Atom-Cage Charge Transfer in Endohedral Metallofullerenes

Letter pubs.acs.org/JPCL

Atom-Cage Charge Transfer in Endohedral Metallofullerenes: Trapping Atoms Within a Sphere-Like Ridge of Avoided Crossings Oksana Tishchenko* and Donald G. Truhlar* Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, 207 Pleasant Street SE, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States S Supporting Information *

ABSTRACT: Endohedral fullerences have great potential for a variety of techological applications. Here we consider B@C60 and show that the amount of charge transfer from the semimetal boron atom to the cage is a strong function of the radial distance of the atom from the center of the fullerene, and it is controlled by multistate conical intersections whose associated ridge of avoided crossings has the topology of a Euclidean sphere. The potential energy surfaces of B@C60 are characterized by two kinds of local minima: those with a boron atom located in the geometric center of the fullerene, and those with a boron atom bound to the fullerene inner wall. At the lowestenergy minimum, at the center, the boron atom is neutral, whereas the transition to the wall is accompanied by an electron transfer from boron to the fullerene cage. The two kinds of minima are separated by a ridge of avoided crossings that forms a surface with a nearly spherical shape. The properties of such systems may be altered by controlling the populations of the two kinds of minima, for example, by application of an external field. Such switchable atom−cage charge transfer may find applications in novel molecular devices. SECTION: Molecular Structure, Quantum Chemistry, and General Theory

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analogue of the circle-like ridge around a caldera is a hypersphere-like ridge, which could again form a trap. Examples of ionic−covalent avoided crossing ridges we have studied recently are those for Ca interacting with benzene or coronene.5 Charge transfer also occurs for metal interactions with graphene.6 Since these molecules are planar, the projection of the ridge on the three Cartesians coordinates of atom A is expected to be locally approximately planar, at a distance from the surface that we may call r0. If the atom approached the curved surface (curved wall) of a fullerene, this shape would be expected to be roughly spherical with the convex side toward A. Suppose, however, that A approached the fullerene wall from the inside, as would be the case for endohedral A. If the radius of the fullerene is larger than r0, one might find a sphere-like avoided crossing ridge inside the fullerene, and the atom A would be effectively trapped by this ridge, which would be sphere-like when projected onto the coordinates of A or hypersphere-like in the full dimensionality of the system. As we will show by electronic structure calculations in this Letter, we have found this to be the case when A is a boron atom and M is buckminsterfullerene (C60), a supersystem with F = 177. The electronic structure of endohedral fullerenes has been widely studied, and the potential for industrial development based on encapsulated metal or semimetal atoms in fullerenes is

harge transfer, especially electron transfer, is one of the most basic processes in chemistry,1 and it plays a major role in many processes where chemistry meets biology or physics. In its simplest manifestations, electron transfer occurs when one forms an ionic bond as well as in interatomic and intermolecular interactions. Consider the case of a metal or semimetal atom A approaching a molecule M (at a distance r) with a low-lying unoccupied orbital. When the ionization potential of A is small and the electron affinity of M is large or only slightly negative, one expects an ionic−covalent potential surface crossing, with the electron transferred from the metal or semimetal to the interaction partner when the geometry is on the “small-r” side.2−4 In fact, the potential surface intersection occurs along a seam of conical intersections of dimension F − 2, where F is the number of internal degrees of freedom of the A−M supersystem, e.g., F is 3N − 6 for a supersystem with N atoms. It would require a seam of dimension F − 1 to divide the internal-coordinate space into well-defined subsystems, so the conical intersection seam does not do that, but the combination of the seam and its shoulders of avoided crossings does divide space into regions that are dominated by ionic electronic configurations and those dominated by electron configurations corresponding to neutral subsystems. An analogy would be a mountain peak, which does not divide a land into two regions, but the mountain peak and its associated mountain range can divide a country. If the mountain range circled back on itself, as in the circle-like ridge around a caldera, a system could be trapped inside the ridge. In more dimensions, the © XXXX American Chemical Society

