Resonant Raman Scattering Cross Sections Research Articles

Time Domain Simulation of (Resonance) Raman Spectra of Liquids in the Short Time Approximation.

Real-time time-dependent density functional theory (RT-TDDFT) and ab initio molecular dynamics (AIMD) are combined to calculate non-resonant and resonant Raman scattering cross sections of periodic systems, allowing for an explicit quantum mechanical description of condensed phase systems and environmental effects. It is shown that this approach to Raman spectroscopy corresponds to a short time approximation of Heller's time-dependent formalism for the description of Raman scattering. Two ways to calculate the frequency-dependent polarizability in a periodic system are presented: (1) via the modern theory of polarization (Berry phase) and (2) via the velocity representation. Both approaches are found to be equivalent for a system of liquid (S)-methyloxirane with the computational settings used. Resulting non-resonance and resonance Raman spectra from the dynamic AIMD/RT-TDDFT approach are compared to the spectra of one gas phase molecule in the harmonic approximation highlighting finite temperature and solvation effects. Using RT-TDDFT to calculate the full frequency-dependent Placzek-type polarizability within one set of simulations covers the non-resonance, near-resonance, and on-resonance regimes on equal footing, thus allowing the calculation of full Raman excitation profiles.

Morphologically Determined Excitonic Properties of Porphyrin Aggregates in Alcohols with Variable Acidity

Self-assembled, excitonically coupled aggregates of 5,10,15,20-tetrakis(4-sulfonatophenyl)porphyrin (TSPP) in acidified alcohols were studied by absorption, resonance light scattering (RLS), and resonance Raman (RR) spectroscopy along with scanning probe microscopy. In ethanol, the major absorption bands of aggregates in 0.5 mM HCl (sample E1) were narrower, with smaller total RLS intensity, compared to those of aggregates in 50 mM HCl (sample E2). RR scattering cross sections were smaller, and depolarization ratio dispersion greater, for E2 than E1. Two distinct types of aggregates at differing acidity in 1-propanol, analogous to the ethanolic samples, but only one type in methanol, were also identified. Atomic force microscopy (AFM) images for E1 showed small, single layered structures (∼5–20 nm diameter, ∼1.5–2 nm thickness). Variable morphologies for E2 included double-layered, elongated structures consistent with collapsed nanotubes (∼25 nm width, ∼3.5–4 nm thickness, ∼100–200 nm length) and single molecule thick sheets (∼50–200 nm in characteristic diameter). The former were also observed in ultrahigh vacuum scanning tunneling microscopy (UHV-STM) images. Aggregate morphology appears to depend on protonation and deprotonation kinetics of porphyrin monomers. Spectroscopic observations suggest that a larger subset of J-band excitonic transitions are significantly active in E2 than in E1. These variations in excitonic properties are attributed to the differing aggregate sizes, shapes, and possibly molecular packing. Formation of long nanotubes appears to require a solvent able to donate two hydrogen bonds, such as water. An open sheet structure is favored otherwise, as in ethanol.

Resonant Raman scattering of polarized and unpolarized x-ray radiation from Mg, Al, and Si

The x-ray resonant Raman scattering (RRS) effect of polarized and unpolarized radiation in the vicinity of the $1s$ absorption threshold of low-$Z$ elements such as magnesium, aluminum, and silicon is investigated. For the polarized and tunable exciting x-ray radiation the plane grating monochromator (PGM) beam line at the PTB laboratory in the BESSY II synchrotron radiation facility was employed, while unpolarized x-ray beams were induced by 1-MeV proton beam irradiation on various pure thick targets. For the latter case, a novel proton-induced x-ray fluorescence scattering chamber was designed and installed at the Tandem accelerator laboratory of the Institute of Nuclear Physics at N.C.S.R. ``Demokritos.'' The total RRS cross sections deduced from both independent excitation modes were found to be in a good agreement, within the experimental uncertainties. The predictions of the existing theory with respect to the dependence of the RRS to the incident beam polarization state is calculated and discussed with respect to the experimental results.

