Dipole Dispersion Research Articles

Theory of the interfacial polarization between isotropic and neutral dielectric bodies

It is shown that, in the case of a planar interface between two different uncharged dielectric bodies, a static difference of potential ΔΦ may be expected across the interface. This quantity is calculated by introducing the nonlinear polarization of the bodies by the surface modes previously used by van Kampen et al. in their theory of the van der Waals attraction between two dielectrics. This leads to a result inversely proportional to the third power of the thickness of the gap between the dielectrics. The proportionality coefficient involves the frequency dependent dielectric constant of the bodies as well as a higher order susceptibility describing their nonlinear (quadratic) polarization. This approach is then found to be consistent with the result of a microscopic model involving the summation of the interatomic dispersion dipole moments appearing in couples involving atoms separated by the interface.

Perturbation theory of interaction dipoles

The dispersion dipole moment on three well-separated atoms is formulated with perturbation theory and evaluated for the Drude model. Then the dispersion force contribution to the adsorption dipole, composed of moments on the adatom and on the substrate, is calculated as a sum of two atom and three atom collision dipoles. The relation to electrostatic results for driven polarization is shown ; comparison is made with image theory analyses of the adsorption dipole.

On the additivity of atomic and molecular dipole properties and dispersion energies using H, N, O, H2, N2, O2, NO, N2O, NH3and 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 Sk , Lk and Ik , 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...

Analytic Coulomb approximations for dynamic multipole polarizabilities and dispersion forces

This paper presents a comprehensive and unified treatment of atomic multipole oscillator strengths, dynamic multipole polarizabilities, and dispersion force constants in a variety of Coulomb-like approximations. A theoretically and computationally superior modification of the original Bates–Damgaard (BD) procedure, referred to here simply as the Coulomb approximation (CA), is introduced. An analytic expression for the dynamic multipole polarizability is found which contains as special cases this quantity within the CA, the extended Coulomb approximation (ECA) of Adelman and Szabo, and the quantum defect orbital (QDO) method of Simons. This expression contains model-dependent parameters determined from ground and excited state ionization potentials and is derived using a powerful approach based on the sturmian representation of a generalized Coulomb Green’s function. In addition, this result is obtained within the ECA and QDO models through an extension of the novel algebraic procedure previously used in obtaining the static polarizability within the ECA, thus demonstrating the equivalence of the two approaches. Static quadrupole and scalar and tensor dipole polarizabilities for a variety of mono and divalent ground and excited state systems within the CA, ECA, and QDO models are compared, when possible, with recent experimental and accurate theoretical work. Except for quadrupole polarizabilities of light divalent systems, agreement for all models is very good. For ground state systems, best accuracy is obtained using the ECA. Illustrative calculation for the dynamic dipole polarizability at real and imaginary frequencies for the He 11S and 21S systems within the ECA is presented and compared with the definitive results of Glover and Weinhold (GW). For He 11S, despite an 8% error in the predicted static polarizability, scaling the dynamic polarizability to the GW static value shows the frequency dependence to be accurately represented. The analytic nature of the ECA allows a wide variety of dispersion force coefficients to be easily calculated. Extensive, but not exhaustive, tabulations of C6, C8, C10, and D9 (three-body) coefficients are given. C6 coefficients involving the He 11S, 21S, 23S systems are compared with the accurate results of GW and, except for interactions of He 12S, excellent agreement is obtained. The discrepancies for He 11S are removed by a simple scaling procedure utilizing the static polarizability. To facilitate scaling of dispersion coefficients, normalized dispersion coefficients are defined. Normalized dipole and quadrupole dispersion coefficients are given for all alkaline earth–alkaline earth pairs. Accurate results for C6 and C8 coefficients are presented for all alkali–alkali pairs and C6 coefficients for alkali–alkaline earth interactions given. Sample C10 and D9 coefficients are listed for the alkalis and hydrogen. Coupling the ECA dynamic dipole polarizability to available discrete oscillator strength distribution data allows C6 coefficients to be obtained for the interaction of alkali, alkaline earth, and metastable helium atoms with the following systems: He, Ne, Ar, Kr, Xe, N, O, H2, N2, O2, NO, N2O, H2O, NH3, and CH4. Finally, C8 coefficients for He–alkali interactions are presented. A significant number of the dispersion coefficients obtained here are not available in the literature. Based on the success of ECA static multipole polarizability predictions, we feel the results presented here are generally the most reliable to date.

Calculation of dipole–dipole dispersion coefficients for liquid metals

Based on simple considerations, the dipole–dipole dispersion coefficients for long-ranged attractive forces in liquid metals are calculated. The derived relation contains parameters such as heat of vaporization and molar volume at 0 K. An analysis of subsequently evaluated van der Waals constants and internal pressure corroborates present estimations. For metals of the same group in the periodic table, the dispersion coefficient is found to be an inverse function of electron density estimated at the boundary of a Wigner–Seitz atomic cell.

