A simple semiempirical model for the static polarizability of ions

A concise analytical model for the static dipole polarizability of ionized atoms and molecules is created for the first time.As input,it requires,alongside the polarizability of neutral counterpart of a given ion,only the charge and elemental composition.This physically motivated semiempirical model is based on a number of established regularities in polarizability of charged monatomic and polyatomic compounds.In order to adjust it,the results of quantum chemistry calculations and gas-phase measurements available for a broad range of ionized multielectron species are employed.To counteract the appreciable bias in the literature data toward polarizability of monoatomic ions,for some molecular ions of general concern the results of the authors'own density functional theory calculations are additionally invoked.A total of 541 data points are used to optimize the model.It is demonstrated that the model we suggested has reasonable(given the substantial uncertainties of the reference data)accuracy in predicting the static isotropic polarizability of arbitrarily charged ions of any size and atomic composition.The resulting polarizability estimates are found to achieve a coefficient of determination of 0.93 for the assembled data set.The created analytic tool is universally applicable and might be advantageous for some applications where there is an urgent need for rapid low-cost evaluation of the static gas-phase polarizability of ionized atoms and molecules.This is especially relevant to constructing the complex models of nonequilibrium chemical kinetics aimed at precisely describing the observable refractive index(dielectric permittivity)of plasma flows.The data sets that support the findings of this study are openly available in Science Data Bank at https://doi.org/10.57760/sciencedb.07526.

A simple semiempirical model for the static polarizability of electronically excited atoms and molecules

We present a semiempirical analytical model for the static polarizability of electronically excited atoms and molecules,which requires very few readily accessible input data,including the ground-state polarizability,elemental composition,ionization potential,and spin multiplicities of excited and ground states.This very simple model formulated in a semiclassical framework is based on a number of observed trends in polarizability of electronically excited compounds.To adjust the model,both accurate theoretical predictions and reliable measurements previously reported elsewhere for a broad range of multielectron species in the gas phase are utilized.For some representative compounds of general concern that have not yet attracted sufficient research interest,the results of our multireference second-order perturbation theory calculations are additionally engaged.We show that the model we developed has reasonable(given the considerable uncertainties in the reference data)accuracy in predicting the static polarizability of electronically excited species of arbitrary size and excitation energy.These findings can be useful for many applications,where there is a need for inexpensive and quick assessments of the static gas-phase polarizability of excited electronic states,in particular,when building the complex nonequilibrium kinetic models to describe the observed optical refractivity(dielectric permittivity)of nonthermal reacting gas flows.

Effects of Electron Donor and Different Solvents on Polarizability and Second Hyperpolarizability of Diradical Complex Involving X(X=B,Al,Ga)

The polarizability（α） and second hyperpolarizability（γ） were systemically investigated for singlet diradical complex involving X（X=B,Al,Ga） atom.The results show that both the α and γ can be effectively tuned by varying the distance R（between compound A and a water molecule） and acceptor atom X.The lone pair of electrons from the O atom of the water molecule entered into the vacant p orbital of atom X,which increased the diradical character and led to the increase of the α and γ values.Furthermore,the polarizable continuum model（PCM） was used to test the effects of H2O and CCl4 solvents on the α and γ values.Both the α and γ values of the studied diradical complex 1a（1b,1c） in H2O and CCl4 were uniformly enhanced.And the solvent effects of H2O on either α or γ were larger than those of CCl4.

Static electric dipole polarizability of lithium atoms in Debye plasmas

The static electric dipole polarizabilities of the ground state and n ≤ 3 excited states of a lithium atom embedded in a weekly coupled plasma environment are investigated as a function of the plasma screening radium. The plasma screening of the Coulomb interaction is described by the Debye-Hiickel potential and the interaction between the valence electron and the atomic core is described by a model potential. The electron energies and wave functions for both the bound and continuum states are calculated by solving the SchrSdinger equation numerically using the symplectic integrator. The oscillator strengths, partial-wave, and total static dipole polarizabilities of the ground state and n ≤ 3 excited states of the lithium atom are calculated. Comparison of present results with those of other authors, when available, is made. The results for the 2s ground state demonstrated that the oscillator strengths and the static dipole polarizabilities from np orbitals do not always increase or decrease with the plasma screening effect increasing, unlike that for hydrogen-like ions, especially for 2s→3p transition there is a zero value for both the oscillator strength and the static dipole polarizability for screening length D = 10.3106a0, which is associated with the Cooper minima.

