Spin–Spin Coupling in Nitrogen Atom Encapsulated C60, C59N, and

Article pubs.acs.org/JPCA

Spin−Spin Coupling in Nitrogen Atom Encapsulated C60, C59N, and Their Respective Dimers Vinit, K.S. Sujith, and C.N. Ramachandran* Department of Chemistry, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand 247667, India S Supporting Information *

ABSTRACT: Density functional theoretical calculations were performed to study the stability and magnetic properties of nitrogen-encapsulated C60, C59N, and their respective dimers at B3LYP/6311G* and B3LYP-GD2/6-311G* levels of theory. For the most stable spin state of each of the above complexes, spin density transfer and spin−spin coupling between different components are investigated. The nature of bonding between the guest and the host is analyzed based on the highest occupied molecular orbital−lowest unoccupied molecular orbital energy gap and the respective molecular orbital diagrams. The analysis of spin density showed that the encapsulated nitrogen retained its atomic state in N@C60 and N@C59N. Depending on the multiplicity of N@C59N, the unpaired electrons of the encapsulated nitrogen are coupled with those of the cage antiferromagnetically or ferromagnetically. The present study also showed that the complex (N@C60)2 can exist in two isoenergetic spin states, namely, 7[(N@C60)2] and 1[(N@C60)2]. In the former, the encapsulated nitrogens are ferromagnetically coupled, whereas they are coupled anti-ferromagnetically in the latter. A similar coupling between the guest species occurs in the nitrogen analogues 7 [(N@C59N)2] and 1[(N@C59N)2]. The stabilization energy of the endohedral nitrogen complexes indicated that the interaction between the guest and the host cage is purely noncovalent.

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a heteroatom such as boron, nitrogen, and phosphorus.26−29 Several theoretical and experimental studies on the electronic structure and stability of various heterofullerenes have been reported.30,31 The nitrogen-doped fullerene C59 N was produced through arc vaporization of graphite in the presence of pyrrole.32,33 Hummelen et al. isolated the heterofullerene dimer (C59N)2 by in situ reduction of C59N+ ion.34 Pichler et al. investigated the electronic structure of azafullerene dimer (C59N)2 using electron-loss spectroscopy, photoemission spectroscopy, and density functional theoretical methods.35 Their study reported that (C59N)2 exists in its trans isomeric form.34,35 Theoretical studies reported that (C59N)2 exists also in the gauche conformation.36 The magnetic properties of fullerenes and their derivatives have taken wide attention recently. The magnetic properties can be induced in a fullerene cage either with the substitution of its carbon atom by a heteroatom as mentioned above or with the encapsulation of guest species having unpaired electrons leading to the formation of paramagnetic fullerene derivatives. Several studies focusing on the encapsulation of paramagnetic species inside fullerene cage have been reported.37−44 These include the pioneering works of Park et al. in which quantum mechanical and density functional methods were used to examine the interaction of encapsulated paramagnetic atoms (4N, 4P, 3O, and 3S) with the host C60 cage.37 Their study showed that the stability of the complex formed is solely due to

INTRODUCTION The endohedral fullerenes have taken wide attention in the scientific community in the last three decades due to their peculiar electronic, magnetic, and optical properties.1,2 The first laboratory discovery of endohedral fullerene was reported in 1985 by Kroto et al., who achieved the encapsulation of La inside C60 by laser vaporization of graphite in a high-pressure supersonic nozzle.3 Following the discovery of La@C60, the encapsulation of several other guest species such as alkali metals, alkaline earth metals, transition metals, some of the pblock elements, noble gases, and various small molecules (H2, H2O, CH4, NH3, etc.) inside fullerenes of various sizes and shapes was reported.1−8 The encapsulation of reactive species inside C60 was a major development due to the stability of the resulting complexes.1−8 Several experimental and theoretical studies have been reported on the encapsulation of reactive species in C60.9−17 One of the most significant achievements in this direction is the encapsulation of highly reactive atomic nitrogen inside C60, in which nitrogen retained its atomic spin state making the complex suitable for quantum computing.4,18 Following the discovery of fullerenes and endohedral fullerenes, several derivatives of these species were obtained through polymerization and substitution reactions. Rao et al. observed that exposure of C60 molecules to UV−visible light led to their dimerization through a [2 + 2] cycloaddition mechanism.19 Theoretical studies on C 60 dimerization supported that [2 + 2] cycloaddition can lead to the formation of a four-membered carbon ring that links two C 60 moieties.20−25 Heterofullerenes are derivatives of fullerenes in which minimum one carbon atom of the cage is substituted by © 2016 American Chemical Society

