Dispersion energy constants C 6(A,B), dipole oscillator strength sums and refractivities for Li,N, O,H2, N2, O2, NH3, H2O,NO and N2O

Accurate values for the orientation-averaged long-range dipole-dipole dispersion energy coefficients, C ₆(A, B), have been determined for all possible pair interactions involving ground state H, Li, N, O, H₂, N₂, O₂, NH₃, H₂O, NO, and N₂O. The calculations have been carried out by employing dipole oscillator strength distributions for these species that have been constructed (except in the case of H) by using discrete oscillator strength, photo-absorption, and high energy inelastic scattering data and by requiring the distributions to reproduce the Thomas-Reiche-Kuhn sum rule and, in the case of the molecules, available accurate refractivity and dispersion measurements for the relevant dilute gases. These oscillator strength distributions were also used to evaluate the refractivity R(λ), as a function of wavelength λ in the visible and ultra-violet region below the ultra-violet absorption thresholds, and the dipole oscillator strength sums S _-2l , l = 1, 2, …, 7, for each atom and molecule. The calculated values of R(λ) provide refractivities for wavelengths, especially in the ultra-violet region, for which accurate experimental data are often not available. The accurate results for C ₆(A, B) and for various dipole oscillator strength sums are used to make self-consistent tests of the adequacy of (1) the C ₆(A, A) bounds provided by Padé approximant methods and (2) various semi-empirical formulae for C ₆(A, B). Some problems that can arise in using other procedures to evaluate the S _-2l and C ₆(A, B) are discussed briefly.     

On the additivity of atomic and molecular dipole properties and dispersion energies using H,N, O,H2, N2, O2, NO,N2O,NH3 and H2O as models

The zeroth-order theory of intermolecular forces is used to derive additivity relations for rotationally averaged molecular dipole properties and dispersion energy constants by assuming that a molecule is comprised of non-interacting atoms or molecules. Some of the additivity rules are new and others, for example the mixture rule for dipole oscillator strength distributions (DOSDs), Bragg's rule for stopping cross sections and Landolt's rule for molecular refractivities, are well known. The additivity rules are tested by using previously constructed DOSDs and reliable values for the dipole oscillator strength sums S_k , L_k and I_k , and dispersion energy constants C ₆, for H, N, O, H₂, N₂, O₂, NO, N₂O, NH₃ and H₂O as models. It is found that additivity is generally unreliable for estimating molecular properties corresponding to k < -2. Generally for k ≥ -2 and for C ₆, and if the hydrogen molecule is used to represent the hydrogen atom in the additivity rules, the additivity relations yield results that are reliable to within ?20 per cent and the estimates improve substantially as k increases. The effects of molecule formation on DOSDs is examined by comparing the various molecular DOSDs with the sum of the DOSDs for the atoms making up the molecules. Molecule formation results in a net decrease in the amount of dipole oscillator strength for low excitation energies and a compensating net increase for higher energies in a region extending from the absorption threshold to about 100 eV. This is shown to imply that estimates of the stopping average energy I ₀, obtained by using bona fide atomic I ₀ values, are lower bounds to the correct molecular I ₀ results.     

N.M.R. studies of cis-1,2-difluoroethylene and vinyl fluoride in a nematic solvent

Constrained anisotropic dipole oscillator strength techniques are used to obtain reliable values for a wide range of anisotropic and isotropic dipole properties of NO, including most anisotropic components of the dipole-dipole dispersion energy coefficients for the interaction of NO with NO, O₂, H₂, N₂, CO, He, Ne, Ar, Kr and Xe. Some of the anisotropic constraints required for our calculations are obtained via dipole sum rules from ab initio, multi-reference configuration interaction wavefunctions for NO. The individual dipole properties of NO considered include the dipole oscillator strength sums S_k , k = 2,1,0(? 1/2)? 2,? 3,? 4,..., the logarithmic dipole sums L_k and mean excitation energies I_k , k = 2(? 1)? 2, and, as a function of wavelength, the dynamic polarizability and its anisotropy, the total depolarizaiton ratio, and the Rayleigh scattering cross-section. Our constrained dipole oscillator strength results are often the only reliable, and often the only available, values for many of the properties and dispersion energies considered.     