Critical radius and dipole polarizability for a confined system

The analytical transfer matrix method （ATMM） is applied to calculating the critical radius τc and the dipole polarizability αd in two confined systems： the hydrogen atom and the Hulthēén potential. We find that there exists a linear relation between τe^1/2 and the quantum number nτ for a fixed angular quantum number l, moreover, the three bounds of αd（αd^K,αd^B,αd^U） satisfy an inequality：αd^K≤αd^B≤αd^U,A comparison betwen the ATMM,the exact numerical analysis, and the variational wavefunctions shows that our method works very well in the systems.

Refractive Index and Electronic Polarizability of Ternary Chalcopyrite Semiconductors

Simple models are proposed for the calculation of refractive index n and electronic polarizability α of AⅠBⅢC2Ⅵ and AⅡBⅣC2Ⅴ compounds of groups of chalcopyrite semiconductors from their energy gap data. The values family and 12 compounds of AⅡBⅣC2Ⅴ family are calculated for the work. The proposed models are applicable for the whole range of energy gap materials. The calculated values are compared with the available experimental and reported values. A fairly good agreement between them is obtained.

Optical Basicity and Polarizability of Nd³⁺-Doped Bismuth Borate Glasses

This paper reports on different physical and optical properties of Nd3+-doped bismuth borate glasses. The glasses containing Nd3+ in (25 - x)Bi2O3:20Li2O:20ZnO:35B2O3:xNd2O3 (where x = 1, 1.5, 2 mol%) have been prepared by melt-quenching method. The amorphous nature of the glasses was confirmed by X-ray diffraction studies. The physical parameters like dielectric constant, refractive index, ionic concentration, oxygen-packing density, inter ionic distance, polaronradius, reflection loss, energy gap, molar refractivity, molar polarizability, electronic polarizability, optical basicity and field strength are computed. On the basis of the measured values of the density and refractive index, the Nd3+ ion concentration in glasses, the polarizability of oxide ions and optical basicity were theoretically determined. The theoretical value of average electronic polarizability and oxide ion polarizability were calculated by using Lorentz-Lorenz formula. Theoretical optical basicity of the glasses is evaluated based on equation proposed by Duffy and Ingram. The metallization criterion has also been calculated on the basis of refractive index and energy gap. The large value of metallization criterion indicates that the glass materials are insulators. The results obtained predict the nature of bonding in the present glasses and provide basis for developing new nonlinear optical material.

Temperature Dependence of Polarizability and Dispersion in Three,Two and One Dimensional Electron Gases

Both temperature dependence of polarizability and plasmon dispersion in unmagnetized metal （or semiconductor） electron gases are investigated in this paper. It is obtained that, with a continuous variation of temperature in a large region, the polarizability and dispersion change non-monotonously. The static polarizability X（q, w =0, μ, T） and dispersion wp（q, T） for finite T in three, two and one dimensional electron gases are calculated numerically. In addition, dispersion relation w（q） at a definite temperature （T ≠0） is similar to that at T = 0.

Nonlinear Polarizability of Erythrocytes in Non-Uniform Alternating Electric Field

Nonlinear polarizability of erythrocytes in non-uniform alternating electric field (NUAEF) was proved theoretically and experimentally by dielectrophoresis method. The paper presents experimental evidence of the nonlinear polarizability of erythrocytes in the non-uniform alternating electric field. The rotation of erythrocyte around its own axis at more than one revolution per second in the non-uniform alternating electric field in the frequency range and the electric field intensity?is the evidence of its nonlinear polarizability. The theoretical analysis of the density of electric charges capable of overcoming the membrane potential was carried out on the basis of statistical mechanics, the thermal equilibrium in which the particle stays. The nonlinear polarizability of the erythrocyte emerges if the voltage on the membrane exceeds?, which was theoretically proved. The alternating electric field from the donor erythrocyte with the amplitude exceeding forms the constant component of the current? in the cytoplasm of the recipient erythrocyte whose energy can be considered as a signal one. The nonlinear equivalent electric circuit of the cell was proposed.