Received: April 14, 2016 Revised: August 15, 2016 Published: August 15, 2016 6990

DOI: 10.1021/acs.jpca.6b03817 J. Phys. Chem. A 2016, 120, 6990−6997

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The Journal of Physical Chemistry A

Figure 1. Optimized geometries of C60, C59N, various endohedral complexes, and their dimers.

sum of the individual spins. The theoretical studies of Gd@C60 by Lu et al. revealed that the complex is most stable in its septet state in which three valence electrons of Gd is transferred to C60. In this complex, the guest and the host are antiferromagnetically coupled as reflected from their spin density values of 6.74 and −1.26 e/au3, respectively.44 In all of the above studies, spin−spin coupling and spin density transfer between the guest and the host are limited to the cage made of carbon atoms. To the best of our knowledge, studies of endohedral complexes of paramagnetic heterofullerenes are not reported. The present work aims to study the stability and the electronic structure of endohedral heterofullerenes N@C60 and N@C59N and their respective dimers in detail. The spin density transfer and the spin−spin coupling between the guest and the host as well as those between the guests in adjacent cages of the above complexes are investigated for their different spin states. The effect of dimerization on the spin of encapsulated nitrogen atoms is discussed. For this purpose, the electronic structures of the most stable spin state of (N@C60)2 and (N@C59N)2 are determined. The nature of bonding between guest and host in the complexes is also analyzed. The results obtained from the present work are expected to help future studies on the development and applications of endohedral complexes of heterofullerenes.

the dispersive interactions between the host and the guest species without the spin density transfer between the components. Recently, Asif et al. investigated the encapsulation of diatomic paramagnetic molecules B2, O2, and Ge2 inside C60 and found that the resulting complexes are stable in their triplet state.38 It has been also reported that the encapsulation of nonmetallic paramagnetic atoms (F and O) inside C60 does not lead to a covalent bond between the guest and the host cage. Moreover, the encapsulated atoms retained the electronic configuration as in their free state.39 Density functional studies of the complex Po@C60 showed that Po is located at the center of the cage and that the complex is most stable in its triplet state with Po atom retaining its free state electronic configuration.40 The spin density value of Po was found to be 1.97 e/au3 suggesting that there is no spin density transfer between Po and the cage. On the other hand, studies of the electronic structure of M@C60 (M = Ca, Sc, and Y) suggested that two s-electrons of Ca, Sc, and Y transfer to the cage, while the d-electrons of Sc and Y remain on the metal atom.41 Dai et al. applied density functional theory to study the defective uranofullerene complex U2@C61, where the defect in C60 cage is induced by adding an extra carbon atom to the cage.42,43 The study showed that the electronic properties of defective uranofullerene U2@C61 are different from those of U2@C60 due to the presence of unpaired electrons on the additional carbon atom. It was revealed that depending upon the site at which the additional carbon is added (i.e., pentagon−hexagon bond or hexagon−hexagon bond), the unpaired electrons of the encapsulated uranium atoms interact with the unpaired electrons of additional carbon either ferromagnetically or anti-ferromagnetically. In the former, the total magnetic field due to the electron spin is enhanced compared to the individual spins, whereas in the latter, it is decreased with respect to the

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COMPUTATIONAL METHODS All calculations reported in this study were performed using the Gaussian 09 program.45 Geometry optimization was performed for C60, N@C60, C59N, N@C59N, and their respective dimers. We used the hybrid density functional B3LYP with and without the Grimme’s empirical dispersion correction (i.e., B3LYP6991

