Open access peer-reviewed chapter

Electronic Structure and Magnetic Properties of N@C60-SWCNT

By Atsushi Suzuki and Takeo Oku

Submitted: October 14th 2010Reviewed: March 2nd 2011Published: July 27th 2011

DOI: 10.5772/16630

Downloaded: 2791

1. Introduction

Single-walled-carbon nanotube (SWCNTs) encapsulating fullerenes as peapods have been considerably interested to apply organic field effect transistor, magnetic device and quantum device (Bailey et. al. 2007, Khlobystrov et. al. 2005). Electronic structure and physical properties of fullerenes within SWCNT as carbon peapods has been studied. Table 1 lists recent works. For instant, the endohedral metallofullerenes nested in the strained nanotube have the electronic structure with the relative energy levels at the different states and produces a spatial modulation of the energy gap (Cho et. al. 2003). A scalable spin quantum computer that combines aspects of electronic and magnetic properties of endohedral fullerenes that enclose small clusters of metal atoms, such as Sc2@C84, La@C82 (as shown in Fig. 1) and Gd@C82, N@C60 and P@C60 encapsulated within SWCNT as peapods has been investigated (Tooth et. al. 2008, Cantone et. al. 2008, Warner et. al. 2008, Cho et. al. 2003, Yang et. al. 2010). The key advantages are that magnetic interactions between electronic spins and nuclear spins in carbon peapods are used. As an example using nitrogen endohedral fullerene N@C60 encapsulated within SWCNT as peapods (see Fig. 2), the nitrogen atom occupies a high-symmetry site at the center of the cage and retains its atomic configuration, and the cage offers protection of the nitrogen electron paramagnetic moment, which is related to electron spins, S=3/2, coupled to be nuclear spin I=1. This material has a high advantage of the NMR quantum computer to control spin gate with decoupling pulses in relaxation time. Morton reported the NMR quantum-computer controlled un-perturbation Rabi oscillation of spin polarization under influence of decoupling process (Morton, et. al. 2005, 2006, 2011). Additionally, nitrogen endohedral fullerene 14N@C60 encapsulated within SWCNT allow to control quantum qubit-gate under a mixture of biding interaction between electron and nuclear spins in the NMR quantum computing. Recently, Yang reported how to efficiently implement the quantum logical gate operations required for universal quantum computation. Transfer of information between qubits had been considered by direct dipole-dipole couplings or by using a mobile electron spin as the bus qubit (Yang et. al. (2010), Meyer et. al. (2004)).

The band structures for infinite periodic chains of C60 and N@C60 are shown in Fig. 2. All the energies are given in units of E -EF for each system. The effects of encapsulated nitrogen on the band structure of C60 have been considered. The results reveal that the nitrogen causes the lowering of the C60 at the LUMO and HOMO levels together with a splitting of the degenerate levels.

ContentsReferences
Fullerene-based quantum computerMorton et. al. (2005), (2006), (2011), Yang et. al. (2010)
Harneit et. al. (2002), Meyer et. al. (2004), Benjamin et. al. (2006)
N@C60-SWCNT, P@C60-SWCNTCho et. al. (2003), Bailey et. al. (2007), Jue et. al. (2007),
Simon et. al. (2006) (2007), Tooth et. al,. (2008), Yang et. al. (2010), Suzuki et. al. (2010), Iizumi et. al. (2010)
Sc@C82-SWCNT, La@C82-SWCNTCho et. al. (2003), Cantone et. al. (2008), Warner et. al. (2008)
Carbon tubesRao et. al. (1997), Khlobystrov et. al. (2005)
C60Schiller et. al. (2006)
N@C60, P@C60, (C59N)2, C59NBuhl et. al. (1997), Fulop et. al. (2001), Kobayashi et. al. (2003),
Abronin et. al. (2004), Schulte et. al. (2007)

Table 1.

Electronic structure and physical properties of fullerenes within SWCNT as carbon peapods

Figure 1.

Local density of states (LDOS) of (a) C82@(17, 0) and (b) La@C82@(17, 0) decomposed into the constituents. Black vertical lines indicate the Fermi level (Ef). Esubf represents the Fermi level with the metal substrate in contact. Isodensity surface plots of the electron accumulation (red) and depletion (blue) are shown for C82-SWCNT (17, 0) and La@C82- SWCNT(17, 0) in (c) and (d), respectively. The values for the red and blue surfaces in (c) are ±0:0035e/eÅ3. Corresponding values in (d) are ±0:0025e/eÅ3. The gray circle in (d) indicates the position of the La atom inside C82. (Cho et. al. (2003))

The gap between HOMO and LUMO is reduced from 1:8 eV of C60 to 1:66 eV of N@C60. The effects of majority and minority spins in the nitrogen basis were found not to have any appreciable further contribution. These small changes to the band gap and Fermi level shifts the support to the evidence that the nitrogen atom is well screened within the cage.

