Theory of the resonance electronic Raman effect

The behaviour of electronic Raman scattering, excited under resonance conditions, is discussed in relation to molecular properties of the ground electronic state, the resonant excited state and the final electronic state. It is shown how the intensity distribution within vibronically structured electronic Raman bands depends on differences of molecular geometry and force field between these states.     

A survey of symmetry point groups and characters of its irreducible representations

In this paper the character tables of irreducible representations of discrete symmetry point groups of general order are arranged.     

The roles of vibronic coupling and the Duschinsky effect in resonance Raman scattering

In most vibronic treatments of resonance Raman scattering it is assumed that the normal coordinates of electronically excited states are not rotated relative to those of the ground state, i.e., the Duschinsky effect is neglected. In the present paper this assumption is critically examined for the case of resonance Raman scattering by a non-totally symmetric vibrational mode. For consistency also the second-order Herzberg-Teller coupling is considered. It is shown that these second-order couplings introduce asymmetry in the excitation profile of appearance similar to that due to nonadiabatic coupling. Also it is shown that even small rotations give rise to noticeable effects in the polarization dispersion curve. Analytical formulas for the Franck-Condon factors and for the Raman tensor (valid for an arbitrary number of normal modes) for the case of small rotations are given, and illustrative calculations of excitation and polarization dispersion curves for a two mode system are presented and discussed.     

Determination of the electro-optic contribution to the Raman scattering tensor of InPS4

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 52, No. 1, pp. 147–150, January, 1990.     

可循环表面增强拉曼光谱基底的制备及其应用

以氨基硅烷为偶联剂,硅酸钠为硅源,合成了一种以金为核,二氧化硅为壳的核壳纳米粒子。通过调节硅酸钠的量,反应温度和反应时间控制二氧化硅壳层厚度,获得理想的表面增强效应。通过研究表面增强拉曼光谱(SERS)信号强度和二氧化硅层厚度之间的关系优化基底的制备条件。采用对巯基苯和联吡啶作为探针分子进行SERS实验,在一定浓度范围内得到SERS信号强度和浓度的对数之间的线性关系,实验结果表明此组装有Au@SiO2的ITO基底作为可循环利用基底可定量分析吸附物种的浓度。     

The rotational resonance Raman spectrum of nitrogen dioxide and the determination of electronic state symmetry from resonance Raman selection rules

The pure rotational Raman spectrum of nitrogen dioxide has been observed and shown to be consistent with existing determinations of molecular parameters. Upon observation at 600 Torr pressure and 0.4 cm⁻¹ resolution a well-defined rotational spectrum is obtained. This spectrum is overlaid with a number of fluorescence lines. The fluorescence lines are separated from the Raman spectrum by a comparison of Stokes and anti-Stokes branches of the rotational spectrum. Out of seven strong fluorescence lines seen with 5145 Å excitation, five probably are identifiable with vibration-rotation fluorescence progressions observed by Abe.The most striking feature of these observations is the potential use of the resonance Raman effect for the analysis of complicated electronic spectra. When this rotational spectrum is observed with excitation by 5309 Å or 5145 Å excitation, the Raman spectrum follows a-axis selection rules and the Q-branches are in the noise level or barely out of it. However, at 4880 Å the ΔK = 2Q-branches become a major feature of a spectrum, indicating that an appreciable part of the absorption at this wavelength is occurring through the operation of b- or c-axis selection rules. These findings are consistent with present notions of a ²B₂ excited state dominating absorption at longer wavelengths, while at shorter wavelengths a ²B₁ excited state becomes important. Given a tunable laser, one could map the relative importance of these two possible selection rules for NO₂ without any theoretical analysis more sophisticated than that presented in this paper.A simplified statement of the selection rules for resonance rotational Raman spectra of asymmetric tops has been developed in the course of this investigation. No attempt has been made to refine the rotational parameters of NO₂ since all of the lines seen areunresolved multiplets. Our data should be regarded as a search spectrum preliminary to investigation on a high resolution instrument.     

