molecular conformations between 30 and 300 K. This order–disorder transition involves a polarization change in the interface and is centered at 125 K as observed with high‐resolution X‐ray photoelectron spectroscopy (XPS). The temperature dependence is described with a thermodynamic model that accounts for disordering with an excitation energy of 74 meV into a high entropy ensemble. All experimental results are supported by density functional theory (DFT).


INTRODUCTION
Fullerenes are archetypal molecular building blocks in nanoscience. Correspondingly carbon shells like C 60 have been studied in detail on surfaces [1][2][3]. Like found in three dimensions [4], the freezing of rotational degrees of freedom also cause phase transitions in two-dimensional systems [5][6][7]. A peculiar phase transition of a monolayer of C 60 on a single layer of h-BN on Ni(111) showed a temperature dependent charge transfer onto C 60 that is triggered by a change in conformation of the molecules with respect to the substrate [8]. This pointed to nonadiabatic effects that may be important for the engineering of electronic or spintronic contacts at the nanometer scale.
Endohedral fullerenes are carbon cages that contain atoms [9]. Species with a similar robustness as C 60 [10] open more opportunities for the exploitation of molecular functionality such as single molecule magnetism [11]. First surface science experiments focused on the electronic properties of multilayer C 80 endofullerenes [12,13], and soon monolayer systems were prepared and observed with scanning probes [14][15][16][17]. At low temperatures the orientation of the endohedral unit is not random [15] and related to the magnetisation [17][18][19]. The orientation of the endohedral units may even be changed by magnetic fields [20]. On the other hand, the incomplete screening of the anisotropic electrostatic potential of the endohedral cluster [21] bears a handle for accessing the magnetisation of the endohedral clusters with electric fields.
Here we report on a phase transition of Sc 2 TbN@C 80 on h-BN/Ni(111) around 125 K. It is related to the change in molecular conformation which is reflected in a change of the angular dependence of the photoemission from molecular orbitals and accompanied by a change of the workfunction, as was the case for C 60 on h-BN/Ni(111). In the present transition, however, we find no charge transfer onto the molecule. Instead, the orbital energies of Sc 2 TbN@C 80 shift parallel to the workfunction i.e. they align with the vacuum level.

EXPERIMENTAL AND THEORETICAL DETAILS Experimental
TbSc 2 N@C 80 molecules with icosahedral I h symmetry of the carbon cage were synthetized and purified as described in Ref. [22] and sublimated onto h-BN/Ni(111) [23], with the substrate kept at 470 K. Like in the case of C 60 [8] this substrate does bind the molecules weakly. The photoemission data were recorded at a photon energy of 600 eV or He Iα (21.2 eV) [24]. The coverage was determined with a layer by layer growth model, with an electron mean free path of 1 nm and from the intensity ratio of the N 1s core levels of the molecule and h-BN [21]. The low energy electron diffraction (LEED) patterns were calibrated with the (0,1) spots of the h-BN/Ni(111) substrate [25]. Scanning tunneling microscopy (STM) was performed at liquid nitrogen temperatures [24].

Theory
Density functional theory (DFT) calculations were performed on the Sc 2 YN@C 80 endofullerene because it is chemically very similar to Sc 2 TbN@C 80 but easier to describe accurately [21]. The calculations on the isolated Sc 2 YN@C 80 cluster were performed with ORCA [26] and the calculations of Sc 2 YN@C 80 /h-BN/Ni(111) using Quantum ESPRESSO [27]; details are given in the supplemental material [25].
We denote the calculated structures h-BN/Ni(111)- , √ 21 and 6 × 6 or "isolated", respectively. We define the condensation energy E c as E c = E tot − E mol − E sub , where E tot is the total energy of the fully relaxed system, E mol the energy of an isolated Sc 2 YN@C 80 molecule, and E sub the energy of the relaxed substrate without molecule. The lock in energy is the energy difference between the highest energy and the lowest energy upon translations of the molecular layer relative to the substrate. We approximate the ionisation potential and electron affinity by the energy eigenvalues of the highest occupied and lowest unoccupied molecular orbital (HOMO and LUMO), respectively.

