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Stability of Group-V Endohedral Fullerenes Leonidas Tsetseris* Department of Physics, National Technical University of Athens, GR-15780 Athens, Greece, and Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, United States ABSTRACT: Most applications of endohedral fullerenes (A@C60) require the retainment of the trapped atoms at the center of C60 cages even after annealing at elevated temperatures. Here we use density-functional theory calculations to identify the atomic-scale mechanisms for loss of group-V elements (namely N, P, and As) from corresponding A@C60 species. We find that the interaction of N@C60 with solvent CS2 or other C60 molecules reduces the N escape activation energy by more than 0.5 eV compared to the case of isolated N@C60’s. These results are in agreement with experimental data on N endohedral loss at 450550 K. In contrast, we find that P@C60 and As@C60 are significantly more robust under annealing due to high P and As escape activation energies.
’ INTRODUCTION The trapping of atoms and small chemical groups inside buckyball cages attracted the attention of researchers soon after the discovery of C60.1 Efforts to insert many different impurities in fullerene molecules have been very active since then and have succeeded with the encapsulation of several elements or atom complexes.2-8 The presence of impurities in the intermolecular space of organic semiconductors is, in general, detrimental for associated electronic devices9 as it is often related to the appearance of charge carrier traps10-13 that degrade transport properties. In contrast, the encapsulation of species in the limited space defined by a fullerene cage opens the possibility of attaining novel functionalities in a controlled way. Applications of endohedral fullerenes include, but are not limited to, magneticresonance imaging,14,15 especially in biomedical sciences, and quantum computing.16-20 Naturally, the existence and stability of spin-polarized states for the trapped species are key requirements for these types of applications. In the case of elemental endohedral fullerenes, stability is often equivalent to retainment of a quasi-atomic configuration at the center of the fullerene cage (we refer to this type of geometries as A@C60). This stability criterion is relevant, for example, to the prototype A@C60’s with A being a group-V element.21-25 Experimental studies22 have shown that annealing of N@C60 samples at 400-600 K results in the loss of the endohedral character for the encapsulated N atoms. The activation energy (Ea) for this process was measured22 equal to 1.57 eV. Similar findings were reported22 for P@C60 with an Ea of 1.2 eV. Moreover, these experiments showed that the disintegration of endohedral N@C60 fullerenes was accelerated by environmental factors, namely the presence of solvents. A more recent study25 also found that the activation temperature for endohedral loss from N@C60 molecules in solution is slightly lower (500 K versus 550 K) than that in the case of N@C60 peapods inside carbon-nanotubes. r 2011 American Chemical Society
Several theoretical studies21,22,24,26-29 have identified the configurations with N or P atoms at the center of C60 molecules as the most stable structures for these group-V endohedral fullerenes. Simulations have also provided details24,26,30-32 about the electronic and magnetic properties of N@C60 and P@C60, in particular about the effect of the cage confinement on the wave functions of the encapsulated atoms. The issue of thermal stability, however, remains unresolved. A number of computational activation energies have been reported;21,22,27 for N escape they are all much larger than experimental values. Moreover, the underlying calculations relied on rigid displacement of the enclosed atom off the central position, ignoring the possibility of other intermediate configurations or the interaction with other molecules. In this article, we use ab initio calculations to identify the atomic-scale details for the encapsulation and escape of group-V atoms from fullerene molecules. The calculated activation energy for N escape from N@C60 is in agreement with measured values when the process is catalyzed by another C60 molecule. This activation energy drops further when the escape is aided by a solvent CS2 molecule. In contrast, Ea’s for N escape from isolated fullerenes are significantly higher than measured values, and so are the activation energies for P escape regardless if the P@C60 molecules are initially isolated or next to another fullerene species. Overall, the results show that the stability of endohedral fullerenes depends strongly on the nature of the encapsulated species and on environmental factors.