Role of interaction energy in the specificity of transcription. I-The Watson Crick G-C base pair template.

The purpose of this work is to show that the selectivity of the nucleotide bases in RNA transcription c an be inferred, in principle, from the DNA base pair - RNA base interaction. The catalytic role of enzymes in this process is, therefore, only to form the sugar - phosphate backbone. A systematic study for the evaluation of the interaction energy of the DNA base pair with the enterant RNA bases have been undertaken to elucidate the aforesaid mechanism. Electrostatic hard sphere approximation of Nash and Bradley 1 has been employed. Non bonded induced dipole and London dispersion forces are not taken into account. The present communication gives the results of computations of the interaction energy of the four RNA bases. The results have been discussed with reference to Stent's and Zubay's schemes of RNA transcription.

A b i n i t i o calculations of the collision-induced dipole in He–H2. I. A valence bond approach

The collision-induced dipole in the system He–H2 is calculated in the multistructure Valence Bond method, using the nonorthogonal monomer orbitals. In the region around the collision diameter, which contributes most to the collision-induced ir absorption, the long range results (the leading terms are the quadrupole-induced dipole on He with R−4 dependence and the dispersion dipole with R−7 dependence) are modified by overlap effects. The short range behavior is determined, moreover, by the appearance of other important terms, the exchange dipole and the overlap-induction dipole on H2, which vanish in the long range. Since all the short range contributions have approximately the same (exponential) dependence on the intemolecular distance, they can be collected and added as a single exponential dipole function to the R−4 and R−7 long range terms. Of the latter terms the R−7 dispersion dipole is of little importance.

Pseudospectral dipole oscillator strength distributions and some related two body interaction coefficients for H, He, Li, N, O, H2, N2, O2, NO, N2O, H2O, NH3, and CH4

Pseudospectral dipole oscillator strength distributions (DOSDs) are presented for ground state Li, N, O, H2, N2, O2, NO, N2O, H2O, NH3, and CH4. The pseudo DOSDs are constructed by requiring the pseudodipole (excitation energy–oscillator strength) pairs to reproduce known values of the dipole oscillator strength sums S (k) evaluated from original DOSDs which are either completely continuous or contain a substantial continuum contribution. The pseudo DOSDs, which are a discrete representation of the original DOSDs, can be used to evaluate a variety of molecular properties in almost a trivial way, without sacrificing accuracy, by using discrete pseudospectral representations of the properties. The pseudostate DOSDs, together with ab initio pseudostates for the ground state H and He atoms, are used to evaluate orientation averaged dipole–dipole dispersion energy constants, C6(a,b), and the corresponding relativistic coefficients, W4(a,b), for all pairs of atoms and molecules taken form H, He, Li, N, O, H2, N2, O2, NO, N2O, H2O, NH3, and CH4. The results are used to assess the accuracy of semiempirical formulae for C6(a,a) and W4(a,a) and of combination rules for C6(a,b) and W4(a,b). The method of using pseudo DOSDs for the evaluation of molecular properties, relative to using the original DOSDs, becomes more important as the number of integrals over DOSDs in the definition of a property increases.

Dispersion dipole between rare-gas atoms

Accurate calculations of the dispersion dipole coefficient D 7 and its components are described for the systems HeH and HeHe, and used to check an approximate formula for D 7 developed in a previous paper [1]. By means of a further approximation for a new atomic property, values of D 7 are obtained for the rare-gas diatoms, based on semi-empirical Van der Waals C 6 coefficients, Hartree-Fock expectation values and sum-rule values for the atoms. The dispersion contributions to the dipole are compared with the Hartree-Fock contributions [35], and at the conventional collision diameters are found to be of comparable magnitude but usually of opposite sign.

On the quantum corrections to the virial coefficients of the equation of state of a fluid

The first quantum correction to the virial coefficients of the equation of state of a fluid is derived in the presence of a weak three-body potential ϕ(i, j, k). Results for the third and fourth virial coefficients are given. Representing the potential energy of interaction of a pair and a triplet, by the Lennard-Jones (12-6) model and the triple dipole dispersion potential model of Axilrod and Teller, the first quantum correction to the third virial coefficient is calculated for many values of T*. The theoretical result is compared with the experimental data of helium.