DOI: 10.1021/acs.jpca.6b03817 J. Phys. Chem. A 2016, 120, 6990−6997

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The Journal of Physical Chemistry A GD2) in conjunction with 6-311G* basis set.46,47 The highest occupied molecular orbital (HOMO)−lowest unoccupied molecular orbital (LUMO) energy gap for C60 predicted by these methods is 2.7 eV in agreement with the value reported experimentally.48,49 The calculated vertical ionization energy (7.63 eV) and vertical electron affinity (2.44 eV) are also found to be in excellent agreement with the corresponding experimental values of 7.6 and 2.46 eV, respectively.50,51 For the complexes N@C59N, (N@C60)2, and (N@C59N)2, possible spin states of each species were considered. The wave functions corresponding to various spin states of different complexes were verified for their stability and confirmed that they are stable. We computed the stabilization energy of each state, and on the basis of that the most stable spin state of each type of the above complexes was determined. The frequency analysis confirmed that the optimized geometry of the most stable state of each type of the complexes corresponds to minima on the respective potential energy surface. The stabilization energy of the complex is calculated as follows:

that the complex N@C60 has stabilization energy of 1.22 and −9.69 kcal/mol at B3LYP and B3LYP-GD2 levels, respectively. It is also observed that the stabilization energy obtained for various spin states of the complex (N@C60)2 at B3LYP/6311G* and B3LYP-GD2/6-311G* levels follow the order 7 [(N@C60)2] = 1[(N@C60)2] > 9[(N@C60)2] > 5[(N@C60)2] > 3[(N@C60)2]. Thus, it can be concluded that in the ground state of (N@C60)2, the encapsulated nitrogen atoms retained their atomic nature. The values of the stabilization energy calculated using B3LYP and B3LYP-GD2 functional indicate that van der Waals interactions play a major role in the stability of these complexes. The stabilization energy calculated for N@C59N for its various spin states (1, 3, and 5) revealed that the triplet and the quintet states of the complex are nearly isoenergetic. Both of these states were found to be stable at B3LYP-GD2 level as evident from the stabilization energy listed in Table 1. The energy difference between triplet and quintet states of N@ C59N is negligible compared to the thermal energy at room temperature, suggesting that the complex can exist in triplet and quintet states. The singlet state of the above complex, where the total zero-spin state arises due to the anti-ferromagnetic coupling between guest and the host cage, was found to be higher in energy. The stabilization energy of the complex (N@C59 N) 2 followed the order 7[(N@C59N)2] = 1[(N@C59N)2] > 5 [(N@C59N)2] > 9[(N@C59N)2] > 3[(N@C59N)2] at both levels of theory. The most stable spin states of N@C59N and its dimer indicate that encapsulated nitrogen retains the atomic nature, despite the presence of a heteroatom of the cage. The low value of stabilization energy for the encapsulation of nitrogen atom in the host cages mentioned above indicates that the guest and the host cage interact via van der Waals interaction. Spin−Spin Coupling between Guest and Host and between Guest Atoms of Adjacent Cages. The calculated values of spin density of the encapsulated nitrogen and the nitrogen of the cage for different complexes studied are listed in Table 2. The spin density difference plots for the complexes are shown in Figure 2. It can be seen from the table that nitrogen atom encapsulated in C60 has a spin density of 2.97 e/au3 keeping the electronic configuration of its free state. This

Estab = Ecomplex − Ecomponents

where, Ecomplex and Ecomponents are the energy of the complex and their components, respectively. The stabilization energy for the most stable complex is further corrected for basis set superposition error (BSSE). For the most stable spin state of (N@C60)2 and (N@C59N)2, the spin density difference is calculated. From the spin density difference distribution and the frontier molecular orbital diagrams, the nature of host−guest interaction present in the complexes is analyzed. The calculated spin density difference distribution and the molecular orbital diagrams of HOMO and LUMO are plotted using the program GaussView 5.52

