Dipole Dispersion Research Articles

A modified Cashion–Herschbach potential for the H 3 potential energy surface

The H 3 potential energy surface has been calculated using the Cashion–Hershbach (CH) potential which contains all orders of two-body Coulomb, exchange, and overlap terms. For collinear configurations, the dominant three-body contribution comes from the Axilrod–Teller–Muto triple–dipole dispersion energy. By adding only this term, properly damped, the saddle point region potential agrees with recent ab initio calculations to within 9×10 −5 a.u. (0.06 kcal/mole).

Dipole moment surfaces and the mid- and far-IR spectra of N2-Ar

An improved theoretical long-range dispersion plus induction dipole moment surface for N2-Ar is presented, and detailed numerical simulations are used to test its predictions against experimental far-IR and mid-IR spectra using two previously-reported potential energy surfaces. As was found in earlier work on the mid-IR spectrum using a pure induction dipole surface, the MMSVmod potential of Jäger et al. [J. Chem. Soc. Faraday Discuss. 97, 105 (1994)] yields distinctly better agreement with both experiments than does the XC-3 potential of Dham et al. [J. Chem. Phys. 103, 8477 (1995)]. However, the new dipole surface yields slightly poorer agreement with certain features of the experimental mid-IR and far-IR spectra, which suggests that the existing theoretical values and derivatives with respect to the bond length of some of the permanent moment and (hyper)polarizability properties of N2 need improvement.

Theoretical investigation of Ca⋅RG, Ca+⋅RG, and Ca2+⋅RG (RG=Ar and Ne) complexes

The ground state structure, harmonic frequency, and dissociation energy for Ca⋅RG, Ca+⋅RG, and Ca2+⋅RG (RG=Ar and Ne) complexes are computed at four theoretical levels [HF, B3LYP, MP2, and MP2(full)] using three different basis sets. The most rigorous method employed was Møller–Plesset second order perturbation with valence plus core electron correlation using 183 basis functions for the calcium–neon complexes and 187 basis functions for the calcium–argon complexes. Correcting the dissociation energies, bond distances, and frequencies for basis set superposition error (BSSE) were done at the most rigorous level of theory by fitting the Morse function to the potential energy curves generated by the counterpoise procedure. At this level of theory, proceeding from the neutral to the doubly charged complexes, the calcium–neon bond distances range from 5.40 to 2.45 Å with dissociation energies (De) from 0.03 to 5.86 kcal/mol. Likewise, the calcium–argon bond distances range from 5.00 to 2.70 Å with dissociation energies from 0.23 to 16.80 kcal/mol as the metal charge increases. Good theoretical agreement is obtained with experimental data when available, while the remaining results can aid in the interpretation of future experiments. In all comparable cases where the calcium–rare gas complexes possess equivalent charge, the argon atom is bound tighter to the metal than the neon atom due to its larger atomic polarizability. An examination of the relationship between dispersion and charge-induced dipole forces is done using these calcium–rare gas complexes.

Dipole dispersion crossover and sonic logs in a limestone reservoir

Analyses of sonic logs in a horizontal well provide new information about mechanical properties of rocks, made possible by recent developments in our understanding of acoustic wave propagation in prestressed formations. Most sections of this horizontal well exhibit azimuthal shear isotropy, indicating isotropic stresses in the plane perpendicular to the well trajectory, leading to stable wellbore conditions. However, two sections show dipole dispersion crossovers that confirm the presence of stress‐induced shear anisotropy caused by a difference between the maximum and minimum stresses in the plane perpendicular to the well trajectory. The two dipole dispersions are obtained by processing the recorded waveforms by a modified matrix pencil algorithm. The fast‐shear direction is estimated from Alford rotation of the cross‐dipole waveforms. One section of the well exhibits the fast‐shear direction parallel to the overburden stress as the maximum stress direction, whereas the other section has the fast‐shear direction parallel to the horizontal stress that is larger than the overburden stress. The cause of this change in the fast‐shear direction is believed to be the well’s penetration into a 3-ft-thick bed with lower porosity and permeability and significantly higher elastic stiffnesses than those in the other part of the homogeneous, high‐permeability reservoir. A stiff bed is likely to have greater stresses in its plane than perpendicular to it, which would make the horizontal stresses greater than the vertical.

