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

Experimental 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.     

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.     

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.     

Diffusion activation energy versus the favourable energy in two-order-parameter model:A molecular dynamics study of liquid Al

In the present work, we find that both diffusion activation energy E_a(D) and E_a(S^ex) increase linearly with pressure and have the same slope (0.022±0.001 eV/GPa) for liquid Al. The temperature and pressure dependence of excess entropy is well fitted by the expression -S^ex(T,P)/k_B=a(P)+b(P)T+c(P)exp(E_f/k_BT), which together with the small ratio of E_f/k_BT leads to the relationship of excess entropy to temperature and pressure, i.e. S^ex≈-cE_f/T, where c is about 12 and E_f (=Δ E-PΔV) is the favourable energy. Therefore, there exists a simple relation between E_a(S^ex) and E_f, i.e. E_a(S^ex)≈cE_f.     

Dynamic polarization of 7Li nuclei in solutions containing radical ions

Dynamic nuclear polarization parameters, obtained at 75 G, are reported for ⁷Li ions in collision with several radical anions and with one radical cation. All systems show large negative ⁷Li N.M.R. enhancements indicative of weak scalar relaxation. However, radical induced relaxation rates derived from ⁷Li T ₁ measurements suggest stronger complexing of lithium ions with radical anions than with the radical cation as would be expected from simple coulombic considerations. Translational modulation of the dipolar interaction best accounts for proton and radical cation dipolar relaxation rates while rotational modulation best accounts for the corresponding radical anion rates; this supports the interpretation above. A model for the lithium radical collision is proposed which implies that, for radical anions, scalar coupling is only apparently weak and that the low ⁷Li scalar relaxation rates observed result from scalar correlation times (τ_c = 10^-8-10^-9 s) longer than any yet observed by this technique. The model predicts that, for certain ranges of τ_c, increasing strength of complex formation should lead to smaller scalar relaxation rates and more negative enhancements, in contrast with the behaviour of fluorocarbons where the reverse was true. The predicted dependence of enhancement upon τ_c also suggests that ⁷Li enhancements should be extremely sensitive to variations in the chemical properties of the system.     

Nonradiative deactivation of the lowest triplet state of naphthalene and its hydroxy derivatives at 77 K

The validity of an inductive resonance theory of energy transfer from the T ₁→S ₀ transition dipole to overtone vibrations of molecular groups containing H and D atoms is experimentally tested for a series of compounds whose conjugation systems are similar in size. To this end, by using kinetic, spectral, and luminescent methods (measurements of the phosphorescence decay times, phosphorescence spectra, ratios between the quantum yields of phosphorescence and fluorescence at 77 K, total quantum yields of fluorescence at 293 K, and ratios between the quantum yields of fluorescence at 293 and 77 K), the deactivation processes of the lowest excited T ₁ and S ₁ states of seven emitting centers (naphthalene, its hydroxy and dihydroxy derivatives, and their monoanions) in solutions in ethanol-h ₆, ethanol-d ₆, and their 2: 1 mixtures with diethyl ether are studied. For all the compounds studied, the rate constants k _r of the radiative T ₁→S ₀ transition and the changes in the overlap integrals of the spectra of phosphorescence and absorption of overtones of CH stretching vibrations are determined. The rate constants of energy transfer k _dd(CH) from the T ₁→S ₀ transition dipole to the stretching vibrations of the CH bonds are calculated without regard for the changes in the localization and orientation of this transition dipole in the compounds under study. The contribution of an individual CH group k _nr(CH) to the total rate constant of nonradiative deactivation of the T ₁ state averaged over the CH groups of the naphthalene ring system is ascertained. A good correlation between the changes in the constants k _nr(CH) and k _dd(CH) in the series of the hydroxy derivatives of naphthalene is found, which is indicative of the inductive resonance mechanism of the energy degradation of the T ₁ state. The deviations from proportionality between the changes in these constants upon passing from naphthalene to its hydroxy derivatives, which correlate with a marked increase in the radiative constant k _nr of the hydroxy derivatives in comparison with naphthalene, indicate changes in the strength and localization of the T ₁→S ₀ transition dipole moment and in its orientation with respect to the plane of the molecule that occur due to introduction of a heteroatom, oxygen, whose lone pair of electrons enters into conjugation with the πelectrons of the naphthalene ring system.     