’ METHOD The calculations employed the density-functional theory (DFT) code VASP.33 Unless stated otherwise, the results we Received: August 31, 2010 Revised: December 31, 2010 Published: February 15, 2011 3528
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present below were obtained with ultrasoft pseudopotentials34 and a local-density approximation (LDA) exchange-correlation (xc) functional. The LDA functional (hereafter called LDA-CA) is based on the Perdew-Zunger parametrization of the Ceperley-Adler xc form.35 Calculations with the LDA-CA functional give a value of 583 Å3 for the volume per molecule in a rhombohedral C60 polymer fullerite crystal.36 The close agreement, less than 2.35% discrepancy, with the experimental value of 597 Å3 suggests the suitability of the LDA-CA functional for the calculations described below, especially those involving fullerene dimers. Selected cases were also tested with projector-augmented waves37,38 and the Perdew-Wang (PW91) xc-functional39 that is based on the generalized-gradient approximation (GGA). The energy cutoff for the plane wave basis was set to 350 eV and large supercells with dimensions of at least 2 nm (3 nm in the case of C60 dimers) were used. Barriers were obtained with the nudged elastic band (NEB) method40 based on experience with similar calculations in various systems.41,42 Within the NEB method, the so-called minimum-energy pathway (MEP) of a process is simulated as a sequence of intermediate structures (termed images) between an initial and a final configuration. In the calculations discussed below we used 16 images for each separate MEP. In some cases, NEB relaxation of the MEP led to intermediate local-energy minimum structures. The path was then split in two MEPs, as described in previous studies.43,44
’ RESULTS Stability of Isolated N@C60. The most stable geometry for a N atom inside a C60 cage is the quasi-atomic N@C60 configuration of Figure 1a with N at the center of the cage. Compared to N@C60, the structures shown in Figure 1b,c, with the N atom attached on the inner side of the fullerene, lie higher in energy by 0.10 and 0.25 eV, respectively. The corresponding GGA-PW91 energy differences are 0.42 and 0.61 eV. Other stable geometries are the N substitutional configurations of Figure 1d,e, and the external bridge structure of Figure 1f. The energies of these structures are lower than that of N@C60 by 0.27, 1.07, and 2.81 eV. With the exception of N@C60, which has a finite magnetic moment (M) of 3 μB, all configurations with a N atom attached in the inner or outer part of the C60 molecule have M of 1 μB. Our finding that the outer N adatom configuration of Figure 1f is more stable than the central N@C60 structure is in agreement with previous ab initio studies21 and differs from the opposite prediction of molecular-orbital calculations.45 Therefore, a N@C60 molecule will transform under sustained annealing to the external bridge configuration of Figure 1f. There are many different possible MEPs for this process, pathways that involve a series of transformations between the above-mentioned structures. We studied several of those sequences and we found that the rate-limiting step for loss of the endohedral N@C60 character is the transformation from the structure of Figure 1b to that of Figure 1d. The energy variation along this escape route is shown in Figure 2. The effective activation energy for N escape is equal to 1.9 eV (2.1 eV) within LDA-CA (GGA-PW91). We note that during the transformation from (a) to (c) the N atom goes through structure (b) which corresponds to the local energy minimum at image 14 of Figure 2. The transformation is then completed with the formation of the structure of Figure 1c which, as shown in Figure 2, is a shallow local-energy minimum. Previous studies21,22 have reported larger Ea’s that range from 2.7 eV upward. The differences may be traced to the fact that
Figure 1. N atoms (shown with arrows) inside and outside a C60 molecule: (a) endohedral N@C60 structure, (b) and (c) on the inner side of the C60 cage, (d) and (e) substitutional N (N replaces a C atom pushing it out to the bridge configurations shown with dotted arrows), (f) N external bridge structure. Color key: C, gray; N, light gray spheres.
Figure 2. Energy variation during escape of N from an initial N@C60 structure. The indexes of structures refer to the configurations of Figure 1. The arrow shows the effective LDA-CA barrier (1.9 eV) for loss of N@C60 species. Energies are referenced with respect to that of structure of Figure 1d.
those studies employed rigid displacements of the N atom off the endohedral central site, a simulation approach that is less reliable than NEB calculations. In addition, intermediate configurations, such as the structure of Figure 1d, were not taken into account. 3529
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Figure 4. N atom (shown with arrows) at the core of a C60-C60 dimer. Color key: C, gray; N, light gray spheres.
Figure 3. C60-C60 dimers with a N atom present (shown with arrows): (a) unlinked N@C60 and C60 pair, (b) [2,2] N@C60-C60 dimer, and (c) N attached on the inner side of one of the C60 molecules. Color key: C, gray; N, light gray spheres.
