Light scattering by anisotropic elliptical objects

The small-angle light scattering in H_v and V_v modes is calculated for elliptical disks with the use of an elliptical coordinate system. The method is general for all degrees of ellipticity, from a circular disk to rodlike extensions, and permits the definition of any desired dipole orientations. The solution is obtained by computer-assisted numeric integration. Two models are considered, an “elliptical” one an “affine deformation” one differing in the orientation of scattering dipoles. The calculated patterns show a significant dependence of the distribution of the scattered intensity on the size and the elliptical axial ratio in both models, permitting the determination of both the size and the degree of ellipticity of the disk from its patterns. In addition, the differences between the calculated results for the two models are sufficiently large to permit the selection of the experimentally appropriate model, at least within the range of moderate degree of ellipticity.     

Frequency-frequency correlation functions and apodization in two-dimensional infrared vibrational echo spectroscopy: a new approach

Ultrafast two-dimensional infrared (2D-IR) vibrational echo spectroscopy can probe structural dynamics under thermal equilibrium conditions on time scales ranging from femtoseconds to approximately 100 ps and longer. One of the important uses of 2D-IR spectroscopy is to monitor the dynamical evolution of a molecular system by reporting the time dependent frequency fluctuations of an ensemble of vibrational probes. The vibrational frequency-frequency correlation function (FFCF) is the connection between the experimental observables and the microscopic molecular dynamics and is thus the central object of interest in studying dynamics with 2D-IR vibrational echo spectroscopy. A new observable is presented that greatly simplifies the extraction of the FFCF from experimental data. The observable is the inverse of the center line slope (CLS) of the 2D spectrum. The CLS is the inverse of the slope of the line that connects the maxima of the peaks of a series of cuts through the 2D spectrum that are parallel to the frequency axis associated with the first electric field-matter interaction. The CLS varies from a maximum of 1 to 0 as spectral diffusion proceeds. It is shown analytically to second order in time that the CLS is the T(w) (time between pulses 2 and 3) dependent part of the FFCF. The procedure to extract the FFCF from the CLS is described, and it is shown that the T(w) independent homogeneous contribution to the FFCF can also be recovered to yield the full FFCF. The method is demonstrated by extracting FFCFs from families of calculated 2D-IR spectra and the linear absorption spectra produced from known FFCFs. Sources and magnitudes of errors in the procedure are quantified, and it is shown that in most circumstances, they are negligible. It is also demonstrated that the CLS is essentially unaffected by Fourier filtering methods (apodization), which can significantly increase the efficiency of data acquisition and spectral resolution, when the apodization is applied along the axis used for obtaining the CLS and is symmetrical about tau=0. The CLS is also unchanged by finite pulse durations that broaden 2D spectra.     

Probing dynamics of complex molecular systems with ultrafast 2D IR vibrational echo spectroscopy

Ultrafast 2D IR vibrational echo spectroscopy is described and a number of experimental examples are given. Details of the experimental method including the pulse sequence, heterodyne detection, and determination of the absorptive component of the 2D spectrum are outlined. As an initial example, the 2D spectrum of the stretching mode of CO bound to the protein myoglobin (MbCO) is presented. The time dependence of the 2D spectrum of MbCO, which is caused by protein structural evolution, is presented and its relationship to the frequency-frequency correlation function is described and used to make protein structural assignments based on comparisons to molecular dynamics simulations. The 2D vibrational echo experiments on the protein horseradish peroxidase are presented. The time dependence of the 2D spectra of the enzyme in the free form and with a substrate bound at the active site are compared and used to examine the influence of substrate binding on the protein's structural dynamics. The application of 2D vibrational echo spectroscopy to the study of chemical exchange under thermal equilibrium conditions is described. 2D vibrational echo chemical exchange spectroscopy is applied to the study of formation and dissociation of organic solute-solvent complexes and to the isomerization around a carbon-carbon single bond of an ethane derivative.     

