Polarizability Of Ground State Research Articles

Contribution of Discrete and Continuum Wave Functions in the Ground State Polarizability of Hydrogen

We analytically derive a discrete radial Green function for a hydrogenic system in terms of associated Leguerre polynomials. We investigate the polarizability of the ground-state hydrogen using the so-called length gauge approximation of electrodynamics. The polarizability is the sum of the polarization matrix elements for the negative and the positive frequency values. We estimate the contribution of discrete wavefunctions to the static ground state polarizability. We found that the contribution of continuum states dominates over that of discrete states to the polarizability by an order of magnitude.

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.

Spectroscopy of the 1001-nm transition in atomic dysprosium

We report on spectroscopy of cold dysprosium atoms on the $1001\,\mathrm{nm}$ transition and present measurements of the excited state lifetime which is at least $87.2(6.7)\,\mathrm{ms}$ long. Due to the long excited state lifetime we are able to measure the ratio of the excited state polarizability to the ground state polarizability at $1064\,\mathrm{nm}$ to be $0.828(0.129)$ by parametric heating in an optical dipole trap. In addition we measure the isotope shifts of the three most abundant bosonic isotopes of dysprosium on the $1001\,\mathrm{nm}$ transition with an accuracy better than $30\,\mathrm{kHz}$.

Pump-induced lensing effects in diode pumped Alexandrite lasers.

It is essential to understand the pump-induced lensing and aberration effects in solid-state lasers, such as Alexandrite, since these set limits on laser power scaling whilst maintaining high spatial TEM00 beam quality. In this work, we present direct wavefront measurements of pump-induced lensing and spherical aberration using a Shack-Hartmann wavefront sensor, for the first time, in a diode-pumped Alexandrite laser, and under both non-lasing and lasing conditions. The lens dioptric power is found to be weakly sub-linear with respect to the absorbed pump power, and under lasing, the lensing power is observed to decrease to 60 % of its non-lasing value. The results are inconsistent with a thermal lens model but a fuller theoretical formulation is made of a combined thermal and population lens model giving good quantitative agreement to the observed pump power dependence of the induced-lensing under non-lasing conditions and the reduced lensing under lasing conditions. The deduced value for the difference in excited to ground state polarizability is consistent with prior measurement estimates for other chromium-doped gain media. The finding of this paper provide new insight into pump-induced lensing in Alexandrite and also provides a basis for a fast saturable population lens mechanism to account for self-Q-switching observed recently in Alexandrite laser systems.

Ferrocene conjugated donor-π-acceptor malononitrile dimer: Synthesis, theoretical calculations, electrochemical, optical and nonlinear optical studies

Abstract The donor-π-acceptor ferrocene conjugated malononitrile dimer [C5H5–Fe–C5H4–C(H) C(CN)–C(NH2) = C(CN)2] (1) has been synthesized and characterized with the aid of analytical and spectroscopic techniques [FT-IR, GC-Mass, 1H and 13C NMR]. The thermal stability of the compound 1 was investigated using thermogravimetric analysis (TGA) and differential thermal analysis (DTA), exhibit the compound is stable up to 180 °C. The photophysical properties were performed by UV–visible and fluorescence spectroscopic methods and the compound 1 exhibited weak fluorescence emission. In addition, the optical band gap (Eg) was calculated using diffused reflectance spectroscopic technique which shows the band gap value of Eg = 3.6 eV. The redox wave of the compound 1 was determined by cyclic voltammetry, revealed that one electron transfer ability of the ferrocene to ferrocenium ion. The experimentally observed HOMO and LUMO values are good agreement with the theoretical calculation by DFT-M06 method using 6–31 + G** as basis set. The solvatochromic studies of compound 1 shows negative solvatochromism due to the high ground state polarizability in presence of cyano acceptors. Further, the nonlinear optical properties were investigated by Q-switched Nd-YAG laser and second harmonic generation efficiency (SHG) using para-nitroaniline (p-NA) as a standard and the results of SHG efficiency is 0.35 times comparable with p-NA.

Electric dipole polarizability ofXe129using the relativistic coupled-cluster and the normal coupled-cluster methods

$^{129}$Xe is an important candidate for the searches of electric dipole moments due to violations of time-reversal and parity violations in diamagnetic atoms. In view of the similarities between the electric dipole moment and the polarizability from the point of view of many-body theory, we have performed rigorous calculations of the ground state polarizability of $^{129}$Xe using a self consistent relativistic coupled-cluster method and the relativistic normal coupled-cluster method. The discrepancy between the results from these two methods is two percent, but each of them differs from the accurate measurement of the polarizability of the ground state of $^{129}$Xe by one percent. Our results clearly suggest that the two theoretical methods, we have employed in this work, can be applied in the future to capture electron correlation effects in the electric dipole moment of $^{129}$Xe to a high degree of accuracy.

