Dynamic polarizability of many-electron systems within a time-dependent density-functional theory

Using the time-dependent extension, proposed by us recently, of the Hohenberg—Kohn—Sham density-functional theory, in the presence of an oscillating electric field, we suggest a Karplus—Kolker-type variation—perturbation method for the calculation of dynamic 2^L-pole polarizability of many-electron systems. As an illustration of the present density-functional formalism, the frequency-dependent dipole polarizability of He atom has been calculated in the frequency range 0 ? ω ? 0.65 au, using local density forms of the exchange and correlation potentials. For ω = 0, the results are numerically better than recent density-functional calculations of the static dipole polarizability of He. The corresponding hydrodynamical formulation, which employs the single-particle density as a basic variable, is also presented.     

Static dipole polarizability of electronically excited molecules: H2(B1Σu+)

The dipole polarizability of H₂(B¹Σ_u⁺) is computed using extended Gaussian basis sets and Hartree-Fock, multiconfiguration Hartree-Fock, and configuration interaction wavefunctions. Electron correlation contributions are found to be significant (≈ 25%) with the largest contribution arising from angular correlation. With a full CI wavefunction, the components of the dipole polarizability were computed to be (in au): α_⊥ = 50 and α_| = 257.     

Ground-state dipole polarizability of lithium hydride. Accurate SCF and CAS SCF calculations

Accurate calculations of the dipole polarizability tensor of lithium hydride are performed using the finite-field perturbation approach in the SCF and CAS SCF method. The SCF results (α_? = 22.1, α_⊥ = 25.4 au) are expected to be very close to the HF values. The CAS SCF calculations predict a positive correlation contribution, giving α_? = 26.3 and α_⊥ = 29.3 au.     

Electric properties of hydrogen iodide: Reexamination of correlation and relativistic effects

The electric dipole moment and the static dipole polarizability of the hydrogen iodide molecule were studied using sophisticated correlated and relativistic methods. Both scalar and spin–orbit relativistic effects were carefully accounted for. We conclude that the large differences between the theoretical and experimental dipole moment, the dipole moment derivative and the polarizability cannot be reconciled by improved account of electron correlation and relativistic effects. The most striking difference between theory and experiment is observed for the polarizability anisotropy. We believe that experimental data, namely the experimental dipole moment (the most recent value is 0.176 au as compared to our best theoretical estimate, 0.154±0.003 au), the parallel polarizability (44.4 and 38.47±0.05 au) and the anisotropy (11.4 and 2.33±0.05 au) must be inaccurate. Experimental and theoretical perpendicular polarizability components (33.0 and 36.14±0.05 au,) and the mean polarizability (36.8 and 36.92±0.05 au) agree better. Our vibrationally corrected relativistic CCSD(T) results represent the most sophisticated predictions of electric properties of HI obtained so far.Contribution to the Björn Roos Honorary Issue     

Water dimer dipole moment

The peculiar properties of the behavior of effective polarizability of water molecules in its saturated vapor are discussed on the basis of the experimental data on the static dielectric constant. It is taken into account that in the region 273 K < T < 485 K there is a mixture of monomers and dimers in the water vapor. The comparison of the theoretical and experimental expressions for the effective polarizability shows that the dipole moment of water dimer is connected with the dipole moment of monomer via relation: d _D = √2d _m. The relative value of the irreducible pair contributions to the polarizability of the dimer is determined.     

Preface

The anisotropic rototranslational scattering spectra of nitrogen gas at high frequency up to 700 cm⁻¹ for several temperatures and from low densities are analyzed in terms of new site–site (M3SV) intermolecular potential and interaction-induced pair polarizability models, using quantum spectral shapes computations. Our theoretical calculations take into account multipole contributions from the mean value and anisotropy of the dipole–dipole polarizability tensor α, two independent components of the dipole–octopole polarizability tensor E and dipole–dipole–quadrupole hyperpolarizability tensor B. The high-frequency wings are discussed in terms of the collision-induced rotational Rayleigh effect and estimates for the dipole–octopole polarizability |E₄| are obtained and checked with recent ab initio theoretical value. Good comparison is found in the frequency range 0–400 cm⁻¹ between the theoretical and experimental spectra. When an exponential contribution [exp(−ν/ν₀)] with ν₀ = 425 cm⁻¹ is considered to model very short-range light scattering mechanisms at room temperature, good agreement is found over the whole frequency range.     

Calculation of the electric susceptibilities of the helium atom

We calculated the static and the dynamic dipole polarizabilities and the static quadrupole polarizability of the helium atom. The results are α = 0.2070 × 10^?24 cm³ for the static dipole polarizability and γ₄ = 0.1038 × 10^?40 cm⁵ for the static quadrupole polarizability.     

