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Novel coupling of molecular rotation and exchange interaction with the nanotube electrons.

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Novel coupling of molecular rotation and exchange interaction with the nanotube electrons.

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  1. Spin-triplet molecule inside carbon nanotubeBogdanova D.A., S.S.MoliverState University Ulyanovsk, RussiaGrant-in-aid 08-03-97000 from Rus. Basic Res. Foundation.To lock a molecule inside a carbon nanotube may be a clever move, if one needs to isolate the molecule, or alternatively, to direct its chemical activity on other prisoner. For example, active spin-triplet molecule, whose phenylene groups mask a delocalized lone electron pair, needs to be islolated in low-temperature inert gas matrix, in order to measure its optical and paramagnetic spectra[Tomioka H., et al. Nature (2001) 412, 626]. Novel effects of exchange interaction of a spin-triplet electron pair with nanotube wall arise, if such a molecule rotates inside nanotube.Control of rotation of such endohedral system may be used in molecular electronics.Another control technique may use an electric current pulse through the nanotube.

  2. Being chemically isolated,endohedral molecule may carry a lone electron pair:Tomioka H., et al. Nature (2001) 412, 626.DePinto J.T., et al. J.Am.Chem.Soc. (2007) 129, 2308.Shiozawa H., et.al. Phys.Rev.Lett. (2009) 102, 04 68 04.

  3. Novel coupling of molecular rotation and exchange interaction with the nanotube electrons. Energy constants refer to spherical top rotation, and exchange interaction depending on molecule distance from the nanotube wall. The simplest model is considered, where integer angular momentum L of entire molecule acts on its principal-axis ort, spin operator S acts on lone electron pair with magneton μ. Magnetic field H0 is aligned with the nanotube axis. [Bogdanova D.A., Moliver S.S. MOLEC–XVII (SPb, Aug. 23–28, 2008) p.110]

  4. The conservation of the total moment's axial z-projection (4) allows one to develop eigenfunctions over spherical harmonics, and 3-component spinor orts. Principal quantum number n orders energies and numerates eigenvectors. We have received matrix secular equations (of infinite order) in analytic form, and then by means of a numerical method have found their approximate solutions with the lowest energies.

  5. Note, that at higher M spherical harmonics with lower L are forbidden in the state expansion. • Thus the lowest energies n=1,2,3 belong to states with M=0,–1,+1.

  6. Hamiltonian matrices can be exactly expressed through the real recurrent coefficients of spherical harmonics. • Only S=1 manifold is applied to electrons spin, since singlet state is considered to have high energy.

  7. Matrix form of the Schroedinger equation on |n,M=0> states. • Equations with L=0,1,2miss some members, according to (6). • Energy scale of the problem: rotational quantum A=ћ2/(2∑MR2)

  8. Matrix form of the Schroedinger equation on |n,M=+1> states. • Equations with L=0,1,2 miss some members, according to (7).

  9. Matrix form of the Schroedinger equation on |n,M=-1> states. • Equations with L=0,1,2 miss some members, according to (8).

  10. Special solution: at zero magnetic field a simple analytical solution (24-25) exists. It is one and the only one eigenstate, in which the molecule has a probability to be found with zero total angular momentum J=0. Other possible results are J=1,2.

  11. Numerical solution: B=2.5A, C=2.6A, L<11, all energies are measured in A. • Special solution (24-25) is marked by squares.

  12. Rates of transitions, stimulated by the high-frequency transversal magnetic field, as in ESR and NMR experiments.

  13. Numerical solution: B=2.5A, C=2.6A, mH0=(0.5–3)A, L<11

  14. Conclusion. • Endohedral-molecule rotations may be excited by techniques of magnetic resonances. Previously only Raman-scattering optics was a success of this kind, however it seems unlikely to cope with a molecule heavier than C2, whose rotation spectra inside C84 were measured • [Krause M., et al. Phys.Rev.Lett. (2004) 93, 13 74 03]. • Since spin-triplet molecules of interest have much bigger moment of inertia, magnetic-resonace interaction should be used to excite their rotations. • ESR and NMR spectroscopies of endohedral molecules • [Carravetta M., et al. Phys.Chem.Chem.Phys. (2007) 9, 4879] • might be redirected to discover exchange interaction. Consider a novel effect, predicted by our calculations: the rotational state of the molecule may be changed by (1) the abrupt magnetic field variations, and (2) control of the level occupation with the use of ESR-like technique.

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