Received: December 6, 2012 Accepted: January 11, 2013

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widely realized.7−19 Previous studies by electronic structure methods usually focused on the ground electronic states at their equilibrium molecular structures, with less attention to global or semiglobal features of the ground or excited state potential energy surfaces. Here we consider the nature of intersecting low-energy electronic states that provide accessible mechanisms for altering charge distribution and are responsible for some unique properties of endohedral fullerenes. This present Letter considers the energies of several electronic states as functions of the location of a boron atom inside the fullerene cage along the radial distance from the center of the cage out toward the fullerene wall. The sphere-like ridges of ionic−neutral avoided crossings discovered here raise additional interesting technological possibilities because a small perturbation that moves the endohedral atom closer to the wall of the fullerene could cause a large change transfer to the cage wall of the fullerene. Additionally, reversing this perturbation would cause the system to revert to a neutral fullerene cage wall. An example of a perturbation would be an external electric field, but the charge transfer may also be promoted by packing effects, pressure, intermolecular interactions, and so on. The large charge transfer expected in response to an electric field perturbation may lead to a large nonlinear polarizability in this kind of system. Such switchable atom−cage charge transfer may find applications in novel molecular devices. Our calculations employ density functional theory (DFT) with the M06-2X20,21 exchange−correlation functional and wave function theory (WFT) calculations using the stateaveraged complete active space self-consistent field method22−26 (SA-CASSCF). All calculations employed the def2SVP27 basis set. All DFT calculations were performed using the Gaussian 09 software,28 and all WFT calculations were performed using the GAMESS software.29 The SA-CASSCF wave function was constructed by distributing three electrons over thirteen active orbitals. The active orbital space consisted of one 2s, three 2p, five 3d, one 3s, and one 3p orbitals on the boron atom and of the two lowest-energy unoccupied orbitals (LUMOs) on the fullerene cage; we denote this active space as (3/13). For the state averaging, the five lowest electronic states were included with equal weights. For analysis, we calculated the partial atomic charge on the boron atom by the Hirshfeld method,30 which is generally less sensitive to the choice of basis set than population analyses and more stable for interior atoms than electrostatic potential fitting. Figure 1 depicts a potential energy profile for one of the states correlating to the 3-fold degenerate p manifold of an isolated boron atom. The profile is presented as a function of the location of the boron atom along a path starting at the geometric center of C60 to the center of a five-membered pentagon, where R is the distance from the center of the ring. One can see the presence of two energy minima: one with the boron atom at the geometric center of C60, and the other with the boron atom placed at a distance R of about 1.75 Å from the center. A barrier of about 25 kcal/mol separates these two minima. The minimum with the boron atom at the center is the lower-energy one, and the peripheral minimum is 10 kcal/mol higher. Also shown in this figure is the Hirshfeld charge on the boron atom as a function of the same geometric parameter R. A sudden shift of charge at a distance corresponding to the top of the barrier indicates charge transfer from the boron atom to the fullerene cage. The charge on the boron atom decreases as the interaction between boron and the carbon atoms of a five-

Figure 1. Cut through the potential energy surface of the ground electronic state (filled circles) and the ground-state Hirshfeld charges (asterisks) as functions of the distance of the boron atom from the center of C60. The cut is for the path connecting the center of the fullerene with the center of a pentagon, and the calculations are carried out by M06-2X.

membered ring develops into what is similar to an pentahapto metal−ligand interaction. Note that the distance (∼R) between the boron atom and the five closest carbons at the peripheral minimum is 1.979 Å, which is considerably smaller than the sum (3.62 Å)31 of their van der Waals radii, but larger than the sum (1.59 Å)31 of the standard single-bond covalent radii. Several electronic states have then been considered in order to elucidate the nature and origin of the two minima with different bonding patterns. The inclusion of at least five electronic states is required due to the degeneracy of the three lowest states, originating from the 2s22p1 electron configuration of the boron atom, and of the two higher-energy states that arise from the transfer of one electron from boron to the doubly degenerate LUMO of the cage. The five lowest electronic states along the same path obtained with adiabatic linear-response time-dependent DFT32 (TDDFT) are shown in Figure 2. Along the path shown, one of the three lowest quasi-

