III SIMPÓSIO INTERDISCIPLINAR FÍSICA +
BIOINFORMÁTICA
22 A 25 DE ABRIL DE 2014
UNIVERSIDADE FEDERAL DE UBERLÂNDIA, UBERLÂNDIA, MINAS GERAIS
Cyclical model for the electron transfer
*Karina H. Paulino Jubilato1 (IC), Elso Drigo Filho1 (PD). 1Instituto de Biociências, Letras e Ciências
Exatas de São José do Rio Preto – UNESP. *karinahpaulino@yahoo.com.br
São José do Rio Preto, São Paulo – Brasil
Rua Cristovão Colombo, 2265 – Jardim Nazareth, CEP 15054-000
Contato: (17)3221-2240
Keywords: Quantum well, cyclical model, electron transfer, tunneling.
INTRODUCTION
In recent years, nanomachines have attracted the
scientific community attention. This interest is
justified by the importance in technological
applications and in the analysis of biological
systems. There are many subjects involving these
structures in biological systems, in particular, we can
analyze the "pumping" of electrons in events related
to the creation and storage of molecular energy as,
for example, photosynthesis.
THEORY
A double square well can be considered as a
simple junction of two wells, where each well has a
simple tip with an infinite barrier and the other a
finite potential. If the wells have the same simple
potential barrier widths the result of the simple
junction of the two wells consists in a symmetric
double well [1]. On the other hand, if the wells simply
have different potential barriers, V0 and V1, for
example, then the result is the asymmetric double
well [2].
The square wells, especially those involving
minimum two (bistable), allow accurate calculations
of tunneling time [3]. In this way, it is possible to use
an asymmetric double well as a model for electron
transfer in a macromolecular system.
The proposed model is composed by a
particular system. The first level, the ground state, is
located only in the well of profundity higher. The
second and third energy levels are localized
between the two wells. Other levels are above the
internal barrier. Using this geometry, the electron
can be transported in a cyclical way.
RESULTS AND DISCUSSION
The energy eigenvalues obtained are shown
in table 1, where E0, E1 and E2 represent energy
levels for the simple well and E*0, E+, E- and E3
represent energy levels of the double well. In the
example analyzed, it is computed the tunneling time
of the 2.2133 x 10-12 s and the transition time of the
4.1885 x 10-16 s.
Table 1. Energy eigenvalues of the asymmetric
double well V1 = 1,5 eV, V0 = 0,675 eV, L = 2,8 nm
e a = 1nm.
Simple Well
Eigenvaleus of
the
energy
(eV)
Double Well
Eigenvaleus of
the
energy
(eV)
E0
0,27715
E*0
0,27740
E1
1,06423
E+
1,06448
E2
1,06444
E-
1,06355
E3
1,56556
CONCLUSIONS
From the eigenvalues obtained here it was
possible to obtain physical quantities for the system
as, for example, the tunneling time and the time of
electronic transition. These times permit us to
conclude that the electron have higher probability of
decay to the ground state of the deeper well than
tunneling back to the shallower one. Exciting the
electron up to the energy level above the internal
barrier it is possible to return the system to the
original configuration. In particular, using the
parameters inspired by biological systems, the times
obtained are closed to experimental measured .
ACKNOWLEDGMENTS
CNPq
____________________
Greiner, W., Quantum Mechanics: na introduction, New York,
Springer-Verlag Press (2001).
2
Paulino K. H., Drigo Filho E., Pulici A. R., Ricotta R. M., Solução
Quântica para o poço duplo quadrado unidimensional assimétrico,
Revista Brasileira de Ensino de Física, 4306, 2010.
3
DeVault, D., Quantum Mechanical Tunneling in Biological
systems, Cambridge University Press (1983).