6.6 Computational Note: Diabatic States for ET and CT Studies
211
radial with respect to the center of the triangle and a component μ p perpendicular
to the ABC plane, as shown in Fig. 6.10. Note that this could be a model for transitions centered in the equatorial ligands of a trigonal pyramid complex. The distance
between the chromophores is R. Show that the excitation transfer dynamics among
the four ligands, such as can be observed after a radiation pulse, has a period
T =
8π R
3
12μ 2
p + 21μ 2
r
.
Calculate the period with R = 15 bohr, μ p = 0.5 a.u., and μ r = 1 a.u.
6.7 Same as the previous problem, but with a square arrangement. Four identical
chromophores A, B, C, and D are placed at the vertices of a square. Their absorption
transition dipoles have a component μ r which is radial with respect to the center of
the square and a component μ p perpendicular to the ABC D plane. The side of the
square has length R. Show that the excitation transfer dynamics among the four
ligands, such as can be observed after a radiation pulse, has a period
T =
4π R
3
4 +
√
2
μ 2
p + 2
3 +
√
2
μ 2
r
.
Calculate the period with R = 15 bohr, μ p = 0.5 a.u., and μ r = 1 a.u.
6.8 Prove Marcus’ relationship, Eq. (6.73).
References
1. Subotnik, J.E., Cave, R.J., Steele, R.P., Shenvi, N.: The initial and final states of electron and
energy transfer processes: diabatization as motivated by system-solvent interactions. J. Chem.
Phys. 130, 234102/1–14 (2009)
2. Voityuk, A.A.: Fragment transition density method to calculate electronic coupling for excitation energy transfer. J. Chem. Phys. 140, 244117/1–7 (2014)
3. Voityuk, A.A.: Interaction of dark excited states. comparison of computational approaches. J.
Phys. Chem. B 119, 7417–7421 (2015)
4. Curutchet, C., Mennucci, B.: Quantum chemical studies of light harvesting. Chem. Rev. 117,
294–343 (2017)
5. Favero, L., Granucci, G., Persico, M.: Dynamics of acetone photodissociation: a surface hopping study. Phys. Chem. Chem. Phys. 15, 20651–20661 (2013)
6. Rohatgi-Mukherjee, K.K.: Fundamentals of Photochemistry. New Age International, New
Delhi (2017)
7. Raišys, S., Kazlauskas, K., Jurši˙ eas, S., Simon, Y.C.: The role of triplet exciton diffusion in
light-upconverting polymer glasses. ACS Appl. Mater. Interfaces 8, 15732–15740 (2016)
8. DeVries, P.L., Chang, C., George, T.F., Laskowski, B., Stallcop, J.R.: Computational study of
alkali-metal - noble-gas collisions in the presence of nonresonant lasers: Na + Xe + ω 1 + ω 2
system. Phys. Rev. 22, 545–550 (1980)
211
radial with respect to the center of the triangle and a component μ p perpendicular
to the ABC plane, as shown in Fig. 6.10. Note that this could be a model for transitions centered in the equatorial ligands of a trigonal pyramid complex. The distance
between the chromophores is R. Show that the excitation transfer dynamics among
the four ligands, such as can be observed after a radiation pulse, has a period
T =
8π R
3
12μ 2
p + 21μ 2
r
.
Calculate the period with R = 15 bohr, μ p = 0.5 a.u., and μ r = 1 a.u.
6.7 Same as the previous problem, but with a square arrangement. Four identical
chromophores A, B, C, and D are placed at the vertices of a square. Their absorption
transition dipoles have a component μ r which is radial with respect to the center of
the square and a component μ p perpendicular to the ABC D plane. The side of the
square has length R. Show that the excitation transfer dynamics among the four
ligands, such as can be observed after a radiation pulse, has a period
T =
4π R
3
4 +
√
2
μ 2
p + 2
3 +
√
2
μ 2
r
.
Calculate the period with R = 15 bohr, μ p = 0.5 a.u., and μ r = 1 a.u.
6.8 Prove Marcus’ relationship, Eq. (6.73).
References
1. Subotnik, J.E., Cave, R.J., Steele, R.P., Shenvi, N.: The initial and final states of electron and
energy transfer processes: diabatization as motivated by system-solvent interactions. J. Chem.
Phys. 130, 234102/1–14 (2009)
2. Voityuk, A.A.: Fragment transition density method to calculate electronic coupling for excitation energy transfer. J. Chem. Phys. 140, 244117/1–7 (2014)
3. Voityuk, A.A.: Interaction of dark excited states. comparison of computational approaches. J.
Phys. Chem. B 119, 7417–7421 (2015)
4. Curutchet, C., Mennucci, B.: Quantum chemical studies of light harvesting. Chem. Rev. 117,
294–343 (2017)
5. Favero, L., Granucci, G., Persico, M.: Dynamics of acetone photodissociation: a surface hopping study. Phys. Chem. Chem. Phys. 15, 20651–20661 (2013)
6. Rohatgi-Mukherjee, K.K.: Fundamentals of Photochemistry. New Age International, New
Delhi (2017)
7. Raišys, S., Kazlauskas, K., Jurši˙ eas, S., Simon, Y.C.: The role of triplet exciton diffusion in
light-upconverting polymer glasses. ACS Appl. Mater. Interfaces 8, 15732–15740 (2016)
8. DeVries, P.L., Chang, C., George, T.F., Laskowski, B., Stallcop, J.R.: Computational study of
alkali-metal - noble-gas collisions in the presence of nonresonant lasers: Na + Xe + ω 1 + ω 2
system. Phys. Rev. 22, 545–550 (1980)