Dipole oscillator strengths,dipole properties and dispersion energies for SiF4

A recommended isotropic dipole oscillator strength distribution (DOSD) has been constructed for the silicon tetrafluoride (SiF₄) molecule through the use of quantum mechanical constraint techniques and experimental dipole oscillator strength data. The constraints are furnished by experimental 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 the molecule. A pseudo-DOSD for SiF₄ is also presented which is used to obtain reliable results for the isotropic dipole-dipole dispersion energy coefficients C₆, for the interaction of SiF₄ with itself and with 43 other species and the triple-dipole dispersion energy coefficient C₉ for (SiF₄)₃.     

E.S.R. spectra of PF4 radicals produced in a single crystal of PF3

E.S.R. spectra of PF₄ radicals were investigated with single crystals of PF₃ made at a low temperature and irradiated with γ-rays. The angular dependence of the spectral lines was satisfactorily analysed in terms of the second-order equations for large couplings of one ³¹P nucleus and two magnetically equivalent ¹⁹F nuclei and of the first-order equation for two ¹⁹F nuclei with small couplings. We conclude that the two magnetically equivalent fluorine nuclei occupy the axial positions of the trigonal bipyramidal structure of the PF₄ radical and the other two fluorine nuclei are in the equatorial positions. Furthermore, the unpaired electron of the PF₄ radical was shown to occupy an orbital consisting mainly of the 2p orbital of each of the two axial fluorine atoms along the F-P-F axis and the 3s and 3p orbitals, directed towards the vacant equatorial position of the central phosphorus atom. The orbital of the unpaired electron can be reasonably represented as a Rundle three-centre non-bonding orbital. The results obtained for the PF₄ radicals not only strongly support the results given for POCl₃ ^- radicals, but also allow us to discuss the electronic structure of phosphoranyl radicals in more detail.     

A coupled cluster study of the magnetisability,rotational g-tensor and quadrupole moment of NF3, PF3 and AsF3

ABSTRACT

A coupled-cluster investigation of magnetic and electric properties of NF₃, PF₃ and AsF₃ provides for a comparison with recent experimental data. For PF₃, achieving reliable values for the magnetisability and rotational g-tensor of PF₃ has been particularly challenging. We report the most accurate calculations to date for PF₃; for the vibrationally corrected anisotropic magnetisability, our extrapolated CCSD(T)/CBS value of ?0.290 a.u is within the uncertainty limits of the most recent experimental value of ?0.286 ± 0.042 a.u. For the rotational g-tensor of PF₃, agreement between theory and experiment for the g_⊥ component is excellent (deviation of less than 0.0006 a.u.). However, the g_|| component remains problematic even though our vibrationally corrected CCSD(T)/CBS value of ?0.0387 a.u is in closer agreement with the recently revised experimental value of ?0.0470 ± 0.0020 a.u. than the original value of ?0.0815 ± 0.0020 a.u. The origin of the remaining discrepancy remains unclear. Dipole and quadrupole moments have also been investigated.     

The 2‐matrix of the spin‐polarized electron gas: contraction sum rules and spectral resolutions

The spin‐polarized homogeneous electron gas with densities ρ_↑ and ρ_↓ for electrons with spin ‘up’ (↑) and spin ‘down’ (↓), respectively, is systematically analyzed with respect to its lowest‐order reduced densities and density matrices and their mutual relations. The three 2‐body reduced density matrices γ_↑↑, γ_↓↓, γ_a are 4‐point functions for electron pairs with spins ↑↑, ↓↓, and antiparallel, respectively. From them, three functions G_↑↑(x,y), G_↓↓(x,y), G_a(x,y), depending on only two variables, are derived. These functions contain not only the pair densities according to g_↑↑(r) = G_↑uarr;(0,r), g_↓↓(r) = G_↓↓(0,r), g_a(r) = G_a(0,r) with r = | r ₁ ‐ r ₂|, but also the 1‐body reduced density matrices γ_↑ and γ_↓ being 2‐point functions according to γ_s = ρ_sf_s and f_s(r) = G_ss(r, ∞) with s = ↑,↓ and r = | r ₁ ‐ r ^′₁|. The contraction properties of the 2‐body reduced density matrices lead to three sum rules to be obeyed by the three key functions G_ss, G_a. These contraction sum rules contain corresponding normalization sum rules as special cases. The momentum distributions n_↑(k) and n_↓(k), following from f_↑(r) and f_↓(r) by Fourier transform, are correctly normalized through f_s(0) = 1. In addition to the non‐negativity conditions n_s(k),g_ss(r),g_a(r) ≥ 0 [these quantities are probabilities], it holds n_s(k) ≤ 1 and g_ss(0) = 0 due to the Pauli principle and g_a(0) ≤ 1 due to the Coulomb repulsion. Recent parametrizations of the pair densities of the spin‐unpolarized homogeneous electron gas in terms of 2‐body wave functions (geminals) and corresponding occupancies are generalized (i) to the spin‐polarized case and (ii) to the 2‐body reduced density matrix giving thus its spectral resolutions.     