Conditions for the existence of double resonance effects in Raman scattering

The condition for the existence of Double Resonance effects in Raman scattering are analyzed. It is shown that the existence of points in the electronic momentum space for which both denominators in the expression for Raman scattering vanish is not sufficient. Based on this analysis, it is shown that double resonance effects cannot show up in Resonant Raman scattering in the vicinity of the E₁ point in InSb.     

Combined dielectric and plasmon resonance for giant enhancement of Raman scattering

Combined dielectric/metal resonators for colossal enhancement of inelastic light scattering are developed and their properties are investigated. It is shown that a record enhancement factor of 2 × 10⁸ can be obtained using these structures. The dielectric resonators are fabricated on Si/SiO₂ substrates where periodic arrays of square 10- to 200-nm-high dielectric pillars are produced via electron-beam lithography and plasma etching. The lateral size a of the pillars varies between 50 and 1500 nm, and their period in the array is 2a. To make a combined dielectric/metal resonator, a nanostructured layer of silver is deposited onto the fabricated periodic dielectric structure by thermal evaporation. It is established that, for a fixed height of the dielectric pillars, the Raman scattering enhancement factor experiences pronounced oscillations as a function of the period (and size) of the pillars. It is shown that these oscillations are determined by the modes of the dielectric resonator and governed by the relation between the excitation laser wavelength and the planar size of the dielectric pillars.     

Raman tensor analysis of hexagonal polyoxymethylene and its application to study the molecular arrangement in highly crystalline electrospun nanofibers

The orientation dependence in space of Raman‐active vibrations in the hexagonal structure of polyoxymethylene (POM) is discussed in terms of Raman tensor elements as intrinsic physical parameters of the lattice. The variation of polarized intensity for the A₁ and the E₁ vibrational modes with respect to the POM molecular orientation is systematically studied, from both theoretical and experimental viewpoints, according to the symmetry assignments of each vibrational mode. A set of working equations including the Raman selection rules associated with the A₁ and the E₁ modes and the orientation distribution function are explicitly formulated and validated by means of a least‐square fitting procedure on experimental data. In addition, an approach based on the introduction of orientation distribution functions is applied to quantitatively assess and compare on a statistical base the molecular orientation of two different types of electrospun POM nanofibers. Copyright © 2012 John Wiley & Sons, Ltd.     

Comparative determination of absolute Raman scattering efficiencies and application to GaN

Absolute Raman scattering efficiencies for first-order light scattering of optical zone-center phonons were determined for cubic and hexagonal GaN. An improved method for the determination of scattering efficiencies by comparative measurement with a standard substance such as BaF₂ was used to minimize the experimental errors substantially. © 1998 John Wiley & Sons, Ltd.     

An axiomatic approach to the number operator and its application to parastatistics

An axiomatic approach to the number operator based on four physically motivated axioms is developed. A connection between the number operator and some generators on representations of group of all unitary transformations of Hilbert space is shown. In consequence, a new generalization of statistics is clarified. In the finite-dimensional case an example of noncommuting number operator is given.     

The Gelfand-Levitan equation and its application to the scattering of neutrons on protons

The Gelfand-Levitan equation for the kernelP(r, r) (withrr) is formulated and then applied for determining the scattering potential in the scattering of slow neutrons on protons (for the case when the dependence of the nuclear forces on the spins can be neglected and onlys-scattering need be considered). The potentials obtained are the same as the Bargmann ones, found by a different method.

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- P(r, r) ( rr). , ( s- ). , .

     

The nature of the vibronic coupling in a metalloporphyrin and its Raman scattering

It has been shown that a Raman line of a nontotally symmetric vibration (b_1g, b_2g, or a_2g) of a metalloporphyrin (D_4h) can be caused, not only by a vibronic coupling between the first ($\text{A}\text{?}$) and second ($\text{B}\text{?}$) excited electronic states but also by a vibronic coupling within one of the electronic states (let us call the former the QS mechanism and the latter the QQ and/or SS mechanism). A simple formulation has been made for each of those different mechanisms, so that a numerical calculation can be made of the excitation profile of a Raman scattering for a given set of coupling constants and damping factors. Next, the result of an examination is given of the excitation profile of the Raman scatterings of some of the b_1g, b_2g, and a_2g vibrations of nickel octaethylporphyrin and nickel octaethyltetrachloroporphryin. Most of the Raman lines of these nontotally symmetric vibrations show a resonance effect only in the Q-band ($\text{A}\text{?}\text{←}\text{X}\text{?}$) region but not in the Soret-band ($\text{B}\text{?}\text{←}\text{X}\text{?}$) region. On the basis of this fact, it has been suggested that those Raman lines are caused mainly by the QQ mechanism rather than the QS mechanism. The observed vibrational structure of an excitation profile also seems to support this suggestion.     

