Chapter 4
Wavepacket Dynamics and Geometrical
Relaxation
Abstract In this chapter we shall present the dynamics that takes place after electronic excitation, under the influence of the new potential energy surface (PES).
Nonadiabatic transitions to other electronic states will be assumed to be slow enough
as to be neglected, so we shall qualify this topic as “adiabatic dynamics.” We shall
examine the basic features of quantum wavepacket dynamics, and we shall find that
some details of the excitation process affect the nature and the time evolution of the
excited state even after the end of the radiation pulse. We shall see how, in certain
conditions, quantum dynamics can be described with classical concepts, that are
easier to grasp and provide the common language of qualitative arguments about
reaction dynamics. The effects of the chemical environment on the dynamics of
excited molecules will also be considered, trying to distinguish between interactions
that change the PES and energy flow processes, i.e., the “static” and the “dynamic”
effects, respectively.
Keywords Franck-Condon excitation · Adiabatic dynamics · Ehrenfest theorem
Intramolecular vibrational energy redistribution · Thermalization · Environmental
effects
4.1 Franck–Condon Excitation
We now explore the excitation by light pulses even shorter than in the previous
chapter, down to few fs, i.e., the realm of “femtochemistry” that was opened in
the 1980s by pioneers such as Ahmed Zewail [1]. A 10 fs pulse has a bandwidth
FWHM ω larger than 1500 cm
−1 , so it can excite simultaneously several vibrational
states, depending on the spacing of the vibrational levels. The “interesting” vibrational modes in photochemistry often have low frequencies, because they are associated with shallower minima than in the ground state: along such coordinates large
amplitude motions occur, leading to conformational changes, isomerizations or other
reactions.
We consider therefore the excitation from the vibronic state ϕ 0 χ 0,u , belonging to
the ground electronic term, to a set of states ϕ k χ k,v with different vibrational quantum
numbers v. According to Eq. (3.74) the excited wavefunction will be
© 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_4
119
Wavepacket Dynamics and Geometrical
Relaxation
Abstract In this chapter we shall present the dynamics that takes place after electronic excitation, under the influence of the new potential energy surface (PES).
Nonadiabatic transitions to other electronic states will be assumed to be slow enough
as to be neglected, so we shall qualify this topic as “adiabatic dynamics.” We shall
examine the basic features of quantum wavepacket dynamics, and we shall find that
some details of the excitation process affect the nature and the time evolution of the
excited state even after the end of the radiation pulse. We shall see how, in certain
conditions, quantum dynamics can be described with classical concepts, that are
easier to grasp and provide the common language of qualitative arguments about
reaction dynamics. The effects of the chemical environment on the dynamics of
excited molecules will also be considered, trying to distinguish between interactions
that change the PES and energy flow processes, i.e., the “static” and the “dynamic”
effects, respectively.
Keywords Franck-Condon excitation · Adiabatic dynamics · Ehrenfest theorem
Intramolecular vibrational energy redistribution · Thermalization · Environmental
effects
4.1 Franck–Condon Excitation
We now explore the excitation by light pulses even shorter than in the previous
chapter, down to few fs, i.e., the realm of “femtochemistry” that was opened in
the 1980s by pioneers such as Ahmed Zewail [1]. A 10 fs pulse has a bandwidth
FWHM ω larger than 1500 cm
−1 , so it can excite simultaneously several vibrational
states, depending on the spacing of the vibrational levels. The “interesting” vibrational modes in photochemistry often have low frequencies, because they are associated with shallower minima than in the ground state: along such coordinates large
amplitude motions occur, leading to conformational changes, isomerizations or other
reactions.
We consider therefore the excitation from the vibronic state ϕ 0 χ 0,u , belonging to
the ground electronic term, to a set of states ϕ k χ k,v with different vibrational quantum
numbers v. According to Eq. (3.74) the excited wavefunction will be
© 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_4
119