118
3 Electronic Excitation and Decay
3.2 Solve the two-state problem with constant V coupling by time-dependent perturbation theory. Compare the TDPT solution with the exact Rabi formula and show
that the approximate solution is accurate for short times, in two cases: (A) |V | | Δε
and (B) Δε = 0.
3.3 Verify that the spectrum/autocorrelation relationships (3.85) and (3.86) also
hold for a continuum spectrum, i.e., that they are consistent with Eqs. (3.88) and
(3.89).
3.4 Derive the Rabi expression (3.98) from the spectrum of two states, one bright
and one dark, given in Eq. (3.100). Make use of the connection between spectrum
and autocorrelation function.
3.5 Derive the expression of the oscillator strength of an absorption or emission
electronic band by applying approximations (3.131) and (3.132) and the normal
coordinate treatment. Use the atomic units system and the formulas of Appendix F.
References
1. Shirley, J.H.: Solution of the Schrödinger equation with a Hamiltonian periodic in time. Phys.
Rev. 138, B979–987 (1965)
2. Einstein, A.: Strahlungs-Emission und -Absorption nach der Quantentheorie. Verhandlungen
der Deutschen Physikalischen Gesellschaft 18, 318–323 (1916)
3. Lakowicz, J.R.: Principles of Fluorescence Spectroscopy. Springer, New York (2006)
4. Andrews, D.L.: Lasers in Chemistry. Springer, Berlin (1997)
5. Merzbacher, E.: Quantum Mechanics. Wiley, New York (1998)
6. Sakurai, J., Napolitano, J.: Modern Quantum Mechanics. Cambridge University Press, Cambridge (2017)
7. Chattarji, D.: The Theory of Auger Transitions. Academic Press, London (1976)
8. Fano, U.: Effects of configuration interaction on intensities and phase shifts. Phys. Rev. 124,
1866–1878 (1961)
9. Bixon, M., Jortner, J.: Intramolecular radiationless transitions. J. Chem. Phys. 48, 715–726
(1968)
10. Cusati, T., Granucci, G., Persico, M., Spighi, G.: Oscillator strength and polarization of the
forbidden n → π ∗ band of trans-azobenzene. A computational study. J. Chem. Phys. 128,
194312/1–9 (2008)
11. Cascella, M., Cuendet, M.L., Tavernelli, I., Rothlisberger, U.: Optical spectra of Cu(II)-azurin
by hybrid TDDFT-molecular dynamics simulations. J. Phys. Chem. B 111, 10248–10252
(2007)
12. Gebauer, R., De Angelis, F.: A combined molecular dynamics and computational spectroscopy
study of a dye-sensitized solar cell. New J. Phys. 13, 085013/1–10 (2011)
13. Srebro-Hooper, M., Autschbach, J.: Calculating natural optical activity of molecules from first
principles. Ann. Rev. Phys. Chem. 68, 399–420 (2017)
14. Kupka, H.: Transitions in Molecular Systems. Wiley-VCH, Weinheim (2010)
15. Peluso, A., Santoro, F., Del Re, G.: Vibronic coupling in electronic transitions with significant
Duschinsky effect. Int. J. Quantum Chem. 63, 233–244 (1997)
16. Toniolo, A., Persico, M.: Efficient calculation of Franck-Condon factors and vibronic couplings
in polyatomics. J. Comput. Chem. 22, 968–975 (2001)
17. Toniolo, A., Persico, M.: A theoretical study of spectroscopy and predissociation dynamics in
nitrosoalkanes. J. Chem. Phys. 115, 1817–1827 (2001)
3 Electronic Excitation and Decay
3.2 Solve the two-state problem with constant V coupling by time-dependent perturbation theory. Compare the TDPT solution with the exact Rabi formula and show
that the approximate solution is accurate for short times, in two cases: (A) |V | | Δε
and (B) Δε = 0.
3.3 Verify that the spectrum/autocorrelation relationships (3.85) and (3.86) also
hold for a continuum spectrum, i.e., that they are consistent with Eqs. (3.88) and
(3.89).
3.4 Derive the Rabi expression (3.98) from the spectrum of two states, one bright
and one dark, given in Eq. (3.100). Make use of the connection between spectrum
and autocorrelation function.
3.5 Derive the expression of the oscillator strength of an absorption or emission
electronic band by applying approximations (3.131) and (3.132) and the normal
coordinate treatment. Use the atomic units system and the formulas of Appendix F.
References
1. Shirley, J.H.: Solution of the Schrödinger equation with a Hamiltonian periodic in time. Phys.
Rev. 138, B979–987 (1965)
2. Einstein, A.: Strahlungs-Emission und -Absorption nach der Quantentheorie. Verhandlungen
der Deutschen Physikalischen Gesellschaft 18, 318–323 (1916)
3. Lakowicz, J.R.: Principles of Fluorescence Spectroscopy. Springer, New York (2006)
4. Andrews, D.L.: Lasers in Chemistry. Springer, Berlin (1997)
5. Merzbacher, E.: Quantum Mechanics. Wiley, New York (1998)
6. Sakurai, J., Napolitano, J.: Modern Quantum Mechanics. Cambridge University Press, Cambridge (2017)
7. Chattarji, D.: The Theory of Auger Transitions. Academic Press, London (1976)
8. Fano, U.: Effects of configuration interaction on intensities and phase shifts. Phys. Rev. 124,
1866–1878 (1961)
9. Bixon, M., Jortner, J.: Intramolecular radiationless transitions. J. Chem. Phys. 48, 715–726
(1968)
10. Cusati, T., Granucci, G., Persico, M., Spighi, G.: Oscillator strength and polarization of the
forbidden n → π ∗ band of trans-azobenzene. A computational study. J. Chem. Phys. 128,
194312/1–9 (2008)
11. Cascella, M., Cuendet, M.L., Tavernelli, I., Rothlisberger, U.: Optical spectra of Cu(II)-azurin
by hybrid TDDFT-molecular dynamics simulations. J. Phys. Chem. B 111, 10248–10252
(2007)
12. Gebauer, R., De Angelis, F.: A combined molecular dynamics and computational spectroscopy
study of a dye-sensitized solar cell. New J. Phys. 13, 085013/1–10 (2011)
13. Srebro-Hooper, M., Autschbach, J.: Calculating natural optical activity of molecules from first
principles. Ann. Rev. Phys. Chem. 68, 399–420 (2017)
14. Kupka, H.: Transitions in Molecular Systems. Wiley-VCH, Weinheim (2010)
15. Peluso, A., Santoro, F., Del Re, G.: Vibronic coupling in electronic transitions with significant
Duschinsky effect. Int. J. Quantum Chem. 63, 233–244 (1997)
16. Toniolo, A., Persico, M.: Efficient calculation of Franck-Condon factors and vibronic couplings
in polyatomics. J. Comput. Chem. 22, 968–975 (2001)
17. Toniolo, A., Persico, M.: A theoretical study of spectroscopy and predissociation dynamics in
nitrosoalkanes. J. Chem. Phys. 115, 1817–1827 (2001)