RESULTS AND DISCUSSION
Incommensurability and low temperature super structure  Figure 2 shows the formation of a C 80 (2×2) low temperature superstructure in the incommensurate monolayer Sc 2 TbN@C 80 on h-BN/Ni(111). The structure forms between 80 and 170 K. Such low temperature ordering or freezing of fullerenes is known from C 60 films, where below 100 K a C 60 (2×2) structure was established [5,6]. For C 60 on h-BN/Ni(111) a ( √ 3 × √ 3) phase was found below 160 K [8]. This indicates that like in three dimensions [4], intermolecular forces lead to ordering of the fullerenes below room temperature in two dimensional systems. The interaction between Sc 2 TbN@C 80 molecules is, however, expected to be more complicated than that between C 60 because the high symmetry of the C 80 cage is broken by the endohedral unit, which is reflected in their appearance as ellipsoids that are weakly distorted from spherical shape and their permanent dipole moments.
In order to better understand the Sc 2 TbN@C 80 on h-BN/Ni(111) system and its differences to C 60 on h-BN/Ni(111) extensive DFT calculations were performed. Table I compares different calculated molecular properties of C 60 and Sc 2 YN@C 80 , which is, except for the paramagnetism of Tb, electronically very similar to Sc 2 TbN@C 80 , that was used in the experiments.   [25]. Therefore, the lock in energy is small compared to thermal energies at the preparation temperature, the binding energy in the freestanding layer, and the adsorption energy of a single Sc 2 YN@C 80 on h-BN/Ni(111). This supports the picture of non-covalent bonding of the molecules to the surface and easy incommensurate layer formation. The orientation of the incommensurate molecular lattice is likely guided by atomic steps in the substrate that run along high symmetry 110 directions.
In Figures 3(c) and (d) the band structure of the valence-and conduction-bands on the carbon cages of Sc 2 YN@C 80 on h-BN/Ni(111) in 6 × 6 and √ 19 cells are shown. While the bands in the former "isolated" structure are flat, the dispersion in the latter, condensed phase is considerable and around the Fermi level of p-type, dispersing downward, with maxima at the Γ point. The large HOMO-LUMO gaps of the molecules become apparent (1.49 and 1.28 eV), where the LUMO is pinned 118 and 81 meV above the Fermi level in the two structures, respectively. For comparison the HOMO-LUMO gap of the free molecule is 1.37 eV. We note that the applied exchange-correlation functional does not match with the experimental gap inferred from optical absorption spectroscopy, where 1.72 eV for Sc 2 YN@C 80 in toluene solution has been measured [28].
Endofullerenes are known to have conformers with local energy minima that are difficult to find with DFT optimization methods. For the search of the lowest energy structure we used an approach where the optimisations start from 120 different conformations [29]. As for C 80 endofullerenes in vacuum [29][30][31] and on surfaces [29] we found different conformers depending on the conformation at the start of the optimization [25]. The calculated workfunction in the lowest energy √ 19 structure is 4.30 eV, while it is 3.55 eV for the substrate without molecules. The standard deviation of the workfunctions of the 120 optimizations is 79 meV and that of the corresponding condensation energies is 68 meV [25]. Within the performed simulations with one molecule per unit cell we found no correlation between workfunction and condensation energy. At this point we speculate that the (2 × 2) molecular ordering, which we could not afford to calculate, might reduce the workfunction by a nonparallel arrangement of the molecular dipoles.
In order to cross check the DFT model and the experimental structures we calculated N 1s photoemission core level binding energies for hexagonal boron nitride on Ni(111), with and without molecules, and the endohedral nitrogen in Sc 2 YN@C 80 on h-BN/Ni(111)-√ 19. In Figure 4 x-ray photoelectron spectroscopy (XPS) data are compared with final state energies that are convoluted with a Gaussian of 470 meV full width at half maximum (FWHM). Inspection increases the confidence that experiment and theory describe very similar physical situations. In contrast to initial state core level calculations of the C 80 cage [21], the final state had to be considered [25]. Self-consistent calculations with a half hole on the N 1s orbital were performed and the resulting eigenvalues were used. From these calculations we reached an excellent agreement of the lowest energy √ 19 structure and the experiment (see Figure 4 and the Table in the supplemental material [25]). The DFT results confirm the assignment of the N 1s core level peaks to the boron nitride and to the endohedral nitrogen species [21]. The broadening of the BN derived N 1s peak upon adsorption of endohedral C 80 predicts that the nitrogen atoms in the BN layer corrugate under the influence of the adsorbed molecules to 0.09 nm [25]. The shift of the BN derived N 1s peak upon adsorption of C 80 is parallel to the work function and is in line with the physisorption picture of h-BN on Ni that involves vacuum level alignment [32]. The chemical shift of the endohedral N 1s peak agrees for experiments at room temperature, but, as we will see below, not for the low temperature case, where (2 × 2) molecular ordering was observed. Figure 5 displays He Iα excited valence band photoe- and that