Photon-matrix molecule interactions

The main cost of this enlianced time resolution compared to fluorescence upconversion, however, is the aforementioned problem of time ordering of the photons that arrive from the pump and probe pulses. Wlien the probe pulse either precedes or trails the arrival of the pump pulse by a time interval that is significantly longer than the pulse duration, the action of the probe and pump pulses on the populations resident in the various resonant states is nnambiguous. When the pump and probe pulses temporally overlap in tlie sample, however, all possible time orderings of field-molecule interactions contribute to the response and complicate the interpretation. Double-sided Feymuan diagrams, which provide a pictorial view of the density matrix s time evolution under the action of the laser pulses, can be used to detenuine the various contributions to the sample response [125]. 

A schematic of the basic principles of a matrix-assisted laser desorption/ion source is shown in Figure 2.35. By the interaction of a focused laser beam with short pulses and a suitable matrix, the energy of the photons is transferred to the matrix molecules. In MALDI mostly pulsed UV (e.g., nitrogen, X = 337 nm, pulse duration 3-10 ns), but also IR lasers (e.g., Er YAG, X = 2.94 (xm or C02, X = 10.6(xm with a higher pulse duration of up to 600 ns) are used. The MALDI mass spectra obtained during soft ionization by UV and IR lasers are identical. The energy density... 

Our present focus is on correlated electronic structure methods for describing molecular systems interacting with a structured environment where the electronic wavefunction for the molecule is given by a multiconfigurational self-consistent field wavefunction. Using the MCSCF structured environment response method it is possible to determine molecular properties such as (i) frequency-dependent polarizabilities, (ii) excitation and deexcitation energies, (iii) transition moments, (iv) two-photon matrix elements, (v) frequency-dependent first hyperpolarizability tensors, (vi) frequency-dependent polarizabilities of excited states, (vii) frequency-dependent second hyperpolarizabilities (y), (viii) three-photon absorptions, and (ix) two-photon absorption between excited states. 

The quantum mechanical approach to light absorption involves evaluating matrix elements of a radiation-molecule interaction operator between initial and final states, subject to the conservation of energy. The cross-section for a photon absorption process in which there is an electronic transition from an initial state (i to a final state f) is given by... 

The matrix element in Eq. (3) involving the operator /2 describes the interaction of the molecule with the incident radiation, and the matrix elements with the operator describes the interaction of the molecule with the scattered radiation. The matrix element products in each term can be read from right to left in a time-ordered sense hence, the resonance term describes the molecule interacting first with a laser photon and subsequently creating a scattered photon, whereas the nonresonance terms reverses the natural order of those two events. 

More important for UV-MALDI might be IP reductions due to matrix-analyte interactions. Matrix-analyte interactions can be stronger than those between matrix molecules, and there is no a priori reason to expect low two-photon efficiencies for such complexes. Kinsel and colleagues have reported several experimental and theoretical studies of this effect in clusters. In one example, strongly reduced IPs for DHB-proline complexes were found, down to 7eV. ° In addition, fragmentation of some complexes after ionization produced protonated analytes.This is an efficient two-photon process that is probably active for certain matrix-analyte combinations. How often it contributes to MALDI is not yet clear, and this cannot be easily predicted in advance. 

In the early 1980s, one of the authors of this chapter began to study argon matrix isolation of radical cations235 by applying the radiolytic techniques elaborated by Hamill and Shida. A central factor was the addition of an electron scavenger to the matrix which was expected to increase the yield of radical cations and the selectivity of the method. For practical reasons, X-rays replaced y-rays as a radiolytic source and argon was chosen as a matrix material because of its substantial cross section for interaction with keV photons (which presumably effect resonant core ionization of Ar). Due to the temporal separation of the process of matrix isolation of the neutral molecules and their ionization, it was possible to obtain difference spectra which show exclusively the bands of the radical cations. 

Rayleigh and Raman scattering are two-photon processes in which absorption of a photon is followed coherently by emission of the same and of a different photon, respectively. They are thus second-order processes if we use a description in which the interaction between matter and radiation is used as a perturbation. The complete second-order treatment (Sushchinskii, 1972 Behringer, 1974) is outside the scope of this contribution. We shall start with the simplified description of the scattering tensor that is familiar from many previous treatments. The scattering tensor describing the Raman transition from the molecular eigenstate / > to /> is represented by a 3 X 3 matrix with (molecule-fixed) Cartesian components (in atomic units, ft = 1)... 

An important aspect in control schemes based on the Stark effect is the choice of the frequency of the control field. It should be chosen such as to ensure a non-resonant interaction with the molecule. In our case, as mentioned in Sect.7.2.1, all the elements of the dipole moment matrix along the z direction are zero by symmetry. However, two-photon transitions between the Si and S2 states can be mediated by the non-zero af2(Q) matrix element. A value of hujc = 1-8 eV, which is high with respect to any two-photon transition between the Si and S2 states was chosen. Calculations with peak intensities of 0,10, 20,30,40 and 50 TW/cm for the control field were performed. The peak intensity of the pump pulse was set to 0.2TW/cm. In order to address various parts of the spectmm, three different photon energies (4.6,4.7 and 4.8 eV) were considered. The TDSE of Eq. (7.27), for each set of parameters was solved using the MCTDH method in the multi-set formalism. In each... 

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