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Atomlike, Hollow-Core–Bound Molecular Orbitals of C60

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Science  18 Apr 2008:
Vol. 320, Issue 5874, pp. 359-362
DOI: 10.1126/science.1155866

Abstract

The atomic electron orbitals that underlie molecular bonding originate from the central Coulomb potential of the atomic core. We used scanning tunneling microscopy and density functional theory to explore the relation between the nearly spherical shape and unoccupied electronic structure of buckminsterfullerene (C60) molecules adsorbed on copper surfaces. Besides the known π* antibonding molecular orbitals of the carbon-atom framework, above 3.5 electron volts we found atomlike orbitals bound to the core of the hollow C60 cage. These “superatom” states hybridize like the s and p orbitals of hydrogen and alkali atoms into diatomic molecule-like dimers and free-electron bands of one-dimensional wires and two-dimensional quantum wells in C60 aggregates. We attribute the superatom states to the central potential binding an electron to its screening charge, a property expected for hollow-shell molecules derived from layered materials.

Charge transport through organic materials occurs efficiently through covalently conjugated π molecular orbital networks, but not when molecules are bound by weak van der Walls forces (1, 2). Buckminsterfullerene (C60) molecular crystal is a typical strongly correlated Mott-Hubbard solid with a high effective electron mass. When intercalated by alkali atoms, C60 can be transformed into metallic, superconducting, insulating, and even magnetic phases (3). A low-temperature scanning tunneling microscopy (LT-STM) study of alkali atom–doped KxC60 monolayers (where x is the number of K atoms) on Au(111) surfaces found a doping-induced reentrant metal-insulator-metal phase transition involving previously unseen orientational ordering of C60 molecules. Wang et al. proposed that electron hopping between the π orbitals of the neighboring molecules creates anisotropic intermolecular interactions, which spontaneously drive the orientational ordering on the weakly interacting Au(111) surface (4, 5).

In an LT-STM study of C60 molecules on Cu surfaces, we found a completely different paradigm for the intermolecular electron delocalization involving isotropic interactions of atomlike electron orbitals centered on the nearly spherical C60 molecules. On Cu surfaces, the strong C60 molecule/substrate interactions hinder the spontaneous orientational ordering and concomitant electron delocalization through the intermolecular π bond hybridization (6). Partial occupation of the lowest unoccupied molecular orbital (LUMO) through chemisorption-induced charge transfer of up to two electrons per molecule facilitates charge transport through the overlayer, but poor intermolecular wave function overlap still hinders it within the overlayer (7, 8).

Thus, it is surprising that in LT-STM images (Fig. 1) above a bias voltage of 3.5 V, we found a transition from the π molecular orbital to a nearly free-electron (NFE)–like character, which is evident in the extensive, wave function delocalization within one-dimensional (1D) and 2D assemblies of C60 molecules. We used LT-STM and density functional theory (DFT) to study the character of C60 molecular orbitals that give rise to these NFE properties. We found that the extensive hybridization involves atomlike orbitals bound by a central potential of the nearly spherical C60 shell. Because this potential is set up by the universal screening and surface dipole fields, we propose that these “superatom” electronic states are a common property of hollow molecules derived by wrapping or rolling of molecular sheets.

Fig. 1.

Topographic (A to C) and dI/dV (D to J) images of LDOS of a single C60 molecule, 1D quantum wire, and 2D quantum well. The quantum well is on a Cu(111) substrate, whereas all other images are for C60 molecules on 7.6 Å–wide bare Cu lines between oxide domains on an O/Cu(110) substrate (6). (K) dz/dV spectra identifying specific tunneling resonances in a single C60 molecule, a molecular dimer, and a C60 island. For potentials up to 3.2 V [(D) and (E)], the LDOS images show intramolecular structure characteristics of the π* orbitals localized on the C atom framework. The complete absence of molecular contrast in the LDOS images taken above 3.5 V for close-packed C60 aggregates is indicative of intermolecular wave function delocalization. The quantum-wire images show the transition from the localized molecular orbital LDOS of LUMO+2 at 2.8 to 3.2 V (E) to the delocalized one of s SAMO at 3.91 V (G). The complementary smooth contrast over both the C60 island (H) and the bare Cu(111) surface (I) regions reflects the NFE properties of SAMOs and IP states. The arrows indicate the bright contrast at the edges and gaps of the quantum-wire antibonding band (G) and the dark contrast at the edge of the quantum-well bonding band (J).