Figure 2.

The relaxed atomic coordinates of N@C60-SWCNT (17, 0). For clarity the carbon atoms of the C60 are shown in red and the nitrogen in blue. The band structures for infinite periodic chains of C60 and N@C60 are shown. All the energies are given in units of E - EF for each system. (Bailey et. al. (2007))

Design of spin labels inside for possible molecular spintronics, which contains of 1D spin chains filling SWCNTs with magnetic endohedral fullerenes of N@C60 and P@C60 as spin qubit have been proposed (Yang et. al. 2010). Jue reported a scheme to implement the two-qubit gates between the nuclear spins of the encapsulated atoms in endohedral fullerenes 15N@C60 or 31P@C60, within today’s magnetic resonance techniques (Jue et. al. 2007). The electronic spin of the N and P ground state is 3/2, while the nuclear spin is either 1/2 (15N, 31P) or 1(14N). The electronic structure at highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO), the magnetic and optical properties of N@C60-SWCNT have been characterized on the basis of magnetic techniques of NMR, ESR and electronic nuclear double resonance (ENDOR) (Benjamin, et. al. 2006) using ab-nitio quantum calculation. The relaxation properties of the 14N nucleus in N@C60 were determined using techniques related to Davies ENDOR which have been proposed for measuring T1 and T2. In order to demonstrate the effectiveness of the bang-bang decoupling scheme in N@C60, a strong environmental interaction has been simulated by applying a strong RF field to drive Rabi oscillations in the nuclear spin; this strong RF field was then decoupled by applying fast phase ‘kicks’ using the π phase gate (Morton et. al. (2006)).

Figure 3 shows Bang-bang control of fullerene qubits by ultrafast phase gates. Morton discussed the benefits of a coupled electron spin to the nuclear spin qubit and demonstrated the ideas using the 14N nuclear spin in the N@C60 molecule. In addition to providing a resource for nuclear spin polarization and detection, the electron spin can be exploited to perform ultrafast nuclear spin phase gates, which can in turn be used to dynamically bang-bang decouple the nuclear spin from unwanted interactions. Figure 4 shows arbitrary nuclear phase gates are implemented by driving two electron spin transitions simultaneously (Morton (2005)). The path of the electron magnetization vector was driven by a microwave field. The corresponding z-magnetizations are displayed as shown in Fig. 4 (a). One transition is driven resonantly, and one strongly detuned. On each cycle, the phase accumulated is proportional to the area enclosed by the path. Both transitions must undergo an integer number of complete cycles to ensure the populations remain unchanged. As shown in Fig. 4 (b), both transitions were detuned by equal and opposite amounts, the population evolution for each is the same, whilst the phase accumulated is of opposite sign. Hence, the relative phase shift can be tuned by controlling the microwave pulse power.

The effect of the non-nearest neighbor couplings has been investigated (Yang et. al. (2010)). Figure 5 show transitions of a single qubit in the presence of couplings to other qubit as a function of the chain length. The uppermost spectrum corresponds to the case of nearest neighbors only [trace (a)]. If non-nearest neighbors are added [see trace (b)], each resonance line splits into seven lines separated by Dnn/8, where Dnn is the coupling between nearest neighbors. The weight of the lines (1:2:3:4:3:2:1) is given by the number of states of the next-nearest neighbors. Adding a third pair of qubits causes an additional splitting of each line into a (1:2:3:4:3:2:1) multiplet, with line separation Dnn/64. With the resolution of the figure [see trace (c)], this appears as a line broadening. The ESR frequency on transitions of a single qubit was appeared in the presence of couplings to other qubit under nearest neighbor. Especially, electronic spin qubits on five molecules of N@C60 in a magnetic field gradient has been simulated. The magnetic parameters of principle g-tensor, hyperfine coupling constant of nitrogen atom and chemical shift of 13C in 14N@C60 within SWCNT for chiral index (n, m) are important to control a quantum qubit-gate of 1D spin in the NMR quantum-computer. In the present work, geometrical effect of diameter and chiral index on the electronic structure, magnetic and optical properties of N@C60-SWCNT have been investigated on the basis of experimental results using ab-initio density functional theory.

Figure 3.

Bang-bang control of fullerene qubits by ultrafast phase gates. (Morton et. al. (2006))

Figure 4.

Arbitrary nuclear phase gates are implemented by driving two electron spin transitions simultaneously (Morton (2005))

Figure 5.