Comparative analysis of the resonant Raman cross sections of pure samples and oxides

AbstractMonochromatic synchrotron radiation was used to study the Raman effect on pure samples of Mn, Fe, and Cu and on oxides such as Mn2O3, Fe2O3, CuO and Cu2O. Energy scannings were carried out for different ranges of energies near the absorption edge of the target element. Theoretical models for the energy distribution of the Raman scattered photons, convoluted with the instrument function, were used to determine the resonant Raman scattering (RRS) cross sections as a function of the incident energy. The results indicate that RRS cross sections for pure samples are similar to those for oxides for the same energy difference from the respective edge, showing that the Raman scattering takes place in the same way in both kinds of samples. Copyright © 2008 John Wiley & Sons, Ltd.

X-ray resonant Raman scattering cross sections of Mn, Fe, Cu and Zn

X-ray fluorescence spectra present singular characteristics produced by the different scattering processes. When atoms are irradiated with incident energy lower and close to an absorption edge, scattering peaks appear due to an inelastic process known as resonant Raman scattering. It constitutes an important contribution to the background of the fluorescent line. The resonant Raman scattering must be taken into account in the determination of low concentration contaminants, especially when the elements have proximate atomic numbers. The values of the mass attenuation coefficients experimentally obtained when materials are analysed with monochromatic x-ray beams under resonant conditions differ from the theoretical values (between 5% and 10%). This difference is due, in part, to the resonant Raman scattering. Monochromatic synchrotron radiation was used to study the Raman effect on pure samples of Mn, Fe, Cu and Zn. Energy scans were carried out in different ranges of energy near the absorption edge of the target element. As the Raman peak has a non-symmetric shape, theoretical models for the differential cross section, convoluted with the instrument function, were used to determine the RRS cross section as a function of the incident energy.

Measurements of Rayleigh, Compton and resonant Raman scattering cross-sections for 59.536 keV γ-rays

The K–L and K–M resonant Raman scattering (RRS) cross-sections have been measured for the first time at the 59.536 keV photon energy in the 70Yb ( B K=61.332 keV), 71Lu ( B K=63.316 keV) and 72Hf ( B K=65.345 keV) elements; B K being the K-shell binding energy. The K–L and K–M RRS measurements have been performed at the 59° and 133° angles, respectively, to avoid interference of the Compton-scatter peak. The Rayleigh and Compton scattering cross-sections for the 59.536 keV γ-rays have also been measured at both the angles in the atomic region 1⩽ Z⩽92. Measurements were performed using the reflection-mode geometrical arrangements involving the 241Am radioisotope as photon source and planar Si(Li) and HPGe detectors. Ratios of the K–M and K–L RRS cross-sections in Yb, Lu and Hf are in general lower than that of the fluorescent Kβ 1,3,5 (K–M) and Kα (K–L) X-ray transition probabilities. Theoretical Rayleigh scattering cross-sections based on the modified form-factors (MFs) corrected for the anomalous scattering factors (ASFs) and the S-matrix calculations are on an average ∼15% and ∼6% higher, respectively, at the 133° angle and exhibit good agreement with the measured data at the 59° angle. Larger deviations ∼30% and ∼20%, respectively, are observed at the 133° angle for the 64Gd, 66Dy, 67Ho and 70Yb elements having the K-shell binding energy in vicinity of the incident photon energy. The measured Compton scattering cross-sections are in general agreement with those calculated using the Klein–Nishina cross-sections and the incoherent scattering function.

Resonance Raman Intensity Analysis of Vibrational and Solvent Reorganization in Photoinduced Charge Transfer

Quantitative analysis of resonance Raman scattering cross sections, together with charge-transfer absorption and emission spectra, can provide detailed information about the changes in nuclear equilibrium geometry undergone by both the electron donor and acceptor and the surrounding solvent in photoinduced charge-transfer processes. The molecular parameters that determine absorption and fluorescence band shapes and resonance Raman cross sections are summarized, and methods for extracting those parameters through spectral modeling are reviewed with emphasis on charge-transfer systems. Applications to the determination of molecular and solvent reorganization parameters to several organic intra- and intermolecular charge-transfer transitions are then presented, and prospects for further development of the technique are discussed.

