238
Appendix G: Animations
The radiation pulse is Gaussian, with the electric field given by:
E(t) = E max e
−t
2 /4τ
2 sin(ω t)
In this simulation, τ = 10 fs. The transition dipole is considered constant and
equal to 1 a.u. The electric field amplitude E max = 0.001 is sufficiently small as
to be in the perturbative regime, but the simulation is numerically exact and does
not make use of perturbation theory.
The excited wavepacket is represented as its squared module, |Θ e (R)|
2 .
• Animation 4.2
The same as in animation 4.1, but with a longer pulse, τ = 60 fs.
• Animation 4.3
The same as in animation 4.1, but with a still longer pulse, τ = 250 fs.
• Animation 4.4
In this animation we show the dynamics of a wavepacket which is created by
electronic excitation by a radiation pulse, just as in the previous ones, but the two
potential energy curves are Morse functions (see Fig. 4.1). Namely:
U g (R) = D g
1 − e
−α g (R−R g )
2
and
U e (R) = D e
1 − e
−α e (R−R e )
2
where R g = 4 bohr, R e = 5.5 bohr, D g = 0.15 a.u., D e = 0.08 a.u., α g = 0.5 a.u.,
and α e = 0.3 a.u. The reduced mass is 30000 a.u.
The radiation pulse is Gaussian, with the electric field given by:
E(t) = E max e
−t
2 /4τ
2 sin(ω t)
In this simulation, τ = 10 fs. The transition dipole is considered constant and
equal to 1 a.u. The electric field amplitude E max = 0.001 is sufficiently small as
to be in the perturbative regime, but the simulation is numerically exact and does
not make use of perturbation theory.
The excited wavepacket is represented as its squared module, |Θ e (R)|
2 .
• Animation 4.5
The same as in animation 4.4, but with a longer pulse, τ = 60 fs.
• Animation 4.6
The same as in animation 4.4, but with a still longer pulse, τ = 250 fs.
• Animation 5.1
This animation shows a wavepacket going through a conical intersection. The
potential energy surfaces are depicted in Fig. 5.6. We simulated the dynamics
in two coordinates, Q S and Q A , and the conical intersection point is at Q S = 3
Appendix G: Animations
The radiation pulse is Gaussian, with the electric field given by:
E(t) = E max e
−t
2 /4τ
2 sin(ω t)
In this simulation, τ = 10 fs. The transition dipole is considered constant and
equal to 1 a.u. The electric field amplitude E max = 0.001 is sufficiently small as
to be in the perturbative regime, but the simulation is numerically exact and does
not make use of perturbation theory.
The excited wavepacket is represented as its squared module, |Θ e (R)|
2 .
• Animation 4.2
The same as in animation 4.1, but with a longer pulse, τ = 60 fs.
• Animation 4.3
The same as in animation 4.1, but with a still longer pulse, τ = 250 fs.
• Animation 4.4
In this animation we show the dynamics of a wavepacket which is created by
electronic excitation by a radiation pulse, just as in the previous ones, but the two
potential energy curves are Morse functions (see Fig. 4.1). Namely:
U g (R) = D g
1 − e
−α g (R−R g )
2
and
U e (R) = D e
1 − e
−α e (R−R e )
2
where R g = 4 bohr, R e = 5.5 bohr, D g = 0.15 a.u., D e = 0.08 a.u., α g = 0.5 a.u.,
and α e = 0.3 a.u. The reduced mass is 30000 a.u.
The radiation pulse is Gaussian, with the electric field given by:
E(t) = E max e
−t
2 /4τ
2 sin(ω t)
In this simulation, τ = 10 fs. The transition dipole is considered constant and
equal to 1 a.u. The electric field amplitude E max = 0.001 is sufficiently small as
to be in the perturbative regime, but the simulation is numerically exact and does
not make use of perturbation theory.
The excited wavepacket is represented as its squared module, |Θ e (R)|
2 .
• Animation 4.5
The same as in animation 4.4, but with a longer pulse, τ = 60 fs.
• Animation 4.6
The same as in animation 4.4, but with a still longer pulse, τ = 250 fs.
• Animation 5.1
This animation shows a wavepacket going through a conical intersection. The
potential energy surfaces are depicted in Fig. 5.6. We simulated the dynamics
in two coordinates, Q S and Q A , and the conical intersection point is at Q S = 3