Monte Carlo calculation of angular transmission functions for small angle scattering

We define an angular transmission function η in the center of mass system. The convolution of the differential cross section σ with η yields the signal in the laboratory system. For the case of elastic small angle scattering by spherically symmetric potentials we calculate η by a Monte Carlo method. Random positions are taken in the beam defining collimators, resulting in a trajectory with a deflection angle at the scattering centre. These deflection angles are transformed to the c.m. system with the small angle tranformation formulae. From the distribution we calculate η as a histogram and the central moments of η. The function η depends on the velocity ratio and on the mass ratio of the scattering partners. We store the results in such a way that the central moments can be calculated afterwards for all mass and velocity ratios. By using the central moments the convolution integral can be reduced to a simple weighted sum of σ-values at different scattering angles. The r.m.s. deviations of the central moments scale with N^{$\text{1}\text{2}$}, with N the number of Monte Carlo trajectories. A typical deviation is 1% in the second order moment for N = 2 × 10⁴, increasing slightly with increasing order of the moments. This method of calculation gives a large degree of freedom for optimisation of the collimation geometry. The use of an angular transmission function defined in the center of mass system gives a good insight in the experimental reflection of the physical events. As an example we apply the method to the case of small angle scattering of Ar as a primary beam by Kr as a secondary beam and the inverse configuration of Kr by Ar.     

The three-body correlation spectral moments in depolarized interaction-induced light scattering of H2 at 297 K

The three-body correlation spectral moments of depolarized interaction-induced light scattering have been measured in normal H₂ at 297 K by means of an analysis of the density behaviour of the spectra between 10 and 300 cm⁻¹. Comparison with classical calculation shows a major discrepancy for the second moment which is attributed to the anisotropic properties of the interacting molecules.     

Elastic forward scattering of high-energy electrons and molecular electron density

The elastic forward scattering of high-energy electrons from molecules has been studied in the second Born approximation. An integral transformation has been adopted to evaluate the second Born integrals analytically without explicit use of molecular wave functions. In the high-energy limit, the differential cross section for the forward scattering is expressed in terms of electric dipole and quadrupole moments, the second moment of charge distribution with respect to the molecular center, and transition dipole moments. All these quantities are shown to be computable from molecular electron densities in the ground state.     

Quantum sum formulae for the collision-induced spectroscopies: Molecular systems as H2-H2

Quantum expressions for the second moment of collision-induced spectra are developed in the low-density limit. Previous work by Moraldi is extended to account for the rotational structure of colliding linear molecules; isotropic interaction is assumed. Computations of the lowest three moments are presented for the case of infrared absorption and Raman scattering of molecular hydrogen pairs at temperatures from 77 to 300 K. The radial distribution functions of pairs, mean energy and angular momentum, which are required for that purpose, are obtained for the case of H₂ molecules interacting with H₂, and compared with their classical counterparts. The simple classical approximations with lowest-order Wigner-Kirkwood quantum corrections serve as an accurate representation of the quantum expressions at large separations and may be sufficient for massive systems at high temperatures.     

Preface

The anisotropic rototranslational scattering spectra of nitrogen gas at high frequency up to 700 cm⁻¹ for several temperatures and from low densities are analyzed in terms of new site–site (M3SV) intermolecular potential and interaction-induced pair polarizability models, using quantum spectral shapes computations. Our theoretical calculations take into account multipole contributions from the mean value and anisotropy of the dipole–dipole polarizability tensor α, two independent components of the dipole–octopole polarizability tensor E and dipole–dipole–quadrupole hyperpolarizability tensor B. The high-frequency wings are discussed in terms of the collision-induced rotational Rayleigh effect and estimates for the dipole–octopole polarizability |E₄| are obtained and checked with recent ab initio theoretical value. Good comparison is found in the frequency range 0–400 cm⁻¹ between the theoretical and experimental spectra. When an exponential contribution [exp(−ν/ν₀)] with ν₀ = 425 cm⁻¹ is considered to model very short-range light scattering mechanisms at room temperature, good agreement is found over the whole frequency range.     