Dipolar Coupling Information in Multispin Systems: Application of a Compensated REDOR NMR Approach to Inorganic Phosphates

Anexperimental strategy has been developed for measuring multiple dipole–dipole interactions in inorganic compounds using the technique of rotational echo double resonance (REDOR) NMR. Geometry-independent information about the dipole couplings between the observe nuclear species S (arbitrary quantum number) and the heteronuclear species I (spin- ) can be conveniently obtained from the experimental curve of ΔS/S₀ versus dipolar evolution time by limiting the analysis to the initial data range 0 < ΔS/S₀ < 0.30. Numerical simulations have been carried out on a three-spin system of type SI₂ in order to assess the effect of the I–I homonuclear dipole–dipole coupling and the influence of experimental imperfections such as finite pulse length and misadjustments of the 180° pulses applied to the I-spin species. The simulations show further that within the initial data range the effects of such misadjustments can be internally compensated by a modified sequence having an additional 180° pulse on the I channel in the middle of the dipolar evolution periods. Experimental ²⁷Al{³¹P} REDOR results on the multispin systems Al(PO₃)₃, AlPO₄, [AlPO₄]₁₂(C₃H₇)₄NF, and Na₃PO₄ confirm the general utility of this approach. Thus, for applications to unknown systems the compensation strategy obviates calibration procedures with model compounds.     

Computation and analysis of the dynamic structure factor S(k, ω) for small wave vectors

Molecular dynamics (MD) calculations have been performed for the Lennard-Jones (12-6) potential function using 2048 particles. Using conventional parameters the results may be compared with those for liquid argon.

The dynamic structure factor S(k, ω) has been determined both by Fourier inversion of the intermediate scattering function F(k, t) and from the longitudinal current-current correlation function C _∥(k, t). Particular attention was paid to the recurrence time of the system. The results for S(k, ω) by the two methods agree within 5 per cent for the whole region of small k-vectors considered. Double Fourier inversion of the van Hove function G(r, t) led to insufficiently accurate results for these small k-values. In view of the present data, the MD-results of Levesque et al. [1] for S(k, ω) have only a qualitative character. These latter data appear to contain truncation errors due to incomplete Fourier transformations.

Using a hydrodynamic assumption for F(k, t) we were able to extract the transport coefficients, the velocity of sound and the ratio of the specific heats in the limit of large wave lengths or small k. The velocity of sound was obtained by exploiting the MD generated anomalous dispersion curve of sound waves. Anomalous dispersion was found to set in for kσ ～ 0·25. A sound speed of 880 ms^-1 has been determined which is in excellent agreement with experimental values for liquid argon. The total error for the MD value amounts to about 5 per cent. In contrast, the ratio of the specific heats γ and the transport coefficients D _T and Γ (thermal diffusivity and sound attenuation) were determinable only with an accuracy of 15 per cent due to the need for larger extrapolations. Nevertheless, we found D _T, Γ and γ in agreement with experimental values within 5-10 per cent.     

On Fusion Algebras and Modular Matrices

We consider the fusion algebras arising in e.g. Wess–Zumino–Witten conformal field theories, affine Kac–Moody algebras at positive integer level, and quantum groups at roots of unity. Using properties of the modular matrix S, we find small sets of primary fields (equivalently, sets of highest weights) which can be identified with the variables of a polynomial realization of the A _r fusion algebra at level k. We prove that for many choices of rank r and level k, the number of these variables is the minimum possible, and we conjecture that it is in fact minimal for most r and k. We also find new, systematic sources of zeros in the modular matrix S. In addition, we obtain a formula relating the entries of S at fixed points, to entries of S at smaller ranks and levels. Finally, we identify the number fields generated over the rationals by the entries of S, and by the fusion (Verlinde) eigenvalues. Received: 7 October 1997 / Accepted: 7 March 1999     

液体核磁共振中由分子间偶极耦合和分子内标量耦合共同作用后的谱图裂分模式

在高极化多自旋液体样品中,同时存在着分子间偶极（D）耦合和分子内标量（J）耦合,它们的共同作用产生了一些原来观测不到的分子间多量子相干信号。而且,信号的裂分模式与只存在J耦合的多自旋体系中观测到的多量子相干信号的裂分模式不同。本文从理论和实验上研究了这些禁阻的共振峰及其独特的裂分模式。为了比较验证,我们以I2S3+X自旋体系为例,结合使用选择和非选择性的射频脉冲序列来获得分子间双量子相干信号的五种裂分模式。进而归纳出对IpSq+Xk (p, q, k = 1, 2, 3,…)自旋体系普适的裂分模式规则。并指出,它们中如(1:0:-1)的裂分模式会放大J耦合裂分,使得J耦合常数的测量更精确,特别在J耦合常数很小或不均匀场中的J耦合常数的测量中具有诱人的应用前景。结果表明理论预测,计算机模拟和实验观测结果三者吻合的很好。     