Intermolecular interactions in methane, carbon tetrafluoride and sulphur hexafluoride

Spherically averaged potential energies of interaction between pairs of methane, carbon tetrafluoride and sulphur hexafluoride molecules have been determined as closely as possible using experimental gaseous viscosity data. Experimental second virial coefficients have then been used to estimate values of the first non zero multipole moment of these molecules. Third virial coefficients calculated with allowance for the triple dipole dispersion interaction agree well with experiment as do calculated self diffusion coefficients for methane.

Three-body interactions and lattice sums in crystals

Lattice sums required for evaluating the effect of the three-body triple dipole dispersion interaction on the elastic constants of face centred cubic crystals are evaluated. Previous calculations omitted a nonzero lattice sum. The present methods may have advantages in terms of rate of convergence.

Long-Range Intermolecular Forces using Gaussian Basis Functions. A Model Calculation

The charge-induced dipole induction energy and the dipole–dipole dispersion energy for the ground state H–H+ and H–H interactions are used as model energies for investigating the feasibility of using Gaussian basis functions to calculate long-range intermolecular forces. The use of various types of Gaussian basis sets to represent the first-order wavefunction, Ψ(1), in the calculation of the interaction energies and the errors introduced into the calculations by using Gaussian representations of the exact zeroth-order wavefunctions for the isolated atoms are considered. Satisfactory long-range forces, at least for the simple interactions considered here, can be obtained by using small Gaussian basis sets to represent the interaction, that is Ψ(1), and/or the zeroth-order wavefunction.

Retarded van der Waals Interactions. I. Simple Atoms

The effect of retardation on the dipole dispersion interaction between atoms has been determined. By the use of accurate frequency-dependent polarizabilities, quantitative calculations of the retardation correction to the interaction of (H, H), (H, He+), (He+, He+), (H, He), and (He, He), as well as to the three-body system (He, He, He), have been made. The procedure used was to evaluate the Casimir–Polder integral for two atoms and its three-body extension directly so as to obtain results correct for all R. Although the corrections to the limiting behavior (1 / R6 for “small” R, 1 / R7 for large R) are not large, they may be of significance for high accuracy measurements in some cases.

Padé Approximants for Two- and Three-Body Dipole Dispersion Interactions

A new method is presented for using theoretical or experimental optical dispersion data to construct bounded estimates to dispersion force coefficients. The bounds are obtained from the Casimir–Polder integral formula and an analytic continuation of the power series expansion of the dynamic multipole polarizabilities for the interacting species. Recognition of the dynamic polarizabilities at imaginary frequency as series of Stieltjes allows construction of the necessary bounded continuations with Padé approximants expressed directly in terms of Cauchy dispersion coefficients. The sequence of bounds obtained incorporates the London and Slater–Kirkwood values in lowest order, and provides improvements to these two well-known bounds in higher order. The method is applied to the two- and three-body dipole interactions of atomic and molecular hydrogen and of helium using theoretical Cauchy dispersion coefficients, and to the inert gases, alkali atoms, and molecular hydrogen, nitrogen, and oxygen using coefficients obtained from optical dispersion and absorption data. Comparison is made with dispersion force estimates obtained from ab initio calculation, semiempirical methods, and molecular beam and low-temperature gas kinetic measurements. In addition to supplying accurate numerical bounds for dispersion force coefficients, the Padé procedure provides the basis for a discussion of previously devised techniques for estimating dispersion force coefficients. The importance of utilizing a proper analytic continuation of the dynamic polarizability in the successful application of these procedures is emphasized. Finally, the accuracy of well-known dispersion force combination rules is discussed within the framework of the Padé procedure, and the relation of the latter to alternative bounding methods which have recently appeared is discussed.

Raman Spectra of Hydrogen and Deuterium Halide Crystals

The crystal Raman Spectra of HCl, DCl, HBr, and DBr have been observed for the lattice and intramolecular vibrational regions. The results for the intramolecular region indicate that the crystal structure of the low-temperature orthorhombic phase is C2v9 − Pn21a with four molecules in a unit cell, containing nonplanar hydrogen-bonded zigzag chains. However, the nonplanarity of the chain is so small that it is not sensitively reflected to the spectra of lattice vibrational region. As a result, the lattice vibrational bands may be assigned adequately based on a planar structure C2v12 − Bb21m, which is the structure determined by neutron diffraction measurement. Normal coordinate calculations have been made by using several kinds of intermolecular potentials. A central force field which assumed dispersion and repulsion forces and dipole–dipole forces failed to explain the observed lattice frequencies. A potential which assumed hydrogen bonding explicitly gave a reasonable fit of the calculated frequencies with the observed ones. The calculations showed that the hydrogen bond involved is relatively weak and high frequencies of the rotational lattice vibrations in spite of the weakness of the hydrogen bond are due simply to a small value of the moment of inertia of the molecule. The Raman spectra of the high-temperature cubic phase showed no strong band in the lattice region and very broad bands in the stretching region. From the results obtained, a model for the molecular reorientational motions in the cubic crystals has been proposed, in which the molecule in the crystal is bound to one of the equilibrium orientational positions, but reorients at random from one equilibrium position to the other before the molecule as a whole completes one cycle of translational oscillation. This model seems to explain the experimental data available.