Even the NEB value of 1.9 eV, however, is considerably larger than the measured22 Ea of 1.57 eV for N loss from N@C60. Moreover, experiments25 on loss of N endohedral character for C60 peapods inside carbon nanotubes found that the process is activated at 550 K, not very different than the temperature range of annealing measurements for C60 in solution or gas phase.22 These facts suggest as an alternative scenario for the thermal instability of N@C60 the interaction of the endohedral molecule with other chemical species, namely neighboring fullerenes or solvent molecules. Stability of N@C60-C60 Dimers. In Figures 3 and 4 we show several configurations of C60-C60 dimers with a N atom present. These structures serve as intermediate steps for the transformation of the original N@C60 geometry to the final arrangement of a chemically bonded fullerene dimer. The rate-limiting step that determines an Ea of 1.42 eV is the formation of the so-called [2,2] C60-C60 dimer of Figure 3b. For a [2,2] dimer without a N atom the binding energy against dissociation to two C60 molecules is 0.4 within LDA-CA and -0.2 eV within GGA-PW91. The LDACA (GGA-PW91) activation energy for [2,2] dimerization (without a N atom) is equal to 1.35 eV (1.81 eV). Given that LDA-CA typically undervalues barriers by a few tenths of an electronvolt, while GGA-PW91 underestimates46 the attractive forces between sp2-based carbon materials, we can infer that the
true Ea for C60 dimerization is about 1.5-1.6 eV. This range is in close agreement with the 1.57 eV value for experiments22 on N endohedral loss. After the dimer is formed, there is a barrier of about 0.9 eV for the N atom to get attached on the inner side of the C60 molecule, as shown in Figure 3c. This step stabilizes the loss of the original 3 μB magnetic moment, since the structure of Figure 3c has an M of 1 μB and its energy is 1.1 eV lower than that of Figure 3a. Following higher-barrier processes the energy can drop further with the formation of the structures shown in Figures 4a,b. These structures have M of 1 μB and they are more stable than that of Figure 3c by 0.1 and 3.7 eV, respectively. N@C60-CS2 Complexes. We now turn our attention to the role of a typical CS2 solvent in enhancing the loss of N@C60 species. In Figure 5 we show several configurations of complexes between a CS2 molecule and a C60 fullerene with a N atom. All structures shown in Figure 5, except for the nonmagnetic geometry of Figure 5e, have M of 1 μB. Figure 5a depicts a CS2 molecule and a proximal C60 molecule with a N atom bonded on the inner side of the cage. As mentioned above, the energy difference and barrier for the generation of this configuration from the N@C60 geometry are 0.1 and 0.9 eV, respectively. Attachment of the CS2 molecule creates the structure of Figure 5b and increases the energy compared to that of Figure 5a by 0.6 eV. The barrier for the (a) to (b) transformation is 1.0 eV. As shown in the energy variation diagram of Figure 6, this transformation is the rate-limiting step for the loss of the endohedral N character from a N@C60-CS2 complex. A second step of comparable barrier leads to the creation of the shallow energy minimum structure of Figure 5c, which lies about 0.3 eV lower than the configuration of Figure 5a. The ensuing, almost barrierless, transformation to the geometry of Figure 6d releases a significant amount of energy (3.7 eV) and makes the loss of the endohedral N character practically irreversible. The energy can drop further (by 0.4 eV) with the formation of the structure of Figure 5f. Figure 5e shows a structure that is 3530
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Figure 7. P atoms inside and outside a C60 molecule. Color key: C, gray; P, light gray spheres.
Figure 5. Complexes between a solvent CS2 molecule and a fullerene with a N atom (shown with an arrow). Color key: C, gray; N, light gray; S, white spheres.
Figure 6. Energy variation for loss of endohedral N from a N@C60CS2 complex. The indexes refer to configurations of Figure 5. Energies are referenced with respect to that of structure of Figure 5d.
intermediate to (d) and (f) and lies 0.15 eV higher in energy than (d). On the basis of these computational results, we obtain an activation energy of 1.1 eV for the loss of the 3 μB moment of N@C60 in the presence of CS2 molecules. We note that this value is significantly lower than the effective activation energy of 1.9 eV for loss of N endohedral character from isolated C60 molecules.