Static dipole polarizability of ytterbium

The static dipole polarizability of the ground state ytterbium atom is calculated using full and approximate relativistic ab initio methods. Our recommended polarizability of 143 au is consistent with experimental atomic spectral data. The corresponding van der Waals coefficient C6 of Yb2, derived using Padé approximants, is 2062 (200) au.     

Collision rotational transfers in NaH A1Σ+ by He,Ar or H2 (and in KH A1Σ+ by H2)

The total and relative rotational transfer cross sections σ_total and σ_Ji-Jf, by collisions of NaH A¹Σ with He, Ar or H₂, are measured from υ′ = 4 and υ′ = 11, J₁′ = 6. The σ_total increase as υ′ increases. They are similar for He and H₂ but much greater for Ar especially at large υ′. In NaH A¹Σ⁺ the bond goes from covalent to ionic as υ′ increases: σ_total is very sensitive to an attractive potential due to the interaction of the permanent electric dipole moment of the molecule with the polarizability of the atom (α_Ar = 11 au, α_He = 1.37 au). The σ_Ji-Jf decrease monotonously as |J_f-J_i| increases and may be fitted by a scaling law. The variation with ΔJ depends on the colliding gas but does not change appreciably with υ′: most of the transfers could take place on the repulsive part of the interaction potential, the shape of which would not depend on υ′.     

Variation of the Intersection Point of the Potential Surface Crossing Induced by the Laser Phase Along the Reaction Path in Ion-Molecule Reactions: Application To Li<Superscript>+</Superscript> + CH<Subscript>4</Subscript>

A laser ion-molecule reaction interaction through both polarizability and dipole moment contribution leads to variation in the intersection point in potential energy surface crossings along the reaction path; the polarizability is maximum and the dipole changes its sign at s = 4 a.u., defining a virtual transition state. Using the gauge representation (electric field gauge) for a wave length λ = 20.6 μm, intensity I = 5×10¹² W/cm², I = 1×10¹³ W/cm², I = 3×10¹³ W/cm², we show here that we can create a laser-induced potential energy surface crossing along the reaction path (s = 7-8 a.u.). We illustrate such effects for the Li H + CH ₃ ⁺ ? Li⁺ + CH₄ reaction which takes the form of inverted Morse (without a barrier) using ab initio methods for calculating the reaction path and electric properties of the ion-molecule reaction.     

A dipole moment study of organo-chalcogen compoun

Analysis of the dipole moments of chalcogenoanisoles, the directions of which are given by those of their p-bromo derivatives, shows that the mesomeric moment decreases on passing from anisole to thioanisole, selenoanisole and telluroanisole (m = 1.1, 0.5, 0.25 and 0.18 D, respectively). In p-nitrochalcogenoanisoles and 1-chalcogenochroman-4-ones the interaction moment follows the reverse order, which is ascribed to the increasing sensitivity of the chalcogen mesomeric moment to the chalcogen atomic number and polarizability. The less-hindered (Te, O)-cis conformation is preferred for 2-acyl-3-methyltellurothiophenes and 3-acyl-2-methyltellurothiophenes (acyl: formyl or acetyl), and 3-formyl-4-methyltellurothiophene. Rotational isomerism in bis(2-furyl), bis(2-thienyl), bis(3-thienyl) and bis(2-selenienyl) ditelluride is also examined, and the dipole moments of 1-chalcogenochroman-4-ones, 2-chalcogenochroman-1-ones and 2-chalco-genochrom-1-ones analyzed.     

Dipole polarizabilities of germanium clusters

Dipole polarizabilities of Ge_n clusters with 2–25 atoms are calculated using finite field (FF) method within density functional theory. The dipole moments and polarizabilities of clusters are sensitively dependent on the cluster geometries and electronic structures. The clusters with low symmetry and large HOMO–LUMO gap prefer to large dipole moments. The polarizabilities of the Ge_n clusters increase rapidly in the size range of 2–5 atoms and then fluctuate around the bulk value. The larger HOMO–LUMO gap may lead to smaller polarizability. As compared with the compact structure and diamond structure, the prolate cluster structure corresponds to a larger polarizability.     

New relationships connecting the dipole polarizability, radius, and second ionization potential for atoms

The atomic dipole polarizability α of the 101 elements from He to No is related to the second ionization potential I? and the Waber-Cromer radius r(WC). Our recommended model is the function α = P?·I??? + P?·r(WC)(3) I?(y). With the parameters P? = 2.26, P? = 3.912, and y = 0.439, it reproduces the polarizabilities of all 101 elements with a mean absolute deviation of 7.5 au.     