In Silico Stark Effect: Determination of Excited-State Polarizabilities of Squaraine Dyes.

The static electric polarizabilities (α) of a quadrupolar squaraine dye are investigated in silico, either as the excess polarizability, i.e., the change from the ground to the lowest excited state, Δα, or as those of the two states separately, depending on the approach. The polarizabilities are worked out by making use of the energy and dipole moment Taylor expansions as a function of the electric field (E), in which α is represented by the quadratic and linear terms, respectively, and also by means of the linear response approach. Dipoles and energies are computed at a few values of the electric field, with different strategies that consider the geometry of the molecule either frozen in the ground state or relaxed at each E value. From a physical standpoint, the most appropriate approach to describing the molecular polarizability depends on the processes in which the molecule is involved: for example, fluorescence methods provide information about relaxed excited states, and absorption methods are used to determine the polarizability changes of excited states frozen in the ground-state conformation. We show that the excited-state polarizability does not strongly differ from the ground-state polarizability when the field is applied along the main axis of the squaraine. In contrast, remarkable differences are found when the field is applied perpendicular to the molecular plane due to a large geometrical distortion of the molecular backbone.

General polarizability and hyperpolarizability estimators for the path-integral Monte Carlo method applied to small atoms, ions, and molecules at finite temperatures

The nonlinear optical properties of matter have a broad relevance and many methods have been invented to compute them from first principles. However, the effects of electronic correlation, finite temperature, and breakdown of the Born-Oppenheimer approximation have turned out to be challenging and tedious to model. Here we propose a straightforward approach and derive general field-free polarizability and hyperpolarizability estimators for the path-integral Monte Carlo method. The estimators are applied to small atoms, ions, and molecules with one or two electrons. With the adiabatic, i.e., Born-Oppenheimer, approximation we obtain accurate tensorial ground state polarizabilities, while the nonadiabatic simulation adds in considerable rovibrational effects and thermal coupling. In both cases, the 0 K, or ground-state, limit is in excellent agreement with the literature. Furthermore, we report here the internal dipole moment of PsH molecule, the temperature dependence of the polarizabilities of ${\mathrm{H}}^{\ensuremath{-}}$, and the average dipole polarizabilities and the ground-state hyperpolarizabilities of ${\mathrm{HeH}}^{+}$ and $\mathrm{H}{{}_{3}}^{+}$.

One- and two-photon detachment ofO−

Cross sections for one- and two-photon detachment of ${\mathrm{O}}^{\ensuremath{-}}(1{s}^{2}2{s}^{2}2{p}^{5}\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{P}^{\mathrm{o}})$ have been determined in a joint experimental and theoretical study. The absolute measurement is based on the animated-crossed-beam technique, which is extended to the case of pulsed lasers, pulsed ion beams, and multiphoton detachment. The ab initio calculations employ $R$-matrix Floquet theory, with simple descriptions of the initial bound state and the residual oxygen atom which reproduce well the electron affinity and ground-state polarizability. For one-photon detachment, the measured and computed cross sections are in good mutual agreement, departing significantly from previous reference experiments and calculations. The generalized two-photon detachment cross section, measured at the Nd:YAG laser wavelength, is in good agreement with the $R$-matrix Floquet calculations. Long-standing discrepancies between theory and experiment are thus resolved.

Measurements of the ground-state polarizabilities of Cs, Rb, and K using atom interferometry

We measured the ground-state static electric-dipole polarizabilities of Cs, Rb, and K atoms using a three-nanograting Mach-Zehnder atom beam interferometer. Our measurements provide benchmark tests for atomic structure calculations and thus test the underlying theory used to interpret atomic parity non-conservation experiments. We measured $\alpha_{\mathrm{Cs}} = 4\pi\epsilon_0 \times 59.45(11) \AA^3$, $\alpha_{\mathrm{Rb}} = 4\pi\epsilon_0 \times 47.44(9) \AA^3$, and $\alpha_{\mathrm{K}} = 4\pi\epsilon_0 \times 42.97(8) \AA^3$. In atomic units, these measurements are $\alpha_{\mathrm{Cs}} = 401.2(7)$, $\alpha_{\mathrm{Rb}} = 320.1(6)$, and $\alpha_{\mathrm{K}} = 290.0(5)$. We report ratios of polarizabilities $\alpha_{\mathrm{Cs}}/\alpha_{\mathrm{Rb}} = 1.2532(10)$, $\alpha_{\mathrm{Cs}}/\alpha_{\mathrm{K}} = 1.3835(9)$, and $\alpha_{\mathrm{Rb}}/\alpha_{\mathrm{K}} = 1.1040(9)$ with smaller fractional uncertainty because the systematic errors for individual measurements are largely correlated. Since Cs atom beams have short de Broglie wavelengths, we developed measurement methods that do not require resolved atom diffraction. Specifically, we used phase choppers to measure atomic beam velocity distributions, and we used electric field gradients to give the atom interference pattern a phase shift that depends on atomic polarizability.