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RESULTS AND DISCUSSION Electronic Structures of N@C60, N@C59N, (N@C60)2, and (N@C59N)2. The optimized geometries of various complexes studied are given in Figure 1. The stabilization energy calculated for the complexes with and without dispersion interactions are listed in Table 1. From Table 1, it can be seen Table 1. Stabilization Energya of Various Endohedral Complexes for Their Different Spin States systems

B3LYP/6-311G* (kcal/mol)

B3LYP-GD2/6-311G* (kcal/mol)

[N@C60] 1 [(N@C60)2] 3 [(N@C60)2] 5 [(N@C60)2] 7 [(N@C60)2] 9 [(N@C60)2] 1 [N@C59N] 3 [N@C59N] 5 [N@C59N] 1 [(N@C59N)2] 3 [(N@C59N)2] 5 [(N@C59N)2] 7 [(N@C59N)2] 9 [(N@C59N)2]

1.22 (3.55) 1.64 52.93 41.81 1.65 (6.37) 41.29 13.81 1.02 (3.08) 1.11(3.22) 2.36 52.14 34.85 2.36 (6.47) 36.64

−9.69 (−7.45) −20.75 30.41 19.16 −20.75 (−15.86) 18.71 14.93 −10.22 (−8.03) −10.13 (−7.92) −20.28 b 11.85 −20.28 (−15.91) 13.69

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Table 2. Calculated Spin Density Values (in e/au3) for Different Types of Nitrogen in Various Systems complexes 4

N 4 [N@C60] 1 [(N@C60)2] 7

[(N@C60)2] [C59N] 3 [N@C59N] 2

a

The BSSE corrected values for the most stable spin states are given in parentheses. bConvergence error. 6992

5

[N@C59N]

1

[(N@C59N)2]

7

[(N@C59N)2]

B3LYP/6-311G*

B3LYP-GD2/6-311G*

3.00 Nencap = 2.97 (Nencap)1 = 2.97 (Nencap)2 = −2.97 (Nencap)1 = (Nencap)2 = 2.97 Ncage = 0.08 Nencap = 2.95 Ncage = −0.08 Nencap = 2.97 Ncage = 0.08 (Nencap)1 = 2.97 (Nencap)2 = −2.97 (Ncage)1 = (Ncage)2 = 0.00 (Nencap)1 = (Nencap)2 = 2.97 (Ncage)1 = (Ncage)2 = 0.00

3.00 Nencap = 2.97 (Nencap)1 = 2.97 (Nencap)2 = −2.97 (Nencap)1 = (Nencap)2 = 2.97 Ncage = 0.08 Nencap = 2.96 Ncage = −0.08 Nencap = 2.97 Ncage = 0.08 (Nencap)1 = 2.97 (Nencap)2 = −2.97 (Ncage)1 = (Ncage)2 = 0.00 (Nencap)1 = (Nencap)2 = 2.97 (Ncage)1 = (Ncage)2 = 0.00

DOI: 10.1021/acs.jpca.6b03817 J. Phys. Chem. A 2016, 120, 6990−6997

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Figure 2. Spin density difference plots for various complexes in their most stable spin states with an isodensity value of 0.0004. The blue color represents the excess of α spin density, and the orange color represents the excess of β spin density.

