Reference Electron Density Research Articles

A Boltzmann Electron Drift Diffusion Model for Atmospheric Pressure Non-Thermal Plasma Simulations

We introduce a fluid computational model for the numerical simulation of atmospheric pressure dielectric barrier discharge plasmas. Ion and neutral species are treated with an explicit drift diffusion approach. The Boltzmann relation is used to compute the spatial distribution of electrons as a function of the electrostatic potential and the ionic charge density. This technique, widely used to speed up particle and fluid models for low-pressure conditions, poses several numerical challenges for high-pressure conditions and large electric field values typical of applications involving atmospheric-pressure plasmas. We develop a robust algorithm to solve the non-linear electrostatic Poisson problem arising from the Boltzmann electron approach under AC electric fields based on a charge-conserving iterative computation of the reference electric potential and electron density. We simulate a volumetric reactor in dry air, comparing the results yielded by the proposed method with those obtained when the drift diffusion approach is used for all charged species, including electrons. We show that the proposed methodology retains most of the physical information provided by the reference modeling approach while granting a substantial advantage in terms of computation time.

A Proposal for Modification of Plasmaspheric Electron Density Profiles Using Characteristics of Lightning Whistlers

Reconstruction of reliable plasmaspheric electron density profiles is important for understanding physical processes in the plasmasphere. This paper proposes a technique that can be applied to correct the plasmaspheric electron density profiles using ray tracing by scrutinizing dispersion analyses of lightning whistlers. The Global Core Plasma Model and the International Reference Ionosphere were introduced as a reference electron density profile. Modifications of this electron density profile were then proposed to satisfy the dispersion characteristics of lightning whistlers measured by satellites in the plasmasphere. We first introduce two kinds of functions to modify the electron density: constant and linear, the linear function is more adequate. We applied our method to two lightning whistler events on 14 August 2017, measured by the Plasma Wave Experiment/Waveform Capture aboard the Arase satellite, and analyzed the dispersion of the observed lightning whistlers. We show how the density modification affects the delay time of the ray path and satisfies the dispersion characteristics under the appropriate adjustments.

Feasibility of Using Boltzmann Plots to Evaluate the Stark Broadening Parameters of Cu(I) Lines.

A linear Boltzmann plot was constructed using Cu(I) lines of well-known atomic parameters. Aligning other spectral lines to the plot was adopted as a viable way to estimate the most probable values of Stark broadening parameters of Cu(I) lines at 330.79, 359.91, and 360.2 nm. Plasma was generated by focusing neodymium-doped yttrium aluminum garnet (Nd:YAG) laser radiation at wavelength 532 nm on a pure copper target in open air. Plasma emission was recorded at delay times of 3, 4, 5, 7, and 10 μs. The in situ optically thin Hα line was used to determine the plasma reference electron density over the entire experiment. Following this method, the missing values of the Stark broadening parameters of the three Cu(I) lines turn out to be about 0.15 ± 0.05 Å (for 330.79 nm transition) and 0.17 ± 0.05 Å (for 359.91 360.20 nm transition) at reference electron density of (1 ± 0.09) × 1017 cm-3 and temperature of 10 800 ± 630 K. The apparent variation in plasma parameters at different delay times was found to scale with electron density and temperature as ∼ne.Te0.166.

Representing Exact Electron Densities by a Single Slater Determinant in Finite Basis Sets.

The premise for Kohn-Sham density functional theory is that the exact electron density can be generated by a set of orbitals in a single Slater determinant. While this is ensured in a complete basis set, it has been shown that it cannot hold in small basis sets. The present work probes how accurately a reference electron density of the full-CI type can be reproduced by a set of orbitals in a single Slater determinant, as a function of the basis set used for the fitting electron density. The key finding is that the fitting error may be significant for basis sets of double- or triple-ζ quality. It is also shown that it is important that the fitting basis set includes the same basis functions as used for generating the reference electron density. The main limitation in a given basis set is the lack of higher order polarization functions. The error for practical purposes becomes insignificant for basis sets of quadruple-ζ or better quality, and this should be the choice when assessing the accuracy of exchange-correlation functionals by comparing electron densities to accurate reference results generated by wave function methods. The methodology in the present work can be used to transform an electron density from a multideterminant wave function into a set of orbitals in a single Slater determinant, and this may be useful for developing and testing new exchange-correlation functionals.