Molecular orbital studies on some 4-substituted pyridine N-oxides and 4-nitroquinoline N-oxide

The electronic structures of a series of 4-substituted pyridine N-oxides and 4-nitroquinoline N-oxide are investigated using the simple Pariser-Parr-Pople (PPP), a modified PPP, IEH and MINDO/2 methods. The electronic absorption band maxima and dipole moments are calculated and compared with experimental values. The photoelectron spectra of these compounds are assigned. The nature of the N-oxide group is characterized using the orbital population distributions. The antifungal activity exhibited by some of these compounds is discussed in terms of the nucleophilic frontier electron densities, superdelocalizabilities and electron acceptor properties. The effect of the electron releasing as well as the electron withdrawing substituents on the physico-chemical properties is explained.     

Microwave spectrum,structure, dipole moment and internal rotation of ethyl fluorosilane

Microwave spectra of the trans and gauche isomers of ethyl fluorosilane and their eleven isotopically substituted species have been measured. The r_s structures of the two isomers were determined from the observed moments of inertia. The molecular structures found for the two isomers in the present study are compared with those of analogous molecules. Dipole moments of the two isomers were determined by Stark-effect measurements and are also compared with those of analogous molecules. The energy difference between the trans and gauche isomers was obtained from the relative intensity measurements of the spectra and the barrier to internal rotation of the methyl group for the gauche isomer was obtained from the A—E splittings of the spectra in the first excited methyl torsional state. The V₃ value was 2775 ± 25 cal mol^?1.     

Surface-enhanced resonance Raman scattering spectra of tetrakis(4-N-methylpyridyl)porphine adsorbed on Ag colloids

The surface-enhanced resonance Raman scattering (SERRS) spectra of tetrakis(4-N-methylpyridyl)porphine (TMPyP(4)) adsorbed on Ag colloids were measured and compared with the resonance Raman scattering (RRS) spectra of TMPyP(4). The surface spectra evidenced the conversion of the adsorbed porphine to Ag(II)TMPyP(4) at pH 7.4 and a conformational change of the adsorbate pH 3.1.     

An investigation of vibrational exciton bands in solid nitrous oxide

Infrared spectra of N₂O crystals containing dilute to isotopic impurities are reported. Information on the second moments and other properties of the vibrational exciton bands has been determined from an analysis of the impurity modes, the LOTO splittings, and a comparison of the transition dipole moments of N₂O with those of CO₂. The effect of the random sense of the molecules on the spectra is discussed.     

Ab initio study of the conformations of chloromethyl formate and fluoromethyl formate

Ab initio calculations are reported for the conformational potential energy surfaces of chloromethyl formate and fluoromethyl formate at minimal basis set level. The halomethyl group is shown to lie Z to the carbonyl group. A plateau on the potential energy surface demonstrates that the halomethyl group can rotate freely. The halogen atom therefore moves from an antiperiplanar (ap) to a synclinal (sp) position with respect to the carbonyl group. The effects on IR spectra and dipole moments are discussed.     

Azulene: polarized absorption in stretched polymers and magnetic circular dichroism

Linear dichroic and magnetic circular dichroic spectroscopy is used to characterize the excited states of azulene. Comparison with crystal spectra underlines the necessity of using two-parameter equations for evaluations of stretched sheet spectra despite some previous claims to the contrary. The MCD spectrum reveals strong vibronic interactions in the second transition.The results are interpreted on the basis of Pariser—Parr—Pople (PPP) type calculations including some with extensive configuration interaction (CI). Calculated signs of the first three B terms spectrum agree with experimental signs irrespective of the details of the PPP model, and even the numerical values are in an order-of-magnitude agreement. Only the calculation with extensive CI gives agreement for signs of higher B terms. It suggest the possible presence of two excited states, but the present experimental evidence for these is insufficient. One of these new states would be best described as a predominantly doubly excited state.The origin of the B terms is traced to contributions due to magnetic mixing of individual zero-order excited states and the results permit determination of the absolute sense of magnetic dipole transition moments between excited states with respect to the sense of the vector product of the electronic dipole transition moments from the ground state to these excited states. A comparison is performed with B terms calculated using finite perturbation technique and gauge-invariant orbitals.     

A dipole moment study of the structures of some ketene acetals

The dipole moments of several acyclic and cyclic ketene acetals have been determined in benzene solution at 293 K using the Halverstadt-Kumler method. For ketene dialkyl acetals (alkyl = Me, Et) the results point to a predominance of the s-cis,s-trans retamer, which disagrees with the conclusions drawn previously from ¹³C NMR chemical shift data, i.e. the s-cis,s-cis form is the more stable species. In the case of 2-methoxyfuran, the dipole moment measurements confirm the previous findings based on the ¹³C NMR spectra, viz the s-cis form is the predominating rotamer. The dipole moments and structures of some other ketene acetals are also discussed.     

