Dipole Dispersion Research Articles

Pairwise and many-body contributions to interaction potentials in Hen clusters

High level ab initio calculations have been carried out to assess the pairwise additivity of potentials in the attractive or well regions of the potential surfaces of clusters of helium atoms. A large basis set was employed and calculations were done at the Brueckner orbital coupled cluster level. Differences between calculated potentials for several interacting atoms and the corresponding summed pair potentials reveal the three-body and certain higher order contributions to the interaction strengths. Attraction between rare gas atoms develops from dispersion, and so helium clusters provide the most workable systems for analyzing nonadditivity of dispersion. The results indicate that the many-body or nonpairwise contributions tend to be less than a few percent of the attractive interaction across regions around the minima of the potential energy surfaces of small clusters. Dipole–dipole–dipole dispersion and dipole–dipole–quadrupole dispersion are noticeable parts of the small three-body terms.

Ab initio dispersion coefficients for interactions involving rare-gas atoms

Calculations of the dynamic dipole, quadrupole, and octopole polarizabilities of Ne, Ar, Kr, and Xe are carried out using both time-dependent coupled Hartree–Fock and many-body perturbation theory methods. Dispersion coefficients are calculated for interactions involving these species. The dynamic polarizabilities are combined with previously published dynamic polarizabilities of H, He, H2, N2, HF, and CO to obtain dispersion coefficients for the interactions involving one of these species and one of Ne, Ar, Kr, or Xe. The dipole–dipole dispersion coefficients agree quite well with the best available semiempirical estimates. The isotropic higher multipole coefficients are in reasonable agreement with previous semiempirical estimates where available, and the anisotropic ones are, in most cases, the first reliable ones to appear in the literature. Nonadditive three-body dispersion coefficients for the Ne3, Ar3, Kr3, and Xe3 interactions are also calculated.

Dipole oscillator strength properties and dispersion energies for acetylene and benzene

Dipole oscillator strength distributions (DOSDs), which are globally reliable, have been constructed for the acetylene and benzene molecules, through the use of quantum mechanical constraint techniques and experimental dipole oscillator strength and molar refractivity data. A recommended isotropic DOSD for each molecule is used to evaluate a wide variety of dipole oscillator stength sums, logarithmic dipole sums, and mean excitation energies, for C2H2 and C6H6. Also obtained are reliable results for the isotropic dipole-dipole dispersion energy coefficients C 6, for the interaction of acetylene and benzene with themselves and with forty-one other species, and for the triple-dipole dispersion energy coefficients C 9, for (C2H2)3 and (C6H6)3. Psuedo-DOSDs for acetylene and benzene are presented which greatly facilitate the evaluation of C 6's and C 9's for a variety of interactions.

C 6 dispersion coefficients in multiconfiguration self-consistent field linear response theory

An algorithm for the evaluation of correlated dipole–dipole dispersion coefficients by direct MCSCF linear response theory is presented. Stepwise construction of a pseudo-state basis using eigenvectors of successive (Cauchy) moments of the linear response function gives an efficient scheme for obtaining polarizabilities at imaginary frequency. The scheme is also useful for polarizabilities on the real axis below the frequency of the first dipole-allowed transition. Sample calculations of C6 coefficients are described for a range of two-electron (H−, He, Li+, Be2+, H2, and H+3 ) and many-electron (Be, N, N2 ) closed- and open-shell systems.

D9 dipole dispersion coefficients

A formula is derived for D 9, the first correction to the usual single-term approximation for the dispersion dipole of a pair of dissimilar atoms. The expression is a Casimir—Polder integral involving dipole and quadrupole polarisabilities, dipole—dipole—quadrupole and dipole— quadrupole—octopole hyperpolarisabilities on each atom. A coupled Hartree—Fock scheme for its ab initio calculation is implemented and static approximation to D 9 show it to be of the same sign as D 7 but larger in magnitude (when both are expressed in atomic units). CHF calculations on H and He give D 9(H +He −)=−3390 au, i.e. over 25 a 2 0 times D 7, and the R −9 local dipole in H…H is over 30 R −2 times the better known R −7 moment.