Transitions of a single qubit in the presence of couplings to other qubits as a function of the chain length. (a) Nearest neighbors only. (b) Nearest neighbors and next-nearest neighbors. (c) Three qubits on each side. (d) Infinite chain, where all but the nearest neighbors are polarized. (Yang et. al. (2010))

2. Quantum chemical calculation

The molecular structures were assembled by CS ChemDraw, CS Chem3D (Cambridge Soft) and Nanotube Modeler (JCrystal Soft). Molecular orbital calculations were carried out by molecular mechanics calculations (MM2) and semi-empirical molecular orbital calculations (Hamiltonian: Parameterized Model Revision 3: PM3). In addition, the isolated molecular structures were optimized by ab-initio quantum calculation using unrestricted Hartree–Fock (UHF) and DFT using UB3LYP with hybrid function LANL2DZ and STO-3G*, 3-31G* and 6-31G* as basis set (Gaussian 03 Inc.). The electronic structure at HOMO, LUMO, LUMO+1 and the HOMO-LUMO band gap (Eg) were calculated. Nitrogen atomic charges of 14N@C60 within SWCNT were estimated using Mulliken population analysis. Wavelength and the exited transition state were calculated by time-dependence of DFT (TD-DFT) with hybrid function UB3LYP and 3-31G* as basis set. Continuously, chemical shift of 13C (δ), principle g-tensor (gxx, gyy, gzz) and principle A-tensor (Axx, Ayy, Azz) in hyperfine coupling constant (hfc) of nitrogen atom were calculated by DFT using NMR/GIAO with hybrid function UB3LYP and 3-31G* as basis set.

3. Results and discussion

3.1. Electronic structure of N@C60-SWCNT

Electronic structure of molecular orbital at HOMO, LUMO, next LUMO+1 and energy levels of N@C60-SWCNT-armchair have been investigated by DFT with hybrid function UB3LYP using 6-31G* as basis set. Molecular orbitals and energy levels of 14N@C60-SWCNT armchair (13, 13), N@C60 and SWCNT are shown in Fig. 6. The molecular orbital of N@C60-SWCNT- zigzag (13, 13) was delocalized on π-electrons at a long axis of SWCNT surface interacted with π-electrons on the N@C60 cage surface as hybrid orbital interaction. The energy level between HOMO-LUMO was smaller than that of original SWCNT. This behavior was due to a mixture of binding interaction with spin distribution.

Molecular orbital of 14N@C60-SWCNT (9, 9) and SWCNT at (a) HOMO, (b) LUMO, (c) LUMO+1 are shown in Fig. 7. The molecular orbital of N@C60-SWCNT-zigzag (9, 9) was delocalized on π-electrons at a long axis of SWCNT surface interacted with π-electrons on the N@C60 cage surface as hybrid orbital interaction. The energy gap of N@C60-SWCNT between HOMO and LUMO was estimated to be 1.16 eV, which was smaller than that of original SWCNT (9, 9) to be 1.24 eV, due to a mixture of binding interaction. Mulliken atomic charge of N in 14N@C60 within SWCNT was 3.8 x 10-5e. This result indicates a slight charge transfer from nitrogen atom to C60 cage within SWCNT. This supports the assertion that the nitrogen is well screened within the C60 cage.

Electronic structures of N@C60-SWCNT-zigzag (14, 0) at (a) HOMO, (b) LUMO and (c) charge distribution are shown in Fig. 8. The molecular orbital were well distributed around the SWCNT interacted with C60 surface cage. Energy gap between HOMO and LUMO was estimated to be 0.87 eV, which indicates semi-conductive behavior. There existed a wide charge distribution on the inner surface of SWCNT, which had π-electron interaction with hybrid orbital on the C60 surface cage.

Figure 9 show molecular orbital of (14N@C60)2-SWCNT-armchair (9, 9) at (a) HOMO and (b) LUMO, calculated by DFT/UB3LYP/STO-3G*. In both cases at HOMO and LUMO, molecular orbital of (14N@C60)2-SWCNT (9, 9) formed a circle ring to distribute on the SWCNT surface. The band gap between HOMO and LUMO was estimated to be 3.72 eV,

Figure 6.

Molecular orbitals and energy levels of 14N@C60-SWCNT armchair (13, 13), N@C60 and SWCNT (Suzuki, el. al. (2010))

Figure 7.

Molecular orbital of 14N@C60-SWCNT (9, 9) and SWCNT at (a) HOMO, (b) LUMO, (c) LUMO+1 and energy levels (Suzuki et. al. (2010)).

Figure 8.

