Faris Gel'mukhanov

Resonant X-ray Raman scattering

Abstract An overview is presented of the theory of X-ray Raman scattering. Second-order perturbation theory for the interaction between matter and light is used as a common starting point, and the consequences of this theory are analytically and numerically analyzed for a variety of experimental situations. The review focuses on results from radiative and nonradiative scattering experiments conducted with 2nd and 3rd generation synchrotron radiation sources during the last couple of years, dealing with atomic, molecular, solid state and surface adsorbate targets. After giving a brief synopsis of relevant experimental techniques, some basic theoretical concepts and principles of X-ray Raman scattering are described, followed by a presentation of the various particular aspects associated with the resonant X-ray scattering process. That is: polarization – interference – role of symmetry – symmetry breaking and energy dependence – dissociation and time dependent interpretations – duration time and frequency detuning – formation of band profiles – Doppler effects – screening and chemical shifts – elastic scattering – solid state theory – application to surface adsorbates – absorption in the Raman mode – direct processes versus resonant X-ray scattering – many channel theory. Each aspect is described by a qualitative picture, a mathematical analysis, and by illustrative examples from experiment combined in some cases with results from simulations. Simple systems are chosen to demonstrate the consequences of various aspects of the theory.

Dynamics of two-photon absorption by molecules and solutions

A dynamic density-matrix based theory of two-photon absorption (TPA) of molecules and solutions is presented. The theory highlights the influence of pulse duration, dephasing, and resonant conditions on the final TPA cross section as well as that of saturation, including a hierarchy of saturation intensities. A breakdown of the conventional identification of TPA with coherent one-step TPA is predicted for the long-pulse regime in which incoherent two-step TPA can even dominate the coherent one-step TPA process. The major role of the solvent is to enhance the off-resonant contributions to TPA furnished by collisional dephasing.

Young's double-slit experiment using core-level photoemission from N2: revisiting Cohen–Fano's two-centre interference phenomenon

The core-level photoelectron spectra of N2 molecules are observed at high energy resolution, resolving the 1σg and 1σu components as well as the vibrational components in the extended energy region from the threshold up to 1 keV. The σg/σu cross section ratios display modulation as a function of photoelectron momentum due to the two-centre interference, analogous to the classical Young’s double-slit experiment, as predicted by Cohen and Fano a long time ago. The Cohen–Fano interference modulations display different phases depending on the vibrational excitations in the core-ionized state. Extensive ab initio calculations have been performed within the Hartree–Fock and random phase approximations in prolate spheroidal coordinates. The dependence of photoionization amplitudes on the vibrational states was taken into account using the Born–Oppenheimer approximation. The ab initio results are in reasonable agreement with the experimental data. The theoretical analysis allows the modulation to be connected with the onset of transitions to the states of increasing orbital angular momentum which occurs at increasing photon energies. Deviation from the Cohen–Fano formula is found for both the experimental and the ab initio results and is attributed to electron scattering by the neighbouring atom. A new formula for the interference modulation is derived within the framework of the multiple scattering technique. It differs from the classical Cohen–Fano formula by the addition of twice the scattering phase of the photoelectron by the neighbouring atom. We demonstrate that

Symmetry assignments of occupied and unoccupied molecular orbitals through spectra of polarized resonance inelastic X-ray scattering

We derive symmetry selection rules for polarized resonance inelastic X-ray scattering (RIXS) in randomly oriented molecules belonging to any of the 32 crystallographic point groups or to the two groups of linear molecules. Compact formulae are derived for cross sections of RIXS processes in randomly oriented molecules for photons of arbitrary polarization; linear, circular or elliptical polarization. It is shown that a specification of polarization ratios of RIXS cross sections yields sufficient information to permit an unequivocal identification of the symmetry species of the occupied and unoccupied molecular orbitals (MOS). The given tabulation of RIXS symmetry selection rules can be used as a quick guide to assign symmetry properties of molecules of experimental interest.

Toward fully nonempirical simulations of optical band shapes of molecules in solution: a case study of heterocyclic ketoimine difluoroborates.

