Dipole Oscillator Strength Distributions Research Articles

Dipole–Dipole Polarizability of the Cadmium 1S0 State Revisited

Experimental results and high-level quantum chemical ab initio calculations of the static polarizability $\alpha_0=\alpha(\omega=0)$ of the cadmium ${^1S_0}$ state are still in marked disagreement. Here we analyze this discrepancy by using experimentally determined dipole oscillator strength distributions (DOSD). It will be shown that within this procedure the experimentally determined static polarizability $\alpha_0$ will shift from $49.7 \pm 1.6~$au to considerably lower values. We now conclude an experimentally determined polarizability of $\alpha_0=47.5 \pm 2.0~$au in much better agreement with the latest calculations of $\alpha_0 \approx 46~$au.

Dipole-dipole polarizability of the cadmium -=SUP=-1-=/SUP=-S-=SUB=-0-=/SUB=- state revisited -=SUP=-*-=/SUP=-

Experimental results and high-level quantum chemical ab initio calculations of the static polarizability α=α(ω=0)) of the cadmium 1S0 state are still in marked disagreement. Here we analyze this discrepancy by using experimentally determined dipole oscillator strength distributions (DOSD). It will be shown that within this procedure the experimentally determined static polarizability α0 will shift from 49.7± 1.6 au to considerably lower values. We now conclude an experimentally determined polarizability of α0 = 47.5 ± 2.0 au in much better agreement with the latest calculations of α0~ 46 au. Keywords: cadmium, polarizability, DOSD

Dipole oscillator strength distributions, sum rules, mean excitation energies, and isotropic van der Waals coefficients for benzene, pyridazine, pyrimidine, pyrazine, s-triazine, toluene, hexafluorobenzene, and nitrobenzene

Experimental, theoretical, and additive-model photoabsorption cross sections combined with constraints provided by the Kuhn-Reiche-Thomas sum rule and the high-energy behavior of the dipole oscillator strength density are used to construct dipole oscillator strength distributions for benzene, pyridazine (1,2-diazine), pyrimidine (1,3-diazine), pyrazine (1,4-diazine), s-triazine (1,3,5-triazine), toluene (methylbenzene), hexafluorobenzene, and nitrobenzene. The distributions are used to predict dipole sum rules S(k) for -6 ≤ k ≤ 2, mean excitation energies I(k) for -2 ≤ k ≤ 2, and isotropic van der Waals C6 coefficients. A popular combination rule for estimating C6 coefficients for unlike interactions from the C6 coefficients of the like interactions is found to be accurate to better than 1% for 606 of 628 cases (96.4%) in the test set.

Medium-induced change of the optical response of metal clusters in rare-gas matrices

Interaction with the surrounding medium modifies the optical response of embedded metal clusters. For clusters from about ten to a few hundreds of silver atoms, embedded in rare-gas matrices, we study the environment effect within the matrix random phase approximation with exact exchange (RPAE) quantum approach, which has proved successful for free silver clusters. The polarizable surrounding medium screens the residual two-body RPAE interaction, adds a polarization term to the one-body potential, and shifts the vacuum energy of the active delocalized valence electrons. Within this model, we calculate the dipole oscillator strength distribution for Ag clusters embedded in helium droplets, neon, argon, krypton, and xenon matrices. The main contribution to the dipole surface plasmon red shift originates from the rare-gas polarization screening of the two-body interaction. The large size limit of the dipole surface plasmon agrees well with the classical prediction.

Static polarizabilities and C6 dispersion coefficients using the algebraic-diagrammatic construction scheme for the complex polarization propagator

An implementation of the damped linear response function, or complex polarization propagator, using the algebraic-diagrammatic construction (ADC) scheme has been developed and utilized for the calculation of electric-dipole polarizabilities and C6 dispersion coefficients. Four noble gases (He, Ne, Ar, and Kr), five n-alkanes (methane, ethane, propane, butane, and pentane), three carbonyls (formaldehyde, acetaldehyde, and acetone), and three unsaturated hydrocarbons (ethene, acetylene, and benzene) have been treated with the hierarchical set of models ADC(2), ADC(2)-x, and ADC(3/2), and comparison has been made to results obtained with damped linear response Hartree–Fock (HF) and coupled cluster singles and doubles (CCSD) theory as well as high-quality experimental estimates via the dipole oscillator strength distribution approach. This study marks the first ADC calculations of C6 dispersion coefficients and the first ADC(3/2) calculations of static polarizabilities. Results at CCSD and ADC(3/2) levels of theory are shown to be of similar quality, with electron correlation effects increasing the molecular property values for all calculations except CCSD considerations of ethene and acetylene (attributed to an overestimation of bond electron density at HF level of theory). The discrepancies between CCSD and ADC(3/2) are partially due to ADC overestimating anisotropies, and discrepancies with respect to experimental values are partially due to the lack of zero-point vibrational effects in the present study.