Molecular orbital of 14N@C60-SWCNT-zigzag (14, 0) at (a) HOMO, (b) LUMO and (c) charge distribution. (Suzuki et. al. (2010))

Figure 9.

Electronic structures of (14N@C60)2-SWCNT-armchair (9, 9) at (a) HOMO and (b) LUMO. (Suzuki et. al. (2010))

which was larger than 1.72 eV, 3.06 eV and 2.11 eV of SWCNT (9, 9), N@C60 and (N@C60)2. Mulliken atomic charge of nitrogen atom in (14N@C60)2-SWCNT (9, 9) was estimated to be 2.998e. This positive charge indicates a considerable charge transfer from nitrogen atom to C60 cage within SWCNT.

3.2. Electronic structure of N@C60

Electronic structure of N@C60 (S=3/2, I=1) at HOMO, LUMO and energy levels are shown in Fig. 10. The molecular orbital was considerably distributed on the C60 surface cage. Mulliken N atom charge was 0.21e, which indicates charge transfer from nitrogen atomic to the C60 surface cage. The energy gap between HOMO and LUMO was estimated to be 3.0 eV, which made agreement with the experimental energy gap of N@C60 (2.7 eV) adsorbed on Cu (887) surface. The molecular structure with the energy levels have been investigated by scanning tunneling microcopy/spectroscopy (STM/STS) and near-edge x-ray absorption fine structure (NEXAFS) spectrum (Schiller, et. al. 2006).

Figure 10.

Electronic structure and molecular orbital of N@C60 at (a) HOMO (a) and (b) LUMO (Suzuki et. al. (2010))

Figure 11.

Electronic structures of (N@C60)2 at (a) HOMO, (b) HOMO-1, (c) LUMO+1, (d) LUMO and (e) spin density. (Suzuki et. al. (2010))

Electronic structures of (14N@C60)2 as dimmer at (a) HOMO, (b) HOMO-1, (c) LUMO+1, (d) LUMO, (e) spin density and Mulliken atomic charge of N1 and N2 are shown in Fig. 11. The molecular orbital of the (N@C60)2 at HOMO and LUMO were partial to distribute between the C60 surface cages. The molecular orbital was interacted with each other on π electron of hybrid orbital. The energy gaps between HOMO and LUMO were estimated to be 2.11 eV, which was smaller than that of N@C60. The dimerization was stable. The molecular orbital at HOMO-1 and LUMO+1 were well distributed around the C60 cage surfaces. The molecular orbital was anti-interacted with each other, due to anti-bonding behavior of isolated molecular orbital of N@C60. Mulliken atomic charge of N1 and N2 in (N@C60)2 were at 0.004299 e and 0.004381 e. The slight values of positive charge were due to slight charge transfer from N atoms to the surface cage of C60.

3.3. Electronic structure of C60N

Electronic structure of C59N (S=1/2, I=1) at HOMO and LUMO are shown in Fig. 12. The molecular orbital were impartially distributed on the C60 cage surface. Mulliken N atomic charge was -0.6e. The negative value indicates considerable charge transfer from C60 cage to nitrogen atom. The energy gap between HOMO and LUMO was calculated to be 1.29 eV, which made agreement with the experimental result of (C59N)2 at 1.1 eV by C K NEXAFS spectrum (Schulte, et. al. 2007). The dimerization of (C59N)2 was stable as compared with isolation of C59N.

Figure 12.

Electronic structure and molecular orbital of C59N at (a) HOMO and (b) LUMO. (Suzuki et. al. (2010))

The single replacement in C59N keeps the bond lengths close to the C60 values (1.40 and 1.45 Å). The dimerization has strong effects as shown in Fig. 13. The charge redistributes itself to weaken the intramolecular bonds of the tetra-coordinated C´ and to strengthen both the N-C bonds on the pentagon and the “double” bonds in the hexagons containing C´-N. This bond turns out to be a relatively weak one, as the electron density distribution emphasizes. In combination with the weak intermolecular C´-C´ bonding, this results in an electronic environment for C´ remarkably different from that of a typical sp3 atom. This fact should account for the missing NMR signal in the sp3 region. Accurate calculations of the carbon chemical shifts would be highly desirable. Their calculations predict a very similar structure for the latter (anti-conformation), apart from the much elongated intermolecular distance (1.675Å). The anti-conformation has been determined also by less sophisticated calculations.

Figure 13.

