138
M. Fukuda et al.
to the electron chirality. While our result supports our conjecture, it cannot yet be
concluded whether our conjecture is correct, since we cannot separate the effect
of the difference between H and Li atoms and that between the chiral and achiral
structures. It can be confirmed that the zeta force distribution is closely related to
the zeta potential distribution and the increase of the zeta potential of C 3 H 2 Li 2 from
C 3 H 4 is inevitably accompanied by the increase of the spin torque.
7.4 Conclusion
In this study, we have studied the spin torque density, the zeta force density, and
zeta potential of allene-structure molecules (C 3 H 4 , C 3 H 2 Li 2 ), whose states are in
the time-independent stationary singlet one. The local picture of the electronic spin
stationary states have been described in terms of these density quantities based on
quantum field theory. We have shown the local spin torque and zeta force distributions of allene-structure molecules. We have pointed out that the distribution pattern
of the zeta potential is not related to the distribution of the electron density. It is
considered that the torque for the electrons in a molecule is dependent on the spin
orbit interaction. Hence we visualize the distribution of the spin orbit interaction in
these molecules and compare the distributions of the spin torque and the zeta force,
in our next work.
In our near future work, the local pictures of the electronic spin are studied for
chiral and achiral molecules, which interact with photons by using the time evolution simulation based on quantum electrodynamics.
Acknowledgements This work was partially supported by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (JSPS) (22550011). M.S. is supported
by a Grant-in-Aid for Young Scientists (B) from JSPS (24760028) and Mizuho Foundation for the
Promotion of Sciences.
References
1. Tachibana A (2001) J Chem Phys 115:3497
2. Tachibana A (2003) In: Brändas EJ, Kryachko ES (eds) Fundamental world of quantum chemistry, a tribute to the memory of Per-Olov Löwdin, vol 2. Kluwer Academic, Dordrecht, p 211
3. Tachibana A (2005) J Mol Model 11:301
4. Tachibana A (2010) J Mol Struct, Theochem 943:138
5. Doi K, Nakamura K, Tachibana A (2006) In: International workshop on nano CMOS. IEEE
Press, New York, pp 209–235
6. Doi K, Mikazuki Y, Sugino S, Doi T, Szarek P, Senami M, Shiraishi K, Iwai H, Umezawa N,
Chikyo T, Yamada K, Tachibana A (2008) Jpn J Appl Phys 47:205
7. Szarek P (2008) PhD dissertation, Kyoto University
8. Fukushima A, Tsuchida Y, Senami M, Tachibana A (2010) Jpn J Appl Phys 49:111504
9. Fukushima A, Sugino S, Tsuchida Y, Senami M, Tachibana A (2010) Jpn J Appl Phys
49:121504
M. Fukuda et al.
to the electron chirality. While our result supports our conjecture, it cannot yet be
concluded whether our conjecture is correct, since we cannot separate the effect
of the difference between H and Li atoms and that between the chiral and achiral
structures. It can be confirmed that the zeta force distribution is closely related to
the zeta potential distribution and the increase of the zeta potential of C 3 H 2 Li 2 from
C 3 H 4 is inevitably accompanied by the increase of the spin torque.
7.4 Conclusion
In this study, we have studied the spin torque density, the zeta force density, and
zeta potential of allene-structure molecules (C 3 H 4 , C 3 H 2 Li 2 ), whose states are in
the time-independent stationary singlet one. The local picture of the electronic spin
stationary states have been described in terms of these density quantities based on
quantum field theory. We have shown the local spin torque and zeta force distributions of allene-structure molecules. We have pointed out that the distribution pattern
of the zeta potential is not related to the distribution of the electron density. It is
considered that the torque for the electrons in a molecule is dependent on the spin
orbit interaction. Hence we visualize the distribution of the spin orbit interaction in
these molecules and compare the distributions of the spin torque and the zeta force,
in our next work.
In our near future work, the local pictures of the electronic spin are studied for
chiral and achiral molecules, which interact with photons by using the time evolution simulation based on quantum electrodynamics.
Acknowledgements This work was partially supported by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (JSPS) (22550011). M.S. is supported
by a Grant-in-Aid for Young Scientists (B) from JSPS (24760028) and Mizuho Foundation for the
Promotion of Sciences.
References
1. Tachibana A (2001) J Chem Phys 115:3497
2. Tachibana A (2003) In: Brändas EJ, Kryachko ES (eds) Fundamental world of quantum chemistry, a tribute to the memory of Per-Olov Löwdin, vol 2. Kluwer Academic, Dordrecht, p 211
3. Tachibana A (2005) J Mol Model 11:301
4. Tachibana A (2010) J Mol Struct, Theochem 943:138
5. Doi K, Nakamura K, Tachibana A (2006) In: International workshop on nano CMOS. IEEE
Press, New York, pp 209–235
6. Doi K, Mikazuki Y, Sugino S, Doi T, Szarek P, Senami M, Shiraishi K, Iwai H, Umezawa N,
Chikyo T, Yamada K, Tachibana A (2008) Jpn J Appl Phys 47:205
7. Szarek P (2008) PhD dissertation, Kyoto University
8. Fukushima A, Tsuchida Y, Senami M, Tachibana A (2010) Jpn J Appl Phys 49:111504
9. Fukushima A, Sugino S, Tsuchida Y, Senami M, Tachibana A (2010) Jpn J Appl Phys
49:121504