4.5 Dynamic Environmental Effects
137
The amount of vibrational energy can be easily larger than after optical excitation,
especially when the molecule lands on the ground-state PES that usually presents
deep minima. As a consequence, the processes of geometrical relaxation, IVR, and
thermalization will take place again in the new PES. Before complete thermal equilibration takes place, in the ground state some processes with large energy barriers
may still occur (“hot ground-state” chemistry) thanks to the residual energy excess.
4.6 Computational Note: Quantum Wavepacket Dynamics
and Classical Trajectories
As we have seen in the previous sections, the adiabatic excited state dynamics depends
on the excitation regime, on the details of the PESs, as well as on static and dynamic
environmental effects. Several processes can be distinguished, ideally and also in ad
hoc experiments, but normally they overlap in time: for instance, IVR can be studied
on its own in rarefied gases, but is intertwined with the vibrational energy loss to
the environment in condensed phase. The complexity of excited state dynamics,
even when limited to the adiabatic regime, can be tackled by simulation methods
that reproduce computationally the time evolution of the excited molecule. Several
methods are available to solve the TDSE for nuclear motion and describe the quantum
wavepacket dynamics, but classical trajectory approaches are also commonly used
because they allow to deal with large systems and long simulation times. More details
about computational methods will be given in Sect. 5.5, where the simulation of fast
nonadiabatic processes is discussed. In fact, such processes cannot be separated from
the nuclear dynamics, so most of the approaches in use for nonadiabatic dynamics
are also suitable and were originally developed for the simpler adiabatic case.
It is however worth to comment here how the classical ansatz is appropriate to
describe nuclear dynamics. We saw in Sect. 4.2 that certain average properties of a
quantum wavepacket (positions, momenta, and their variances) obey the same equations of motion as in classical mechanics. This is the basis for replacing quantum
with classical dynamics, which is done by running swarms of classical trajectories
with the same initial distributions of coordinates and momenta as in the quantum
wavepacket. The above average properties offer a rather complete description of the
dynamics as far as the wavepacket is well localized. The stationary vibrational states
in molecules are in fact fairly localized, and ultrashort pulses create equally localized
wavepackets in the excited PESs. So, in the short time the adiabatic quantum dynamics is well reproduced by a swarm of trajectories. At longer times, the wavepackets
tend to delocalize, so their properties are not anymore described satisfactorily by
the simple averages and variances of positions and momenta (think for instance of
a wavepacket that splits into different reaction channels). Phenomena such as tunneling or the interference of different components of a wavepacket are not properly
described by classical mechanics, although ad hoc corrections have been envisaged
[18, 19]. The differences in the quantum and classical microcanonical and canonical
137
The amount of vibrational energy can be easily larger than after optical excitation,
especially when the molecule lands on the ground-state PES that usually presents
deep minima. As a consequence, the processes of geometrical relaxation, IVR, and
thermalization will take place again in the new PES. Before complete thermal equilibration takes place, in the ground state some processes with large energy barriers
may still occur (“hot ground-state” chemistry) thanks to the residual energy excess.
4.6 Computational Note: Quantum Wavepacket Dynamics
and Classical Trajectories
As we have seen in the previous sections, the adiabatic excited state dynamics depends
on the excitation regime, on the details of the PESs, as well as on static and dynamic
environmental effects. Several processes can be distinguished, ideally and also in ad
hoc experiments, but normally they overlap in time: for instance, IVR can be studied
on its own in rarefied gases, but is intertwined with the vibrational energy loss to
the environment in condensed phase. The complexity of excited state dynamics,
even when limited to the adiabatic regime, can be tackled by simulation methods
that reproduce computationally the time evolution of the excited molecule. Several
methods are available to solve the TDSE for nuclear motion and describe the quantum
wavepacket dynamics, but classical trajectory approaches are also commonly used
because they allow to deal with large systems and long simulation times. More details
about computational methods will be given in Sect. 5.5, where the simulation of fast
nonadiabatic processes is discussed. In fact, such processes cannot be separated from
the nuclear dynamics, so most of the approaches in use for nonadiabatic dynamics
are also suitable and were originally developed for the simpler adiabatic case.
It is however worth to comment here how the classical ansatz is appropriate to
describe nuclear dynamics. We saw in Sect. 4.2 that certain average properties of a
quantum wavepacket (positions, momenta, and their variances) obey the same equations of motion as in classical mechanics. This is the basis for replacing quantum
with classical dynamics, which is done by running swarms of classical trajectories
with the same initial distributions of coordinates and momenta as in the quantum
wavepacket. The above average properties offer a rather complete description of the
dynamics as far as the wavepacket is well localized. The stationary vibrational states
in molecules are in fact fairly localized, and ultrashort pulses create equally localized
wavepackets in the excited PESs. So, in the short time the adiabatic quantum dynamics is well reproduced by a swarm of trajectories. At longer times, the wavepackets
tend to delocalize, so their properties are not anymore described satisfactorily by
the simple averages and variances of positions and momenta (think for instance of
a wavepacket that splits into different reaction channels). Phenomena such as tunneling or the interference of different components of a wavepacket are not properly
described by classical mechanics, although ad hoc corrections have been envisaged
[18, 19]. The differences in the quantum and classical microcanonical and canonical