Dispersion dipoles, quadrupoles and electric-field gradients

Dispersion dipoles, quadrupoles and electric-field gradients at nuclei can be represented as integrals of frequency-dependent monomer polarisabilities and hyperpolarisabilities and are therefore accessible in ab initio calculations that combine finite-field and analytic methods. Static approximations lead to a physical interpretation of the size and sign of the induced properties calculatedfrom the exact formula. A coupled-Hartree-Fock implementation is described and results are presented for pairs involving H, He, Ne, Ar and CH 4

Reliable isotropic and anisotropic dipolar dispersion energies, evaluated using constrained dipole oscillator strength techniques, with application to interactions involving H2, N2, and the rare gases

Molecular dipole oscillator strength distributions (DOSDS), which are reliable in the sense of yielding accurate results for the various dipole properties of molecules, can be constructed if sufficient input information is available. The DOSDS are constructed from extensive experimental and theoretical information, including oscillator strength and photoabsorption cross section data, and are constrained to reproduce accurate refractivity measurements of the relevant dilute gases and to satisfy oscillator strength sum rules. The techniques for obtaining the DOSDS, and related properties, are well established for the evaluation of reliable isotropic dipolar dispersion energies. In this paper they are extended to the evaluation of anisotropic dipole properties, with particular emphasis on anisotropic dispersion energies. The approach used will be illustrated with applications involving H2, N2, and the rare gases. Also included will be brief discussions on (i) the use of reliable results for the dipole–dipole and triple–dipole dispersion energies in constructing complete two- and many-body potential energies and (ii) the advantages of constrained DOSD methods, relative to other approaches, for determining all the dipole properties of molecules.

Dispersion dipoles and dispersion forces: Proof of Feynman’s ‘‘conjecture’’ and generalization to interacting molecules of arbitrary symmetry

This paper provides the first explicit, general proof that the leading-order dispersion forces between two interacting molecules result from the attraction of nuclei in each molecule to the dispersion-induced change in the electronic charge density of the same molecule. The proof given here holds for molecules of any symmetry, provided that overlap between the charge distributions is small. New sum rules for the nonlinear response tensors are also obtained, after consideration of the long-range limit. A perturbation analysis gives the dispersion-induced polarization in each molecule in terms of nonlocal, nonlinear response tensors taken at imaginary frequencies. Forces on the nuclei are computed from a reaction-field expression for the dispersion energy, in terms of polarizability densities. Recent work has shown that the derivative of the polarizability density with respect to a nuclear coordinate is linked to an integral involving the nonlinear response tensor and the dipole propagator, and this link provides the key to the proof.

Dispersive orientational dipole relaxation in thermally stimulated depolarization currents

We show that dipole orientational relaxation in thermally stimulated depolarization currents (TSDC) from alkali-containing glass can be explained by requiring broad distribution of dipole relaxation events. This requirement originates in the structural disorder of the material. Shlesinger-Montroll's theory in the framework of continuous-time random-walk is applied to the case of dispersive rotational motions of dipole relaxation. The Williams-Watts function is obtained for orientational dipole decay. The TSDC is calculated and is in good agreement with our experiment.

Triplet dipoles in the absorption spectra of dense rare gas fluids. II. Long range interactions

A model calculation is presented to evaluate the long range dispersion dipole occurring when three nonoverlapping dissimilar atoms interact. Deviation from pairwise additivity is taken into account by a simplified theory based on electrostatic arguments. By comparing the long range triplet dispersion dipole with the one resulting from exchange overlap effects previously investigated [J. Chem. Phys. 90, 650 (1989)], it is shown that a cancellation between both contributions occurs in the vicinity of the van der Waals separation. The far infrared spectra of dense rare gas fluids are next generated by molecular dynamics simulation including long range dispersion and short range overlap dipoles. An estimate of the expected absorption in liquid krypton is given, αmax =3.6×10−9 cm−1 am−2, which might give some hope to experimentalists. As far as rare gas mixtures are concerned, the model calculation reproduces surprisingly well the experimental absolute spectral density of a Kr–Ar liquid mixture (15% Kr, 135 K) over a large domain of frequency but fails to reproduce the low frequency dip. Nevertheless, irreducible three-body dipoles contribute significantly to the spectrum. The difficulty of obtaining accurate results from an approximate model is emphasized and a guideline for further improvements is sketched.