Dielectric relaxation in clathrates

Dielectric parameters (permittivity and loss factors) have been measured for clathrates based on ice (gas hydrates), quinol and Dianin's compound with particular attention to the frequency and temperature ranges displaying the reorientational dipole dispersion of the guest molecules. Many such processes conformed to the simple Debye form. Enthalpies (in kcal mole–1) and entropies (in cal mole–1 deg.–1) of activation for this reorientation were evaluated from Eyring's rate equation, and effective dipole moments (in D) for the guest were derived from the Böttcher-Onsager equation.[graphic omitted]

Total Collision Cross Sections for the Interaction of Atomic Beams of Alkali Metals with Gases

Total collision cross sections (Q) for the interaction of atomic beams of K and Cs with a number of molecules were measured with an apparatus of 30″ angular resolution. Although absolute determinations of Q are difficult, relative values are readily obtained (±3%). Results are reported as the ratio (Q*) of the cross section for a given molecule to that of argon for the same beam atom. Seventy-seven molecules (of varied complexity and reactivity) were studied with K and 16 with Cs beams. Q* ranged from 0.29 to 2.8. The data were correlated using the Massey-Mohr theory, assuming an attractive intermolecular potential V(r) = —C/r6. For this case Q=b(C/vr)2/5, where vr is the relative velocity and b a known constant. C was estimated from standard formulas for the London dispersion and dipole-induced dipole forces, using known refraction and dipole moment data. The theoretical values of Q differ by a nearly constant factor from the experimental results; thus values of Q* are predicted with good accuracy. The deviation between Qcalc* and Qobs* was &amp;lt;±3% for 57% (and &amp;lt;±10% for 87%) of the molecules. Most of the large deviations occurred for the light gases.

Gamma Rays from the Nuclear Photoeffect in Carbon, Oxygen, and Copper

A NaI crystal was used to study the spectra of gamma rays associated with the giant resonance cross section of the nuclear photoeffect in carbon, oxygen, and copper. The x-ray source was a bremsstrahlung beam whose energy was varied from 19 to 61 Mev. Cross sections for elastic, and mixed elastic and inelastic scattering were measured at 135\ifmmode^\circ\else\textdegree\fi{} to the x-ray beam. The copper cross section has a magnitude which is well predicted by particle photoproduction cross sections coupled with a dipole dispersion theory. The elastic scattering cross section for carbon can be predicted in a similar fashion, but the oxygen cross section cannot. For oxygen, the observed cross section is much larger than the predicted one and this result is explained if narrow, isolated, resonances are an important part of the oxygen photonuclear cross section. The different behavior of carbon and oxygen which is found is consistent with other experiments. The angular dependence of the oxygen elastic scattering cross section near 22 Mev is predominantly dipole with a possible quadrupole admixture. For oxygen, an inelastic scattering cross section was observed which has a threshold at about 26 Mev, a peak at about 30 Mev, and is due to transitions to a state (or states) near 6 Mev. It is interpreted as the result of an overlap of two giant resonance cross sections---one for the ground state and one for the excited state. The consequences of this interpretation to the theory of the nuclear photoeffect is discussed. The yield of gamma rays from ${\mathrm{O}}^{15}$ and ${\mathrm{N}}^{15}$ which follow neutron or proton emission was also studied and several lines were observed, but none above 6.5 Mev. The photonuclear cross sections associated with these lines are estimated to be 45% of the whole photonuclear cross section at 23 Mev.

Theory of Dyeing Polyester and Polyacrylic Fibers1

These two fiber classes are similar in that both are dyed by disperse-type dyes; however, polyacrylic fibers can be dyed with anionic dyes if positive sites are provided. This can be done, for example, by using fiber containing ammonium groups. Alterna tively, positive sites in the form of bound cuprous ions can be produced by treatment of the fiber with cuprous salts. In either case, ion exchange occurs in which colorless anions and dye amons compete for positive sites in the fiber. In contrast, disperse dyes, which are used on all common fibers except cellulose and wool, require no specific dyeing sites. In polyethylene terephthalate, the dyeing reac tion behaves like a simple solution in the tiber, with dipole interactions and dispersion forces probably very important. The rate of dyeing of polyethylene terephthalate tends to be inconveniently slow, and organic compounds called carriers are used frequently to increase the rate. They are effective by mcreasing the diffusion rate of dye through the fiber.