Spectral behaviour of the two-photon absorption coefficient in ZnO,CuCl and Bi4Ge3O12

Summary The spectral behaviour of the direct interband two-photon absorption coefficient α⁽²⁾ in ZnO, CuCl and Bi₄Ge₃O₁₂ has been investigated in a large excitation energy range. The experimental results have shown that the α⁽²⁾ spectral behaviour is well described by a parametric formula containing terms with different energy dependence. In particular, for 2ħω-E _g>≈400 meV, the first experimental evidence of 2ħω-E _g)^5/2 dependence has been obtained. As a consequence, each of the various models proposed to predict the α⁽²⁾ dispersion curve gives the correct energy dependence in a limited energy range, due to the poor approximation made in the evaluation of dipole matrix elements. To explain the spectral dependence of the two-photon absorption coefficient, consideration of all the intermediate states is required, with the energy dependence of the dipole matrix elements properly considered. It is shown that the greatest contributions to the oscillator strength come from transitions totally allowed at the critical points. Work partially supported by M.P.I.     

Dipole oscillator strength properties and dispersion energies for CI2

A recommended isotropic dipole oscillator strength distribution (DOSD) has been constructed for the chlorine molecule through the use of quantum mechanical constraint techniques and experimental dipole oscillator strength and molar refractivity data. It has been used to evaluate a variety of dipole oscillator strength sums, logarithmic dipole oscillator strength sums, and mean excitation energies for the molecule. A pseudo-DOSD for C1₂ is also presented which is used to obtain reliable results for the isotropic dipole-dipole dispersion energy coefficients C₆, for the interaction of Cl₂ with itself and forty-two other species, and the triple-dipole dispersion energy coefficient C₉ for (Cl₂)₃.     

The variable viscoelasticity oscillator

The complex dynamics of a variable viscoelasticity oscillator is studied using the novel concept of Variable‐Order (VO) Calculus. The damping force in the oscillator varies continuously between the elastic and viscous regimes depending on the position of the mass. The oscillator considered here is composed of a linear spring of stiffness k that inputs a restitutive force F_k = ‐k x, a VO damper of order q(x(t)) that generates a damping force F_q = ‐c_q ??^q(x(t)) x, and a mass m. A modified Runge‐Kutta method is used in conjunction with a trapezoidal numerical integration technique to yield a second‐order accurate method for the solution of the resulting VO Differential Equation (VODE). The VO oscillator is also modelled using a Constant Order (CO) formulation where a number of CO fractional order differentials are weighted to simulate the VO behavior. The CO formulation asymptotically approaches the VO results when a relatively large number of weights is used. For the viscoelastic range of 0 ≤ q ≤ 1, the dynamics of the oscillator is well approximated by the CO formulation when 5 or more fractional terms are included (e.g., 0, 1/4, 1/2, 3/4, and 1).     