quintet states of N@C59N. The values of spin density (Table 2) also suggest that there is no spin density transfer from trapped nitrogen to that of the cage in both spin states of the complex. The spin densities of nitrogen of the cage (Ncage) in triplet and quintet states of N@C59N are −0.08 and 0.08 e/au3, respectively. This indicates that ferromagnetic or antiferromagnetic spin−spin coupling occurs between the guest and the host in N@C59N depending upon the spin states of the complex. For the quintet state of (N@C59N)2, the two confined nitrogen atoms possess the spin densities of 2.91 and 2.97 e/au3 compared to −0.08 and −0.01 e/au3 for the nitrogens of the cages as listed in Table S1 of Supporting Information. This indicates that there is no transfer of spin density from the trapped nitrogen to its host cage, an observation similar to the case of triplet state of N@C59N. However, in the higher-energy quintet state 5[(N@C59N)2], spin density transfer from one cage to another is observed as depicted in Figure S1 of the Supporting Information. A similar spin density transfer between the host cages is also observed for the higher-energy state of 9 [(N@C59N)2]. This holds true for the quintet and nonet states of (N@C60)2. However, in the lower-energy septet state, the excess of α-electron spin density resides only on the encapsulated nitrogens without any transfer to the host cage. Thus, in 7[(N@C59N)2] the unpaired electrons on each guest species are ferromagnetically coupled. In contrast to the septet state, in the singlet state of (N@C59N)2, anti-ferromagnetic coupling occurs between the spin of encapsulated nitrogens of adjacent cages. Thus, it can be concluded that in N@C59N and in its dimer, the presence of nitrogen of the cage does not assist the spin density transfer between the guest and the host. The complex (N@C59N)2 can be considered to be formed by the dimerization of two N@C59N radicals with the pairing of unpaired electron of each cage, as elucidated from the analysis of the spin density difference plots shown in Figure 2. Although the spin density difference plot indicates an excess spin density

suggests that there is no spin density transfer from the encapsulated nitrogen to the host cage. Since nitrogen retains its spin in N@C60, it is important to know how the presence of a nitrogen atom in an adjacent cage affects the spin of an encapsulated nitrogen. Considering the fact that spin density of the nitrogen of 7[(N@C60)2] is equal to that of the nitrogen in N@C60, it can be concluded that there is no transfer of spin density between the guest species or between the guest species and the host. This is also confirmed from the spin density difference plot of septet state of (N@C60)2, where the spin density difference is distributed only on nitrogen atoms, suggesting a ferromagnetic coupling between them. In the singlet state of (N@C60)2, spin of the unpaired electrons of nitrogen atoms in the adjacent cages are anti-ferromagnetically coupled as evident from their spin density values of 2.97 and −2.97 e/au3 obtained from the broken symmetry calculations as explained in the Supporting Information. The values of spin density and its distribution for other higher electronic states of (N@C60)2 are given in Table S1 and Figure S1, respectively, in the Supporting Information. The complex N@C59N has two different types of nitrogen atoms, one that is encapsulated in the cage (Nencap) and the other that substitutes one of the carbon atoms (Ncage) of the cage. Thus, we analyzed the spin density associated with both types of nitrogen atoms of the complex in its triplet and quintet states. A comparison of spin−spin coupling between the encapsulated nitrogen and the cage in N@C59N with that between the encapsulated nitrogens of (N@C59N)2 showed some interesting results. For C59N in its ground state, the spin density is distributed over the entire cage rather than only on nitrogen atoms that possess a spin density of only 0.08 e/au3, suggesting that the unpaired electron is delocalized over all atoms of the cage. We examined the nature of coupling between the encapsulated nitrogen and the paramagnetic C59N cage in the complex N@C59N. The encapsulated nitrogen atom (Nencap) has nearly the same value of spin density in triplet and 6993

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The Journal of Physical Chemistry A on the host cage of N@C59N, no such excess α or β spin density is observed in any of the cages of dimer for its singlet and septet states, suggesting the pairing of electrons during dimerization. Nature of Bonding between the Guest and the Host. The frontier molecular orbitals of a complex can give valuable information about the nature of interaction between its component species. Thus, the HOMO and LUMO of the complexes are analyzed. The energy gap between the frontier molecular orbitals of various complexes mentioned above is listed in Table 3, and the diagrams of the frontier molecular