Derivation of the RPA (Random Phase Approximation) Equation of ATDDFT (Adiabatic Time Dependent Density Functional Ground State Response Theory) from an Excited State Variational Approach Based on the Ground State Functional.

The random phase approximation (RPA) equation of adiabatic time dependent density functional ground state response theory (ATDDFT) has been used extensively in studies of excited states. It extracts information about excited states from frequency dependent ground state response properties and avoids, thus, in an elegant way, direct Kohn-Sham calculations on excited states in accordance with the status of DFT as a ground state theory. Thus, excitation energies can be found as resonance poles of frequency dependent ground state polarizability from the eigenvalues of the RPA equation. ATDDFT is approximate in that it makes use of a frequency independent energy kernel derived from the ground state functional. It is shown in this study that one can derive the RPA equation of ATDDFT from a purely variational approach in which stationary states above the ground state are located using our constricted variational DFT (CV-DFT) method and the ground state functional. Thus, locating stationary states above the ground state due to one-electron excitations with a ground state functional is completely equivalent to solving the RPA equation of TDDFT employing the same functional. The present study is an extension of a previous work in which we demonstrated the equivalence between ATDDFT and CV-DFT within the Tamm-Dancoff approximation.

Structural Determinants of Tau Aggregation Inhibitor Potency

Small-molecule Tau aggregation inhibitors are under investigation as potential therapeutic agents against Alzheimer disease. Many such inhibitors have been identified in vitro, but their potency-driving features, and their molecular targets in the Tau aggregation pathway, have resisted identification. Previously we proposed ligand polarizability, a measure of electron delocalization, as a candidate descriptor of inhibitor potency. Here we tested this hypothesis by correlating the ground state polarizabilities of cyanine, phenothiazine, and arylmethine derivatives calculated using ab initio quantum methods with inhibitory potency values determined in the presence of octadecyl sulfate inducer under reducing conditions. A series of rhodanine analogs was analyzed as well using potency values disclosed in the literature. Results showed that polarizability and inhibitory potency directly correlated within all four series. To identify putative binding targets, representative members of the four chemotypes were added to aggregation reactions, where they were found to stabilize soluble, but SDS-resistant Tau species at the expense of filamentous aggregates. Using SDS resistance as a secondary assay, and a library of Tau deletion and missense mutants as targets, interaction with cyanine was localized to the microtubule binding repeat region. Moreover, the SDS-resistant phenotype was completely dependent on the presence of octadecyl sulfate inducer, but not intact PHF6/PH6* hexapeptide motifs, indicating that cyanine interacted with a species in the aggregation pathway prior to nucleus formation. Together the data suggest that flat, highly polarizable ligands inhibit Tau aggregation by interacting with folded species in the aggregation pathway and driving their assembly into soluble but highly stable Tau oligomers.

Theory Study on Polarizability and Dipole Moment of W<sub>m</sub>B<sub>n</sub>(m+n≤7) Clusters

Geometric structure of WmBn(m+n7) clusters are optimized by using the density functional theory at the B3LYP/LANL2DZ level. For the ground state configurations, polarizability and dipole moment are analyzed. The calculated results show that: Δα varies with W atom which present turbulence change; W2B3cluster is nonpolar, WB5cluster has the strongest polarity, W5B2cluster has the weakest polarity, symmetry of clusters influence polarizabilities and dipole moment.

Molecular structure and solvent effects on the dipole moments and polarizabilities of some aniline derivatives

This work presents the quantum chemical studies of the effects of substituents and solvents on the ground state molecular geometry, dipole moments, polarizabilities and frontier orbital energies of aniline (A), N-methylaniline (NMA), N-ethylaniline (NEA), N,N-dimethylaniline (DMA) and N,N-diethylaniline (DEA) towards understanding their structure–property relationship. The ground state molecular geometry, dipole moments, polarizabilities and frontier orbital energies of A, NMA, NEA, DMA and DEA were computed by use of the ab initio restricted HF–DFT self-consistent field method (B3LYP) with 6-31G* basis set in vacuum, ethanol and tetrahydrofuran. The results of the B3LYP/6-31G* calculations revealed that these properties are enhanced upon successive substitution with size and number of alkyl groups at the amino group of the molecules, and as the dielectric constant of the solvents decrease. It was also found that for all the molecules, the enhanced ground state molecular geometry, dipole moments and polarizabilities upon substitution or solvent effect are associated with a decrease in the EHOMO−ELUMO (optical) gap. The lower optical gap, higher dipole moments and polarizabilities with increased size and planarity illustrates increased reactivity and ground state electro-optic (non-linear optical) activity of the molecules upon substitution, and as the dielectric constant of the solvents decreased. Of the studied molecules, DEA was found to exhibit the most electro-optic activity and reactivity.