This study demonstrates that a hybrid density functional theory/molecular mechanics approach can be successfully combined with time-dependent wavepacket approach to predict the shape of optical bands for molecules in solutions, including vibrational fine structure. A key step in this treatment is the estimation of the inhomogeneous broadening based on the hybrid approach, where the polarization between solute and atomically decomposed solvent is taken into account in a self-consistent manner. The potential of this approach is shown by predicting optical absorption bands for three heterocyclic ketoimine difluoroborates in solution.

Core excitations of naphthalene: Vibrational structure versus chemical shifts

High-resolution x-ray photoelectron emission (XPS) and near-edge x-ray absorption fine structure (NEXAFS) spectra of naphthalene are analyzed in terms of the initial state chemical shifts and the vibrational fine structure of the excitations. Carbon atoms located at peripheral sites experience only a small chemical shift and exhibit rather similar charge-vibrational coupling, while the atoms in the bridging positions differ substantially. In the XPS spectra, C-H stretching modes provide important contributions to the overall shape of the spectrum. In contrast, the NEXAFS spectrum contains only vibrational progressions from particular C-C stretching modes. The accuracy of ab initio calculations of absolute electronic transition energies is discussed in the context of minute chemical shifts, the vibrational fine structure, and the state multiplicity.

Vibrational scattering anisotropy in O2 -- dynamics beyond the Born–Oppenheimer approximation

Born–Oppenheimer and Franck–Condon approximations are two major concepts in the interpretation of electronic excitations and modeling of spectroscopic data in the gas and condensed phases. We r ...

Screening in resonant X-ray emission of molecules

Abstract We explore the effects of screening in resonant X-ray emission from molecules by means of unconstrained multiconfigurational self-consistent field optimizations of each state involved in the resonant and nonresonant X-ray processes. It is found that, although screening can produce shifts in transition energies of a few eV, its effect on the transition intensities is relatively minor. Using results from the investigated molecules, we find that the screening is quite dependent on the type of molecule-saturated versus unsaturated-and on the core site, but depends little on the particular core shell for a given core site. A differential core level screening, relating to the X-ray chemical shift, can still be noted. The consequence of the findings for analysing general resonant X-ray emission spectra is discussed.

The principles of infrared-x-ray pump-probe spectroscopy. Applications on proton transfer in core-ionized water dimers

In this paper we derive the basic physics underlying infrared-x-ray pump-probe spectroscopy (IR, infrared). Particular features of the spectroscopy are highlighted and discussed, such as dependence on phase of the infrared pulse, duration and delay time of the x-ray pulse, and molecular orientation. Numerical applications are carried out for the water dimer using wave packet techniques. It is shown that core ionization of the donor oxygen of the water dimer results in a drastic change of the potential with the global minimum placed in the proton transfer region. The results of the modeling indicate that IR-x-ray pump-probe spectroscopy can be used to study the dynamics of proton transfer in this core-ionized state, and that, contrary to conventional core level photoelectron spectroscopy, x-ray core-ionization driven by an IR field is a proper method to explore the proton transfer in a system like the water dimer. We observe that the trajectory of the nuclear wave packet in the ground state potential well is strongly affected by the absolute phase of the IR pulse.

Optical limiting for microsecond pulses

We present a dynamical theory of nonlinear absorption and propagation of laser pulses with duration in the microsecond time domain. The general theory is applied to fullerene C(60) because of its good optical limiting properties, namely, a rather low ground state absorption and a strong triplet-triplet absorption. It is shown that sequential absorption involving strong triplet-triplet transitions is the major mechanism of nonlinear absorption. The intrinsic hierarchy of time scales makes an adiabatic solution of the coupled rate equations valid, which therefore can be reduced to a single dynamical equation for the ground state population. The slow evolution of this population is defined by an effective rate of population transfer to the triplet state and by the pulse duration. The propagation effect plays an important role in the optical power limiting performance. The intensity of the field as well as the population of the triplet state decreases during the pulse propagation, and a weakened nonlinear sequential two-photon absorption is followed by a linear one-photon absorption which gradually becomes the dominating process. The competition between these qualitatively different processes depends on the field intensity, the length of the absorber, and the concentration. The pulse propagation is studied by solving numerically the two-dimensional paraxial field equation together with the effective rate equation for the ground state population.