Synthesis of silver nanowires via electroplating technology and its surface enhanced Raman scattering effect

This very paper is focusing on the preparation of silver nanostructures and the surface enhanced Raman scattering effect of the silver nanostructures produced. Via electroplating technology, silver nanowires and nanoparticles were prepared on silicon wafers. Characterization was performed by X-ray diffraction, scanning electron microscope, transmission electron microscope equipped with X-ray energy dispersion spectroscope and selected area electron diffraction, which reveals that the formation of silver nanostructures depends on the over-potential. The produced silver nanowires are of crystalline FCC structure and grow in 〈0 1 1〉 direction. The growth mechanism has been further discussed. The surface enhanced Raman scattering effect is achieved with the silver nanostructures produced.     

Facile preparation of Au/Ag bimetallic hollow nanospheres and its application in surface-enhanced Raman scattering

In this paper, an Au/Ag bimetallic hollow nanostructure was obtained by using SiO₂ nanospheres as sacrificial templates. The nanostructure was fabricated via a three steps method. SiO₂@Au nanospheres were first synthesized by the layer-by-layer technique, and then they were coated with a layer of Ag particles, finally, the Au/Ag bimetallic hollow nanospheres were obtained by dissolution of the SiO₂ core by exposure in HF solution. Several characterizations, such as transmission electron microscopy (TEM), scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDX) and UV visible absorption spectroscopy were used to investigate the prepared nanostructures. The effectiveness of these Au/Ag bimetallic hollow nanospheres as substrates toward surface-enhanced Raman scattering (SERS) detection was evaluated by using rhodamine 6G (R6G) as a probe molecule. We show that such Au/Ag bimetallic hollow nanospheres structure films which consisting of larger interconnected aggregates are highly desirable as SERS substrates in terms of high Raman intensity enhancement. The Au/Ag bimetallic hollow nanostructured aggregate, interconnected nanostructured aggregate and nanoscale roughness are important factors responsible for this large SERS enhancement ability.     

Optical properties of sub-wavelength dielectric gratings and their application for surface-enhanced Raman scattering

We fabricated and measured the far-field optical properties of a sub-wavelength Si₃N₄ (silicon nitride) two dimensional grating. Frequency-dependent transmission measurements from a white-light source revealed that both transverse magnetic (TM) and transverse electric (TE) modes were excited on the grating. We determined the dispersion relations of the modes by tilting the sample with respect to the incoming light beam and measuring the frequency shift of the absorption features. By comparing to a simple model, we determined the effective refractive index for the TM and TE modes and the geometrical constants for the grating. This information enables gratings with desired optical properties to be designed and fabricated. The application of the sub-wavelength grating for surface-enhanced Raman scattering (SERS) is demonstrated.     

Tip-enhanced Raman scattering: Influence of the tip-surface geometry on optical resonance and enhancement

The tip-sample distance (z) dependence of tip-enhanced Raman scattering (TERS) has been investigated. The intensities of both, the Raman lines and the broad TERS background, exhibit strong decays with increasing z, which are nearly complete within 10 nm withdrawal of the STM tip in z direction. Interestingly, the maximum of the broad Lorentzian-shaped TER background is substantially blue shifted in energy with z. This effect is ascribed to a corresponding blue shift of the energies of localized plasmon modes upon tip retraction. Both experimental results fit very well data of a simple theoretical near-field model.     

The relationship of angle resolved light scattering from surface optical resonances to the surface enhanced Raman effect

For a given mildly rough Ag surface, the angle resolved pattern bears the same shape for elastic light scattering, for Raman scattering from adsorbed pyridine or cyanide, or for the luminescence background. This result suggests that surface enhanced Raman scattering is closely related to topographically related surface optical resonances.