Stuff for the 2nd paper

Figures

The following figures must be openned with Xmgr. All the data sets in the figure files can be retrieved using Xmgr.

• new1.fig Comparison of the results by the TREA and the exact propogation
  Eta=2, MD trajectory A, E_D=E_A=-10 eV
  Conclusion: The TREA appears to work for stronger coupling cases, and fail for weaker coupling cases, within a given period (~1 ps).
• new2.fig Comparison of the results by the TREA and the exact propogation
  Eta=1, MD trajectory A, E_D=E_A=-10 eV
• new3.fig Maxima of |rho(i,+/-)| (i!=+,-)
  for different donors and acceptors as a function of time: Eta=1, MD trajectory A, E_D=E_A=-10 eV
• new4.fig Maxima of |rho(i,+/-)| (i!=+,-)
  for different donors and acceptors as a function of time: Eta=2, MD trajectory A, E_D=E_A=-10 eV
• new5.fig f₁ and f₂
  when the donor and acceptor energy level approaches and enters the conduct band, as a function of time: Eta=2, MD trajectory A, Met121-Lys122
• new7.fig f₁ and f₂
  when the donor and acceptor energy level approaches and enters the conduct band, as a function of time: Eta=1, MD trajectory A, Met121-Lys122
• new6.fig Bridge HOMOs and LUMOs
  for different donors and acceptors. This figure shows that the fluctuations of HOMOs and LUMOs are about 0.5 eV. (Note: These fluctuations are much greater than an k_BT. Because they are NOT electronic energy, it is risky to relate their magnitudes to that of an k_BT. Theoretically, k_BT should be compared with the kinetic energy of the nuclei plus the electronic energy of the system, both of which cannot be, unfortunately, accurately treated within the framework of our semiempirical model.)
• new8.fig Comparison of the TREA, TEEA and the exact:
  121Met-122Lys, MD trajectory A, E_D= E_A=-10, Eta=2.
• new9.fig Eigen wave function propogations Psi₊(t) and Psi_-(t) when E_D and E_A approach and enter the conduct band, when K(i,+/-) (i!=+,-) are turned on and off. 121Met-122Lys, MD trajectory A, Eta=2
• newa.fig Comparison of the TREA, TEEA and the exact:
  121Met-123Gly, MD trajectory A, E_D= E_A=-10, Eta=2.
• newb.fig Comparison of the TREA, TEEA and the exact:
  121Met-123Gly, MD trajectory A, E_D= E_A=-10, Eta=1.
• newc.fig Comparison of P_DA(t) by the TREA and the exact propogation:
  121Met-122Lys, MD trajectory A, E_D= E_A=-10, Eta=2 when E_D and E_A(t) approach and enter the conduct band.
• newd.fig Comparison of P_DA(t) by the TREA and the exact propogation:
  121Met-122Lys, MD trajectory A, E_D= E_A=-10, Eta=1 when E_D and E_A(t) approach and enter the conduct band.
• newe.fig Maxima of |rho(i,+/-)| (i!=+,-) as a function of time: Eta=2, MD trajectory A, when E_D=E_A approach and enter the conduct band.
  Conclusion: The positions of the peaks in this figure correspond to the poles of the Green function at that time. When the donor and acceptor energies enter the conduct band, they have plenty of chances to resonate with the dense energy levels in the band.
• newf.fig Real and imaginary part of the eigen wave functions, when K(i,+/-) (i!=+,-) are turned on and off, 121Met-125Leu, Eta=1, Ed=Ea=-10 eV.
• newg.fig Real and imaginary part of the eigen wave functions, when K(i,+/-) (i!=+,-) are turned on and off, 121Met-122Lys, Eta=2, Ed=Ea=-10 eV.
  Conclusion: The contributions to eigen space propogation by the imaginary couplings between the two eigenstates +,- and the others are likely independent of the distance between donor and acceptor, and they lead to the disagreement between the TREA and TEEA. Because of their existence, the magnitude of propogation given by the TEEA will never be smaller than a certain value (10^-4 for Eta=2, it is dependent on the couplings) whereas the TREA result will become smaller and smaller when the acceptor gets further and further away from the donor. At some point, one might never be able to derive a two-state approximation of whatsoever kind.
• newi.fig P_DA(t), when K(i,+/-) (i!=+,-) are turned on and off, 121Met-122Lys, Eta=2, Ed=Ea=-10 eV. Compared with the exact propogation, the TREA result is negligible. However, the TREA result is similiar to the superexchange contribution. When K(i,+/-) (i!=+,-) are turned off, the noisy components get filtered off.
  Conclusion: Occupancy diffusion from the +,- eigenstates to the others is responsible for the discrepancy between the TEEA and the TREA.