orbitals of various complexes are presented in Figure 3. It can be seen that the energy gap between HOMO and LUMO of C60 (2.75 eV) is nearly unaffected by the encapsulation of nitrogen atom inside C60. From the molecular orbital diagrams of C60 and N@C60, it is also clear that the frontier molecular orbitals of N@C60 are mainly formed from the atoms of the host cage. This is understandable because the molecular orbitals derived from nitrogen are lower in energy because of its higher electronegativity. Similarly, the HOMO−LUMO energy gap (2.48 eV) of host (C60)2 in (N@C60)2 is also unaffected by the encapsulation of nitrogens. Like in N@C60, the frontier orbitals of (N@C60)2 are formed mainly from carbon atoms of the cage as evident from Figure 3. The unperturbed frontier molecular orbitals of the host species of N@C60 and (N@C60)2 as well as the calculated values of respective stabilization energy indicate that the interaction between the guest and the host is noncovalent in nature. The HOMO−LUMO energy gap for C59N was found to be 1.27 eV, and it remained the same for the triplet and quintet states of N@C59N. For N@C59N, the energy gap is considered for either α- or β-spin orbitals depending on the spin state of the complex. The reason for choosing the α-spin orbital energy gap for the quintet state and β-spin orbital energy gap for triplet state of N@C59N can be explained on the basis of the spin density difference plot and the HOMO−LUMO energy levels given in Figure 2 and Figure S2, respectively. The figures clearly illustrate that, unlike 5[N@C59N], 3[N@C59N] has β-spin density on the host cage. It is also clear from Figure 3 that the HOMO of all these complexes is centered on the host cage. Thus, for 3[N@C59N], the HOMO−LUMO energy gap for βspin orbital is considered. Figure 3 shows that HOMO and LUMO of 5[N@C59N] has no contribution from the

Table 3. Calculated HOMO−LUMO Energy Gap for Various Complexes in Their Most Stable Spin States systems 4

C60 [N@C60]

7

(C60)2 [(N@C60)2]

2

[C59N]

3

[N@C59N]

5

[N@C59N]

7

(C59N)2 [(N@C59N)2]

α β α β α β α β α β α β

B3LYP/6-311G* (eV)

B3LYP-GD2/6-311G* (eV)

2.75 2.74 2.66 2.48 2.48 2.43 1.27 2.46 2.45 1.25 1.27 2.44 2.21 2.22 2.12

2.74 2.74 2.66 2.47 2.47 2.41 1.27 2.45 2.45 1.25 1.27 2.44 2.20 2.20 2.10

Figure 3. Isodensity surface plots of α-spin highest occupied and lowest unoccupied molecular orbitals of the complexes with an isodensity value of 0.02. For triplet state of 3[N@C59N], the β-spin orbitals are shown. 6994

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The Journal of Physical Chemistry A encapsulated nitrogen, although there is a slight contribution of the encapsulated nitrogen atom toward HOMO and LUMO of 3 [N@C59N] complex. The HOMO−LUMO energy gap of (C59N)2 was found to be 2.21 eV, which is unaffected by the encapsulation of nitrogen atoms inside the cages. The respective HOMO and LUMO of (C59N)2 and (N@C59N)2 are quite similar in appearance as evident from Figure 3. As mentioned for the other endohedral complexes, the HOMO and LUMO of (N@C59N)2 are mainly contributed by the carbon and nitrogen atoms of the cage. This along with the low stabilization energy of −20.28 kcal/mol for (N@C59N)2 indicates the lack of covalent interaction between the guest species and host cage. The stability of the complex arises mainly because of the dispersion interaction between the component species. The effect of dimerization on the HOMO−LUMO energy gap of C60, N@C60, C59N, and N@C59N was examined, and it was found that the HOMO−LUMO energy gap for C60 and N@C60 is decreased by ∼0.27 eV on forming their respective dimers. For the complexes C 59 N and N@C 59 N, the dimerization led to an increase in the HOMO−LUMO energy gap by ∼0.95 eV in agreement with the enhanced stability of the dimer. In the above discussion, the encapsulation of nitrogen is considered only for the trans isomer of (C59N)2 based on the earlier experimental results, although a gauche isomer of slightly lower energy (∼0.5 kcal/mol) is reported theoretically.34−36 The experimental studies of Hummelen et al. reported that the dimer (C59N)2 shows only 30 lines in 13C NMR suggesting a highly symmetric structure.34 The studies of Pitchler et al. also support (C59N)2 trans form.35 However, to examine whether the orientation of the host cage affects the spin−spin interaction between the guest species, we also studied the encapsulation of two nitrogen atoms in the cages of the gauche isomer of (C59N)2 for the singlet and the septet states. The results of the above calculations are listed in Table S2 of the Supporting Information. From the values of spin density of nitrogen obtained for the endohedral complexes of gauche and trans isomers it can be concluded that the orientation of the cage has no significant effect on the interaction between the encapsulated guest species.