A simple damping function for the three-atom dispersion energy

A simple procedure is used to construct the damping functions for extending the Axilrod–Teller–Muto triple dipole dispersion energy for arbitrary three-atom systems to smaller distances. The new damping functions incorporate the Tang–Toennies two-body damping functions at the appropriate united atom limits. The accuracy of the damping function is illustrated by comparing with ab initio and third-order perturbation calculations of the H 3 three-body polarization energy.

Constant pressure path integral molecular dynamics studies of quantum effects in the liquid state properties of n-alkanes

A computer simulation study of quantum effects in methane, butane, and octane is presented. Each molecular system is examined at three state points in the liquid region using novel extended system, multiple time step, constant pressure, path integral molecular dynamics methodology. In addition, the results of classical calculations are reported to provide a useful reference. Liquid butane is used as a test case on which to compare the predictions of two empirical force fields, CHARMM22 and AMBER95. Comparisons are made to experiment. Briefly, the models predict that quantum effects lead to an increase in molar volume of approximately 2 cm3/mole (i.e., relative to a classical calculation). However, a slight unphysical hydrogen–deuterium isotope effect is, also, observed. This may be caused by an incorrect parametrization of the anisotropy of the potential or by a reduction in the magnitude of the intermolecular induced dipole-induced dipole dispersion coefficient with increasing isotope mass that has not been parametrized in the force fields. In addition, the results show an interesting zero-point energy effect. The intramolecular regions of the radial distribution function exhibit less structure at lower temperatures than at higher temperatures. This is the inverse of the prediction of the model in the classical limit. The quantum effect occurs because the bulk density decreases faster than the intramolecular degrees of freedom lose zero-point energy as temperature increases in the highly harmonic intramolecular potential model employed in the calculations. Nonetheless, the phenomena is not likely to be an artifact and careful experiments could observe it. Finally, the efficiency of the path molecular dynamics methods employed in the studies are demonstrated on both serial and parallel computers.

Solvent Effects on Ultraviolet Absorption and Circular Dichroic Spectra of Helical Polypeptides and Globular Proteins. Calculations Based on a Lattice-Filled Cavity Model

Solvent effects on the electronic absorption and circular dichroic spectra of helical polypeptides and globular proteins are modeled by placing the molecule in a spherical cavity in a continuous dielectric medium and filling voids in the cavity with a simple cubic lattice of solvent molecules. Effects on the amide π−π* spectra near 200 nm are treated. The interactions among the solute atoms, solute chromophores, and discrete solvent molecules are treated by the partially dispersive dipole interaction treatment applied previously to the isolated molecules, while the dielectric continuum is treated by a rigorous reaction field formalism. Calculations are given for helical polypeptides αR-(Ala)10, (Pro)10 II, βP-(Abu)6×3, βA-(Abu)6×3 and globular proteins erabutoxin, cytochrome c, and myoglobin. Predicted solvent effects are generally small, but include potentially measurable increases in intensities of CD bands in αR-(Ala)10, (Pro)10 II, and the three proteins, and hypochromic shifts in the absorption bands of β-sheets.

Long-range, collision-induced dipoles of Td–D∞h molecule pairs: Theory and numerical results for CH4 or CF4 interacting with H2, N2, CO2, or CS2

Compressed gases and liquids containing molecules of Td and D∞h symmetry absorb far-infrared radiation, due to transient dipole moments induced during molecular collisions. In earlier theoretical work on far-infrared absorption by CH4/N2 mixtures, good agreement was obtained between calculated and experimental spectra at low frequencies, but at higher frequencies—from 250 to 650 cm−1—calculated absorption intensities fell significantly below the experimental values. In this work, we focus on an accurate determination of the long-range, collision-induced dipoles of Td⋯D∞h pairs, including two polarization mechanisms not treated in the earlier line shape analysis: dispersion and nonuniformity in the local field gradient acting on the Td molecule. Since these mechanisms produce transitions with ΔJ=±3 or ±4 for CH4 and ΔJ=0 or ±2 for N2, their inclusion is expected to increase the calculated absorption intensities in the high frequency wings for CH4/N2 mixtures. This should improve agreement with the experimental spectra, and permit more accurate determination of anisotropic overlap terms in the collision-induced dipole. We give numerical values for the long-range dipole coefficients of CH4 or CF4 interacting with H2, N2, CO2, or CS2; the dipole coefficients have been derived with spherical-tensor methods and evaluated using single-molecule moments and susceptibilities from recent ab initio calculations or experiments. The dispersion dipoles are given rigorously in terms of integrals involving the imaginary-frequency polarizability α(iω) and the hyperpolarizabilities β(0;iω,−iω) and B(0;iω,−iω). To obtain numerical estimates for the dispersion dipoles, we have developed constant-ratio approximations that require only the static susceptibilities and C6 van der Waals coefficients.