Doppelresonanzuntersuchungen zum Stark-Effekt des 4s 4p 3 P 1-Terms im Ca I-Spektrum

The influence of an electric field on the Zeeman-splitting of the 4s 4p ³P₁-level was investigated using the double resonance method. From the r.f.-resonance signals the tensor polarizability of the 4s 4p ³ P ₁-level was deduced to be α_ten(³ P ₁)=3.2(8) kHz/(kV/cm)². This value is used for an estimate of the oscillator strength of the infrared transition between the multiplets 4s 4p ³ P and 4s3d ³ D. Taking into account measured oscillator strengths of electric dipole transitions from the³ P ₁-level to other low lying levels one obtainsf(4s 4p ³ P→4s 3d ³ D)=0.09.     

Density functional theory study of homologous organometallic molecules of the [RhXL2]2 (X = Cl,Br, or I; L = CO,PH3, or PF3) type

Density functional theory generalized gradient approximation calculations, which were tested in our previous detailed study of [RhCl(PF₃)₂]₂ (Seuret et al., 2003, Phys. Chem. chem. Phys., 5, 268–274), were applied for a series of homologous organometallic compounds of the [RhXL₂]₂ (X = Cl, Br, or I; L = CO, PH₃, or PF₃) type. Various properties of the studied compounds were obtained. Optimized geometries of [RhCl(PH₃)₂]₂ and [RhCl(CO)₂]₂ are in very good agreement with available experimental data. Geometries of other compounds as well as other properties (thermochemistry of selected fragmentation channels, barriers to structural changes, frontier orbitals) which are not available experimentally were predicted. All the considered compounds are not planar. Enforcing planarity of the central [RhX]₂ moiety requires only a small energetic cost ranging from 2.2 to 3.9 kcal mol^?1. The analysis of frontier orbitals indicates that the metals provide the most favourable site for the electrophilic attack in all considered compounds. The analysis of the shape of the lowest unoccupied molecular orbitals indicates that the halogens and ligands provide the most favourable site for the nucleophilic attack for [RhCl(CO)₂]₂ or [RhCl(PF₃)₂]. For [RhBr(PF₃)₂]₂, [RhI(PF₃)₂]₂ and [RhCl(PH₃)₂]₂, the nucleophilic attack on the halogen is less probable. Except for [RhCl(CO)₂]₂, the least energetically expensive decomposition channel involves initial separation of ligands. For [RhCl(CO)₂]₂, its decomposition into the RhCl(CO)₂ fragments was found to be the least energetically expensive fragmentation reaction which is probably one of the reasons for the known catalytic activity of this compound.     

Structural and optical properties of thermally evaporated 2-(2,3-dihydro-1,5-dimethyl-3-oxo-2-phenyl-1H-pyrazol-4-ylimino)-2-(4-nitrophenyl)acetonitrile thin films

The structural and optical properties of as-deposited and γ-rays irradiated 2-(2,3-dihydro-1,5dimethyl-3-oxo-2-phenyl-1H-pyrazol-4-ylimino)-2-(4-nitrophenyl)acetonitrile (DOPNA) thin films have been reported. The structural properties of as-deposited and γ-rays irradiated DOPNA thin films are characterized by Fourier transformation infrared, X-ray diffraction and transmission electron microscope techniques. The transmittance, T(λ), and reflectance, R(λ), are measured at the normal incidence of light by a double beam spectrophotometer in the wavelength range 200-2200 nm. The refractive and absorption indices have been calculated. The dispersion parameters such as dispersion energy, oscillator energy and dielectric constant at high frequency are evaluated. The data of the absorption coefficient are analyzed in order to determine the type of inter-band electronic transitions and the optical band gap of the films. Other optical absorption parameters, namely, the extinction molar coefficient, oscillator strength and the electric dipole strength, are also calculated.     

Perturbation allowed transitions in the infrared spectrum of 14ND3: determination of the K-dependent parameters in the ground state

ABSTRACT

Accurate values of the K-dependent constants ^{( i )} C, ^{( i )} D_K and ^{( i )} H_K in the ground state of ¹⁴ND₃, with i = s, a, have been determined for the first time thanks to the detections of ‘perturbation allowed’ transitions in the ν₁, ν₂, ν₃, ν₄ and 2ν₄ infrared bands. The rotation–inversion and inversion transitions from the literature, together with 7289 ground state combination differences from the infrared vibration–rotation–inversion transitions have been simultaneously analysed. The adopted rotation–inversion Hamiltonian includes distortion constants up to the eighth power and the Δk = ±3 and Δk = ±6 interaction terms. Precise values of the diagonal constants and of the Δk = ±3 interaction coefficients have been obtained. Accurate values of the ground state term values have been calculated for both s and a levels up to J = 21.     