Determination of resonance Raman scattering cross sections of laser dyes using a traveling-wave amplifier

Determination of resonance Raman scattering cross sections of laser dyes using a traveling-wave amplifier

A novel divided cell for quantitative Raman and resonance Raman spectroscopy

A novel four nuclear magnetic resonance (NMR)-tube holder is described for quantitative Raman and resonance Raman spectroscopy. This cell has advantages over other divided cell designs in producing high precision quantitation and eliminating off-axis errors. Raman spectra were obtained for both absorbing and nonabsorbing solutions, and the results compared to those obtained using a single tube holder. The relative Raman intensities in a 1:1 mixture of benzene and chloroform taken in the single holder were within 6% of those of the pure solvents taken with the four NMR tube holder. The resonance Raman scattering cross section of chromate was determined to be within 6% of the value obtained from a single-tube holder. All of these errors in accuracy and precision are within the errors normally associated with the quantitative measurement of Raman cross sections. These results show that the four-tube holder can be used for precise and accurate measurement of both Raman and resonance Raman scattering.

Measurement of KL and LM resonant Raman scattering cross sections with a proton-induced x-ray beam

The resonant Raman effect has been described as an inelastic scattering process occurring when the energy of the exciting x-ray beam approaches from below the energy of an absorption edge of a target element. It produces a scattered photon with a characteristic maximum energy and the emission of an inner-shell electron. A high monochromatic x-ray beam produced by protons was utilized for the measurement of the KL type of resonant Raman scattering (RRS) cross sections in V and Cr and of the LM ones in La and Ce. In the case of V and Cr targets, the fluorescence yields of the KL-RRS process were also extracted, while the fine-structure splitting in a LM-RRS spectrum was observed for the first time. The influence of RRS into different topics of x-ray spectrometry, like the quantitative x-ray flourescence analysis, the theoretical calculations of the mass attenuation coefficients or the shape of characteristic x-rays emitted from low Z thick targets, is also discussed.

Effect of distortion and displacement of potential surfaces on resonance Raman scattering

A general formulation for the resonance Raman scattering cross section which includes the effects of displacements as well as distortions of the potential energy surfaces is developed. The resonance Raman spectra are numerically calculated to demonstrate the effect of the distortions.

System–bath relaxation theory approach to nonadiabatic coupling effects on condensed phase electronic absorption spectra

Separation of a many-body system into a primary system plus a bath of background modes enables approximate calculation of electronic absorption spectra and zero-temperature resonance Raman scattering cross sections in cases where there is nonadiabatic coupling between two or more Born–Oppenheimer excited-state potential surfaces. In particular, the low-resolution optical line shape theory recently developed to describe curve-crossing phenomena [D. G. Evans and R. D. Coalson, J. Chem. Phys. 99, 6264 (1993)] is extended to systems where there is a primary nuclear coordinate mode that is characterized by large excited-state displacements and an ensemble of weakly displaced bath modes. The accuracy of the resulting approximation scheme is illustrated using the spectroscopic spin-boson model, in which all surfaces are harmonic, and path integral techniques can be used to obtain exact results. Application to more complicated systems is discussed.

An experimental study of radiation-induced pure dephasing: ArF excited emission of O2

The effects of incoherent incident light on both nonresonant and resonant secondary radiation (RSR) are demonstrated for the spontaneous emission of O2. ArF excimer radiation (FWHH∼120 cm−1) is resonant with several rovibronic features of the v′=4 band of the Schumann–Runge absorption system. Off-resonant contributions to the RSR spectrum are Raman-like (v″=1) but carry the linewidth of the incident incoherent radiation. Purely resonant emission features are found to be entirely fluorescence-like (v″≥6). Other RSR vibrational bands of O2 exhibit contributions of both types of emission including interferences between Raman (off-resonant) and fluorescence (resonant) amplitudes. The observed depolarization ratios also reflect these various emission characters. The RSR spectra of O2 excited by incoherent (ArF) driving fields are contrasted with that due to monochromatic excitation. Convolution of the incident spectral density with a rovibronic Kramers–Heisenberg irreducible tensor treatment of resonance Raman scattering cross sections is shown to capture all the observed RSR emission characteristics.

