Bond softening

Theoretical description of bond softening can be traced back to early work on dissociation of diatomic molecules in intense laser fields.

[1] While the quantitative description of this process requires quantum mechanics, it can be understood qualitatively using quite simple models.

In the presence of light, the molecule may absorb a photon (violet arrow), provided its frequency matches the energy difference between the ground and the excited states.

The excited state is unstable and the molecule dissociates within femtoseconds into hydrogen atom and a proton releasing kinetic energy (red arrow).

The number of photons is very large but only a few curve repetitions need to be considered in this very tall ladder, as shown in Fig.

In the region of the anticrossing the molecule is in a superposition of the ground and the excited states, continuously exchanging energy with the laser field.

As the internuclear separation increases, the molecule absorbs energy and the electronic wavefunction evolves to the antibonding state on the femtosecond timescale.

When the dissociation is fast and the gap is small, a diabatic transition may occur where the system ends up on the other branch of the anticrossing.

In a vacuum chamber, the pulses were focused on molecular hydrogen under low pressure (about 10−6 mbar) inducing ionization and dissociation.

As the neutral H atom was taking the other half of the photon energy, this was an unambiguous confirmation of the bond softening process leading to the 1ω, 2ω and 3ω dissociation limits.

Figure 1: Two theoretical models of a molecule interacting with laser field. At low intensity (a) it is convenient to plot molecular energy curves and indicate photon transitions with vertical arrows. At high intensity (b) it is more appropriate to "dress" the molecular curves in photons and consider photon transitions at the curve crossings.
Figure 2: Distortion of molecular energy curves dressed in photons for increasing laser intensity. Curve crossings become anticrossings, which induces bond softening. The distorted curves have been calculated from undistorted ones [ 2 ] in Matlab using Hamiltonian diagonalisation.