The polarizability of a pair of hydrogen atoms at long range

The coefficients of R^?6 and R^?9 in the long-range expansion of the parallel and perpendicular components of the polarizability of a pair of hydrogen atoms at a separation R have been calculated. The results are A⁽⁶⁾₆ = 2558.59. A⁽⁶⁾_⊥ = 1268.25, A⁽⁸⁾₆ = 90639.5 and A⁽⁸⁾_⊥ = 22010.3 au. The values of A⁽⁶⁾₆ and A⁽⁶⁾₆ and A⁽⁶⁾_| are somewhat larger than previous theoretical estimates and much larger than the classical values of 729 and 182.25 au. The terms in R^?8 arise from distortion associated with the dispersion forces and from the field of the quadrupole moment induced by the field-gradient at each atom.     

On the dipole and higher polarizabilities of Ne(1S)

The dipole polarizability and the higher-order polarizabilities of Ne(¹S) are calculated in the LCAO SCF approximation. The higher polarizabilities are found to be strongly basis-set dependent. Our final values for α, C, B and γ are 2.37, 2.04, -13.6 and 78 (in atomic units).     

Electric field gradients in EuScFe garnets

The electric quadrupole interactions at the octahedral, tetrahedral, and dodecahedral sites in the Eu_3?ySc_2+yFe₃O₁₂ (0 ≤ y ≤ 0.5) garnet system were studied with ⁵⁷Fe and ¹⁵¹Eu Mössbauer spectroscopy. The electric field gradient tensor at the three sites was calculated using a monopole-point-dipole model. It is shown that the dipole contribution to the electric field gradient tensor is not negligible even for very small values of the oxygen dipole polarizability. The importance of the overlap and second-order 4f contributions is discussed.     

Hartree—Fock—Slater functions as basis for one-electron perturbation calculations for molecules: I. Calculation of ground state electric dipole polarizabilities

The analysis of the decoupling of Hartree—Fock—Slater SCF perturbation equations for an external field is undertaken. The points of departure from the corresponding Hartree—Fock perturbation equations are stressed. Both formal and numerical results suggest that the fully uncoupled Hartree—Fock—Slater expression is a less drastic approximation than the same Hartree—Fock one. The uncoupled expression for the ground state electric dipole polarizability is calculated for CO, N₂, ethylene, acethylene and trans-butadiene in the dipole length—dipole length, dipole velocity—dipole length and dipole velocity—dipole velocity alternative formulations with an ab initio Hartree—Fock—Slater SCF basis set. The results compare well with other non-empirical results and the dipole velocity-dipole length results are in remarkably good agreement with experiments.     

Polarizability effect in silatranes and related compounds

The dipole moments (μ) of the molecules, the dipole moments (μ_DA) and the length (d_DA) of the Si ← N bonds, and the electrochemical oxidation potentials (E_p) of Si-substituted silatranes, the dipole moments (μ^hs) of the molecules of Si-substituted 3-homosilatranes as well as the enthalpies of formation (ΔH⁰) of the intermolecular complexes of SiF₄ with aniline derivatives depend not only on the inductive and resonance effects, but also on the polarizability of substituents which can be characterized by the σ_α constants.     

A sum-over-state scheme of analysis of hyperpolarizabilities and its application to spiroconjugated molecular system

The static first and second hyperpolarizabilities of a number of spiromolecules with varying degree of polarity have been calculated at the HF and MP2 level using the 6-31+G* basis set and the B3LYP/6-31+G* optimized geometry. The variation of mean second hyperpolarizability in these molecular systems has been explained in terms of the ground state dipole moment, mean linear polarizability and second-order polarizability. A number of relationships among these quantities have been derived in the framework of the sum-over-state scheme and the generalized Thomas–Kuhn sum rule. The spiroconjugation results in the significant increase of the mean polarizability. The appreciable enhancement of first hyperpolarizability due to the spiroconjugation between two dipolar monomer units has been accounted for the rather significant increase of the mean polarizability tensor and the ground state dipole moment. The relatively larger value of the average second hyperpolarizability of the spiroconjugated molecules compared to that of the corresponding monomers arises from the rather significant increase of the nonaxial component γ _xxyy . The replacement of spirocarbon by spirosilicon results in the enhancement of the cubic polarizability manifold. The donor–acceptor substituted spirocompounds are predicted to be the superior third-order nonlinear optical (NLO) phores. The nature of π-conjugation in the monomer units around the spirocenter shows a strong modulation of the NLO properties of spirocompounds. The influence of electron correlation on the NLO properties at the MP2 level has been found to be rather significant.