Spin Properties of Transition-Metallorganic Self-Assembled Molecules Page: 24 of 47
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Donor bath Acceptor bath
Donor Acce for
E = E
Figure 12: Schematic diagram showing the donor-acceptor correlation and its effect on
the donor and acceptor baths. The donor and the acceptor are attached to a molecule,
represented by the long bar, which mediates the interaction between the two baths, resp-
resented by the two ring areas.
polyproline, where acoustic phonons are the main low-energy excitations,
1 eigR e-Rl
x Nx 2 d 2 2) 3
IqI -'N 3vq q -
where #3 1/kBT with kB being the Boltzmann constant and T temperature, R =
R1 - R2 is the molecular contour length between donor and acceptor, and hwoq 1 has
been used. Here we have introduced a low-momentum cut-off -, which is due to the
finite length of a molecule. For a flexible molecule, is determined by a persistence length
beyond which the bending become significant. Defining F as the correlation strength, we
can write
x = e-R. (7.1)
Hence a correlation between the donor and acceptor fluctuations entails an effective cou-
pling between the two baths, (Q1,Q2 ) - 0, where Qa are normal coordinates in bath
i1.
To describe the interacting baths, we augment the noninteracting HO, which can be
written in terms of normal coordinates, HO = Z,(PA + LjQi ), by a crossing term
Hb = Hb - Z Yw QaQ2a. (7.2)
Under this new Hamiltonian of the baths, (Q1aQ2 ) can be evaluated via
(Q1Q2) = dQ dQ2AQ Q2-eH __ aY)
j #~wj(1 - 7!23
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Yu, Zhi Gang. Spin Properties of Transition-Metallorganic Self-Assembled Molecules, report, June 30, 2010; United States. (https://digital.library.unt.edu/ark:/67531/metadc1014357/m1/24/: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.