Ultrafast Molecular Dynamics

Time-Resolved Concidence Imaging Spectroscopy

Time-resolved photoelectron spectroscopy is a powerful tool for investigating a broad range of photochemical and photophysical problems. In some cases, however, a measurement of the photoelectron spectrum alone is not enough to obtain a full understanding of the photochemical reaction. Time-resolved photoelectron-photoion coincidence imaging spectroscopy (CIS) is a recently developed technique that provides an unprecedented level of detail for such cases. The spectrometer allows us to make time, energy and angle-resolved measurements of photoelectrons and photoions, providing data which gives us the fullest possible picture of the photochemical reaction. By measuring photoions in coincidence with photoelectrons we gain information on kinetic energy correlations and have the ability to mass select to disentangle photoelectron spectra correlated with different product channels. Finally, coincidence measurements (or measurements from an aligned sample) also allow us to step from the lab frame into the molecular frame, removing the effects of orientational averaging from the measurements, so providing the clearest possible picture of the photochemical process from the molecule’s point of view.

Figure 1: Potential energy curves for the states relevant to the photoelectron spectroscopy study of UV dissociation of the NO-dimer

Example: UV dissociation of the NO-dimer

The power of this technique is nicely illustrated by some recent experiments on the dissociation of the NO-dimer at wavelengths around 200 nm[1]. A detailed study of the dynamics using photoelectron spectroscopy has revealed that from the initial bright state, the electronic excitation briefly passes through an intermediate state before the dimer dissociated into two NO molecules, one in the electronic ground state and one in the first excited state. The CIS technique was used to obtain valuable information about the electronic symmetry of the intermediate state as well as the vibronic couplings leading to dissociation.

Figure 2: Mass selected photoelectron spectra

Mass selected photoelectron spectra

In photoelectron spectroscopy complications may arise when several fragmentation channels are possible - in favorable cases the spectra associated with each channel are separated into clearly distinguishable peaks, but in other cases they may overlap. In the case of the NO-dimer only one channel is observed at the chosen probe wavelength and Koopmans' correlations favour ionization into a single ion state. At zero delay between the pump and probe pulses complications arise due to the competition between resonant and non-resonant ionization. Frank-Condon factors for the resonant path favour ionization into the pre-dissociative continuum in the ion, while creation of the bound dimer-ion is more favorable for the non-resonant path. When electrons and ions are measured in coincidence it is, however, straightforward to extract the photoelectron spectra corresponding to ionization into the pre-dissociative states and the dimer-ion respectively as shown in Figure 2.

Kinetic energy correlations

The imaging technique allows us to measure not only the mass but the full recoil velocity vector of each charged fragment. From the coincident data we may thus build a electron-ion kinetic energy correlation map. This is shown in figure 3 for a range of different pump-probe delays. Firstly, this map gives a great amount of information about the energy partitioning in the fragments: energy conversion requires that

KE(electron) + KE(ion) + Eint(ion) + IP = hn(pump) + hn(probe),
thus, constant internal energy contours will appear as anti-diagonal lines in the map. The maps in figure 3 show an evolution from broad and featureless at early delays to a clear, horizontal line building up at later delays. The lack of features at early delays is a consequence of ionization into the pre-dissociative continuum of the dimer-ion. The horizontal stripe seen at later delay times marks the appearance of NO(A) products from dissociation on the neutral excited state surfaces. The NO(A) state is a Rydberg-type state that strongly favor delta(v) = 0 ionization to NO(X)+ leading to nearly mono-energetic electrons. By selecting events with electron energies in the window corresponding to NO(A) products (and subtracting the continuous background) we can monitor how the recoil energy of the fragments evolves with time. This is shown in Figure 4. Via energy conservation this means that we monitor how the internal energy distribution of the fragments evolves as a function of time. Figure 4 shows that, for the dissociation of the NO-dimer, fragments that are formed at short pump-probe delay times have high internal-energy whereas fragments formed at long delays have little or no vibrational excitation. This is a direct measurement of vibrational redistribution of energy using time-resolved product state distributions.

Figure 3: Electron-ion kinetic energy correlation map

Figure 4: Time evolution of the internal state distribution for the NO(A) products


Photoelectron angular distributions

Photoelectron angular distributions (PADs) contain information on the symmetry of the states involved in the ionization process, but only if measured in the frame of the molecule. In the laboratory frame, orientational averaging can wash out the information contained in the PADs. Coincidence imaging of ions and electrons is a perfectly suited tool for measuring molecular frame PADs. If the axial recoil approximation is valid, the recoil direction of the fragments in the dissociative process directly reveals the orientation of one (bond) axis in the molecule at the time of dissociation. When the recoil direction of the electron measured in coincidence with such a fragment, we may transform the velocity of the electron into the recoil frame (which differs from the molecular frame by azimuthal averaging around the recoil direction). Figure 5 compares measured lab and recoil frame PADs in the NO-dimer dissociation. Clearly, the recoil frame distribution contains a richer structure than the lab frame distribution. More important is the fact that while the lab frame distribution hardly shows any time-dependence, there are small, but significant changes in the recoil frame distribution. Careful analysis of these angular distributions strongly suggests that the intermediate state in the dissociation process is a Rydberg 3py state.

Figure 5: Lab frame vs recoil frame photoelectron angular distributions

3D Photoelectron Imaging from Aligned Molecules

The coincidence experiment described above allows us to record the time-resolved photoelectron spectrum, the energy correlations between ions and photoelectrons, and enables reconstruction of the PADs in the recoil frame. In order for this final step to work use is made of the axial-recoil of fragments to reconstruct the dissociation event in the recoil frame - along the NN bond axis in the case of the NO dimer. Another way to relate the molecular frame to the lab frame is to fix the molecule in space by aligning the molecule prior to the pump-probe measurement. This technique can be advantageous because axial-recoil is not required.

Example: MF-PADs from fixed-in-space CS2 molecules

Figure 6.

Another example of the power of MF-PADs is seen from the CS2 measurements [Science: 323, 1464 (2009)]. In this case an intense IR pulse was used to transiently align the molecules. Pumping at 201.2 nm enabled the preparation of a 2-level vibrational wavepacket in the excited state (figure 6), creating a system which undergoes a quantum beat. The levels coherently prepared are both mixed stretching and bending modes, but with differing amounts of stretch and bend; the evolution of the wavepacket causes the molecule to pass through linear and bent geometries. The bending of the molecule allows mixing of the bright state electronic character with a close-lying dark state, hence the electronic character evolves on the same timescale as the vibrational quantum beat.

The photoelectron spectrum shows the quantum beat at low electron kinetic energies – this is the sinusoidal oscillation overlaid on the exponential decay of the signal – but this beat is not observed at low kinetic energies (figure 7). In the MF-PADs the beat is also observed, in this case as a change of the angular form of the PAD which is related to the electronic evolution of the excited state (figure 8). This conclusion is confirmed by the fact that changes in the MF-PAD are observed at all kinetic energies, despite the loss of observable modulation in the photoelectron spectrum. This highlights the separation of the observables: the photoelectron spectrum reflects the nuclear dynamics through changing Franck-Condon factors while the MF-PAD is most sensitive to changes in the electronic character through the electronic part of the ionization matrix elements.

Figure 7.
Figure 8.

1: Science: 311, 219 (2006)