2026-09-20T06:47:28Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/497512022-01-13T07:54:21Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Troy Van Voorhis.
Song, XiaoGeng, Ph. D. Massachusetts Institute of Technology
Massachusetts Institute of Technology. Dept. of Chemistry.
Massachusetts Institute of Technology. Department of Chemistry
2009-11-06T16:29:46Z
2009-11-06T16:29:46Z
2009
2009
http://hdl.handle.net/1721.1/49751
456576017
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemistry, 2009.
Includes bibliographical references (leaves 127-137).
In this dissertation, we discuss two methods developed during my PhD study to simulate electron transfer systems. The first method, the semi-classical approximation, is derived from the stationary phase approximation to the path integral in the spin-coherent representation. The resulting equation of motion is a classical-like ordinary differential equation subject to a two-ended boundary condition. The boundary value problem is solved using the "near real trajectory" algorithm. This method is applied to three scattering problems to compute the transmission and reflection probabilities. The strength and weakness of this approach is investigated in details. The second approach is based on the generalized Langevin equation, in which the quantum transitions of electronic states are condensed into a linear regression equation. The memory kernel in the regression equation is computed using a second perturbation expansion. The perturbation is optimized to achieve the best convergence of the second order expansion. This procedure results in a tow-hop Langevin equation, the THLE. Results from a spin-boson system validate the THLE in a wide range of parameter regimes. Lastly, we tested the feasibility of using Monte Carlo sampling to compute the memory kernel from the spin-boson system and proposed a smoothing technique to reduce the number of sampling points.
by XiaoGeng Song.
Ph.D.
137 leaves
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by
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http://dspace.mit.edu/handle/1721.1/7582
Chemistry.
Nonadiabatic electron transfer in the condensed phase, via semiclassical and Langevin equation approach
Thesis
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<Abstract>In this dissertation, we discuss two methods developed during my PhD study to simulate electron transfer systems. The first method, the semi-classical approximation, is derived from the stationary phase approximation to the path integral in the spin-coherent representation. The resulting equation of motion is a classical-like ordinary differential equation subject to a two-ended boundary condition. The boundary value problem is solved using the "near real trajectory" algorithm. This method is applied to three scattering problems to compute the transmission and reflection probabilities. The strength and weakness of this approach is investigated in details. The second approach is based on the generalized Langevin equation, in which the quantum transitions of electronic states are condensed into a linear regression equation. The memory kernel in the regression equation is computed using a second perturbation expansion. The perturbation is optimized to achieve the best convergence of the second order expansion. This procedure results in a tow-hop Langevin equation, the THLE. Results from a spin-boson system validate the THLE in a wide range of parameter regimes. Lastly, we tested the feasibility of using Monte Carlo sampling to compute the memory kernel from the spin-boson system and proposed a smoothing technique to reduce the number of sampling points.</Abstract>
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