Pressure-induced resonance Raman scattering in Ga1−xInxAs/Ga1−yAlyAs strained quantum-well structures

Pressure-tuned resonance Raman scattering (RRS) experiments in Ga1−xInxAs/Ga1−yAlyAs strained-layer quantum-well samples with x=0.15 and y=0.15, on a GaAs substrate, are reported. The photoluminescence (PL), 2LO-, and LO-phonon Raman-scattered intensities were followed as a function of pressure using the diamond cell. In backscattering geometry and with (100) samples, three sharply defined 2LO-phonon resonances are observed, at 2.1, 3.8, and 5.2 GPa, with 647.1-nm excitation (ℏωL=1.916 eV), and these are identified to be from the AlGaAs, GaAs, and InGaAs layers, respectively. At the above pressures, the 2LO peak of the layer falls right on top of the PL peak of the corresponding layer, revealing that the resonance occurs when E0=ℏωS (2LO). For the LO-phonon intensity, maxima are observed at 2.8 and 4.7 GPa, respectively, from the AlGaAs layer and GaAs substrate. While the LO-resonance profile (pressure versus phonon intensity) for the AlGaAs layer is narrow, the profile of the GaAs substrate layer is highly asymmetric. The InGaAs LO-resonance is totally masked by the strong GaAs LO phonon. The pressure dependence of the E0 gap, determined from PL data, reveals that the resonance condition for 2LO is E0=ℏωS (2LO) and, for LO, E0=ℏωL. Results with samples of different Al content and ℏωL are consistent with the above conditions. A brief discussion of the theory of the RRS cross section is given, and it is suggested that the observed 2LO-resonance scattering is dominated by Frölich interaction, and that it could be a double resonance. The asymmetry in the LO resonance of the GaAs substrate, we believe, is due to the pressure-induced transparency, and this is a problem when dealing with pressure-tuned RRS, in multiple-quantum-well structure with GaAs or AlGaAs substrates. The usefulness of the 2LO resonance in locating the E0 gap is indicated, and the indistinguishability between luminescence and Raman scattering at the center of the 2LO resonance is pointed out. The need to study photoluminescence and Raman scattering in pressure-tuned RRS experiments is emphasized.

Depolarization ratios of resonance Raman scattering in the gas phase

All three scattering invariants, isotropic, antisymmetric, and anisotropic, contribute to the resonance Raman (RR) activity of randomly oriented gas phase scatterers as shown in a sum-over-all-rovibronic-states approach regardless of the symmetry of the vibrational transition. Thus, in the gas phase, totally symmetric modes may have Raman depolarization ratios (ρ)>3/4 and nontotally symmetric modes may have ρ≠3/4 for resonance excitation frequencies. Large ρ dispersion effects are predicted when the RR scattering cross section is dominated by the contribution of a single vibronic band. The extent of this purely rotational effect sensitively depends on the excitation frequency and the resonant dephasing rate. These depolarization ratio effects are demonstrated by the resonance Raman scattering of CH3I (B state) and NH3, ND3 (A state) for both a and e vibrational bands as well as for J (NH3) and K (CH3I) resolved rovibrational features.

Resonant Raman Scattering of synchrotron X-rays by xenon: Test of angular and polarization dependence of RRS

Using monochromatized synchrotron radiation with variable photon energyEi=33.94keV...34.54keV, Resonant Raman Scattering (RRS) by free Xenon atoms (B1s=34.566keV) was investigated. The measured double-differential RRS cross sections are in excellent agreement with those calculated in the non-relativistic dipole approximation, modified by some relativistic corrections, and including the interference corrections predicted by Tulkki and Aberg. Within the experimental error of 5 % the RRS cross section is found to be independent of the scattering angle and of the polarization of the incident photons.