We investigated the electronic structure of C60 molecules on Cu(111) and partially oxidized Cu(110)-(2×1)-O surfaces (6, 9). By imaging chemisorbed C60 overlayers with constant-current scanning (Fig. 1, A to C) (10), we identified isolated-molecule, 1D wire, and partial 2D monolayer structures. We found the unoccupied states that mediate electron tunneling through C60 molecules by recording the distance-voltage (z-V) scans at different positions and numerically differentiating them to obtain dz/dV spectra such as that shown in Fig. 1K (11, 12). Finally, we explored the electronic nature of specific dz/dV resonances by imaging the local density of states (LDOS) with differential conductance (dI/dV) scanning (Fig. 1, D to J).

Our dz/dV spectroscopic survey from single C60 molecules to three molecular layers on O/Cu(110) and Cu(111) surfaces is consistent with previous assignments of the peaks at 1.5 and 2.8 to 3.2 V to the LUMO+1 and LUMO+2 states with π* antibonding molecular orbital character [energies or bias potentials are referenced to the Fermi level (EF)] (7, 8, 13, 14). The LUMO+2 images (Fig. 1, D and E) map through-molecule electron-tunneling pathways that depend on the surface-specific orientation of C60 molecules and the spatial distribution of their π* molecular orbitals (7, 13, 15).

By contrast to these molecular orbital–resolved images, at potentials of 3.5 V and higher, the unoccupied states extend over the entire 1D and 2D assemblies (Fig. 1, G, H, and J). Such wave function delocalization gives similar contrast to the image of the complementary bare-metal region where, at 4.36 V, tunneling occurs through the intrinsic free-electron–like image potential (IP) state of the Cu(111) surface (Fig. 1I) (16).

Strong electron delocalization for molecular quantum wells on the C60/Au(111) surface has also been reported by Zhu et al. (14). By angle- and time-resolved two-photon photoemission (2PP), Zhu et al. found a state at 3.7 eV with energy-momentum dispersion characterized by an effective mass only 1.4 times that of a free electron. On the basis of their DFTcalculations performed with an atomic-orbital basis set, Zhu et al. attributed the delocalized state to the intermolecular hybridization of the LUMO+2 or LUMO+3 states.

To explain the marked change in the LT-STM images from the localized orbitals of LUMO+2 to the highly delocalized ones for the next higher-energy state, we performed plane-wave DFT calculations (1720) for isolated fullerenes of different sizes, fullerenes with endohedral doping (21), and for C60 dimers. In Fig. 2, we have reproduced the well-known π* antibonding LUMO orbitals of the sp2 hybridized C atom network (13). In addition, we found diffuse orbitals, which, according to their angle-averaged wave functions in Fig. 2, are attached to the empty C60 core rather than the C atom shell and have nodes at the π orbital density maxima. On the basis of their radial nodes, these core-bound states have the principle quantum number n = 3, whereas the σ and π orbitals correspond to n = 1 and 2 (19). Because they evoke the spherical harmonic shape of s, p, and d symmetry atomic orbitals corresponding to the orbital angular momentum quantum numbers l = 0, 1, and 2, we dub them the superatom molecular orbitals (SAMOs).

Fig. 2.

(A) Calculated LUMO to LUMO+4 and s, p, and d SAMO wave functions for isolated C60 and Li@C60 molecules. The angle-averaged occupied-state wave functions find the σ and π electron probability at, as well as above and below, the C atom surface plane, whereas the SAMO probability density is centered on the hollow molecular core. The SAMO radial nodes appear at the π electron density maxima, as required by the n = 3 principle quantum number and the Pauli exclusion principle. The black line gives the angularly averaged DFT potential, V(r), showing the deep well of the C atom shell and the shallow screening potential of the hollow C60 core (expanded five times). (B and C) C and Li atom localized and delocalized DOS for C60 and Li@C60. Charge transfer of the 2s electron from Li [yellow in center of C60 for Li@C60 in (A)] to the LUMO of C60 causes the reference energy to shift between (B) and (C). Hybridization with the Li atomic orbitals lowers the energy of SAMOs with respect to the undoped case. s′ refers to an n = 4 state.