In other words, a solvent CS2 molecule acts as an efficient catalyst for N@C60 disintegration. It also accelerates N@C60 loss compared to interactions with neighboring fullerene molecules, since the activation energy in the latter case is 0.32 eV higher in energy than the 1.1 eV value. Stability of P@C60 and As@C60. Unlike N@C60, there is a large energy difference between a P@C60 with P at the center of the fullerene and the structure with P attached on the inner side of the C60 molecule. In particular, the former configuration is more stable than the latter by 1.47 eV (1.70 eV) within LDA-CA (GGA-PW91). These two structures are depicted in Figure 7a,b. The buckled substitutional geometry of Figure 7c lies about 0.8 eV higher in energy than P@C60. On the other hand, the external P bridge of Figure 7d is more stable than P@C60 by 2.0 eV. With the exception of P@C60, which bears a magnetic moment of 3 μB, all other structures have M equal to 1 μB. Escape of P from the C60 cage can proceed through the transformations of P@C60 to the inner adduct of Figure 7b and then to the external adatom structure of Figure 7c. The activation energy for this transformation, however, is more than 5 eV. The large Ea value shows that annealing, even at extreme temperatures, cannot activate the escape of P from isolated C60 molecules. But, even in the case of C60-C60 dimers, the escape routes have activation energies of several electronvolts. In other words, unlike the case of N@C60, we could not identify a MEP for P escape that has an Ea as low as the reported22 experimental value of 1.2 eV. Since P has a larger covalent radius than N, it seems unlikely (though the results of this work cannot rule out completely the possibility) that P can go through the C60 cage with an Ea that is lower than that for N. In the case of As, the inner adduct is unstable and transforms spontaneously to the endohedral configuration As@C60 with As at the center of the C60 cage. Compared to As@C60, an As structure of the type of Figure 7c is less stable by 1.5 eV. The lowest-energy As configuration is the external bridge of the form of Figure 7d; its energy difference to the As@C60 geometry is 1.5 3531
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’ CONCLUSIONS Based on the above, endohedral P@C60 and As@C60 species are significantly more robust than N@C60, and they could, thus, be used in applications for which thermal stability is a critical issue. As in the case of O trapped inside fullerene molecules,13 though P and As exohedral structures are more stable, endohedral species that are trapped during growth or irradiation will remain encapsulated for very long periods of time. On the other hand, N@C60 molecules are also relatively stable when isolated, but their loss of endohedral N atoms can be accelerated by neighboring C60 and solvent CS2 molecules. Both these findings on environmental dependence explain corresponding experimental data.22,25 Such data include the measured activation energy of 1.57 eV for N endohedral instability in the case of gas phase fullerene species, as well as the temperature range for N endohedral loss in C60 peapods. We have also seen that the formation of a C60-C60 dimer is the rate-limiting step for N loss, and that a subsequent transformation to an inner adduct has a lower barrier of about 0.9 eV. This value suggests that fullerene dimers formed at low temperatures by nonthermal means, such as ball milling or pressure, can retain their N endohedral character with M = 3 μB. The scenario explains related findings23 on the persistence of N@C60 structures at 80 K, even after dimerization has occurred. We should finally note that the accuracy of the reported binding energies and transformation barriers can be further improved in future studies that will include an explicit treatment of dispersion interactions or the use of hybrid functionals for the description of electronic exchange and correlation. Examples of such studies on different endohedral systems, namely C60 and C70 fullerenes with hydrogen molecules trapped inside, have been reported recently47-49 and highlighted the importance of corrections related to van der Waals interactions, especially in the case of GGA xc-functionals. In summary, we have provided atomic-scale details for the reaction pathways that lead to loss of endohedral character from group-V A@C60 molecules. The calculated energies and barriers of transformations explain pertinent experimental data and reveal the dependence of thermal stability on environmental factors like the presence of solvent molecules or other fullerene species. P@C60 and As@C60 can retain an endohedral character for temperatures much higher than the ones needed for the activation of N endohedral loss. ’ AUTHOR INFORMATION Corresponding Author
*Phone number: þ30-210-7723046. E-mail:
[email protected].
’ ACKNOWLEDGMENT The calculations used resources of the EGEE and HellasGrid infrastructure. Useful discussions with Dr. K. Porfyrakis are acknowledged.
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