Lindhard's polarization parameter and atomic sum rules in the local plasma approximation: a case for excited states

ABSTRACTIn this work, we analyze the effects of Lindhard polarization parameter, χ, on the sum rule, , within the local plasma approximation (LPA) as well as on the logarithmic sum rule , in both cases for the system in an initial excited state. We show results for a hydrogenic atom with nuclear charge Z for the spherically symmetric (l=0) states with n=1, 2 and 3 with p=−1,0,1, and 2. Our calculations are complemented with comparisons to the exact results for this system for the ground state. As a natural extension of our treatment, we report analytical results for helium-like systems in terms of a screened charge for the ground state. Our study shows that by increasing χ, the sum rule for p<0 decreases while for p>0 it increases, and the value p=0 provides the normalization/closure relation which remains fixed to the number of electrons for the same initial state. When p is fixed, the value of increases as the initial excited state increases for p<0 and decreases for p>0. Thus, when using a specific value of χ to adjust to a particular sum rule value, the sum rule becomes unbalanced for other values of p. Our results show that the dipole oscillator strength distribution, within the LPA, provides good results for the sum rules for excited states.

Constrained dipole oscillator strength distributions, sum rules, and dispersion coefficients for Br2 and BrCN

Dipole oscillator strength distributions for Br2 and BrCN are constructed from photoabsorption cross-sections combined with constraints provided by the Kuhn-Reiche-Thomas sum rule, the high-energy behavior of the dipole-oscillator-strength density and molar refractivity data when available. The distributions are used to predict dipole sum rules S(k), mean excitation energies I(k), and van der Waals C6 coefficients. Coupled-cluster calculations of the static dipole polarizabilities of Br2 and BrCN are reported for comparison with the values of S(-2) extracted from the distributions.

Inelastic cross-sections and energy loss properties by non-relativistic heavy ions in zirconium dioxide

A formalism for the inelastic cross-section for electronic collisions of protons and heavier ions in a material is developed based on a quadratic extrapolation of the experimentally based dipole oscillator strength distribution (DOSD) of the material into the energy momentum plane. The approach is tested by calculating various energy loss properties in zirconium dioxide. Mean free path, stopping power and continuous slowing down approximation (csda) range are predicted as a function of ion energy for various incident ions, with the stopping powers compared to experimental data to assess the effectiveness of the methodology. The DOSD is straightforwardly obtained from the experimentally measured energy loss function data below 80eV and atomic photo-absorption cross-section data above 100eV. Agreement between the results of the calculation for stopping power and the experimental data is within 10% for all ions when compared for energies greater than the Bragg peak. The discrepancy is larger below the peak due to limitations in the methodology, especially the failure to make corrections for the Barkas and higher order effects and the lack of charge cycling cross-section data.

Dipole properties of PH3, PF3, PF5, PCl3, SiCl4, GeCl4, and SnCl4

ABSTRACTExperimental and theoretical photoabsorption cross sections combined with constraints provided by the Kuhn–Reiche–Thomas sum rule, the high-energy behaviour of the dipole oscillator strength density, static dipole polarisabilities, and molar refractivity data when available are used to construct dipole oscillator strength distributions for PH3, PF3, PF5, PCl3, SiCl4, GeCl4, and SnCl4. The distributions are used to predict dipole sum rules S(k), mean excitation energies I(k), and van der Waals C6 coefficients.

Construction of Constrained Dipole Oscillator Strength Distributions

Abstract A brief review is given of how a constrained dipole oscillator strength distribution (DOSD) is constructed from experimental and possibly theoretical photoabsorption cross-sections with constraints provided by molar refractivity data and the Kuhn–Reiche–Thomas sum rule. Some recent refinements including the imposition of the correct high-energy behavior on the DOSD for homoatomic molecules are discussed and extended to the general molecular case. A sample application to pyridine is given.