For (C59N)2: Isodensity hypersurfaces of (a) the electron density and (b) the HOMO. Values (in au) are 0.2 (a); 0.002 (dark) and 0.0005 (light) (b). (Andreoni et. al. (1996))

3.4. Electronic structure of (C60)3 as trimmer

Electronic structure of the C2h symmetry trimmer, (C60)3 based on the P4 peanut has been studied (Beu 2006). The HOMO and LUMO energies obtained with the PBE (HCTH) functional are respectively EHOMO=-0.175 (-0.179) a.u. and ELUMO=-0.171 (-0.173) a.u. The distribution of the Mulliken charges in the two waist regions are similar to those of the dimmer (between -0.030 e and +0.056 e for the PBE functional). Figure 14 shows geometrical structure and HOMO-orbital (isovalue 0.01) of the C2h symmetry C60 trimer, (C60)3 based on the P4 peanut. The HOMO-orbital qualitatively showed the same behavior, bridging the cages. A transverse nodal plane through the middle of the central cage seems to limit the delocalization of the electrons. Anyway, for all methods the HOMO-LUMO gap of the trimmer was significantly reduced as compared to the dimmer, (C60)3, continuing the monotonous decrease with respect to the C60 monomer.

3.5. Geometrical effect of N@C60-SWCNT, SWCNT, N@C60 and C59N on electronic structure

Geometrical effect of N@C60-SWCNT, SWCNT, N@C60 and C59N on the electronic structure has been investigated by DFT using UB3LYP. Table 2 lists comparison between N@C60-SWCNT, (N@C60)2-SWCNT, SWCNT, (N@C60)2, N@C60 and C59N on energy levels at HOMO, LUMO and band gap (Eg). The energy levels of N@C60-SWCNT were affected by diameter and chiral index. The energy levels of N@C60-SWCNT compared with SWCNT had effected with increasing diameters. Especially, the energy gap of N@C60-SWCNT was smaller than those of SWCNT, N@C60 and C59N. This behavior would be originated in narrowing energy gap based on molecular interaction between N@C60 and SWCNT. These behaviors of 14N@C60-SWCNT were considerably closed to those in density of state (DOS), which calculated with a tight binding model for SWCNT armchair. Electronic density of states (DOS) calculated with a tight binding model for SWCNT armchair (8, 8), (9, 9), (10, 10), and (11, 11) are shown in Fig. 16. The HOMO-LUMO gaps of SWCNT (n, n) for n = 9-13 as metal were inverse proportion to the diameters (Rao, et al. 1997). The energy gap of (N@C60)2-SWCNT (9, 9) was extend to be 3.72 eV as compared with that of N@C60-SWCNT (9. 9), due to instable dimmer within SWCNT. As reference, the energy gap of dimmer, (14N@C60)2 was estimated to be 2.11 eV, which was smaller than that of 14N@C60, due the stable formation.

Figure 14.

Geometrical structure and HOMO-orbital (isovalue 0.01) of the C2h symmetry C60 trimer, (C60)3 based on the P4 peanut. (Rue (2006))

Table 2.

Comparison of N@C60-SWCNT, (N@C60-SWCNT)2, SWCT, (N@C60)2, N@C60, and C59N on energy levels (Suzuki, et. al. (2010))

Figure 15.

Electronic density of states (DOS) calculated with a tight binding model for SWCNT armchair (8, 8), (9, 9), (10, 10), and (11, 11). The Fermi energy is located at 0 eV. Wave vector–conserving optical transitions can occur between mirror image spikes, that is, v1→c1 and v2→c2. (Rao, et al. (1997))

Table 3.

Excited state transitions of N@C60-SWCNT (9, 9), calculated by TD-DFT. (Suzuki, et. al. (2010))

Excited state transitions of N@C60-SWCNT were investigated by TD-DFT quantum calculation. Table 3 list excited state transitions of N@C60-SWCNT (9, 9), calculated by TD-DFT. The wavelength converted from the exited energy levels were estimated to be 1703 nm and 1061 nm, which were closed to experimental results of C59N-SWCNT by UV-vis NIR spectra and 2D PL contour maps as shown in Fig. 16 (a) (Iizumi, et. al. 2010). The optical behavior displayed the broad peaks around 2000 nm and 1000 nm, which could be assigned as the first (E11M) and second (E22M) van Hove transition on Raman spectroscopy with density of state using tight binding model (Rao, et al. 1997). As showed in Fig. 16 (b), the 2D PL contour maps of (C59N)2-SWCNT demonstrated that the emission and excited wavelength were around 1730 nm and 1000 nm. The slight different value between theoretical and experimental results would be originated in narrowing band gap based on molecular interaction between N@C60 and SWCNT.

Figure 16.

a) UV-vis NIR spectra, b) 2D PL contour maps of NC59-SWCNT. (Iizumi et. al. (2010))

Table 4.