Resonance Raman scattering from molecules with a nonequilibrium vibronic distribution

Expressions for the differential cross section of the resonance Raman scattering from molecules in which initially prepared nonequilibrium vibronic levels undergo vibrational and/or electronic relaxations are derived by using the generating function method. Two kinds of the initial nonequilibrium vibronic distributions, single vibronic level and Poisson ones are taken into account. A displaced harmonic oscillator model for the initial and resonant vibrational states and a linear vibrational quantum number dependence of the relaxation constants are adopted in deriving the cross sections. Model calculations of the time-resolved resonance Raman scattering cross sections and of the excitation profiles of the nth order Stokes and anti-Stokes Raman bands are performed by using the derived expressions. The results of the calculation indicate that the anti-Stokes Raman bands make a significant contribution to the resonance Raman scattering from the nonequilibrium vibronic distributions. It is suggested that measurements of the excitation profiles are useful for analyzing the nonequilibrium distribution initially prepared and the subsequent relaxation mechanism.

Theory of Time-resolved Resonance Raman Scattering from Vibrationally Hot Molecules

Abstract A theory of time-resolved resonance Raman scattering (RRS) from molecules is developed. The time-resolved RRS cross section is defined as a product of the time-dependent vibronic energy distribution and the scattering cross section from the single vibronic level. The theory is applied to the time-resolved RRS from vibrationally hot molecules whose vibronic distribution characterized by a canonical distribution with temperature higher than that of the heat bath relaxes to the equilibrium one in the presence of a collisional vibrational relaxation. Analytical expressions for the time-resolved RRS cross section are derived within a displaced harmonic oscillator model. It is shown that in the strong coupling case the intensities of the Stokes and anti-Stokes Raman bands in the rigorous resonance case vary inversely as the time-dependent average vibrational occupation number. Some model calculations are performed to illustrate the time-dependent intensity changes of the Raman bands.

Two‐Phonon Resonance Raman Scattering and Quantum Interference Effects in Polar Semiconductors in High Magnetic Fields

AbstractThe EHP contribution to the two‐phonon resonance Raman scattering (RRS) cross‐section is calculated for a polar semiconductor located in a high magnetic field H. This contribution is of order α, where α is the Fröhlich electron (hole)‐LO phonon coupling constant (in the case H = 0 the cross section is of order α2). This α‐dependence results from the quasi one‐dimensional motion of the electron (hole) in a high magnetic field. For such a polar semiconductor as InSb (α ≈ 0.013 ≪ ≪ 1) a high magnetic field leads to a sharp increase of the secondary radiation intensity. The two‐phonon RRS cross section is an oscillating function of the magnetic field H and (or) of the incident light frequency ω1. The oscillations exist due to the increase of the density of states near the Landau zone bottom. It is shown that in the vicinity of a number of values of the magnetic field H = H0/L, where H0 = mecωLO/|e|, (me(e) = effective mass (charge) of electron, L = 1/2, 1, 3/2, 2, …, there is a number of additional contributions of interferential character to the cross section, which lead to a resonance decrease of the secondary emission intensity.

Resonant Raman Scattering of synchrotron X-rays by neodymium: Observation of fine structure in K-L-RRS and of K-N-RRS

Using monochromatized synchrotron radiation with variable photon energyEi =43.01...43.35 keV, Resonant Raman Scattering (RRS) by Neodymium atoms (K-shell binding energyB1s=43.57 keV) was investigated. For the first time the fine structure splitting in a K-L-RRS spectrum due to the energy difference of the L2 and L3 subshells was observed. In addition, the first observation of K-N-RRS in the spectrum of scattered photons is reported. The measured double-differential RRS cross sections are, on an absolute scale, in very good agreement with those calculated in the non-relativistic dipole approximation, modified by relativistic corrections.