Activity Trends in Desoxy Anthrapyrazoles: The Influence of Molar Volume, Polarizability and Lipophilicity of N₂C₅Side Chains on Their Anticancer Response

QSAR methodology was used to assess the effects of lipophilicity (logP), molar volume (MV) and polarizability (pl) of the side chains at N2 and C5 of 20 known desoxy anthrapyrazoles on their in vitro anticancer activity expressed as the negative logarithm of the inhibitory concentration of 50% of L1210 murine leukemia cell line (1/logIC50). The main data set shows poor correlations between biological response and the descriptors with exception of MV of the C5 side chain, where a moderate correlation was discerned ( =0.60, n = 18, two outliers). To extract more information regarding mechanism, the main data set was visually classified to three clusters depending on N2 side chain. Cluster 1 containing six 5-substituted 2-[(2-hydroxyethyl) amino] ethyl anthrapyrazoles;cluster 2 contains ten 5-subsitutes 2-(diethyl amino) ethyl anthrapyrazoles and cluster 3 contains four anthrapyrazoles with miscellaneous substituents at both N2 and C5. For cluster 1, MV and pl of C5 show high correlation with biological response (R2’s = 0.75 and 0.72 respectively) while logP gives a weak correlation (R2 = 0.44). For cluster 2, the correlations of logP and pl of C2side chain are higher (=0.66 and 0.62 respectively) compared with MV (=0.16). Cluster 3 shows very poor correlation with all descriptors (~0.3). This indicates mechanistic distinction between the three clusters. Derived descriptors which represent the difference between the descriptors of N2 and C5 side chains where used to explore the presence of interplay between these descriptors in affecting variability of the biological response.

Calculations of atomic polarizability for beryllium using MCDHF method

Based on the fully relativistic multiconfiguration Dirac-Hartree-Fock(MCDHF)method and the corresponding program package GRASP2018,a new program for calculating the polarizabilities is developed.As the first application,the static electric-dipole polarizabilities of the ground state 2s^(2)^(1)S_(0) and excited state 2s2p^(3)P_(0) of beryllium are calculated.By means of these polarizabilities,the blackbody radiation(BBR)shift of the 2s2p^(3)P_(0)→2s^(2)^(1)S_(0)clock transition is determined.The present results agree very well with other available theoretical results.

RELATION BETWEEN THE OPTICAL ANISO-TROPY INDEX AND THE POLARIZABILITY ELLIPSOID OF ATOM GROUPS

The optical anisotropy index is a new conception which has been proposed by the author of this paper on the basis of the Gladstone refractivity (i.e. specific energy by Larsen). The conception is very useful for studying the structural-optical mineralogy. The polarizability ellipsoid of atom groups in minerals may be obtained from the optical anisotropy index; conversely, when the crystal structure, orientation, and the polarizability ellipsoid of atom groups are known, the optical anisotropy index of the minerals may be calculated, and then three principal refractive indices, and the optical axis angles may be calculated, too. The calculated values of optical properties are in very good agreement with the experimental values. This calculation method is much simpler thanBragg’s for the carbonates, and the precision of calculated values is much higher than that of Bragg’s. The principle of calculation method is suitable for all the minerals containing some strong anisotropic atom groups, besides

Comprehensive study of electronic polarizability and band gap of B_(2)O_(3)-Bi_(2)O_(3)-ZnO-SiO_(2)glass network

Quaternary glasses were successfully fabricated using melt quenching technique based on the chemical compound composition(x)Bi_(2)O_(3)–(0:5-x)ZnO-(0.2)B_(2)O_(3)–(0.3)SiO_(2),where(x=0.1,0.2,0.3,0.4,0.45)mole.The sources of SiO_(2)was produced from rice husk ash(RHA)at 99.36%of SiO_(2).The Urbach energy was increased from 0.16 eV to the 0.29 eV as the mole of Bi_(2)O_(3)increased in the glass structure.The indirect energy band gap is indicated in decrement pattern with 3.15 eV towards 2.51 eV.The results of Urbach energy and band gap energy that were obtained are due to the increment of Bi^(3+)ion in the glass network.The refractive indexes for the prepared glasses were evaluated at 2.36 to 2.54 based on the Lorentz–Lorentz formulation which correlated to the energy band gap.The calculated of molar polarizability,electronic polarizability and optical basicity exemplify fine complement to the Bi_(2)O_(3)addition in the glass network.The glass sample was indicated in amorphous state.

Magic wavelengths for 6s_(1/2)→5d_(3/2,5/2)transitions of Yb~+ions

The wave functions,energy levels and matrix elements of Yb+ions are calculated using the relativistic configuration interaction plus core polarization(RCICP)method.The static and dynamic electric dipole polarizabilities of the ground state and low-lying excited states are determined.Then,the magic wavelengths of the magnetic sublevel 6s_(1/2,m=1/2)→5d_(3/2,m=±3/2,±1/2)and 6s_(1/2,m=1/2)→5_(d5/2,m=±5/2,±3/2,±1/2)transitions in the linearly,right-handed,and left-handed polarized light are further determined.The dependence of the magic wavelengths upon the angle between the direction of magnetic field and the direction of laser polarization is analyzed.

