Chapter 3
Electronic Excitation and Decay
Abstract This chapter deals with the optical excitation processes that bring about
transitions between electronic states and with some of the dynamical processes that
may follow. The excited states created by photon absorption can be nonstationary
under two basic aspects: first, they can undergo radiationless electronic transitions
(nonadiabatic dynamics), and second, internal motions can occur in the new potential energy surface as the nuclear wavefunction or “wavepacket” evolves in time
(adiabatic dynamics). After presenting the basic aspects of optical excitation, in this
chapter we shall consider the slow radiationless transitions between electronic states
caused by nonadiabatic or spin–orbit couplings. The adiabatic dynamics, i.e., the
nuclear motion in a single potential energy surface, will be dealt with in the next
chapter. Finally, in Chap. 5 we shall tackle the ultrafast nonadiabatic transitions that
occur when two or more PESs are close in energy. In such events, the nonadiabatic
dynamics and the nuclear motion are inextricably coupled. To begin with, we shall
introduce and make use of some important formalisms, such as the time-dependent
perturbation theory or the relationship between autocorrelation functions and spectra.
In presenting such concepts and tools, we shall focus rather on their physical meaning
and their applicability to real phenomena, than on the mathematical formalism.
Keywords Rabi oscillations · Time dependent perturbation theory
Autocorrelation function · Franck-Condon factors · Fermi golden rule
Quasi-continuum
3.1 Constant and Time-Dependent Perturbations
Several common phenomena in molecular physics can be described as a system,
initially in a stationary state, being perturbed by an external force that drives a
dynamical response. For instance, the source of perturbation can be a static electric
or magnetic field, a light pulse, or the interaction with an approaching molecule. If
we call ˆ
H
(0) the Hamiltonian of the unperturbed system, and ˆ
V the perturbation,
then the complete Hamiltonian is
ˆ
H = ˆ
H
(0)
+ ˆ
V
(3.1)
© Springer International Publishing AG, part of Springer Nature 2018
M. Persico and G. Granucci, Photochemistry, Theoretical Chemistry
and Computational Modelling, https://doi.org/10.1007/978-3-319-89972-5_3
79
Electronic Excitation and Decay
Abstract This chapter deals with the optical excitation processes that bring about
transitions between electronic states and with some of the dynamical processes that
may follow. The excited states created by photon absorption can be nonstationary
under two basic aspects: first, they can undergo radiationless electronic transitions
(nonadiabatic dynamics), and second, internal motions can occur in the new potential energy surface as the nuclear wavefunction or “wavepacket” evolves in time
(adiabatic dynamics). After presenting the basic aspects of optical excitation, in this
chapter we shall consider the slow radiationless transitions between electronic states
caused by nonadiabatic or spin–orbit couplings. The adiabatic dynamics, i.e., the
nuclear motion in a single potential energy surface, will be dealt with in the next
chapter. Finally, in Chap. 5 we shall tackle the ultrafast nonadiabatic transitions that
occur when two or more PESs are close in energy. In such events, the nonadiabatic
dynamics and the nuclear motion are inextricably coupled. To begin with, we shall
introduce and make use of some important formalisms, such as the time-dependent
perturbation theory or the relationship between autocorrelation functions and spectra.
In presenting such concepts and tools, we shall focus rather on their physical meaning
and their applicability to real phenomena, than on the mathematical formalism.
Keywords Rabi oscillations · Time dependent perturbation theory
Autocorrelation function · Franck-Condon factors · Fermi golden rule
Quasi-continuum
3.1 Constant and Time-Dependent Perturbations
Several common phenomena in molecular physics can be described as a system,
initially in a stationary state, being perturbed by an external force that drives a
dynamical response. For instance, the source of perturbation can be a static electric
or magnetic field, a light pulse, or the interaction with an approaching molecule. If
we call ˆ
H
(0) the Hamiltonian of the unperturbed system, and ˆ
V the perturbation,
then the complete Hamiltonian is
ˆ
H = ˆ
H
(0)
+ ˆ
V
(3.1)
© Springer International Publishing AG, part of Springer Nature 2018
M. Persico and G. Granucci, Photochemistry, Theoretical Chemistry
and Computational Modelling, https://doi.org/10.1007/978-3-319-89972-5_3
79