Fermionic entropy of the vortex state in d-wave superconductors

In d-wave superconductors the electronic entropy associated with an isolated vortex diverges logarithmically with the size of the system even at low temperatures. In the vortex array the entropy per vortex per layer, S _V , is much larger than k _B and depends on the distribution of the velocity field v _s around the vortex. If there is a first-order transition upon a change of the velocity distribution, then there will be a big entropy jump ΔS _V ∼k _B at the transition. This entropy jump comes from the electronic degrees of freedom on the vortex background, which is modified by the vortex transition. This can explain the big jump in the entropy observed in the so-called vortex-melting transition [A. Junod, M. Roulin, J-Y. Genoud et al., Physica C, to be published], in which the vortex array and thus the velocity field are redistributed. The possibility of the Berezinskii-Kosterlitz-Thouless transition in the 3-dimensional d-wave superconductor due to the fermionic bound states in the vortex background is discussed. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 6, 465–469 (25 March 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Dielectric properties of a mixture of dipolar hard spheres

A theory for the dielectric constant, ε, of a fluid mixture of dipolar hard spheres is formulated by generalizing the methods developed by Ramshaw and Wertheim for the pure fluid case. The resulting expression for ε depends on the pair distribution functions, g _αβ(r ₁, θ₁, r ₂, θ₂) for a dipolar mixture. Due to the unavailability of exact representations for these dipolar pair distribution functions, the results of the mean spherical approximation are employed in the formalism developed. Numerical results are given for ε as calculated from the pair distribution functions for a spherical volume of macroscopic dimensions. The compositional dependence of the ε obtained in this way for a specific mixture is compared with the corresponding properties of the well established theories of Clausius-Mossotti-Debye and Onsager. In addition, the relative importance of the dipole moment and size of the hard sphere parameters in determining ε for a dipolar mixture (the correlative behaviour of which is described by the mean spherical approximation) is evaluated. It is found that the differences in hard core diameters can be largely ignored, in that ε for an ‘effective’ single component fluid can be given to within 2–5 per cent relative error (at worst) of the mean spherical approximation's result. Such an ‘effective pure fluid’ is described as having the same polarization content as the actual mixture being considered. Thereby, the properties of the effective fluid are determined by the quantity y = 4πβ(m ₁ ² ρ₁ + m ₂ ² ρ₂)/9 where m_i and ρ _i are the dipole moment and number density of component i in the binary mixture, with β = (kT)^-1.     

Estimating the entropy of liquids from atom–atom radial distribution functions: silica,beryllium fluoride and water

Molecular dynamics simulations of water, liquid beryllium fluoride and silica melt are used to study the accuracy with which the entropy of ionic and molecular liquids can be estimated from atom–atom radial distribution function data. The pair correlation entropy is demonstrated to be sufficiently accurate that the density–temperature regime of anomalous behaviour as well as the strength of the entropy anomaly can be predicted reliably for both ionic melts as well as different rigid-body pair potentials for water. Errors in the total thermodynamic entropy for ionic melts due to the pair correlation approximation are of the order of 10% or less for most state points, but can be significantly larger in the anomalous regime at very low temperatures. In the case of water, the rigid-body constraints result in larger errors in the pair correlation approximation, between 20 and 30%, for most state points. Comparison of the excess entropy, S _e, of ionic melts with the pair correlation entropy, S ₂, shows that the temperature dependence of S _e is well described by T ^?2/5 scaling across both the normal and anomalous regimes, unlike in the case of S ₂. The residual multiparticle entropy, ΔS = S _e ? S ₂, shows a strong negative correlation with tetrahedral order in the anomalous regime.     

Liouville Equation for Turbulent Gases

The Hamiltonian H and Hamilton equations of motion are derived for the Fourier amplitudes p _k and q _k of the canonical conjugate fields p and q defined by p = mν and ? q /?t = nν where ν( r , t ) and n ( r, t ) are the velocity and density fields of ideal, compressible gases in the state of fully developed turbulence. A Liouville equation is presented for the distribution function f ( p _k , q _k ; { k }) in the multidimensional phase space formed by the scalar components of the set { k } of wave mode vectors p _k and q _k . Though the theory is highly idealized since viscous and thermal dissipation are not taken into account, it may be considered as a first attempt at extending statistical mechanics to random continuous media. As an application, that stationary solution f = f(H) of the Liouville equation is calculated, which maximizes the turbulence entropy. It is shown that the distribution of the velocity and density fluctuations of compressible gases is Gaussian in fully developed turbulence, in agreement with the experiments.     