Analytical Model of Electron Density and Its Machine Learning Inference.

We present an analytical model representation of the electron density ρ(r) in molecules in the form of expansions of a few functions (exponentials and a Gaussian) per atom. Based on a former analytical model of ρ(r) in atoms, we devised its molecular implementation by introducing the anisotropy inherent in the electron distribution of atoms in molecules by means of proper anisotropic functions. The resulting model named A2MD (anisotropic analytical model of density) takes an analytical form highly suitable for obtaining the electron density in large biomolecules as its computational cost scales linearly with the number of atoms. To obtain the parameters of the model, we first devised a fitting procedure to reference electron densities obtained in ab initio correlated quantum calculations. Second, in order to skip costly ab initio calculations, we also developed a machine learning (ML)-based predictor that used neural networks trained on broad molecular datasets to determine the parameters of the model. The resulting ML methodology that we named A2MDnet (A2MD network-trained) was able to provide reliable electron densities as a basis to predict molecular features without requiring quantum calculations. The results presented together with the low computational scaling associated to the A2MD representation of ρ(r) suggest potential applications to obtain reliable electron densities and ρ(r)-based molecular properties in biomacromolecules.

Excitation energies from particle-particle random phase approximation with accurate optimized effective potentials.

The optimized effective potential (OEP) that gives accurate Kohn-Sham (KS) orbitals and orbital energies can be obtained from a given reference electron density. These OEP-KS orbitals and orbital energies are used here for calculating electronic excited states with the particle-particle random phase approximation (pp-RPA). Our calculations allow the examination of pp-RPA excitation energies with the exact KS density functional theory (DFT). Various input densities are investigated. Specifically, the excitation energies using the OEP with the electron densities from the coupled-cluster singles and doubles method display the lowest mean absolute error from the reference data for the low-lying excited states. This study probes into the theoretical limit of the pp-RPA excitation energies with the exact KS-DFT orbitals and orbital energies. We believe that higher-order correlation contributions beyond the pp-RPA bare Coulomb kernel are needed in order to achieve even higher accuracy in excitation energy calculations.

Accurately extracting the signature of intermolecular interactions present in the NCI plot of the reduced density gradient versus electron density.

An electron density (ED)-based methodology is developed for the automatic identification of intermolecular interactions using pro-molecular density. The expression of the ED gradient in terms of atomic components furnishes the basis for the Independent Gradient Model (IGM). This model leads to a density reference for non interacting atoms/fragments where the atomic densities are added whilst their interaction turns off. Founded on this ED reference function that features an exponential decay also in interference regions, IGM model provides a way to identify and quantify the net ED gradient attenuation due to interactions. Using an intra/inter uncoupling scheme, a descriptor (δginter) is then derived that uniquely defines intermolecular interaction regions. An attractive feature of the IGM methodology is to provide a workflow that automatically generates data composed solely of intermolecular interactions for drawing the corresponding 3D isosurface representations.

Minimal Basis Iterative Stockholder: Atoms in Molecules for Force-Field Development

Atomic partial charges appear in the Coulomb term of many force-field models and can be derived from electronic structure calculations with a myriad of atoms-in-molecules (AIM) methods. More advanced models have also been proposed, using the distributed nature of the electron cloud and atomic multipoles. In this work, an electrostatic force field is defined through a concise approximation of the electron density, for which the Coulomb interaction is trivially evaluated. This approximate "pro-density" is expanded in a minimal basis of atom-centered s-type Slater density functions, whose parameters are optimized by minimizing the Kullback-Leibler divergence of the pro-density from a reference electron density, e.g., obtained from an electronic structure calculation. The proposed method, Minimal Basis Iterative Stockholder (MBIS), is a variant of the Hirshfeld AIM method, but it can also be used as a density-fitting technique. An iterative algorithm to refine the pro-density is easily implemented with a linear-scaling computational cost, enabling applications to supramolecular systems. The benefits of the MBIS method are demonstrated with systematic applications to molecular databases and extended models of condensed phases. A comparison to 14 other AIM methods shows its effectiveness when modeling electrostatic interactions. MBIS is also suitable for rescaling atomic polarizabilities in the Tkatchenko-Scheffler scheme for dispersion interactions.