X-ray spectra and electronic structure of several ternary chalcogenides and their solid solutions

The electronic energy structure of substitution solid solutions CuGa(S_xSe_1−x)₂ is studied within wide limits of sulfur concentration x in the onion sublattice. The SK absorption spectrum is calculated for CuGaS₂ in a high-order multiple scattering approximation using the FEFF7 program. For all concentrations x, partial densities of states are calculated in a full multiple scattering approximation by the local coherent potential method. The calculation schemes for the filled and vacant states are employed, which differ in a choice of the crystalline potential. The effect of a vacancy on the SK level on the density of the free Sp states is considered. The theoretical K absorption spectra and densities of states of CuGaS₂ are compared with the experimental X-ray and X-ray photoelectron spectra. The calculated curves are in good agreement with the experiment. It is established that the densities of the S and Se p states change smoothly with varying concentration of anions. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 6, pp. 1076–1082, November–December, 1998.     

Vibrational relaxation in the group IVA trimethylmetal chlorides

The temperature dependence of the polarized and depolarized Raman spectra of the ν₂, ν₄, ν₆ and ν₇ modes were measured for t-butyl chloride and the analogous group IVA trimethylmetal chrlorides (silicon, germanium and tin). Analysis of the lineshapes revealed that isotropic second moments and vibrational relaxation times for a given mode remained approximately constant through the series. This tranferability of relaxation parameters between molecules extended to modulation times calculated from the Kubo formalism. The above results are in contrast to earlier studies on molecules of dissimilar structure. They provide some preliminary evidence that the mechanism of vibrational relaxation may be the same for equivalent modes in members of the series.     

Theoretical study on contribution of charge transfer effect to surface-enhanced Raman scattering spectra of pyridine adsorbed on Ag(n) (n = 2-8) clusters

We investigate surface-enhanced Raman scattering (SERS) spectra of pyridine–Ag_n (n = 2–8) complexes by density functional theory (DFT) and time-dependent DFT (TDDFT) methods. In simulated normal Raman scattering (NRS) spectra, profiles of pyridine–Ag_n (n = 2–8) complexes are analogical with that of isolated pyridine. Nevertheless, calculated pre-SERS spectra are strongly dependent on electronic transition states of new complexes. Wavelengths at 335 nm, 394.8 nm, 316.9 nm and 342.6 nm, which are nearly resonant with pure charge transfer excitation states, are adopted as incident light when simulating pre-SERS spectra for pyridine–Ag_n (n = 2–8) complexes, respectively. We obtain enhancement factors from 10³ to 10⁵ in pre-SERS spectra compared with corresponding NRS spectra. The obvious increase in Raman intensities mainly result from charge transfer resonance Raman enhancement. A charge difference densities (CDDs) methodology is adopted in describing chemical enhancement mechanism. This methodology aims at visualizing charge transfer from Ag_n (n = 2–8) clusters to pyridine on resonant electronic transition, which is one of the most direct evidences for chemical enhancement mechanism.     

Regularity modes in Raman spectra of polyolefins: Part II. Polyethylene and ethylene copolymers

In this work, the thermal behavior of the regularity modes in Raman spectra of polyethylene with different densities and random ethylene/1-hexene copolymers with varying content of comonomer are studied. We demonstrate especially that the vibrational modes at 1062 and 2850 cm^↙1 are related to a critical sequence length of trans-conformers of 6⬜8 CH₂ groups, while the modes at 1130, 1170, 1295, and 2883 cm^↙1 indicate a critical sequence length of trans-conformers of 18 CH₂ groups. Upon increasing the 1-hexene content in the ethylene/1-hexene copolymers, the evolution of the intensities of the Raman modes at 1062, 1130, 1170, 1295, and 1417 cm^↙1, normalized to the intensity of the band at 2850 cm^↙1, is similar to the evolution of the intensities of the same modes in the Raman spectra of low density polyethylene at increasing temperature. This observation however contrasts with that in the Raman spectra of polyethylenes with middle and high densities. We suppose that these results can be explained by similarities in the structure of non-crystalline areas of low density polyethylene and the ethylene/1-hexene copolymers, which contain significant amounts of short sequences of trans-conformers.     