Electric/magnetic deformations of S3 and AdS3, and geometric cosets

We analyze asymmetric marginal deformations of SU(2)_k and SL(2,ℝ)_k WZW models. These appear in heterotic string backgrounds with non‐vanishing Neveu–Schwarz three‐forms plus electric or magnetic fields, depending on whether the deformation is elliptic, hyperbolic or parabolic. Asymmetric deformations create new families of exact string vacua. The geometries which are generated in this way, deformed S³ or AdS₃, include in particular geometric cosets such as S², AdS₂ or H₂. Hence, the latter are consistent, exact conformal sigma models, with electric or magnetic backgrounds. We discuss various geometric and symmetry properties of the deformations at hand as well as their spectra and partition functions, with special attention to the supersymmetric AdS₂ × S² background. We also comment on potential holographic applications.     

Dipole ordering and ionic conductivity in NASICON-Type Na<Subscript>3</Subscript>Cr<Subscript>2</Subscript>(PO<Subscript>4</Subscript>)<Subscript>3</Subscript> structures

The aspects of structure, dipole ordering, and ionic conductivity of the Na₃Cr₂(PO₄)₃ crystal with the four polymorphic phases (α, α', β, and γ) have been investigated. The features of the α-Na₃Cr₂(PO₄)₃ crystal structure and its dipole ordering and relaxation polarization in the low-temperature α and α' phases have been refined. The occurrence of Na₃Cr₂(PO₄)₃ dipole ordering in the α and α' phases and high ionic conductivity in the β and γ phases is attributed to the structural changes in the rhombohedral [Me₂(PO₄)₃]^–3_3∞ crystal frame upon phase transformations α → α', α' → β, and β → γ. A model for explaining the dipole ordering and ionic conductivity phenomena in Na₃Cr₂(PO₄)₃ is proposed.     

Variational transition state theory with multidimensional tunnelling and kinetic isotope effects in the reactions of C2H6, C2H5D and C2D6 with .CCl3 to produce CHCl3 and CDCl3

ABSTRACT

Rate constants for the reactions of C₂H₆, C₂H₅D and C₂D₆ with .CCl₃. for the production of CHCl₃ and CDCl₃ (k₁, k₂, k₃ and k₄) were computed using variational transition state theory coupled with hybrid-meta density functional theory (MPWB1K) over the temperature range of 200–2900 K. The ground-state vibrational adiabatic potential was plotted for all channels. Small- and large-curvature tunnelling were determined to include quantum effects in the calculation of rate constants. Harmonic vibrational frequencies along the reaction path were calculated in curvilinear coordinates with scaled frequencies. Anharmonicity was included in the lowest-frequency torsion. The position of formation and dissociation of bonds was specified using the variation in harmonic vibrational frequencies along the reaction path. Representative tunnelling energy and the thermally averaged transmission probability at 298 K (P(E)exp?( ? ΔE/RT)) were determined for the reactions in which tunnelling is important. The kinetic isotope effect was used to calculate the considerable contributions of tunnelling and vibration. The expressions for rate constants were determined using nonlinear least-square fitting over the temperature range of 200–2900 K.     

Potential tunable white-emitting phosphor LiSr4(BO3)3:Ce3+, Eu2+ for ultraviolet light-emitting diodes

A novel Ce³⁺/Eu²⁺ co-activated LiSr₄(BO₃)₃ phosphor has been synthesized by traditional solid-state reaction. The samples could display varied color emission from blue towards white and ultimately to yellow under the excitation of ultraviolet (UV) light with the appropriate adjustment of the relative proportion of Ce³⁺/Eu²⁺. The resonance-type energy transfer mechanism from Ce³⁺ to Eu²⁺ in LiSr₄(BO₃)₃:Ce³⁺, Eu²⁺ phosphors is dominant by electric dipole–dipole interaction, and the critical distance is calculated to be about 29.14 Å by the spectra overlap method. White light was observed from LiSr₄(BO₃)₃:mCe³⁺, nEu²⁺ phosphors with chromaticity coordinates (0.34, 0.30) upon 350 nm excitation. The LiSr₄(BO₃)₃:Ce³⁺, Eu²⁺ phosphor has potential applications as an UV radiation-converting phosphor for white light-emitting diodes.     