Chemical shifts of 13C with multicity in 14N@C60-SWCNT, SWCNT and 14N@C60 (Suzuki et. al. (2010))

Figure 17.

The measured chemical shift of (a) SWCNT, (b) and (c) DWCNT (Simon et. al. (2007)).

3.6. Magnetic properties of N@C60-SWCNT, N@C60 and C59N.

The magnetic parameters of chemical shift, principle g-tensor, A-tensor in hyperfine coupling constant (hfc) of N@C60-SWCNT and N@C60 have been studied by NMR, electron paramagnetic resonance (EPR) and electron nuclear double resonance (ENDOR) spectroscopy (Simon, et. al. 2006, 2007). Especially, chemical shifts of 13C with multicity of N@C60-SWCNT (13, 13), N@C60 and original SWCNT have been investigated. Table 4 lists chemical shifts of 13C with multicity in 14N@C60-SWCNT, 14N@C60 and SWCNT. Comparison results of the chemical shift between N@C60-SWCNT, SWCNT and N@C60 were investigated. As listed in Table 4, line position of N@C60-SWCNT shifted out at degenerated position with 39, 51, 26, 47 multicity states in a low magnetic field. Effect of chiral index on the chemical shifts of 13C in 14N@C60-SWCNT is shown in Fig. 17. The chemical shifts positions of N@C60-SWCNT shifted out with decreasing the diameters. The calculated results were considerably closed to the experimental results (Simon, et. al. 2007). These results were originated in a lack of 2s spin density distribution, spin-local orbital interaction and π electron interaction between N@C60 and inner surface on SWCNT. The electronic spin-nuclear spin interaction based on unsymmetrical distribution of 2p spin orbital influenced the chemical shift position separated with splitting lines under a low magnetic field.

The chemical shifts of 13C with multicity in optimized molecular structure will be calculated. The chemical shift will be constructed with a total sum of four terms as below:

σ  = σdia + σpara+ σFC+ σSDE1

where σdia is diamagnetic term, σpara is paramagnetic term, σFC is Fermi contact interaction, σSD is spin dipole-interaction with angle dependence on 2p spin density distribution. The magnetic behavior of the chemical shift will be mainly based on the diamagnetic term and the spin-dipole interaction. Especially, the chemical shifts of N@C60-SWCNT compared with C59N and (C59N)2 have been quantitatively analyzed on the basis of the experiment using ab-initio DFT calculation.

Figure 18.

Electronic structure of C59N at (a) HOMO and (b) LUMO. (Suzuki et. al. (2010))

Electronic structure and calculated chemical shifts of 13C and multicity in parentheses for the atoms in the close environment in C59N are shown in Fig. 18 and 19. The calculated chemical shifts of 13C in C59N separated in the range of 126 ppm and 152 ppm. The chemical shift of C near N atom suggests at 136.22 ppm with multicity at 5.0. The behavior would be arisen from electron-nuclear spin interaction based on spin density distribution at HOMO. The 13C chemical shifts of (C59N)2 compared them with the experimental spectrum. Comparison

Figure 19.

Calculated chemical shifts of 13C and multicity in parentheses for the atoms in the close environment in C59N. (Suzuki et. al. (2010))

between the calculated 13C chemical shifts of (C59N)2 and the experimental spectrum is showed in Fig. 20. The value for the saturated carbon atom (C’), 83.1 ppm, is refined to 85.3 ppm with the TZP/DZ basis, is in reasonably good agreement with the experiment (90.3 ppm), as is the value for the corresponding carbon atom in C59NNH, 68.4 ppm (TZP/DZ) versus 72.1. Figure 21 shows 13C chemical shifts for the atoms in the close environment of N: (a) (C59N)2, (b) C59NH, and (c) indole. There was a substantial de-shielding of the saturated carbon atom in going from C59NH to (C59N)2, both in the experimental and theoretical data using the electronic density distribution.

Figure 20.

chemical shifts (C59N)2: (a) experimental spectrum and (b) computed values at the DZ level (Buhl et. al. (1997))

Figure 21.

chemical shifts for the atoms in the close environment of N: (a) (C59N)2, (b) C59NH, and (c) indole. Experimental data are in boxes. Note that in the three cases the location and magnitude of the ”extrema” are similar (Buhl et. al. (1997))

The magnetic interaction with the electron spins will be explained. The Hamiltonian can be formulated by Eq. 2.

H = gbeS H  gNbNI H + S A I + S D S + I Q I E2

The five terms represent the following interactions: electronic and nuclear Zeeman interaction, the hyperfine of the spin nuclear interaction, the fine structure of the spin-spin interaction and the nuclear quadrupole.