Kβ X-ray emission spectroscopy offers unique chemical bonding insights: revisiting the electronic structure of ferrocene

Kβ X-ray emission spectroscopy (XES) is emerging as a powerful tool for the study of chemical bonding. Analyses of the Kβ XES of ferrocene (Fc) and ferrocenium (Fc(+)) are presented as further demonstrations of the capabilities of the technique. Assignments of the valence to core (V2C) region of these spectra as electric dipole-allowed cyclopentadienyl (Cp) → Fe 1s transitions demonstrate that XES affords electronic structural insight into the energetics of ligand-based molecular orbitals (MOs). Combined with K-edge X-ray absorption spectroscopy (XAS), we show that XES can provide analogous information to photoemission spectroscopy (PES). Density functional theory (DFT) analyses reveal that the V2C transitions in Fc/Fc(+) derive their intensity from Fe 4p admixture (on the order of 5-10%) into the Cp-based MOs from which they originate. These 4p admixtures confer bonding character to the Cp-based a(2u) and e(1u) MOs to at least the extent of backbonding contributions to frontier MOs from higher-lying Cp π* MOs.     

Proton dynamics in hydrogen-bonded systems

The proton mean kinetic energy Ke(H) in various systems was calculated between 5 and 320 K using a semi-empirical (SE) approach. The SE calculation relies on the harmonic approximation and decoupling between the various modes, where the input data of the internal and external frequencies were taken from inelastic neutron scattering (INS) and IR/Raman experiments. The studied systems included ordinary H₂O phases, water of crystallisation in sulphate salts, adsorbed water and water confined in various samples of pore dimensions less than 20 Å. These included some zeolites, periodic mesoporous organosilicas (PMOs), beryl, Bikitaite and single- and double-wall carbon nanotubes. All SE calculated Ke(H) values were close to that of pure ice/liquid water, for which a good agreement was found with the deep inelastic neutron scattering (DINS) measurements. However, for water in Beryl at 5 K and ice in carbon nanotubes, at 170 K, large deviations from DINS results were found. Some insight into this problem may be gained by comparing those deviations with recently studied anharmonic systems involving proton double well potentials: Rb₃H(SO₄)₂ and KH₂PO₄, where an excellent agreement was obtained between SE calculations and DINS measurements.     

Estimation of trace elements in some medicinal plants used in anti‐cancer drugs by PIXE

A trace elemental analysis was carried out in various parts of 12 anticancer medicinal plants, using the PIXE (particle‐induced X‐ray emission) technique. A 3‐MeV proton beam was used to excite the samples, and spectra were recorded using a Si (Li) detector. Data analysis was done using the GUPIX software. The elements Cl, K, Ca, Ti, V, Mn, Fe, Ni, Cu, Zn, Br and Sr were identified, and their concentrations estimated. The results of the present study provide justification for the usage of these medicinal plants in the development of anticancer drugs. Copyright © 2012 John Wiley & Sons, Ltd.     

Comment to “Dynamics of supercooled confined water measured by deep inelastic neutron scattering”

We comment on the findings of “Dynamics of supercooled confined water measured by deep inelastic neutron scattering”, by V. De Michele, G. Romanelli, and A. Cupane [Front. Phys. 13, 138205 (2018)]. We show that the current sensitivity of the deep inelastic neutron scattering (DINS) method, cannot detect with confidence small differences in the proton kinetic energy, Ke(H), involved in a liquid-liquid transition in supercooled water confined in nanoporous silica. We also critisize the calculation of Ke(H) carried out in Front. Phys. 13, 138205 (2018).     

Convergence in law of random sums with non-random centering

We extend results obtained in Kruglov,⁽⁷⁾ and Finkelstein and Tucker⁽³⁾ to obtain necessary and sufficient conditions for convergence in law of random sums of non-identically distributed independent random variables under non-random centering. Thei.i.d. case is also considered for random variables attracted to a stable law. Necessary and sufficient conditions for convergence in law of these random variables under non-random centering, and in some cases, under non-random norming, are also obtained. The distribution functions for the limit laws are determined as well, generalizing results of Robbins.⁽¹⁰⁾ Supported in part by The State University of New York and United States Information Agency Grant No. IA AEMP69193692.     

Mechanism of protein folding

The first stage of protein self-organization—the formation of a fluctuating secondary structure in the unfolded protein chain—is considered. The stereochemical theory is presented enabling one to calculate helix-coil and β-structure-coil equilibrium constants. It is shown that the most probable localization of fluctuating α- and β-structure in the unfolded protein chain corresponds to the native localization of these structures. The formation of large α- and β-structural blocks is observed, each of them including several native α-helices or β-strands.