Figure 2. Energies of the five lowest electronic states by TDDFT/ M06-2X as functions of the distance from the center of the C60 molecule to the center of a hexagon. The reference state for the TDDFT calculation is shown as filled circles. 423

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degenerate states (which are degenerate in an isolated boron atom) undergoes an avoided crossing with the two higher-lying states; this corresponds to an electron transfer from the 2p orbital of the boron atom to an orbital delocalized over a large portion of the fullerene cage. In the same range of R, all five electronic states are energetically close and show local maxima and minima in the state-to-state gaps, which indicates the existence of nearby conical intersections.33 Similar calculations have been performed using a SACASSCF wave function (Figure 3). The surfaces are

Figure 4. Cuts through the potential energy surface of the ground electronic state as functions of distance from the center of the fullerene to the center of a C−C bond between two carbon hexagons (filled squares), to the center of a hexagonal carbon ring (open circles), and to the center of a pentagonal carbon ring (asterisks), calculated by M06-2X.

minima in all three cases are also nearly equidistant from the fullerene center, and since these minima are energetically close, the locus of points that form the “minimum-energy-surface” for the peripheral “minimum” is apparently close to a spherical valley (spherical trough). Motion in that trough is similar to the previously discovered34,35 circular motions of two La atoms within the round Ih C80 fullerene cage.

Figure 3. SA-CASSCF energies of the five lowest electronic states as a function of the distance from the center of the cage. The five states have equal weights. The cut is for the path connecting the center of the fullerene with the center of C−C bond between two hexagons.

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ASSOCIATED CONTENT

S Supporting Information *

qualitatively similar to those shown in Figure 2. The state crossings take place at higher energies due to the lack of dynamic electron correlation in a CASSCF wave function. It is interesting to compare the present results to the case of Ca atoms interacting with π electrons of smaller molecules such as coronene, benzene, and ethylene; those systems showed qualitatively similar structure of the ground electronic state potential energy surface except that there are three minima, corresponding to the neutral partners, single electron transfer, and two-electron transfer.5 The novel and fascinating feature of the endohedral fullerenes in this respect, though, is dictated by unique shapes of the fullerene molecules that gives rise to the particular topology of the avoided crossing ridge. Specifically, what in the former case (e.g., of benzene molecule interacting with metal atom) was a hyperplane-like ridge becomes in the case of endohedral fullerenes a hypersphere-like ridge. For boron, there is clearly an avoided crossing ridge both outside the fullerene and inside it. For more electropositive atoms, the position at the center of the cage may already be close enough to the wall that the entire range of geometries inside the cage is in the “small-r” region so that there is only a ridge on the outside. To demonstrate that the shapes of the ridges for the B@C60 system are similar to spheres, Figure 4 shows cuts through the ground electronic state potential energy surface as functions of the distance R from the center of C60 in three different directions. One can see from Figure 4 that the energy maxima corresponding to the avoided crossing ridge occur at approximately the same distance R, which indicates that this ridge too has a sphere-like shape. Furthermore, the energy

Geometry and energies in hartrees for one point on each curve in each figure. This material is available free of charge via the Internet http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (O.T.); [email protected] (D.G.T.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported in part by the National Science Foundation under Grant No. CHE09-56776 and by the Air Force Office of Scientific Research by Grant No. FA9550-11-10078. An award of computer time was provided by the Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program; this research used resources of the Argonne Leadership Computing Facility at Argonne National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract DEAC02-06CH11357.

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