Energy level diagram for isotropic atomic 14N@C60 in a strong external magnetic field is shown in Fig. 22 (A). This Hamiltonian yields the 12-level system illustrated in Fig. 22 (A). The first split shows the four possible values of the electronic spin, and these are each split into the three possible values of I. The splitting of the nuclear energy levels has been investigated. The principle value of g-tensor will be mainly estimated by second perturbation. Δgii related to spin local interaction with energy interaction between paramagnetic and nearest neighbor interaction.

gii= ge+ ΔgiiE3
gii= ge{1+m|φm|Li|φp|2ϵpϵm} E4
Δgii=gii2= ζαΔEiE5

The hyperfine coupling strength of A-tensor is constructed with a sum of isotropic and anisotropic hyperfine interaction.

Atensor = Aiso+ AiiE6
Aiso= 8π/3 gnμNρ(0)E7
Aii=gNμN(3cos2θ1)r3ρ(r)dv E8

The isotropic hyperfine interaction, Aiso will be related on the 2s spin density distribution, ρ (0), as described by Eq. 7. The anisotropic hyperfine interaction, A’ii–tensor has influence of the 2p spin density distribution with angle dependence on a direction of the electron nuclear interaction, as noted in Eq. 8. A quantitative relation between the π−electron spin density and the isotropic hyperfine coupling constant has been discussed. For planar π−radical (e.g., CH3 radical), this relation has been known as noted by Eq. 9.

Aiso= Qrp gE9

where ρ π is the π-electron density on the C atom and Q = 45 G. A future of non-planar radicals including C59N is the “umbrella effect characterized by (i) deviation of the C atom containing the unpaired electron from the plane and (ii) partial change in the hybridization of this C atom, which becomes intermediate between sp2 and sp3 (Abronin et. al. 2004). The spin-spin interaction with zero field constant, S D S is mainly originated in the dipole-dipole interaction, as noted by fifth term in Eq. 2. In the quadruple nuclear interaction, I Q I, the quadruple coupling constant, Q of nitrogen atom with more than I = 1 on nuclear quadruple resonance (NQR) will be dependence on magnetic interaction between electric quadruple moment, e Q and electric field gradient (EFG). The electric quadruple moment, e Q will be related on deviation of nuclear charge distribution. The magnetic parameters of g-tensor, A-tensor in the hyperfine coupling constant and the quadruple coupling constant of nitrogen atom will be under the spin nuclear interaction, e Q, EFG and the spin density distribution.

Figure 22.

A) 14N@C60 has electron spin S = 3/2 and nuclear spin I = 1 which together provide a rich 12-level structure. Considering only the first-order hyperfine interaction, the three electron transitions associated with a particular nuclear spin projection are degenerate. Adding the second order corrections (δ = a2/B) lifts the degeneracies for the MI = ±1 lines. (B) Continuous wave EPR spectrum of high purity N@C60 in degassed CS2 at room temperature. Each line in the triplet signal is labeled with the corresponding projection MI of the 14N nuclear spin. (C–E) Zoom-in for each of the three hyperfine lines reveals further structure. Stars (*) mark the line split by 13C hyperfine interactions with C60 cage. Measurement parameters: microwave frequency, 9.67 GHz; microwave power, 0.5 μW; modulation amplitude, 0.2 μT; modulation frequency, 1.6 kHz. (Simon et. al. (2006))

3.7. Calculated magnetic parameters

The EPR spectrum of 14N inside N@C60 consists of three lines centered at electron g-factor, split by a 14N isotropic hyperfine interaction. Table 6 lists magnetic parameters of g-tensor, A-tensor in hfc and Mulliken N atomic charge of N@C60-SWCNT (13, 13), (9, 9), (N@C60)2, N@C60 and C59N, calculated by ab-nitio DFT quantum calculation. The magnetic parameters such as principal g-tensor, hfc and Mulliken N atomic charges in N@C60-SWCNT (9, 9) were estimated to be 2.00093-98, 3.8-6.0 and 3.8×10-5, respectively. The calculated magnetic parameters of N@C60-SWCNT were discussed on the basis of the experimental results as shown in Fig. 23. The slight un-symmetrical values of hfs on N@C60-SWCNT would be originated in anisotropy spin-dipole interaction and π electron interaction between N@C60 and inner surface on SWCNT. In this case, a few percent of the values of ρ (2 s) and ρ (2 p) on nitrogen in N@C60-SWCNT will be expected by the values of AN (2 s) and (2 p) of 14N to be 557 G and 17.8 G at the ρ (2 s) = 1 and ρ (2 p) = 1. The calculated values of hfs in N@C60-SWCNT, N@C60 and C59N was in proportion to the spin-dipole interaction, a few percent of contribution from the 2p spin density distribution with a lack of 2s spin density distribution, obeyed by Fermi contact parts. The nuclear quadruple interaction of 14N (I = 1) in N@C60-SWCNT was negligible due to a slight value of EFG based on charge transfer from the CNT to C60 with a slight value of the Mulliken atomic charges. The principle g-tensor, hfc and Mulliken nitrogen atomic charges on N@C60-SWCNT (9, 9) as compared with N@C60 and C59N were decreased. These results would be dependence with geometrical effects of N@C60-SWCNT (n, n) for chiral index on π-electron interaction in cooperation with the magnetic interaction between electron spins, S = 3/2 and nuclear spin, I = 1.