Infrared transitions of C2D6 from v 4 to the interacting system v 4+ v 6, v 4+ v8, v 3+ 2v 4: rotational analysis,and torsional splitting in the v 3+ 2v 4 and v 3+ v 4 states

The hot infrared transitions of C₂D₆ from the υ₄(A_1u ) to the υ₄ + υ₆(A_2g ) and υ₄ + υ₈(E _g ) vibrational states, observed from 960 to 1180 cm^?1, have been rotationally analysed on a high-resolution Fourier transform spectrum (full width at half-maximum about 0·0030 cm^?1). The vibration-rotation interactions affecting the upper vibrational states are very similar to those of the corresponding cold system. A strong x,y Coriolis interaction between υ₄ + υ₆ and υ₄ + υ₈, with K-level crossing, generates large displacements of the rotational components of both vibrational states, tuning them to additional local resonances in several spectral regions. Thus l resonances with Δl = ±2, Δk = ±1 occur within υ₄ + υ₈. A x,y Coriolis-type resonance between υ₄ + υ₈(?l,K ? 1) and υ₃ + 2υ₄(K) occurs at K = 11,12,13, and a further coupling of υ₄ + υ₈(+l,K + 1) and υ₃ + 2υ₄(K + 3) is most effective at K = 11 and 12. These resonances induce torsional splittings on the perturbed levels of υ₄ + υ₈ and allow us to determine the torsional splittings in the υ₃ + 2υ₄ state. The vibration-rotation constants of υ₄ + υ₆, υ₄ + υ₈ and υ₃ + 2υ₄, several interaction parameters and the torsional splitting of υ₃ + 2υ₄ have been determined by least-squares fit of 1391 observed transition wavenumbers, with an overall standard deviation σ = 0·75 × 10^?3 cm^?1. The vibrational wavenumbers found for the four torsional components of (υ₃ + 2υ₄)? υ₄ are υ(E_3d) = 1040·961 82(809)cm^?1, υ(A_3d) = 1041·218 27(865)cm^?1, υ(E_3s) = 1041·225 23(662)cm^?1 and υ(A_1s) = 1041·407 77(633)cm^?1. These are anomalous for both the order of the torsional components and the magnitudes of their separations. We believe that this is mainly due to the interactions of υ₃ + 2υ₄ with the torsional manifolds with υ₃ = 0 and υ₃ = 2, through the vibration-torsion Hamiltonian term (?V ₆/?q ₃)q ₃cos (6γ)]/2. The further observation of a few doublets of υ₈ and υ₃ + υ₄ at resonance provides information on the torsional splitting of the latter state.     

Subterahertz electrodynamics of (TMTSF)2X (X = ClO4, PF6) salts

The terahertz-subterahertz spectra of the complex permittivity and dynamic conductivity of polycrystalline (TMTSF)₂ClO₄ and (TMTSF)₂PF₆ samples are measured quantitatively. The spectra of (TMTSF)₂ClO₄ have absorption lines at frequencies of 7 and 30 cm^?1. The obtained temperature dependences of the line parameters in the range 5–300 K cast some doubt on the earlier concept of their phonon origin. An excitation is detected at temperatures below 20 K in the frequency range near 30 cm^?1, and its nature is related to the activation of a transverse acoustic phonon caused by the folding of the Brillouin zone due to the ordering of noncentrosymmetrical anions below 20 K. An increase in the carrier relaxation rate is found in this temperature range, which indicates a close relation between the electron and phonon subsystems in (TMTSF)₂ClO₄. Sings of additional low-energy excitations that should manifest themselves at frequencies below 1–2 cm^?1 are detected. (TMTSF)₂PF₆ containing centrosymmetrical anions has no absorption lines in the frequency range 3–20 cm^?1 and the temperature range 5–300 K.