Femtosecond studies chemistry in the fast lane

Excitation from the ground state to the repulsive covalent state, well above the crossing point, results in passage through the crossing region as the molecule vibrates. Thus, some of the trajectories cross onto the ionic curve (i.e. they follow the upper dashed curve in 

Wave packets are a useful concept when dealing with laser excitation processes on the femtosecond and picosecond time-scales, and they fit well with our intuitive way of thinking about molecular motion. In essence, they allow us to visualize how a molecular system evolves with time. 

Owing to the short pulse width of a femtosecond laser the energy/firequency spread is large, as required by the uncertainty principle, i.e. 

For example, for At = 85 fs one finds AP = 400 cm Thus, rather than exciting a single stationary state of a molecule, as in high-resolution spectroscopy, several states are excited coherently, i.e. a superposition of states (a linear combination) is formed and this is clearly a non-stationary state of the molecule. 

We must, therefore, use the Schrodinger equation in its time-dependent form to describe the motion of the molecule, with the wave packet being initially localized on the PES, in space and time. If discrete travelling-wave solutions of the Schrodinger wave equation are combined, then they can be used to construct the required wave packet, which localizes it to a transient pulse. Assuming that a single-frequency wave solution of the time-dependent Schrodinger equation can be written as y(r, t) =A sin( r — rot), then the superposition wave-packet solution is Y (r, t) = 

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