Empirically constructed dynamic electric dipole polarizability function of magnesium and its applications

The dynamic electric dipole polarizability function for the magnesium atom is formed by assembling the atomic electric dipole oscillator strength distribution from combinations of theoretical and experimental data for resonance oscillator strengths and for photoionization cross sections of valence and inner shell electrons. Consistency with the oscillator strength (Thomas-Reiche-Kuhn) sum rule requires the adopted principal resonance line oscillator strength to be several percent lower than the values given in two critical tabulations, though the value adopted is consistent with a number of theoretical determinations. The static polarizability is evaluated. Comparing the resulting dynamic polarizability as a function of the photon energy with more elaborate calculations reveals the contributions of inner shell electron excitations. The present results are applied to calculate the long-range interactions between two and three magnesium atoms and the interaction between a magnesium atom and a perfectly conducting metallic plate. Extensive comparisons of prior results for the principal resonance line oscillator strength, for the static polarizability, and for the van der Waals coefficient are given in the Appendix.

On the dipole polarisability and dipole sum rules of ozone

Ab initio calculations of the dipole polarisability and other Cauchy moments of the dipole oscillator strength distribution (DOSD) of ozone are reported to help resolve discrepancies between theory and experiment. A number of coupled-cluster methods based on a Hartree–Fock reference function, multiconfiguration-reference configuration interaction methods, and perturbatively corrected, complete-active-space self-consistent field methods are used. The C DOSD of Kumar and Thakkar is probably preferable to their B1 distribution. Our best estimate of the mean polarisability is atomic units.

Long-range correlation energies from frequency-dependent weighted exchange-hole dipole polarisabilities

Long-range correlation energies are calculated using an approximation of the single-particle density-density response function of the system that leads to an expression requiring only occupied orbitals and eigenvalues. Dipole-dipole polarisabilities and isotropic leading-order dispersion coefficients obtained from this approximation are shown to be in a reasonable agreement with corresponding values from the experiment or dipole oscillator strength distributions. The localised polarisabilities were used to calculate a long-range correlation correction to a hybrid-generalised gradient approximation functional using a proper damping function at short ranges. It was found that the hybrid density-functional theory+dispersion method obtained in this way has a comparable accuracy than high-level ab initio wave function methods at a much lower computational cost. This has been analysed for a number of systems from the GMTKN30 database including subsets for noncovalently bound complexes, relative energies for sugar conformers and reaction energies and barrier heights of pericyclic reactions of some medium sized organic molecules.

Dipole polarizability, sum rules, mean excitation energies, and long-range dispersion coefficients for buckminsterfullerene C60

Experimental photoabsorption cross-sections combined with constraints provided by the Kuhn–Reiche–Thomas sum rule and the high-energy behavior of the dipole-oscillator-strength density are used to construct dipole oscillator strength distributions for buckminsterfullerene (C60). The distributions are used to predict dipole sum rules Sk, mean excitation energies Ik, the frequency dependent polarizability, and C6 coefficients for the long-range dipole–dipole interactions of C60 with a variety of atoms and molecules.

Linear Response and Measures of Electron Delocalization in Molecules

The concept of localization and delocalization in molecules is discussed in terms of the response of the electronic system to an external perturbation. It is argued that both the spatial organization of electrons in pairs and the spatial distribution of the response intensity, reflect main features of the correlated motion of electrons, ultimately described by the pair distribution function of electrons. Various measures, derived from the linear charge density response function, are able to characterize localization in a rigorous way, in close analogy to the approach followed in solid state physics. Keywords: Electron localization, linear response, Resta localization index, bond order, localized orbitals, exchange hole, distributed polarizabilities, fluctuation-dissipation theorem, POLARIZABILITY, EXCHANGECORRELATION HOLE, Hartree-Fock (HF), Kohn-Sham (KS), TDCHF (time-dependent coupled Hartree-Fock), dipole oscillator strength distributions (DOSD), Delocalization Indices, MOLECULAR ORBITAL LOCALIZATION CRITERIA

Ozone: Unresolved discrepancies for dipole oscillator strength distributions, dipole sums, and van der Waals coefficients

Dipole oscillator strength distributions (DOSDs) for ozone are constructed from experimental photoabsorption cross-sections combined with constraints provided by the Kuhn-Reiche-Thomas sum rule, the high-energy behavior of the dipole-oscillator-strength density, and molar refractivity data. A lack of photoabsorption data in the intermediate energy region from 24 to 524 eV necessitates the use of a mixture rule in that region. For this purpose, a DOSD for O(2) is constructed first. The dipole properties for O(2) are essentially the same as those obtained in earlier work even though most of the input data is from more recent experiments. A discrepancy is found between the refractivity data and photoabsorption data in the 10-20.6 eV range for ozone. A reliable ozone DOSD of the sort obtained for many other species remains out of reach. However, it is suggested that the true dipole properties of ozone lie between those predicted by two distributions that we present.