Spectroscopic measurement of Stark broadening parameter of the 636.2 nm Zn I-line

In this article we will present an attempt to measure the Stark broadening parameter of the Zn I-line at 636.23 nm utilizing the optical emission spectroscopy (OES) technique, taking into consideration the possibility of existence of self absorption. This method is standing on comparison of the Lorentzian FWHM and spectral line intensity of the unknown Stark broadening parameter line (Zn I-636.23 nm—in our case) to a well known Stark parameter line (e.g. Zn I-lines at 472.2, 481 and 468 nm) at a reference electron density of 2.7 × 1017 cm-3 and temperature of 1 eV. We have utilized the emission spectral data acquired from well diagnosed plasma produced by the interaction of Nd: YAG laser at wavelength of 1064 nm with ZnO nanomaterial target in open air. The results indicates that the Stark broadening of the Zn I-line at 636.23 nm is centered at 5.06 ± 0.03 ? with a 25% uncertainty at the given reference plasma parameters. The knowledge of the Stark broadening parameter of the 636.23 nm line may be important in the diagnostics of the laser plasma experiments especially in the absence of the Hα-line.

Simple and exact approach to the electronic polarization effect on the solvation free energy: Formulation for quantum-mechanical/ molecular-mechanical system and its applications to aqueous solutions

We present a simple and exact numerical approach to compute the free energy contribution δμ in solvation due to the electron density polarization and fluctuation of a quantum-mechanical solute in the quantum-mechanical/molecular-mechanical (QM/MM) simulation combined with the theory of the energy representation (QM/MM-ER). Since the electron density fluctuation is responsible for the many-body QM-MM interactions, the standard version of the energy representation method cannot be applied directly. Instead of decomposing the QM-MM polarization energy into the pairwise additive and non-additive contributions, we take sum of the polarization energies in the QM-MM interaction and adopt it as a new energy coordinate for the method of energy representation. Then, it is demonstrated that the free energy δμ can be exactly formulated in terms of the energy distribution functions for the solution and reference systems with respect to this energy coordinate. The benchmark tests were performed to examine the numerical efficiency of the method with respect to the changes in the individual properties of the solvent and the solute. Explicitly, we computed the solvation free energy of a QM water molecule in ambient and supercritical water, and also the free-energy change associated with the isomerization reaction of glycine from neutral to zwitterionic structure in aqueous solution. In all the systems examined, it was demonstrated that the computed free energy δμ agrees with the experimental value, irrespective of the choice of the reference electron density of the QM solute. The present method was also applied to a prototype reaction of adenosine 5'-triphosphate hydrolysis where the effect of the electron density fluctuation is substantial due to the excess charge. It was demonstrated that the experimental free energy of the reaction has been accurately reproduced with the present approach.

SU-FF-T-631: Deviation of Electron Density with CT Simulator Image Reconstruction Kernels and Its Impact On Dosimetry in Radiotherapy