guest atoms indicates electron spin dipolar coupling rather than spin exchange coupling between two spin centers in agreement with the findings of recent experimental studies on similar systems.53,54 The examination of the HOMO−LUMO energy gap and the molecular orbital diagrams of the complexes confirmed that no covalent interaction exists between the host and the guest species. In all cases, the HOMO−LUMO energy gap is unaffected by the encapsulation of nitrogen atom. Thus, the stability of the complex is entirely due to the dispersion interaction between the encapsulated nitrogen atoms and the host cage. It is also found that the formation of (C59N)2 and (N@C59N)2 from their respective units leads to an increase in the HOMO−LUMO energy gap in contrast to the corresponding change for (C60)2 and (N@C60)2. In conclusion, taking nitrogen-encapsulated fullerenes as a prototype of two spin center molecules, we have studied the stability, magnetic properties, and nature of interaction between two paramagnetic guest species encapsulated in adjacent cages. The effect of a heteroatom on the surface of the cage in the interaction was also examined using an experimentally viable system.

CONCLUSION Density functional theoretical studies were performed to investigate the structure, stability, and magnetic properties of nitrogen-encapsulated complexes of C60, C59N, and their respective dimers. The triplet and quintet states of N@C59N are nearly isoenergetic suggesting that the complex can exist in either spin state. For the most stable spin state of each of the complexes, the spin−spin coupling and the spin density transfer between the guest and the host cage and those between guest species of adjacent cages are investigated. In the triplet state of N@C59N, the spin density of the encapsulated nitrogen and that of the host cage is anti-ferromagnetically coupled, opposite to the ferromagnetic coupling in its quintet state. The present study also showed that the complexes (N@ C60)2 and (N@C59N)2 are stable both in their septet and singlet states. Unlike in metallofullerenes, in the above complexes, there is no electron transfer between the guest and the host species. This suggests that the zero total spin for the singlet state arises due to the anti-ferromagnetic coupling between the guest species, in contrast to anti-ferromagnetic coupling of core@shell systems. The large distance between the

*E-mail: [email protected]. Phone: +91-1332284773.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b03817. Details of the anti-ferromagnetic singlet-state calculations of the complexes, spin density values for the less stable states of the complexes considered, spin density difference plots for the unstable spin states of the complexes, HOMO and LUMO plots for the α-spin orbitals of 3[N@C59N] and the β-spin orbitals of the relevant complexes, HOMO−LUMO energy levels for the C59N and its nitrogen-encapsulated endohedral complexes, the comparison of the energy and spin density values of nitrogen for the singlet and septet states of the complexes for trans and gauche forms (PDF)

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AUTHOR INFORMATION

Corresponding Author Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Vinit is grateful to University Grants Commission, New Delhi, India, for a junior research fellowship. C.N.R. acknowledges Science and Engineering Research Board, Department of Science and Technology, India, and Sponsored Research and Industrial Consultancy, Indian Institute of Technology Roorkee, for the research grants SB/S1/PC-019/2013 and CMD/FIG/100604, respectively.

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DEDICATION Dedicated to Prof. N. Sathyamurthy on the occasion of his 65th birthday. §

REFERENCES

(1) Lu, X.; Feng, L.; Akasaka, T.; Nagase, S. Current status and future developments of endohedral metallofullerenes. Chem. Soc. Rev. 2012, 41, 7723−7760.

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DOI: 10.1021/acs.jpca.6b03817 J. Phys. Chem. A 2016, 120, 6990−6997

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DOI: 10.1021/acs.jpca.6b03817 J. Phys. Chem. A 2016, 120, 6990−6997