Heterodyne coincidence spectroscopy

A new type of light-scattering experiment, which should measure directly the triple static structure factor S ⁽³⁾ (k, q) of a fluid, is proposed. S ⁽³⁾(k, q) is the full spatial Fourier transform of the equilibrium triplet distribution function g ⁽³⁾(r ₁, r ₂, r ₃). The experiment may also be used to study dynamic correlation functions of the form <a_k (t)a_q (t′)a_k_q(t″)> (where a_k () is the kth spatial Fourier component of the density), thereby giving new information on mode-mode coupling. The method obtains its information from triple correlations in the arrival of scattered photons at three detectors. The detectors must be operated in the heterodyne mode (i.e. with a local oscillator); the scattering volume must be much larger than the volume over which molecular positions are correlated. Comparison is made with previous analyses of other multi-detector experiments.     

von Neumann entropy signatures of a transition in one-dimensional electron systems with long-range correlated disorder

We study the von Neumann entropy and related quantities in one-dimensional electron systems with on-site long-range correlated potentials. The potentials are characterized by a power-law power spectrum S(k) μ\propto 1/k ^α, where α is the correlation exponent. We find that the first-order derivative of spectrum-averaged von Neumann entropy is maximal at a certain correlation exponent α _m for a finite system, and has perfect finite-size scaling behaviors around α _m . It indicates that the first-order derivative of the spectrum-averaged von Neumann entropy has singular behavior, and α _m can be used as a signature for transition points. For the infinite system, the threshold value α _c = 1.465 is obtained by extrapolating α _m .     

Coherence transfer between nuclear spins in paramagnetic systems: effects of nucleus—electron dipole—dipole cross-correlation

In nuclear magnetic resonance of paramagnetic systems, cross-correlations between the fluctuations of a nucleus—nucleus dipole—dipole coupling I^k I^l and a nucleus—electron dipole coupling I^kS induces cross-relaxation and makes it possible to generate bilinear terms in the density matrix of the type 2I^k _xI^l _z from coherence I^k _x that can lead to ‘relaxation-allowed’ coherence transfer between two nuclei I^k and I^l . In this paper these effects are demonstrated in a complex involving a fragment of double-stranded DNA and two chromomycin molecules complexing a paramagnetic cobalt ion. Analytical expressions are given for the cross-correlation rates in particular conditions, while the extension to anisotropic g tensors or zero field splittings are addressed. It is shown that relaxation-allowed coherence transfer leads to characteristic signals in double-quantum filtered correlation spectroscopy (DQF—COSY), but not in total correlation spectroscopy (TOCSY). Analytical expressions are unable to reproduce the observed cross-peak patterns. A careful numerical study reveals that in the high spin Co(II) complex studied here, the cross-correlation dynamic shift contribution is of the same order of magnitude as the cross-correlation rate, a value much larger than what can be computed assuming isotropic Brownian motion and complete separation between the electron spin and the lattice.     

Thermodynamics of phonon-stabilized Fermi distributions with application to uranium

Since phonons are built on the free energy of electrons, their frequencies can be altered by thermal electronic excitations, implying that thermal electronic excitations can alter the phonon entropy. The effect of this extra phonon entropy on electronic distribution functions and thermodynamic properties is calculated in the limit of classical vibrations. The phonon entropy stabilizes electrons above the Fermi level by more than the usual k _B T. The thermodynamic coupling of electron and phonon degrees of freedom allows far more heat capacity than in equivalent independent systems. The method developed is used to explain uranium data from the literature.     

Inversion relations,phase transitions and transfer matrix excitations for special spin models in two dimensions

The infrared and Raman active phonons (k=0) of orthorhombic TbF₃ and of isomorphous HoF₃ have been observed and attributed to the different irreducible representations of the factor groupD _2h. Moreover we investigated crystal-field excitations of the 4f-configuration of the Rare-Earth-ions and effects of their interaction with optical phonons, especially as a function of an external magnetic field. The infrared reflection spectra of these materials not only display reststrahlen bands of electric dipolar but also of magnetic dipolar type with a characteristic shape of the latter bands.On entering the ferromagnetic ordered state pertinent symmetry reductions (D _{2hC 2h}) become evident in the system of electronic transitions and optical phonons in TbF₃ by a change of selection rules and a magnetization-induced transfer of transition intensities to new components of the transition dipole or of the Raman polarizability tensor. These observations are in accordance with general symmetry considerations.The delocalization of the crystal-field excitations results in a Davydov splitting of the single-ion transitions.