Time-dependent correlations in an inhomogeneous one-component plasma

Sum rules describing perfect screening at equilibrium in a classical plasma are extended to the time-displaced structure function of an inhomogeneous one-component plasma. We find that there are long-wavelength modes which oscillate undamped with a single frequency , being an angular average of the squared plasma frequency at infinity. Our results are derived heuristically, allowing also for quantum effects, from linear response theory, and rigorously from the classical BBGKY hierarchy under some reasonable assumptions on the spatial decay of correlations. Special cases are investigated, in particular plasmas bounded by walls of varied shapes.This laboratory is associated with the CNRS.     

Interior transmission eigenvalue problem with refractive index having C2-transition to the background medium

The interior transmission eigenvalue problem for scalar acoustics is studied for a new class of refractive index. Existence of an infinite discrete set of transmission eigenvalues in the case that the acoustic properties of a domain D???? ⁿ are allowed to have a C ²-transition to the homogeneous background medium is established. It is shown that the transmission problem has a weak formulation on certain weighted Sobolev spaces for this class of refractive index. The weak formulation and the discreteness of the spectrum is justified by using the Hardy inequality to prove compact imbedding theorems. Existence of transmission eigenvalues is demonstrated by investigating a generalized eigenvalue problem associated with the weak formulation.     

Excitation profiles of resonant coherent Raman scattering by impurity molecules

The amplitudes and the excitation profiles of coherent resonant Raman scattering (coherent anti‐Stokes and Stokes Raman scattering (CARS and CSRS)) by impurity centers in crystals and/or molecules in solutions are studied, taking into account the coherence of the excited mode and the inhomogeneity of the environment. The CARS and CSRS excitation profiles can directly be related to one‐photon absorption when using the transform theory known from spontaneous resonant Raman scattering. The enlargement of the amplitude of the active mode reveals itself in an enhancement of the vibrational overtones. At large amplitudes, a splitting in the profiles caused by the contribution of two turning points of a strong coherent vibration is observed. The inhomogeneous broadening is different in the excitation profiles of CARS and CSRS. The overlapping contributions to spectrally narrow and broad transitions lead to Fano peculiarities. The effects are illustrated by model calculations. Copyright © 2011 John Wiley & Sons, Ltd.     

Relation between the Slater–Kohn–Sham orbitals generated by the one-body potential V(r) of DFT and the Löwdin natural orbitals for inhomogeneous electron liquids

The Löwdin natural orbitals (NO) are defined as those orbitals which bring the first-order density matrix of a correlated electron assembly into diagonal form. Another one-particle density matrix with the same diagonal elements is the single-particle idempotent Dirac density matrix generated by the one-body potential of density functional theory. Here, we compare the off diagonal form of γ expanded in terms of the Slater–Kohn–Sham (SKS) orbitals generated by V(r) with the NO expansion of Löwdin for general inhomogeneous electron liquids. In particular, the equation of motion of the correlated γ is corrected from that of γ _s , both now containing the one-body potential V(r). To illustrate the theory presented here, we first construct an approximate, albeit accurate, correlated 1DM for the ground state of the He atom and display connections between the resulting NOs and the SKS orbitals. The second example we discuss, but now quite briefly, is that of the inhomogeneous electron liquid in crystalline Si, where the NO expansion is available from the literature.     

一类三对角矩阵任意正整数幂的计算

给出一类带有一个零行或两个零行的三对角矩阵的任意正整数幂的一般表达式.本文所用的方法较Leonaite和Rimas的方法简单,而结果既简洁又更具一般性.     

Use of the Richardson extrapolation in optics of inhomogeneous layers: Application to optical characterization

A new approach to calculation of optical quantities of inhomogeneous layers is presented. In this approach, the Richardson extrapolation is used to improve the accuracy of the method, in which the inhomogeneous layer is approximated by a stack of thin homogeneous layers. The results presented in this paper are based on the assumption that the media are isotropic and the inhomogeneity is along the axis normal to the boundary. The results obtained by the new method are compared with those obtained without the Richardson extrapolation. The Richardson extrapolation brings significant improvement in accuracy, especially if the number of approximating layers is large. Moreover, the method using the Richardson extrapolation proceeds in steps with an error estimate available in each step; thus, the calculation can be stopped when the desired accuracy is reached. The use of the method is illustrated by means of the optical characterization of strongly inhomogeneous film of non‐stoichiometric silicon nitride.     

Inhomogeneous electron liquid in the free-space building block Li2C2 plus its dimer and trimer

Quantum-chemical calculations are first reported on the building block Li₂C₂. Two low-lying isomers are predicted, and hence the equilibrium ground-state geometry by the coupled cluster method (CCSD). The ground-state is non-linear, contrasting with the other planar isomer. The dimer (Li₂C₂)₂ is then examined by the Hartree–Fock plus second-order Møller–Plesset (HF+MP2) method. The ground-state geometry is predicted to have C₄ on a linear chain. As to the trimer, the C₆ atoms are predicted at the same ab initio level to lie on a hexagon. But the Li atoms prefer each to bond to two C atoms, rather than reproduce the geometry of benzene. Finally, some contact is made with a recent density functional theory study of solid lithium carbide under pressure.     

Ellipsometric characterization of inhomogeneous non‐stoichiometric silicon nitride films

Variable‐angle spectroscopic ellipsometry is employed for the optical characterization of non‐stoichiometric silicon nitride thin films exhibiting inhomogeneity formed by refractive index and extinction index changes through the film thickness. For all the film samples, the best fit of the experimental data is achieved if, in addition to the inhomogeneity, an overlayer or roughness of the upper boundary is included. However, distinguishing of these two defects is found not to be possible. The influence of working gas ratio, deposition temperature and on/off time on the film properties is studied. The refractive index and extinction coefficient is found to increase with increasing working gas ratio and less significantly with decreasing deposition temperature. It is also found that the inhomogeneity increases with decreasing deposition temperature, and the deposition rate of the films decreases with increasing working gas ratio. The influence of the on/off time on the film properties is practically unimportant. Copyright © 2013 John Wiley & Sons, Ltd.     

Modeling absorption spectra of molecules in solution

The presence of solvent tunes many properties of a molecule, such as its ground and excited state geometry, dipole moment, excitation energy, and absorption spectrum. Because the energy of the system will vary depending on the solvent configuration, explicit solute–solvent interactions are key to understanding solution-phase reactivity and spectroscopy, simulating accurate inhomogeneous broadening, and predicting absorption spectra. In this tutorial review, we give an overview of factors to consider when modeling excited states of molecules interacting with explicit solvent. We provide practical guidelines for sampling solute–solvent configurations, choosing a solvent model, performing the excited state electronic structure calculations, and computing spectral lineshapes. We also present our recent results combining the vertical excitation energies computed from an ensemble of solute–solvent configurations with the vibronic spectra obtained from a small number of frozen solvent configurations, resulting in improved simulation of absorption spectra for molecules in solution.