Conformational preferences of endohedral metallofullerenes on Ag, Au, and MgO surfaces: Theoretical studies

In this report, we study the ordering of C60, Sc3N@C80, and Dy2ScN@C80 molecules on different metallic and dielectric surfaces such as Ag(100), Au(111), and MgO(100). By using DFT techniques, we can classify different types of cage‐to‐surface arrangements and their relative energies. Using a proposed homogenous sampling of the conformational space for the M3N cluster, we determine a potential energy map that is capable of providing a structural distribution for a given energy window. We find that Coulomb interaction is a dominant force that governs the system's stability and order. However, a deep analysis of the charge density rearrangements reveals that even though the integral charges may be considered as a qualitative control parameter, it fails to provide quantitative data due to the importance of spatial characteristics of charge densities.

general and nitride cluster fullerenes in particular 10,11 are among leaders in withstanding such perturbations, [12][13][14][15][16] as the magnetically active cores are protected by fullerene cages, which are adapted to absorb the most of destructive effects. 17 It was shown, for example, that the charge fluctuations will mostly involve the fullerene cage rather than the cluster inside.
Similar to other Ln-based SMM systems, the EMF magnetic anisotropy is determined by the charge anisotropy of the local environment, which still can be randomly changed upon such SMM-substrate interaction, even if the local charge arrangements will be preserved. Recently, we have shown to what extent a very weak electrostatic interaction can control the inner cluster orientation in Y x Sc 3Àx N@C 80 when hosted by Ni(OEP). 18 In this report, we conduct a comprehensive investigation of inner cluster ordering in the Dy 2 ScN@C 80 and Sc 3 N@C 80 molecules while hosted by inorganic surfaces Ag(100), Au(111), and MgO(100) taking into account surface proximity, the fullerene cage orientation, and the cluster conformation. Following the relative energy criteria, we found that similar to Dy 2 ScN@C 80 Rh 111 ð Þ j and Sc 3 N@C 80 Cu 110 ð Þ j systems 12,19 the metal surfaces tend to order M 3 N clusters in parallel orientation, while the MgO surface enforces vertical orientations. This suggests that any magnetic moment measurements sensitive to ordering (such as XMCD or MLD) will likely find the order formations in the single molecular layers of Dy 2 ScN@C 80 on the metals and nonordered state response on MgO. 14 Furthermore, we have addressed in detail the effect of fullerene-to-surface proximity with emphasis on relative orientations and the charge density separation between the

| RESULTS AND DISCUSSIONS
First, we outline the scope of the problem and thereby emphasize some obvious shortcomings in common strategies of similar research, and thus formulate an approach that we will use to accomplish the reproducibility goal of obtaining theoretical data.
Here, our aim is to construct potential energy surface (PES) fold that is complex enough to track and select thermodynamically stable conformational isomers within a certain energy range. As the system of interest consists of MOI and a surface, from a whole set of available degrees of freedom the angle between positive normal to the Dy 2 Sc plane and z-axis will be used. Such a single control parameter is sufficient to follow the conformational changes in the system due to cluster rotation. We have employed a similar strategy while studying Thus, before a conformational analysis of the inner cluster, we have to position the MOI optimally next to the surfaces. To limit the number of possible cases some assumptions have to be made. Here, we use the fact that the cage and surfaces interact stronger than the cluster and cage. This assumption is easy to justify, as it is known that in the isolated M 3 N@C 80 , M 3 N rotates freely. 18 This allows focusing solely on one nonspecific orientation of the cluster while studying the relative positions of MOI on the atomic grid.
The distance between MOI and the surfaces is defined as the dif-  (Table 1). Edges [6] and [5,6] of the cages were selected as reference points-the C-C bonds through which two hexagons and hexagon and pentagon faces are joined. Other reference points include vertices [6] and [5,6], with a transparent logic behind the names. Furthermore, the surfaces also provide additional options like the void or metal sites for the Ag, Au surfaces, and Mg or O sites for the MgO case. Overall, 12 systems for Sc 3 N@C 80 and 6 for C 60 were considered as initial guesses, which are summarized in Table 1. Also, the inner cluster orientation initially was parallel to the surfaces but free to change during optimization. Figure 1A,B show the energy distribution following the complete optimizations of MOI Surfaces j systems with ID geometries (Table 1) as initial guesses. As mentioned before, due to the local nature of the optimization procedure, most of the minima are found in close proximity to the starting geometry. Also, the inner Dy 2 ScN cluster remained in the same relative orientation. Thus, almost all 12 distinct cases can be seen with just some little twist to the original geometries ( Figure 2 for isolated fullerenes adsorbed on the surface. 24 Although, the more detailed studies of C 60 on surfaces revealed a possibility of surface reconstruction (atomic reorganization of underlying layers) as well as the formation of dimples and so-called nanopits. 25,26 As it was already affirmed the initial geometries for Sc 3 N@C 80 were set on the optimal distance. After the optimization process the moleculesurfaces gap-dz, and the distance between the two closest atoms from MOI and a surface d(M-C) were evaluated again and provided in Table 2.
We also analyzed Bader charges 27,28 accumulated on the MOI. It is worth pointing out, though, that the charge transfer is affected little by relative molecular orientations, but by the distance to the surface. Furthermore, in the case of C 60, the charge transfer appears to be bigger which could be seen in the case of Ag(100) or MgO(100) surfaces (Table 2). These charge transfer values for the Ag(100) are in good agreement with other calculations. 29 The values reported for Ag(100) and Au(111) and defined by direct integration lay relatively close to those given in Table 2. 24 To have a better perception of the connection between the charge transfer intensity and the type of the surface, the same study was conducted for the trial MOIs on the different surface faces ( Furthermore, the direction of charge transfer on Au is rather curious and requires deeper consideration. Therefore the real space charge density redistribution (depletion and accumulation) was computed by subtracting from the total densities the densities of isolated MOI and surfaces: These difference electron densities for most stable C 60 Surfaces j and Sc 3 N@C 80 Surfaces j on Au(111) are shown in Figure 3. Expectedly, the density rearrangement is more prominent in the contact area