Purpose: Fifteen image reconstruction kernels are provided in Siemens Somatom Sensation Open CT Scanner to produce the images with different levels of edge definition and quantity of noise. After conversion of CT number, planning system assigns electron density to each volume of interest for dose calculation. This study quantitatively investigated the variation of tissue electron density with kernels and its impact on dosimetry in radiotherapy.Method and Materials: CIRS electron density reference (EDR) phantom, RPC lung phantom, and a lungcancer patient were scanned in our CT scanner. The projection data was saved for image reconstruction with 8 selective kernels including “least noise” kernel and “best edge definition” kernel. All images were loaded in Pinnacle planning system to calculate the values of electron density relative to water (EDRTW). For PTV and each OAR, generalized equivalent uniform dose(GEUD) were computed from each image set. Three clinical treatment plans were used (one 6MV IMRT plan, two 3D conformal plans using 6MV and 23MV respectively). Same MUs were delivered and dose calculation included heterogeneity correction. The comparison was made for electron density and GEUD for target and various OARs. Results: Values of EDRTW measured from EDR phantom, RPC phantom, and the lungcancer patient vary with kernels from −3.5% to 12.6%, −2.3% to 1.1%, and −1.9 to 9.6%, respectively. Larger fluctuations in values of EDRTW were observed in lower density materials and organs. But the fluctuations of values of EDRTW caused less than 2.0% changes in GEUD in both Phantom and the patient studies. Conclusions: Utilization of EDR phantom for CT density table check could vary 12% from Kernel to Kernel. The dosimetry impact from selection of kernels is small on the lungcancer patient treatments when adaptive convolution algorithm is used. Because it is systematic error, the impact deserves our attention.

Molecular geometry and symmetry from a differential geometry viewpoint

Relations between an earlier generalization of molecular symmetry called symmorphy and a molecular equivalence based on diffeomorphisms of electron density functional graphs (the so-called DFG equivalence introduced in our previous work) are analyzed. Any two DFG-equivalent electron density functions can be derived from one another by a suitable transformation of the spatial coordinates and the electronic charge density scale; the classes of DFG equivalence are the orbits of a group of linear operators operating in the space of electron density functions. Within the symmorphy framework, the symmetry group is derived from the symmorphy group by taking an intersection of a subgroup of the symmorphy group and the group of isometries for a natural choice of the Riemannian metric tensor. The Riemannian metric properties provide a choice for a suitable reference electron density function for each class of equivalent densities. Such reference densities serve as tools for a systematic classification of the infinite family of electron densities of molecular conformations. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64: 669–678, 1997

Universal behaviour of the electronic transport

The universal behavior of the electronic transport in solids is discussed. It is shown that these findings can be interpreted by a general quantum transport model. It is based on a generalization of the Bohr quantum condition, resulting in a reference length ae = 7.25 nm and a reference electron density of 3 × 1015 m-2, which limits the electron current. It is shown that the limitation is supported by experimental data. The priority of the formulation of the square of the electric charge as e2 = αh is discussed. It leads to a new system of units. The formulations of the reference values of all electromagnetic quantities are given. It is shown that the data of the Aharonov Bohm effect of 1/f noise confirm the presented statements.

Shortcomings in our understanding of the lower ionosphere as revealed by an analysis of radiowave absorption measurements

Empirical relationships derived from an extensive series of equatorial ground-based radiowave absorption measurements are analysed in terms of our current understanding of the basic processes that control the formation and behaviour of the lower ionosphere. Multi-frequency absorption and virtual height measurements are combined with the results of a rocket borne experiment to construct an equatorial noontime reference electron density profile corresponding to the conditions of a non-flaring sun at solar cycle maximum. The enhancement in this electron density profile, and hence in the absorption of radio waves, as the solar 1–8 Å flux increases by moderate amounts is then calculated from our knowledge of the ion production and loss processes. In order to bring the calculated increase of absorption into agreement with the empirically established relationship ( Gnanalingam, 1974), we find it necessary to reduce by a factor of about 5 the Meira (1971) nitric oxide densities below 90 km. Attention is drawn to the wide disparity between the effective recombination coefficient and the average dissociative recombination coefficient for the known ion composition in both the molecular and cluster ion regions of the lower ionosphere. The factor of 5 reduction in the nitric oxide profile required to explain the solar control of absorption, however, largely eliminates this disparity in the cluster ion region. Our analysis of the diurnal variation of radiowave absorption and virtual height also reveals a gross discrepancy between the calculated and measured variations. In order to resolve this discrepancy, a mechanism is needed which would cause the electron density in the 95–105 km region to decrease with increasing solar zenith angle faster than is predicted by the present theory of ion production and loss processes in this region. Also presented in this work is an ad hoc model of the diurnal variation of the electron density profile which is consistent with the measured diurnal variation of radiowave absorption and virtual height.