To confirm that the SAMOs calculated for free C60 molecules give rise to atomlike orbitals on Cu surfaces, we searched for the l > 0 counterparts and explored how SAMOs hybridize into delocalized bands. Figure 3 shows dI/dV images taken at several energies above 3 V for a C60 molecule isolated in a Cu trough on the O/Cu(110) surface (6). The LDOS images corresponding to the three indicated regions of the dI/dz spectra of Fig. 1K (3.5 to 4.3, 4.6 to 4.9, and ≥5.0 V) exhibit distinct monopolar (quantum number m = 0), dipolar (m = 1), and quadrupolar (m = 2) symmetry, corresponding to their dominant s, p, and d orbital character, respectively (m is the surface projection of l). On the basis of the m = 0 symmetry and energy, we attribute the 3.70 and 4.15 V images to the s and pz SAMOs. The s SAMO has a characteristic dark spot (diminished LDOS) in registry with the topmost pentagon of the C60 molecule, whereas the pz SAMO is more compact. The broken symmetry at the surface hybridizes the s and pz SAMOs into a bonding (3.70 V) and an antibonding (4.15 V) pair. The anisotropy of the O/Cu(110) surface lifts the degeneracy of the m = 1 SAMOs; the repulsion by the oxide domains along the Math azimuth destabilizes the py SAMO with respect to the px SAMO. Finally, based on its appearance, we assign the 5.0 V image to hybridization of the py and dyz SAMOs. Because several p-d hybrid orbitals are likely to fall into a narrow energy range, the assignment of d SAMOs is uncertain.

Fig. 3.

dI/dV mapping of an individual C60 molecule's SAMOs. As the measurement voltage is increased, the dI/dV images of a single C60 molecule evolve from the π* molecular orbital character of LUMO+2 to the core-centered s, pz, px, py, and dyz SAMO character. The characteristic dark spot on the s SAMO occurs above the top C60 pentagon. Tunneling through the image potential states of the substrate is responsible for the bright contrast above the metal and the oxide domains.

Having confirmed the existence of hydrogen or alkali atomlike SAMOs, we then explored their hybridization into delocalized states of superatomic matter. Figure 4 presents the calculated wave functions and observed images of s and p SAMOs hybridizing into σ and π symmetry bonding and antibonding orbitals of superatom dimers. The molecular orbitals derived from SAMOs, like those of an H2 molecule, can be classified by their nodal pattern in and orthogonal to the molecular plane. The 3.5 to 4.3 V region encompasses the bonding and antibonding hybridization of the s and pz SAMOs. The 4.60 to 4.95 V region shows a progression from the σ bonding of px SAMOs to the π* antibonding of the px and py SAMOs. Above 4.90 V, the dimer orbitals are more diffuse and may have additional d SAMO character. Though obscured by congestion and broadening, the comparison between the dz/dV spectra of the monomer and the dimer (Fig. 1K) suggests that the hybridization-induced shifts are small (<0.2 V). By contrast to SAMOs, the LUMO+2 dimer images in Fig. 4 show little evidence of the intermolecular hybridization that could give rise to NFE character.

Fig. 4.

Hybridization of the superatom orbitals of individual C60 molecules into the corresponding molecular orbitals of C60 dimers was investigated by DFT calculations and dI/dV imaging. The calculated orbitals are for isolated dimers, whereas the experimental LDOS images are for dimers on Cu troughs. The Hatom–like sand p SAMOs combine to form σ and π symmetry bonding and antibonding molecular orbitals resembling those of an H2 molecule. The correspondence between the calculated probability densities and measured LDOS is proposed on the basis of the observed nodal patterns. Overlap of several bands complicates assignments, particularly at higher measurement potentials. The dimer images show how the SAMO character evolves into the NFE properties of superatom matter. By contrast to SAMO images, LUMO+2 does not show substantial hybridization-induced changes in the LDOS.