Influences of adsorptions of some inorganic molecules on electronic, optical, and thermodynamic properties of Mg_(12)O_(12) nanocage: A computational approach

According to density functional theory, we investigate the effects of BF3, BF4, BCI3, A1F3, AICI3, A1Br3, 13eF3, GaF3, GaC13, GaBr3, NO3, BS2, BSO, BO2, F2, PFs, PC15, and ASF5 molecules on the geometric, electronic, linear, and nonlinear optical properties of an Mg12012 nanocage. The thermodynamic stability and feasibility of the adsorption process are investigated by analyzing the free energy. It is shown that the adsorptions of almost all molecules on the Mg12OI2 surface are exothermic. The calculations of the polarizability of these nanoclusters show that among the studied molecules, BeF3 has the largest influence on the polarizability value （a≈315 a.u., the unit a.u. is short for atomic unit）. The static first hyperpolarizability （β0） value is increased in the presence of these superhalogens. This increase is greatest for BeF3 and BF4 of which the highest value of the first hyperpolarizability （βO≈ 5775 a.u.） is related to a BeF3_c（e@Mgl2Ol2） nanocluster. The adsorption position is a key to estimating the value of increasing the first hyperpolarizability.

Molecular Structure, Vibrational Assignments and Non-Linear Optical Properties of 4,4’ Dimethylaminocyanobiphenyl (DMACB) by DFT and <i>ab Initio</i>HF Calculations

In the present study, structural properties of 4,4’ dimethylaminocyanobiphenyl (DMACB) have been studied extensively by using ab initio Hartree Fock (HF) and density functional theory (DFT) employing B3LYP/B3PW91 exchange correlation levels of theory. The vibrational frequencies of DMACB in the ground state have been calculated by using Hartree Fock level and density functional method (B3LYP/B3PW91) with 6-31G(d, p), basis set. Nonlinear optical (NLO) behavior of the examined molecule is investigated by the determination of the electric dipole moment μ, the polarizability α, and the hyperpolarizability β by using the B3LYP/B3PW91 methods.

The evaluation of temporal electronic structures of nonresonant Raman excited virtual state of thiourea

An algorithm has been introduced to calculate molecular bond polarizabilities of thiourea, which supply essential electronic information about the nonresonant Raman excited virtual states. The main dynamical behaviour of the excited virtual states of thiourea is that the Raman excited electrons tend to flow to the N-H bonds and C-N bonds from the S-C bonds because of the electronic repulsion effect. The difference in Raman excited electron relaxation time of thiourea under 514.5-nm and 325-nm excitations has been observed, which quantitatively shows that the Raman scattering process is dependent on the wavelength of the pumping laser. Finally, the distribution of the electrons at the final stage of relaxation is given out through the comparison between the bond electronic densities of the ground states and the bond polarizabilities after deexcitation.

Ab initio calculations for the absorption spectra and polarizabilities of small sulfur clusters

Absorption spectra for Sn clusters （n=2...8） are calculated using an adiabatic time-dependent density functional formalism within the local density approximation （LDA）. We compare the calculated spectra with those computed using a simple LDA approach. The time-dependent LDA （TDLDA） spectra display a significant blue shift with respect to the LDA spectra. The calculated spectra present a variety of features that can be used for comparison with future experimental investigations. We also obtain a significant threshold absorption, which can distinguish between different ground states of the sulfur clusters. In addition, the polarizabilities of the clusters are calculated by using the higherorder finite-difference pseudopotential density functional method in real space. We find that the polarizabilities of the clusters considered are higher than the value estimated from the ＇hard sphere＇ model using the bulk static dielectric constant. The computed polarizabilities per atom tend to decrease with increasing cluster size. The polarizabilities are closely related to the HOMO-LUMO gaps and the geometrical configurations.

Static dipole polarizabilities of Sc_n (n ≤15) clusters

The static dipole polarizabilities of scandium clusters with up to 15 atoms are determined by using the numerically finite field method in the framework of density functional theory. The electronic effects on the polarizabilities are investigated for the scandium clusters. We examine a large highest occupied molecular orbital -- the lowest occupied molecular orbital （HOMO-LUMO） gap of a scandium cluster usually corresponds to a large dipole moment. The static polarizability per atom decreases slowly and exhibits local minimum with increasing cluster size. The polarizability anisotropy and the ratio of mean static polarizability to the HOMO-LUMO gap can also reflect the cluster stability. The polarizability of the scandium cluster is partially related to the HOMO-LUMO gap and is also dependent on geometrical characteristics. A strong correlation between the polarizability and ionization energy is observed.