Some details of REMPI spectroscopy

Resonance enhanced multiphoton ionization (REMPI) spectroscopy has been subject of a number of excellent reviews, tutorials and book chapters. There is sample information in the literature – detailing every aspect of the technique. We are just highlighting a couple of aspects of REMPI which are more or less related to APLI.

The schematic energy level diagram in Figure 1 is illustrating a number of processes that may affect the overall ionization efficiency of REMPI schemes: Resonant excitation within a ro-vibrational manifold of an electronically excited state increases the ion yield by orders of magnitude as compared to non-resonant excitation (case a). On the other hand, inter-molecular relaxation processes depleting the initially populated intermediate level (e.g., form a singlet into a triplet state, case c) may reduce this enhancement considerably. The difference between case a) and case b) is simply that the photon density in the former is much lower; thus the molecule has some time to relax within the electronically excited state. Upon increasing the photon density, the numbers of photons interacting per time interval with the molecule increases also. As a result, the period between the initially two well separated absorption processes decreases, and becomes eventually smaller than the molecular relaxation time. Under such high photon flux conditions, however, there is no way to tell the molecule to stop absorbing further photons once the ionization region is reached; on the contrary, the density of available ionic states of a molecule is usually rather high, and more than two photons are readily absorbed.

Before continuing, we should address the different time domains regarding REMPI processes. In the above example, a laser pulse is used that is orders of magnitude longer than the duration of any intra-molecular relaxation process within an electronic manifold. It simply means that we are working with pulsed nano-second laser light. The single reason is that APLI is based on ns excitation. Ultra-fast, multi-photon excitation (i.e., applying laser pulse widths that are shorter (tens of fs) than any intra-molecular relaxation process) is discussed in reviews; many exciting applications are thinkable, but this is beyond the scope of this discussion. The fundamental difference between ultra-fast fs- and conventional ns-excitation is that in the latter case, the nuclei in the molecule are able to change their position within the timeframe of the pulse (in fact, they can oscillate several hundred times), whereas in the former case all nuclei positions are basically static; only electron density is forced to change within the timeframe of the light pulse. Temporally well separated from the excitation pulse, the nuclei start to “slowly” re-orientate according to the new electronic configuration. Furthermore, the power density within a fs laser pulse can be extremely large. As an example: A typical 10-ns laser pulse with 10 mJ of energy generates 1 MW; a 25 fs pulse with 5 µJ energy, 0.2 GW! Upon focusing a fs laser beam, TW power densities are easily achievable. As a downside, we may want to note that the optical resolution severely suffers from the short pulse duration owing to Heisenberg’s Uncertainty Principle; in the above example, at a wavelength around 800 nm the spectral width would be on the order of 30 nm.

The total energy acquired through multiphoton absorption (“ladder climb”) eventually leads to dissociation of the parent ion (Figure 1b, upper part). Rate constants for the unimolecular decay of electronically highly excited ions yield lifetimes on the order of ps. If the laser pulse width is several ns, the generated fragments (“ladder switch”) can also further absorb multiple photons (“ladder climb”) and further fragment (“ladder switch”), and so on. In this way, strongly absorbing molecules can even be atomized.

Finally, case d) was not discussed yet. It appears as if this is a more common situation when performing REMPI of non-aromatic organic compounds with functional groups acting as chromophores in the near UV. The dissociative character of such bound-state transitions stems from the frequently encountered situation that electrons in bonding orbitals within the chromophoric group are excited to orbitals with anti-boding character at the energy level of the first photon. The repulsive curve in Figure 1 d) illustrates this situation. Within a timeframe of ps, the molecule is entirely dissociated into neutral fragments D_n. It is very tough, even at rather high photon fluxes, to promote the dissociating molecule (i.e., the transition state of this unimolecular process) to the ionization region; not only do Franck-Condon factors become increasingly less favorable when moving along the reaction coordinate, but also the required wavelength changes (compare to case c; here just one selected wavelength is promoting the molecule from T₁ into the ionic ground state, if possible). As a result, if the absorption cross section leading to dissociation is high, then hardly any ionic signal is detected upon excitation with ns lasers. Instead, one could think about detecting the neutral fragments D_n; in fact, this approach can be applied, particularly in combination with ion imaging techniques.