In larger aggregates, SAMOs hybridize into 1D quantum wires (Fig. 1G) and 2D quantum wells (Fig. 1, H and J). Electron delocalization within these extended structures is responsible for the vanishing molecular contrast and other telling features. Whereas s SAMO–derived images show uniform contrast, the m = 1 quantum well on Cu(111) (4.60 V) (Fig. 1J), reflecting its origin in the hybridization of the degenerate px and py SAMOs, has nodes centered on C60 molecules. Furthermore, near the edges of 1D chains and 2D islands (Fig. 1, G and J), the energy-dependent bonding and antibonding hybridization gives rise to distinct dark or bright boundary states (22).

Having established that above 3.5 V SAMOs dominate the STM dI/dV images of single and aggregated C60 molecules, we next considered their physical origin. Emergence of the atomic-orbital character in a molecular system requires a central potential. For example, atomlike molecular Rydberg states exist because weakly bound electrons interacting with a molecular ion through the long-range Coulomb potential essentially do not penetrate into the molecular core. The SAMOs, however, are distinct from Rydberg states because their probability density resides substantially— and, for the s SAMO, dominantly—within the hollow C60 core. Considering the C60 molecule as a hollow dielectric shell whose screening properties are described by the angle-averaged DFT potential in Fig. 2, we can reproduce the radial shapes but not the exact energies of the LUMO and SAMO wave functions.

To explore the origin of SAMOs, we solved the Schrödinger equation using the form of the angle-averaged DFT potential but varying the relative core and shell contributions. These calculations show that the shell potential dominantly gives rise to the n = 2 HOMO (highest occupied molecular orbital) and LUMO orbitals, whereas the nearly constant attractive screening potential extending 0.25 nm from the molecular center is essential for the existence of the n = 3 SAMOs (19, 23). The energy and shape of SAMOs also depend on the C atom shell potential, which locates the radial nodes at the π orbital density maxima.

The origin of the central potential within the C60 core can be traced to the screening of an electron charge through the short-range exchange and correlation and the long-range Coulomb interactions. At a solid/vacuum interface, these many-body interactions give rise to a series of IP states that converge to the vacuum level and have NFE properties parallel to the surface (24). For 2D molecular sheets such as graphene and hexagonal BN, IP states should exist on both sides and hybridize into symmetric and antisymmetric linear combinations (25, 26). Stacking molecular sheets to form quasi-2D solids causes IP states to hybridize into interlayer bands characterized by a probability-density peak between and NFE properties parallel to the sheets (25, 26).

Topological distortion of molecular sheets (that is, wrapping or rolling them into 1D or 0D molecules) also affects the bilateral IP states; the favorable screening of the concave surface stabilizes the interior IP state with respect to the exterior one. Also, a dipole directed along the surface normal that is created by the curvature-induced hybridization of the σ and π molecular states contributes an additional attractive potential (2628). The resulting internal potential gives rise to SAMOs, which can be thought of as 0D interlayer states, whereas the external IP potential is responsible for the more weakly bound Rydberg states (29). Viewed as a consequence of the universal surface screening and dipole potentials, SAMOs emerge as a general property acquired by rolling and wrapping 2D layered materials into 1D nanotubes and 0D hollow molecules.

The 2PP band dispersions (14) and LT-STM images of delocalized wave functions together demonstrate that SAMOs impart metal-like conductivity to the excited anion states of self-assembled C60 structures. Because these properties derive from the topological modification and assembly, we postulate that SAMOs can impart previously unseen electronic and optical properties to other layered materials. For example, the conduction bands of the hexagonal BN and BN nanotubes have NFE interlayer-state character (26). The SAMO properties also can be tuned through the cage size or intercalation. In Fig. 2, we present the calculated SAMO orbitals and the C and Li atom localized and delocalized density of states (DOS) for Li@C60, which illustrate that an endohedral Li atom in the center of a C60 molecule stabilizes the s SAMO to 1.2 eV above EF. In other calculations on single-wall carbon nanotubes, the internal doping with a positive charge was shown to stabilize an interlayer-derived NFE state by more than 3 eV to below EF (27). Because the image and dipole potentials are universal properties of the curved molecular sheets, the NFE states analogous to SAMOs should be a general property of hollow molecules such as fullerenes.

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