A molecular description of how noble gases and nitrogen bind to a model site of anesthetic action.

How some noble and diatomic gases produce anesthesia remains unknown. Although these gases have apparently minimal capacities to interact with a putative anesthetic site, xenon is a clinical anesthetic, and argon, krypton, and nitrogen produce anesthesia at hyperbaric pressures. In contrast, neon, helium, and hydrogen do not cause anesthesia at partial pressures up to their convulsant thresholds. We propose that anesthetic sites influenced by noble or diatomic gases produce binding energies composed of London dispersion and charge-induced dipole energies that are sufficient to overcome the concurrent unfavorable decrease in entropy that occurs when a gas molecule occupies the site. To test this hypothesis, we used the x-ray diffraction model of the binding site for Xe in metmyoglobin. This site offers a positively charged moiety of histidine 93 that is 3.8 A from Xe. We simulated placement of He, Ne, Ar, Kr, Xe, H2, and N2 sequentially at this binding site and calculated the binding energies, as well as the repulsive entropy contribution. We used free energies obtained from tonometry experiments to validate the calculated binding energies. We used partial pressures of gases that prevent response to a noxious stimulus (minimum alveolar anesthetic concentration [MAC]) as the anesthetic endpoint. The calculated binding energies correlated with binding energies derived from the in vivo (ln) data (RTln[MAC], where R is the gas constant and T is absolute temperature) with a slope near 1.0, indicating a parallel between the Xe binding site in metmyoglobin and the anesthetic site of action of noble and diatomic gases. Nonimmobilizing gases (Ne, He, and H2) could be distinguished by an unfavorable balance between binding energies and the repulsive entropy contribution. These gases also differed in their inability to displace water from the cavity. The Xe binding site in metmyoglobin is a good model for the anesthetic sites of action of noble and diatomic gases. The additional binding energy provided by induction of a dipole in the gas by a charge at the binding site enhanced binding.

Effects of borehole stress concentrations on dipole anisotropy measurements

We show both experimentally and theoretically how stress concentrations affect the velocity field around a borehole, and how the velocity field influences dipole anisotropy measurements. At low frequencies the dipole mode is sensitive to the far‐field stresses primarily, so standard sonic log interpretation correctly yields the direction of maximum stress. At higher frequencies, the dipole mode is sensitive to near‐field stress concentrations such that the fast polarization direction is aligned with the direction of minimum tectonic stress. These effects combine to produce a crossover in the dipole dispersion curves measured in the fast and slow directions. With broad‐band dipole data, the dispersion crossover can be used as an indicator of stress‐induced anisotropy dominating over weak intrinsic anisotropy.

Nonadditive three-body dipoles of inert gas trimers and H2⋯H2⋯H2: Long-range effects in far infrared absorption and triple vibrational transitions

Nonadditive, three-body dipoles are detected experimentally in far-infrared absorption by inert gas mixtures and in triple transitions, the absorption of a single photon by three molecules, each of which becomes vibrationally excited. In this work, we use perturbation theory to derive the nonadditive, three-body dipole of molecules A, B, and C of arbitrary symmetry, interacting at long range. Our results include linear induction, hyperpolarization, dispersion, and concerted induction–dispersion effects, with direct overlap damping. We derive exact, new equations for the dispersion and induction–dispersion dipoles, in terms of the polarizabilities and hyperpolarizabilities of A, B, and C, integrated over imaginary frequencies. With these, we obtain accurate numerical results for the dipoles of inert gas trimers and trimers containing H2, isotropically averaged over the orientations of the molecular axis. For application to heavier systems, we develop a new constant-ratio approximation, relating three-body dipoles to the van der Waals interaction energy coefficients C6 and C9, the static polarizability α, and the static dipole2-quadrupole hyperpolarizability B. For the test cases in this work, this approximation gives the integrals appearing in the induction–dispersion dipoles with root-mean-square errors of 10–14 %, and the integrals in the pure dispersion dipoles with root-mean-square errors of 1–4 %. Our numerical results for the dipoles of inert gas trimers should be useful in molecular dynamics simulations of far-infrared absorption, and in extracting information on intercollisional interference from the absorption line shapes.