The REMPI processes discussed so far rely on step-wise excitation of the molecule. For many aromatic hydrocarbons, this approach works perfectly well. We have also seen, however, that for a large number of other molecules, this scheme is often not favorable. One way around this problem is, of course, direct excitation of energetically higher lying states: After leaving the bound state region, we enter the Rydberg region (this picture is dramatically over-simplified!). Electrons promoted to Rydberg orbitals tend to have non-bonding character. If the molecule is still bound when electron density is removed from the ground state, we can expect that the excited molecule is stable. Furthermore, the low-Rydberg region is far less congested as compared to the bound state as well as the high-Rydberg energy range. Thus, it appears as if this energy range is very promising for REMPI. Figure 2 a) illustrates this situation. One problem remains, however: this energy region corresponds to wavelengths well below the tunable range of commercially available laser systems (i.e., λ < 200 nm). Of course it ispossible to generate tunable VUV radiation, but only with many constraints rendering analytical applications rather difficult. In addition to many instrumental issues, one practical aspect is the very strong absorption of these wavelengths by air.

Figures 2 b - d) illustrate an alternative approach, which is often used in REMPI of small molecules, both for analytical as well as spectroscopic applications: Simultaneous resonant absorption of two (or more) photons, followed by ionization from the excited state with one (or more) photons. The simplest and most widely applied case is shown in Figure 2 b), a (2+1) REMPI process, which is discussed in more detail below. Figures 2 c) and d) are (3+1) and (2+2) REMPI processes, respectively. In all these schemes, the photon density needs to be orders of magnitude larger than in the resonant (1+1) case; power densities of 10¹⁰ W/cm² and above appear to be sufficient. For REMPI involving TPA processes, two important things have to be considered: First, the values of σ_n for multiphoton absorption are so small that if linear absorption is present it usually dominates. In other words, beware of strongly absorbing repulsive intermediate states! Second, at such high power density levels, absorption of a third photon readily occurs because this step merely represents a resonant excitation into the dense ionization region. We than encounter the same situation as depicted in Figure 1 b): with ns laser pulses, there is hardly a way to prevent further absorption of photons by the parent ion. This means that in many cases of REMPI involving TPA, extensive ionic fragmentation occurs.

The (2+2) REMPI process shown in Figure 2 c) is less frequently applied; in this case frequency doubling of the radiation would probably also allow (1+1) excitation (caveat: selection rules!), which is by far more sensitive. (3+1) REMPI (Figure 2 d) is rarely applied for analytical applications; the required power density is again raised by orders of magnitude as compared to (2+1) REMPI. For spectroscopic applications, particularly if the concentration of the analyte can be simply increased to get above the actual detection limit, such processes are sometimes useful. We should keep in mind that besides absorption cross sections, power densities, and lifetimes, selection rules also play important roles in determining the overall REMPI response, particularly for small molecules.

In summary, (1+1) and (2+1) REMPI schemes appear to be the most widely applied multiphoton excitation processes. We have tried to explain this situation by inspecting the dynamics of the excitation steps. Provided favorable spectroscopic features exist, overall resonant, multi-step schemes [e.g., (1+1), (1+1+1), or two-color (1+1’+1) REMPI] result in very efficient ion generation. In case of (1+1) REMPI, the parent ion signal intensity is modulated according to the spectroscopy involved at the energy level of the first photon. This is one of the most powerful features of ns REMPI and leads to a two-dimensional analytical technique: The first dimension is spectroscopic, the second is mass spectrometric; besides optical selectivity, we also get mass selectivity.

If TPA is involved, the power density has to be raised by orders of magnitude. In this case, efficient ion production is also observable, most probably accompanied by ionic fragmentation. Nevertheless, even upon extensive ionic fragmentation, all fragment ions carry the spectroscopic signature of the resonantly excited intermediate state(s) of the neutral precursor. Provided the matrix is not too complex, two dimensional analysis frequently leads to unambiguous results.