Theoretical Study on Raman Spectra of Aqueous Peroxynitric Acid

Using density functional theory and polarizable continuum models, we study the Raman spectra of aqueous peroxynitric acid. The calculated results indicate that the solvent effect has significant influence on the electric dipole transition moments between the ground and excited electronic state and Raman polarizabilities. The theoretical Raman spectra agree well with the experimental results. From the experimental depolarization ratio, we can conclude that peroxynitric acid is not a plane molecule. We also find that the hydrogen bond can enhance IR intensity of hydroxyl group by several times.

Dispersion and polarization interactions of the strontium atom

Dispersion coefficients involving the 5s 2 1 S e and 5s5p 1,3P o states of strontium are determined from a large basis configuration interaction calculation. Dispersion coefficients are presented for the strontium dimer and also for strontium interactions with hydrogen and the rare gases. Polarizabilities and oscillator strengths from some low lying states are also given. The ground state polarizability and that of the 5s5p 1P o and 5s4d 1D e states are very similar in size.

The theory study of electronic structures and spectram properties of WnNim(n+m≤7; m=1, 2) clusters

Possible geometrical structures of WnNim (n+m≤7; m=1, 2) clusters have been optimized by using the density functional theory (B3PW91) at the LANL2DZ level. For the ground state structures, the NBO,vibration frequencies, spectrum and polarizability are studied. The calculated results show: the hybrid phenomenon is very strong within W and Ni atoms, while weak in the W-Ni atoms. In the process of forming alloy clusters, the charge transfer happens owing to the interaction of W and Ni so that most of Ni atom is positive and while W atom is negative. The optical properties indicated, the number of the vibrational peak is the most in the IR and Raman of W6Ni cluster, the IR and raman absorption peak of W5Ni2 is the strongest and the IR absorption peak of W2Ni has only one; the bonding between atoms shows stronger with the increasing of W content in the WnNim (n+m≤7; m=1, 2) clusters.

Calculation of parity-nonconserving amplitude and other properties ofRa+

We have calculated parity nonconserving 7s - 6d_{3/2} amplitude E_PNC in 223Ra+ using high-precision relativistic all-order method where all single and double excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Detailed study of the uncertainty of the parity nonconserving (PNC) amplitude is carried out; additional calculations are performed to estimate some of the missing correlation corrections. A systematic study of the parity conserving atomic properties, including the calculation of the energies, transition matrix elements, lifetimes, hyperfine constants, quadrupole moments of the 6d states, as well as dipole and quadrupole ground state polarizabilities, is carried out. The results are compared with other theoretical calculations and available experimental values.

Blackbody radiation shift of the Al+ clock transition

The blackbody radiation shift of the Al+ 3s2 1Se 0 ↦ 3s3p 3P○ 0 clock transition is evaluated. The polarizabilities of the two states are determined by means of configuration interaction calculations in conjunction with oscillator strength sum rules. The ground state polarizability was 24.14 ±0.12 a.u. while the metastable state polarizability was 24.62 ±0.25 a.u. The derived frequency shift at 300 K was Δν= -0.0042 ±0.0032 Hz. Some auxiliary sum rules are evaluated that allow for the conversion of a finite frequency polarizability difference to a static polarizability difference.

An ab initio and TD-DFT study of solvent effect contributions to the electronic spectrum of Nile Red

A CIS and TD-DFT study using a polarizable continuum solvent model has been conducted to assess non-specific solvent effects on the spectral shifts in Nile Red (NR). The results in this paper show that the electronic band shifts of Nile Red are a consequence of both a field effect on the transition energy and an effect due to a solvent induced geometry change. The S0-->S1 transition experiences a large red-shift with increasing solvent polarity but is relatively insensitive to geometric change. The TD-B3LYP assessment of the S0-->S2 transition yields a blue shift with increasing solvent polarity but a red shift due to the solvent induced geometry change. Ground state dipole moments and polarizabilities are also shown to increase with solvent polarity. CIS optimization of the first excited state of NR is reported, but the solvent effects suggest a locally excited state may have been obtained. Further studies are needed to assess the role of a TICT state.