Experimental values of A-tensor in hfs on N@C60 and C59N are shown in Fig. 23 and 24. The symmetrical structure of N@C60 had isotropic value of magnetic parameters. The experimental results of N@C60 compared with C59N (Fulop et. at. (2001)) were considerably closed to the calculated results (Harneit et. al. (2002)). The unsymmetrical structure of C59N affected the principle lines at several states, which splitting by anisotropy hyperfine interaction. Spin density distribution of paramagnetic azafullerene, C59N have been calculated (Abronin et. al. 2004, Schrier et. al. 2006). Based on hyperfine coupling constants for 14N and 13C nuclei in C59N, the spin density distribution of the unpaired π-electron in C59N was mainly localized around the nitrogen atom. Mulliken charge transfer of nitrogen atom in C59N was calculated to be -0.6 e. This result indicates a considerable value of charge transfer from C60 to N atom. The magnetic parameters of the anisotropic molecular structure would be strongly attributed from the spin-dipole interaction with 2p spin density distribution. Considerably, molecular design of the endohedral fullerenes within SWCNT varied with geometry structure is important to control the quantum spin qubit, splitting the magnetic parameters including g-tensor, A-tensor of hfc and the chemical shifts in the NMR quantum computer.

Elementsg-tensor
(gxx, gyy, gzz)
hfc / G
(Axx, Ayy, Azz)
Mulliken N atomic
charges / e
14N@C60
-SWCNT
(13, 13)
2.00119
2.00119
2.00117
2.4
2.4
1.3
-0.004521

14N@C60
-SWCNT
(9, 9)
2.00098
2.00098
2.00093
6.0
6.0
3.8
0.000038
(14N@C60)2
Dimmer
1.99775
1.99776
1.99785
4.6
4.6
15.0
0.004299, 0.004381
14N@C60

2.00490
2.00490
2.00490
4.5
4.5
4.5
0.211512
C59N

2.00545
2.00511
2.00356
2.4
2.5
7.6
-0.605804

Table 5.

g-tensor, hfc and Mulliken N atomic charge of 14N@C60 –SWCNT (Suzuki et. al. (2010)).

Figure 23.

ESR spectra of (a) SWCNT, (b) N@C60 and (c)-(d) N@C60-SWCNT at triplet state. (Simon et. al. (2007)).

Table 6.

Spin properties of the endohedral C60 fullerenes with electron spin S = 3/2 (Harneit et. al. (2002))

Figure 24.

Motionally narrowed ESR spectrum of tumbling C59N substituted in C60 at 290 K and 9 GHz (Fulop et. al. 2001.).

4. Conclusion

Design of spin labels for the NMR quantum computer that contained 1D spin chains filling SWCNT with N@C60 has been proposed. The electronic structure, chemical shift, g-tensor, A-tensor of hfc would be influenced by geometrical structure, varied with diameter and chiral index. The magnetic properties were originated in spin density distribution with π-electron interaction between N@C60 and inner surface on SWCNT and CT. The slight un-symmetrical values of A-tensor in hfs on N@C60-SWCNT (9, 9) would be originated in anisotropy spin-dipole interaction and π-electron interaction between N@C60 and inner surface on SWCNT. The values of A-tensor in hfc would be in proportion to the 2 p spin distribution based on the spin-dipole interaction with a lack of 2 s spin density distribution, obeyed by Fermi contact parts. The magnetic parameters of the anisotropic structure would be strongly influenced by the spin-dipole interaction with a slight distribution of the 2 p spin density. Molecular design of the endohedral fullerenes within SWCNT as peapods is important to control quantum qubit, splitting the principle lines based on hyperfine interaction as the NMR quantum computer.

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Atsushi Suzuki and Takeo Oku (July 27th 2011). Electronic Structure and Magnetic Properties of N@C60-SWCNT, Electronic Properties of Carbon Nanotubes, Jose Mauricio Marulanda, IntechOpen, DOI: 10.5772/16630. Available from:

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