Bichromophoric hemicyanine dyes as fluorescence probes applied for monitoring of the photochemically initiated polymerization

The spectroscopic properties of series homodimmeric hemicyanine dyes based on (p-N,N-dimethylaminostyryl)benzothiazolium, (p-N,N-dimethylaminostyryl)benzoxazolium, (p-N,N-dimethylaminostyryl)-2,3,3-trimethyl-3H-indolium residues were determined. The absorption and fluorescence spectra of the dyes under study were measured in different polarity solvents at room temperature. On the basis of the solvatochromic behavior the ground state (μ_g) and excited state (μ_e) dipole moments of bis-(N,N-dimethylaminostyryl) derivatives were evaluated. The dipole moments (μ_g and μ_e) were estimated from solvatochromic shifts of absorption and fluorescence spectra as function of dielectric constant (ε) and refractive index (n) of applied solvents. The absorption and fluorescence spectra are only slightly affected by the solvent polarity. The analysis of solvatochromic behavior of the fluorescence spectra as a function of Δf (ε, n) revealed that the emission occurs from a high polarity excited state. The large dipole moment changes along with the red-shifted fluorescence, as the solvent polarity is increased, demonstrates the formation of an intramolecular charge transfer state (ICT). Six bichromophoric hemicyanine dyes, possessing benzothiazole, benzoxazole or indolinium group linked by 5 or 10 methylene groups were evaluated as fluorescence probes applied for monitoring of the polymerization process. The study on the changes in fluorescence intensity and spectroscopic shift of studied compounds were carried out during photochemically initiated polymerization of 2-ethyl-2-(hydroxymethyl)-propane-1,3-diol triacrylate (TMPTA).     

Second-sphere coordination in non-spherical anion binding: Synthesis, characterization and X-ray structure of cis-diazidobis(ethylenediamine)cobalt(III) 2-chloro,5-nitrobenzenesulphonate monohydrate

The dipole, quadrupole, and other second moments have been determined at the equilibrium structures of the halogen azides, isocyanates, and isothiocyanates, for both principal axes and inertial axes. The theoretical procedures used are Möller–Plesset (MP2) and DFT (B3LYP) methodologies, with TZVP and cc-pVTZ basis sets. There is systematic variation in the calculated directions of the dipole moments in the present series, where B3LYP and MP2 methodologies show differences up to ∼20° for the directions. This discrepancy is largest in ClN₃, but quite significant for several other compounds, such as XNCO (where X = Cl, Br and I). The dipole moments of the compounds rotate through a wide angle, as the halogen changes; in contrast, the axes of the second moments rotate to a much smaller degree. The properties are compared with the limited microwave spectral data so far available, in the hope that the present study will encourage further experimental study. There is an urgent need for new experimental data on the dipole moment a,b-components for these compounds.     

Electron energy structure and X-ray spectra of wide-band GaN, AlN, and AlN-GaN semiconductors

The electronic energy structure of GaN, AlN, and AlGaN crystals with the wurzite structure is calculated by the local coherent potential method using the cluster version of the MT-approximation within the framework of the multiple scattering theory. The calculated densities of electron states are compared with XPS spectra of gallium and aluminum, AlL _{II, III} XES, and also with K-spectra of gallium and AlL _{II, III} XAFS absorption. The comparison of the electronic structure of Al_xGa_1?x N crystals and binary GaN and AlN and the interpretation of their features are performed. The concentration dependence of the width of the upper subband of the valence band and the band gap in Al_xGa_1?x N (x = 0, 0.25, 0.5, 0.75, 1) crystals on the content of aluminum is studied and its non-linear character shown.     

Observation of transient resonance raman spectra of the S1 state of trans-stilbene

Transient resonance Raman spectra of trans-stilbene in n-hexane have been obtained using two pulsed lasers at 266 and 585 nm. The former was used to pump the molecule to the first excited singlet state (S₁) and the latter to proble spontaneous Raman scattering in resonance with the S_n ← S₁ electronic transition. The dependence of the pump and probe laser power, the temporal behavior, and the excitation profile of the spectra clearly indicate that they are due to the S₁ state of trans-stilbene.