| Conformation trends of Dy 2 ScN Surfaces j
The optimal configurations EG1, EU1, and EM1 (see Figure 1) were used as frameworks for the subsequent analysis of Dy 2 ScN cluster rotation along with the Fibonacci nodes. The resulting energy distributions are provided in ESI, Figure 4. The most stable geometries from this set helped us rationalize experimental observables in Krylov et al. 16 The effect of the surfaces is very pronounced. There relative F I G U R E 1 Energy distribution for the optimized structures with different cage orientations toward the surfaces (see Table 1), for (A) Sc 3 N@C 80 Surfaces j and (B) C 60 Surfaces j T A B L E 1 Orientation guesses for the optimal cage orientation search Thus, in this case, the energy spread is twice as small ($25 meV) if compared to the metal surfaces.
These scatter plots show the position of distinct minima of PES along the Θ degree of freedom. The small energy differences between neighboring pairs of the optimized conformers indicate the possibility of the cluster rotation (assuming the Bell-Evans-Polanyi principle is valid and the barriers between the nearest conformers are proportional to the enthalpy). Nevertheless, these folded PESs ( Figure 4) have a visible clustering along the Θ coordinate with energy preference of certain angles of Dy 2 ScN clusters relative to an underlying surface. Therefore, if employed experimental techniques have sufficiently high energy resolution (δε) and the system is under thermodynamic control, we can separate conformers From the data in Figure 4, we find that δε border value should be below 50 meV (which corresponds to 2k B T at room temperature) so the system Dy 2 ScNC 80 order would be distinguishable on different surfaces.
Thus, for metals, the conformers closer to Θ = 0 value would dominate the sampling. At the same time, for the MgO surfaces, there are 2 preferential orientations at nearly 40 and 75 . On a whole, both these finding are consistent with experimental observation. 16 Also, we find the energy overlap between cage location isomers and cluster conformers for a given cage orientation- Figures 1A and 4. As  (bottom row). Here, the red isosurfaces (isovalue = XYZ e/Å 3 ) correspond to accumulation of electron densities and while the blue ones correspond electron density depletion. The intermixed nature of charge separation in the system makes it difficult to rely on integrated values and on-site (atomic) properties surfaces (the charge transfer is color-coded in the scatter plot in Figure 4). Even though the spread of the charge transfer values ( max MOI P iЄMOI q i À min MOI P iЄMOI q i ) is humble 0.1e, one can read the trend clearly. This correlation is more pronounced in the case of the Au(111) surface, where the charge transfer gradually decreases with Θ and destabilizes the system.

| Difference densities in
On the Ag(111) surface, the charge transfer reverses direction in terms of Bader analysis. However, as we have eluded before, these integral values may be deceptive and the real space density analysis may be more helpful. Accordingly, the difference electron densities were obtained (Equation (1)) and are shown in Figure 5 for the two most stable and most unstable conformers on these surfaces. The overall appearance of δρ(r) is similar to one in cases of the trial MOIs and concentrate mostly in the contact area, or, more precisely, in the gap between MOI and the surface.
In the case of Au(111), two domains formed with most of density depletion on carbon cage and accumulation on the surface. In the Ag(100) case, δρ(r) forms intertwined net with alternating pockets of density depletion and accumulation as we have seen before in the case of C 60 Au j 111 ð Þ system, which generalizes the observation.
Furthermore, we find a similar topology of δρ(r) account for very different local properties. For example in Figure 5 (the gold surface case) the Bader charge predicted for the most stable and most unstable conformer have a two-fold difference in terms of Bader charges (Σ iЄMOI q i = À0.14 and Σ iЄMOI q i = À0.26), however, the spatial order of δρ(r) is identical. Thus, in this case, concluding the exact amount of charge transfer in terms of the localized model will be an inadequate approach. Nevertheless, it should be noted, that spatial ordering of δρ(r) forces inner clusters to avoid the regions of π-systems distortion in the cage. For metals, it means the parallel orientation of the cluster toward the surfaces. For less electronically distorted MgO the small perturbation region surfaces as attractor instead, making perpendicular order more preferable ( Figure 5).

| CONCLUSIONS
In conclusion, we provided an inclusive DFT study of the functional fullerene-based molecules (C 60 , Sc 3 N@C 80 , Dy 2 ScN@C 80 ) ordering next to metal (Au, Ag) and dielectric (MgO) surfaces-the MOI Surface j systems. We investigated systems stability as a function of the surface  Figure 3, the red isosurfaces (isovalue = 0.1 e/Å 3 ) correspond to accumulation of electron densities and while the blue ones correspond electron density depletion proximity, the fullerene cage orientations toward the surfaces and the cluster conformation. We found that the relative energy scale for surfaces positioning is roughly 0.5 eV and coincides with the energy scale of the inner cluster rotation ( max Θ E Θ i ð ÞÀE Θ iþ1 ð Þ j j $ 0:4 eV). We find that cluster ordering in EMF is controlled by overall charge distribution in the systems. However, having analyzed the charge delocalization in terms of local properties and real space distributions, we found very similar topological trends in electron densities but very different local atomic properties. Thus, we conclude that the local atomic properties cannot be used as a guide and real space densities are more reliable properties.

DATA AVAILABILITY STATEMENT
All structural information that supports the findings of this study is available in the local database at IFW, Dresden, and will be provided upon request.