Dipole oscillator strength distributions with improved high-energy behavior: Dipole sum rules and dispersion coefficients for Ne, Ar, Kr, and Xe revisited

The construction of the dipole oscillator strength distribution (DOSD) from theoretical and experimental photoabsorption cross sections combined with constraints provided by the Kuhn-Reiche-Thomas sum rule and molar refractivity data is a well-established technique that has been successfully applied to more than 50 species. Such DOSDs are insufficiently accurate at large photon energies. A novel iterative procedure is developed that rectifies this deficiency by using the high-energy asymptotic behavior of the dipole oscillator strength density as an additional constraint. Pilot applications are made for the neon, argon, krypton, and xenon atoms. The resulting DOSDs improve the agreement of the predicted S(2) and S(1) sum rules with ab initio calculations while preserving the accuracy of the remainder of the moments. Our DOSDs exploit new and more accurate experimental data. Improved estimates of dipole properties for these four atoms and of dipole-dipole C(6) and triple-dipole C(9) dispersion coefficients for the interactions among them are reported.

Dipole oscillator strength distributions, properties and dispersion energies for the dimethyl, diethyl and methyl–propyl ethers1

Isotropic dipole oscillator strength distributions (DOSDs) have been constructed for the dimethyl, diethyl and methyl–propyl ether molecules through the use of quantum mechanical constraint techniques and experimental dipole oscillator strength data. The constraints are furnished by molar refractivity data and the Thomas–Reiche–Kuhn sum rule. The DOSDs are used to obtain recommended values for a variety of isotropic dipole oscillator strength sums, logarithmic dipole oscillator strength sums, and mean excitation energies for the molecules. Pseudo-DOSDs for the ethers are also constructed and used to obtain reliable results for the isotropic dipole–dipole dispersion energy coefficients for all two-body interactions of the ethers with each other and with fifty other species. In addition reliable results are also obtained for the triple–dipole dispersion energy coefficients for all three-body interactions involving the ethers. 1Dedicated to Anthony Stone, an excellent scientist and friend, on the occasion of his 70th birthday.

Dipole oscillator strength distributions, properties, and dispersion energies for ethylene, propene, and 1-butene

A recommended isotropic dipole oscillator strength distribution (DOSD) has been constructed for the ethylene molecule through the use of quantum mechanical constraint techniques and experimental dipole oscillator strength (DOS) data; the DOS data employed are recent experimental results not available at the time of the original constrained DOSD analysis of this molecule. The constraints are furnished by molar refractivity data and the Thomas–Reiche–Kuhn sum rule. The DOSD is used to evaluate a variety of isotropic dipole oscillator strength sums, logarithmic dipole oscillator strength sums, and mean excitation energies for ethylene. Pseudo-DOSDs for this molecule, and for propene and 1–butene, which are based on an earlier constrained DOSD analysis for these molecules, are developed. They are used to obtain reliable results for the isotropic dipole–dipole dispersion-energy coefficients C6, for the interactions of the alkenes with each other and with 47 other species, and the triple-dipole dispersion-energy coefficients C9 for interactions involving any triple of molecules taken from ethylene, propene, and 1–butene.Key words: alkenes, dipole properties, pseudo-states, dipole–dipole and triple-dipole dispersion energies, long-range additive, non-additive interaction energies.

Directional Dependence of the Mean Excitation Energy and Spectral Moments of the Dipole Oscillator Strength Distribution of Glycine and Its Zwitterion

In this contribution, we consider the interaction of glycine, a small, model biomolecule, and its zwitterion with fast ion radiation. The object of the study is to determine the differences in properties among various conformers and orientations of the neutral molecule and the zwitterion and to determine if these differences will have implications in terms of radiation protection and radiation therapy. To this end, quantum mechanical calculations were carried out on three conformers of the neutral molecule and two of the zwitterion to determine both the isotropic and directional components of the moments of the dipole oscillator strength distribution in each case. It is these moments that determine the interaction of swift radiation with a molecule.