A simplified mathematical model for the electron transfer in photosystem II by path integral method based on Markov model


  • Sarayut Pantian Faculty of Science and Technology, Thepsatri Rajabhat University, Meung, Lopburi province 15000


Electron transfer, Path integral, Markov model, Photosynthesis


The mathematical model for the electron transfer in photosystem II is built by path integral method with nonlocal harmonic oscillator potential. The results show that the amplitude of propagator and wave function depend on time. By the way, the trend of wave function is according to wave function with the constant forced harmonic oscillator. The energy is more than twice the energy value obtained from spectroscopy technique. The probability of electron transfer to another energy level state is then determined using the Markov method which found that the electron has the greatest probability of not changing its energy level, 0.53 at x = 1.5 angstrom.


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เอกพัน จันผง, อัฏฐชัย ถาวรสุวรรณ, วิทยา ทิพย์อักษร และ นิคม ชูศิริ. 2551. อินทิกรัลตามเส้นทางสำหรับกึ่ง

ฮาร์มอนิกออสซิลเลเตอร. วารสารมหาวิทยาลัยทักษิณ. 11(2): 24-29.

Blankenship, R. E. 2002. Molecular mechanisms of photosynthesis. 2nd Edition. Oxford, UK: Blackwell


Chanana, N., Menon, V. J. and Singh, Y., 1994. Path integration of a general two time action

involving local and nonlocal harmonic oscillator potentials. J. Chem. Phys. 101: 651–661.

Fine, S., Singer, Y., 1998. The hierarchical hidden markov model: Analysis and applications.

Machine Learning. 32 (1): 41–62.

Hall, D. O. and Rao, K.K..1999. Photosynthesis. 6th Edition. Cambridge, UK: Cambridge

University Press.

Lee, W. H., Lim, C., Ban, E., Bae, S., Ko, J., Lee, H. S., Min, B. K., Lee, K. Y., Yu, J. S. and Ho, H. S.,

W@Ag dendrites as efficient and durable electrocatalyst for solar-to-CO conversion

using scalable photovoltaic-electrochemical system. Applied Catalysis B: Environmental.

: 120427.

Liang, X. T. 2010. Excitation energy transfer: Study with non-Markovian dynamics. PHYSICAL

REVIEW E. 82 : 051918.

Niels, H. D., Giulio, C., Alvin, T. Y. and Thomas, R. B., 1997. Femtosecond Dynamics of Excited-

State Evolution in [Ru(bpy)3]2+. Science. 275(5296): 54-7.

Pach ́on, L. A and Brumer, P., 2011. The Physical Basis for Long-lived Electronic Coherence in

Photosynthetic Light Harvesting Systems. J. Phys. Chem. Lett. 21 (2) : 2728–2732.

Sa-yakanit, V., Choosiri, N. and Robkob, U. 1987. Exact Propagator of a Two-Dimensional

Random System. Physical Rev.B. 37 (18) : 10851-10853.





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