1 3
Theor Chem Acc (2015) 134:149
DOI 10.1007/s00214-015-1747-y
REGULAR ARTICLE
The exchange coupling between the valence electrons of the
fullerene cage and the electrons of the N atoms in N@C
−1,3
60
L. Udvardi
1
Received: 15 June 2015 / Accepted: 19 October 2015 / Published online: 17 November 2015
© Springer-Verlag Berlin Heidelberg 2015
limitations of using endohedral fullerenes as quantum
information carriers. Mehring et al. [ 9 ] pointed out experimentally the entanglement of the nuclear spin and the electronic spin of the encaged N atom. A detailed review of
group V endohedral fullerenes can be found in Ref. [ 10 ].
The changes in the characteristic EPR signal of the quartet electronic spin of the N atom make it an ideal probe for
monitoring chemical reactions of C 60 [ 11 ]. During the last
decades, a great deal of excitement has been brought by
the discovery of the superconductivity of the alkali-doped
fullerenes. In this type of fullerene compounds, the valence
electrons of the ionized alkali atoms partially occupy the
bands formed by the LUMOs of the C 60 molecules. The
applicability of the quartet atomic state of the N atom
as a spin label depends on the strength of the interaction
between the 2 p electrons of the N atom and the valence
electron of the fullerene cage. An interaction which is small
compared to the hyperfi ne interaction results in a line width
effect of the EPR signal, and the N@C 60 is a good candidate for a spin labeling agent. In the case of strong coupling, the EPR signal of the system is completely changed
and the lines corresponding to the valence electrons of the
N atom are hard to identify in the signal of the paramagnetic system.
The interaction between the 2 p electrons of the N atom
and the valence electrons of the C 60 can be described by
a Heisenberg-like effective Hamiltonian H int = JS N S C 60
where S N and S C 60 denote the spin operator for the valence
electrons of the N atom and for the C 60 , respectively, and J
is the exchange coupling characterizing the strength of the
interaction. The aim of the present paper is to determine
theoretically the exchange coupling appearing in the effective Hamiltonian. The exchange coupling plays a role in the
description of the transport through magnetic molecules
[ 12 , 13 ], which is particularly interesting from the point of
Abstract MCSCF calculations are performed in order to
determine the exchange coupling between the 2 p electrons
of the N atom and the LUMOs of the fullerene cage in the
case of mono- and tri-anions of N@C 60 . The exchange
couplings provided our calculations are in the range of
1.5 meV which is large compared to the hyperfi ne interaction. The strong coupling can explain the missing EPR signal of the nitrogen in paramagnetic anions.
Keywords Fullerene · Exchange coupling
1 Introduction
Since the discovery of the fi rst endohedral fullerene [ 1 ],
the variety of endohedral structures has been extended tremendously [ 2 ]. Many metal atoms can be encapsulated by
using discharge techniques or ion implantation. In all cases,
the metal atom interacts strongly with the fullerene and acts
as an electron donor occupying an ’off-centered’ position
inside the cage. In contrast, the nitrogen in N@C 60 is situated at the center of the molecule and retains its S = 3/2
spin quartet atomic state [ 3 , 4 ]. This amazing property of
the encapsulated N atom triggered several research on its
possible application in quantum computing and spin labeling. Several publications [ 5 – 8 ] studied the promise and
Published as part of the special collection of articles “Festschrift
in honour of P. R. Surjan”.
* L. Udvardi
udvardi@phy.bme.hu
1
Department of Theoretical Physics , Budapest University
of Technology and Economics , Budafoki út 8 ,
Budapest 1111 , Hungary
145
Reprinted from the journal
Theor Chem Acc (2015) 134:149
DOI 10.1007/s00214-015-1747-y
REGULAR ARTICLE
The exchange coupling between the valence electrons of the
fullerene cage and the electrons of the N atoms in N@C
−1,3
60
L. Udvardi
1
Received: 15 June 2015 / Accepted: 19 October 2015 / Published online: 17 November 2015
© Springer-Verlag Berlin Heidelberg 2015
limitations of using endohedral fullerenes as quantum
information carriers. Mehring et al. [ 9 ] pointed out experimentally the entanglement of the nuclear spin and the electronic spin of the encaged N atom. A detailed review of
group V endohedral fullerenes can be found in Ref. [ 10 ].
The changes in the characteristic EPR signal of the quartet electronic spin of the N atom make it an ideal probe for
monitoring chemical reactions of C 60 [ 11 ]. During the last
decades, a great deal of excitement has been brought by
the discovery of the superconductivity of the alkali-doped
fullerenes. In this type of fullerene compounds, the valence
electrons of the ionized alkali atoms partially occupy the
bands formed by the LUMOs of the C 60 molecules. The
applicability of the quartet atomic state of the N atom
as a spin label depends on the strength of the interaction
between the 2 p electrons of the N atom and the valence
electron of the fullerene cage. An interaction which is small
compared to the hyperfi ne interaction results in a line width
effect of the EPR signal, and the N@C 60 is a good candidate for a spin labeling agent. In the case of strong coupling, the EPR signal of the system is completely changed
and the lines corresponding to the valence electrons of the
N atom are hard to identify in the signal of the paramagnetic system.
The interaction between the 2 p electrons of the N atom
and the valence electrons of the C 60 can be described by
a Heisenberg-like effective Hamiltonian H int = JS N S C 60
where S N and S C 60 denote the spin operator for the valence
electrons of the N atom and for the C 60 , respectively, and J
is the exchange coupling characterizing the strength of the
interaction. The aim of the present paper is to determine
theoretically the exchange coupling appearing in the effective Hamiltonian. The exchange coupling plays a role in the
description of the transport through magnetic molecules
[ 12 , 13 ], which is particularly interesting from the point of
Abstract MCSCF calculations are performed in order to
determine the exchange coupling between the 2 p electrons
of the N atom and the LUMOs of the fullerene cage in the
case of mono- and tri-anions of N@C 60 . The exchange
couplings provided our calculations are in the range of
1.5 meV which is large compared to the hyperfi ne interaction. The strong coupling can explain the missing EPR signal of the nitrogen in paramagnetic anions.
Keywords Fullerene · Exchange coupling
1 Introduction
Since the discovery of the fi rst endohedral fullerene [ 1 ],
the variety of endohedral structures has been extended tremendously [ 2 ]. Many metal atoms can be encapsulated by
using discharge techniques or ion implantation. In all cases,
the metal atom interacts strongly with the fullerene and acts
as an electron donor occupying an ’off-centered’ position
inside the cage. In contrast, the nitrogen in N@C 60 is situated at the center of the molecule and retains its S = 3/2
spin quartet atomic state [ 3 , 4 ]. This amazing property of
the encapsulated N atom triggered several research on its
possible application in quantum computing and spin labeling. Several publications [ 5 – 8 ] studied the promise and
Published as part of the special collection of articles “Festschrift
in honour of P. R. Surjan”.
* L. Udvardi
udvardi@phy.bme.hu
1
Department of Theoretical Physics , Budapest University
of Technology and Economics , Budafoki út 8 ,
Budapest 1111 , Hungary
145
Reprinted from the journal