of the endohedral nitrogen is increased by a factor of 5. The N 1s final state energy in Sc2YN@C80 from DFT is matched to the experimental binding energy in Sc2TbN@C80 [25]. mission data and the corresponding secondary electron cutoff of Sc 2 TbN@C 80 on h-BN/Ni(111) at 30 and 300 K. The workfunction increases with temperature from 3.95 to 4.20 eV. This shift is also reflected in the energy of the HOMO and it indicates vacuum level alignment of the Sc 2 TbN@C 80 molecular orbitals, which is in line with a non-covalent bonding to the substrate. The HOMO peak of Sc 2 TbN@C 80 on h-BN/Ni(111) occurs at relatively high binding energies of 2.30 and 2.04 eV at 30 and 300 K. They are larger than the optical HOMO-LUMO gap of Sc 2 YN@C 80 and indicative for a strong on site Coulomb interaction U [1,33]. In multilayer Sc 3 N@C 80 [12] the HOMO was found at ≈1.73 eV binding energy.
In contrast to C 60 on h-BN/Ni(111) [8] we find no hint on temperature induced charge transfer, namely no partial filling of the LUMO that was seen as extra intensity at the Fermi level. The valence band data show, however, anisotropy of the molecular orbitals at low temperature, while no anisotropy is visible at room temperature. Such intensity variations are known as ultra-violet photoelectron diffraction (UPD) effects [34][35][36] and indicate orientational order of the molecules at low temperatures. Behaviour of the molecular conformation with temperature Figure 6 shows XPS of Sc 2 TbN@C 80 on h-BN/Ni(111) between 30 K and room temperature. The N 1s and the Sc 3p 3/2 core levels are observed. The N 1s level of the endohedral unit displays relative to the N 1s levels of the BN substrate sharper and at lower binding energy. The BN N 1s orbitals of the substrate have constant binding energy (±25 meV), while those of the atoms in the molecules follow the workfunction, i.e. show the same energy shift as the secondary cut off and the HOMO molecular orbitals in Figure 5. This means that the BN N 1s energy does not follow the temperature dependence of the vacuum level, while the one of the molecular layer on top of h-BN does.
We assign the observed behaviour of the workfunction to the onset of endohedral rotation and different dipole components p z along the surface normal. The workfunction change ∆Φ and ∆p z are connected via the Helmholtz equation ∆Φ = −n∆p z e/ 0 , where n is the areal density of the corresponding dipole component ∆p z and e the elementary charge. Taking the calculated gas phase dipole moment of Sc 2 YN@C 80 of 0.25 D we would get a workfunction increase of 92 meV in a √ 19 unit cell in going from a configuration where the dipole points antiparallel to the surface normal to an isotropic configuration with a zero average dipole moment.
The temperature dependence of the core level binding energies that are parallel to the workfunction allows to extract thermodynamic properties of the Sc 2 TbN@C 80 on h-BN/Ni(111) phase transition. Specifically, we consider for the molecular conformations two energy levels that are separated by ∆E = E 1 − E 0 . While E 0 is set to be non-degenerate (N 0 = 1), the degeneracy of E 1 is N 1 (see Figure 6(c)). As it can be seen from the calculations in the supplementary material [25], the assumption of two conformational energies only is a simplification, though the "smooth bend" of the order parameter does not allow for reliably fitting of more than four independent parameters. At thermal equilibrium we obtain the occupation n 0 of the lowest energy state E 0 , and the occupation of state E 1 , n 1 = 1 − n 0 . If the measured core level energies E B are taken to express the order parameter i.e. the weighted sum E B = n 0 E B0 + n 1 E B1 , we may derive E B0 , E B1 , ∆E and N 1 from the measured data. E B0 describes the system at T=0 or n 1 = 0 and E B1 is the core level energy if all molecules were excited, i.e. n 1 = 1. From n 0 (T ) the relevant thermodynamic quantities ∆E and N 1 are determined. The solid lines in Figure 6(d) show the fits of the N 1 degenerate two level model for the N 1s and the Sc 2p 3/2 core levels of Sc 2 TbN@C 80 on h-BN/Ni(111). The fit-parameters are ∆E = 74 ± 6 meV, E B0 − E B1 = 310±40 meV and the degeneracy N 1 = 1300±700. As expected E B0 − E B1 is in line with the work function shift. The energy ∆E has the order of magnitude of the scatter of E c for the calculated conformations of Sc 2 YN@C 80 on h-BN/Ni(111) [25]. This means that the transition has the energy scale of different molecular conformations of Sc 2 YN@C 80 /h-BN/Ni(111). The large degeneracy N 1 reflects the large C 80 (2 × 2) unit cell at low temperature and indicates a strong contribution of the entropy to the free energy of the system above the ordering temperature.

CONCLUSIONS
We observed a temperature induced workfunction shift of Sc 2 TbN@C 80 on h-BN/Ni(111) centered at 125 K. This shift is related to the disappearance of a Sc 2 TbN@C 80 (2×2) LEED structure. The transition is an order disorder transition with onset of rotation of the endohedral clusters. This conclusion bases on angular dependent valence band photoelectron spectroscopy. DFT calculations, predict the lattice constant of Sc 2 YN@C 80 , a permanent dipole moment, describe the N 1s XPS spectrum in the Sc 2 YN@C 80 (1×1) phase and propose different conformers with an energy distribution that is in line with a model for the temperature dependence of the molecular core level binding energies.