Reliable anisotropic dipole properties and dispersion energy coefficients for NO, evaluated using constrained dipole oscillator strength techniques

Reliable anisotropic dipole properties and dispersion energy coefficients for NO, evaluated using constrained dipole oscillator strength techniques

Reliable anisotropic dipole properties and dispersion energy coefficients for NO, evaluated using constrained dipole oscillator strength techniques

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 Sk , k = 2,1,0(− 1/2)− 2,− 3,− 4,..., the logarithmic dipole sums Lk and mean excitation energies Ik , 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.

Reliable anisotropic dipole properties, and dispersion energy coefficients, for O2 evaluated using constrained dipole oscillator strength techniques

Constrained anisotropic dipole oscillator strength techniques are used to obtain reliable values for a wide range of anisotropic and isotropic dipole properties of O2, including the dipole–dipole dispersion energy coefficients for the interaction of O2 with 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, multireference configuration interaction (CI) wave functions for the ground state of O2. The individual dipole properties of O2 considered include the dipole oscillator strength sums Sk, k=2,1,0(−1/2)−2,−3,−4,..., the logarithmic dipole sums Lk and mean excitation energies Ik, k=2(−1)−2, and, as a function of wavelength, the dynamic polarizability and its anisotropy, the total depolarization ratio, the Rayleigh scattering cross section, and the Verdet constant. Our constrained dipole oscillator strength results are often the only reliable, and sometimes the only available, ones for many of the properties and dispersion energies considered.

A Simplified Perturbed Hard-Sphere Model for the Activity Coefficients of Amino Acids and Peptides in Aqueous Solutions

A simple perturbed hard-sphere model has been developed to correlate the activity coefficients of amino acids and peptides in aqueous solutions. The perturbation terms are those due to dispersion forces and dipole−dipole interactions. These interactions are represented by a Lennard-Jones (6−12) and a Keesom expression, respectively. Dipole moments of amino acids and peptides, calculated by a quantum mechanical approach using the Hyperchem molecular modeling software, are reported. The model can accurately correlate the activity coefficients of amino acids and peptides in aqueous solutions. The model was used to correlate and predict the solubilities of amino acids in aqueous solutions at different temperatures. New values of Δg and Δh of solution of amino acids are reported.

A density functional theory study of frequency-dependent polarizabilities and Van der Waals dispersion coefficients for polyatomic molecules

A method for calculating frequency-dependent polarizabilities and Van der Waals dispersion coefficients, which scales favorably with the number of electrons, has been implemented in the Amsterdam Density Functional package. Time-dependent Density Functional Theory is used within the Adiabatic Local Density Approximation (ALDA). Contrary to earlier studies with this approximation, our implementation applies to arbitrary closed-shell molecular systems. Our results for the isotropic part of the Van der Waals dispersion energy are of comparable quality as those obtained in TDCHF calculations. The ALDA results for the relative anisotropy of the dipole dispersion energy compare favorably to TDCHF and MBPT results. Two semi-empirical ways to calculate the dispersion energy anisotropy are evaluated. Large bases which include diffuse functions are necessary for a good description of the frequency-dependent properties considered here.

Reliable isotropic and anisotropic dipole properties, and dipolar dispersion energy coefficients, for CO evaluated using constrained dipole oscillator strength techniques

Abstract Constrained anisotropic dipole oscillator strength methods are applied to obtain reliable results for a wide selection of anisotropic and isotropic dipole properties of CO and for the dipole-dipole dispersion energy coefficients for the interaction of CO with CO, N 2 , H 2 , He, Ne, Ar, Kr and Xe. The properties of CO evaluated 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 depolarization ratio, the Rayleigh scattering cross section, and the Verdet constant. Our constrained dipole oscillator strength results are often the only reliable, and sometimes the only, results available for many of the anisotropic dipole properties and dispersion energies considered in this paper.

Effect of three-body forces on the statics and dynamics of SF6–(Rg)n and (Rg)13 clusters

Molecular dynamics and Monte Carlo simulations are used to examine the effect on the structural properties of heterogeneous SF6–(Ar)n and SF6–(Kr)n clusters, and on the melting behavior of heterogeneous SF6–(Ar)n and homogeneous (Ar)13 and (Kr)13 clusters, of including the three-body Axilrod–Teller–Muto triple–dipole dispersion energies in the total potential energy surface governing the dynamics of the system. The behavior of these systems is governed by potentials constructed from the best available two-body interactions, and from accurate constrained dipole oscillator strength values for the triple–dipole dispersion energy coefficients reported here for the first time. The structural studies show that (virtually) all isomers are destablized by inclusion of the three-body terms, with the ‘‘stacked’’ or ‘‘nonwetting’’ structures being destablized relatively more than isomeric ‘‘monolayer’’ or ‘‘wetting’’ structures. However, the qualitative trends in relative stability are unchanged; in particular, the preference for the SF6 to be fully solvated in larger clusters formed with Ar, but to lie on the surface of larger clusters formed with Kr, remains unchanged. In contrast, the melting temperatures of the stacked and monolayer isomers of the heterogeneous SF6–(Ar)12 cluster undergo substantial change on inclusion of the three-body terms, the former dropping from ca. 30 to 22 K and the latter from 10 to 6 K. The melting temperatures of the homogeneous (Ar)13 and (Kr)13 icosahedral isomers also decreased on inclusion of the three-body interactions, and the resulting values are quite different than those obtained using the commonly accepted ‘‘effective’’ two-body LJ(12,6) pair potentials for these systems.

Calculation of the dispersion-dipole coefficients for interactions between H, He, and H2

Collisions between atoms and molecules create an induced dipole moment which, at long range separations, stems, in part, from the van der Waals interactions between the colliding species. This contribution is known as the dispersion dipole moment and is of the order R−7, where R is the separation between particles. Although there have been several approximate calculations of the dispersion-dipole coefficients which govern this contribution, and are the counterparts to the van der Waals dispersion-energy coefficients, there have been few ab initio calculations. In this article we present highly accurate results, based on explicitly electron-correlated wave functions, for the dispersion-dipole coefficients pertaining to interactions between pairs chosen from H, He, and H2. We also obtain values with some of the currently used approximate formulas. A comparison shows that these values differ, in general, by a significant amount (∼20–∼40 %) from the accurate ones. We also tabulate values of the dipole–dipole-quadrupole polarizability tensor (B) for imaginary frequency (iω) for a range of frequencies appropriate to a 64-point Gauss–Legendre quadrature for H, He, and H2. These values were used in certain numerical integrations we made to verify our original results which had been obtained by analytic integration—they may, however, be useful in other contexts. For H–H2 and H2–H2, these are the only ab initio calculations of the dispersion-dipole coefficients of which we are aware.

Thermal diffusion factors and intermolecular potentials for noble gas–SF6 systems

Experimental thermal diffusion factors for equimolar mixtures of He–, Ne–, Ar–, Kr–, and Xe–SF6 have been measured in the temperature range from 225 to 500 K. The data were obtained in a 20-tube trennschaukel, or ‘‘swing separator.’’ The systems containing the four lighter noble gases all exhibited a ‘‘normal’’ thermal diffusion factor, αT, i.e., concentration of the heavy species, SF6, in the cold region of the apparatus and increase of αT with temperature. Xe–SF6, the system with the smallest mass difference, exhibited ‘‘abnormal’’ behavior. The spherically symmetric Pack potentials were used to calculate the thermal diffusion factor with reasonable success. Recently published dipole–dipole dispersion coefficients were used to construct intermolecular potentials of the Hartree–Fock-dispersion functional form with individually damped attractive terms. The potentials, when tested against the available transport and thermodynamic data, improved the fit to experiment in almost all cases.