Far-infrared laser spectroscopy of van der Waals bonds: a powerful new probe of intermolecular forces

Our objective in these studies is to provide a detailed characterization of the structures and internal dynamics of weakly bound complexes as the requisite first step toward the ultimate goal: obtaining details three-dimensional intermolecular potential-energy surfaces for molecular weak interactions. The current state of the art limits us to studies of binary systems, but several groups are currently seeking to extend both the theory and experiments to address ternary and quaternary complexes. This will afford a detailed examination of the many-body effects (e.g., Axelrod -Teller triple dipole dispersion interaction), which becomes of potential importance in models of the chemistry of liquids.

Dipole moments in rare gas interactions

A hybrid model is used to calculate the dipole moments of care gas dimers and trimers. The exchange and polarization interactions are obtained with a single-configuration self-consistent-field (SCF) calculation and the dispersion contribution to the dipole is obtained by perturbation theory. The SCF dipoles for the trimers are found to compare well with values modeled by an exchange quadrupole-induced dipole mechanism. The dispersion dipole for the ArKr dimer is found to be significant compared to the exchange contribution even in the region of the equilibrium separation. Values of the B hyperpolarizability are evaluated for Ne, Ar, Kr, and Xe which allows the perturbation calculation of the dispersion dipole for any pair of rare gas atoms.

Dipole oscillator strength properties and dispersion energy coefficients for H2S

Globally reliable dipole oscillator strength distributions (DOSDs) have been constructed for the H2S molecule in its ground state. An adopted DOSD is used to evaluate a variety of dipole oscillator strength sums Sk, logarithmic dipole sums Lk, and mean excitation energies Ik, for H2S; these dipole properties are important in various physical processes. It is also used to obtain reliable results for the dipole–dipole dispersion energy coefficients C6 for the interaction of H2S with itself, and with thirty-nine other atoms and (mostly) molecules, and the triple-dipole dispersion energy coefficient C9 for (H2S)3. A pseudo-DOSD for H2S is presented which facilitates the evaluation of C6's, and in particular C9's.

Correlation and prediction of gas–liquid partition coefficients in hexadecane and olive oil

A cavity theory of solution has been used to derive an equation for the correlation and prediction of Ostwald solubility coefficients (as log L values) of solutes in hexadecane and olive oil: log L= a + bV+ c(MR)+ dµ2 The endoergic work of creating a cavity in the solvent is given by bV, where V is a solute volume, and the exoergic solute–solvent interactions are given by c(MR) and dµ2, being dispersion and dipole-induced dipole (or dipole–dipole) effects, respectively; MR and µ are the solute molar refraction and dipole moment. When applied to 84 log L values for a wide variety of solutes in hexadecane, the standard deviation in log L is only 0.18 log units, and for 52 non-acidic solutes in olive oil the corresponding standard deviation is 0.23 log units. Comparison of calculated and observed log L values on olive oil for a number of hydrogen-bond-donor solutes shows that hydrogen bonding from the solute to the basic olive oil is negligible for solute CHCl3, but contributes about 20% of the total solute–olive oil interaction energy for alcohol solutes, viz. ∼ 2 kcal mol–1.

Ab initio calculation of the dipole moment of He-Ar and the collision-induced absorption spectra.

For the study of induced dipole moments, the collisional He-Ar complex is treated as a molecule in self-consistent-field (SCF) and size-consistent coupled-electron-pair approximation (CEPA) calculations. The basis superposition error is effectively avoided by using nonorthogonal local orbital sets. The results suggest that the SCF plus approximate dispersion dipoles commonly considered may be at best in accidental agreement with experiment because of fortuitous cancellation: for He-Ar, the hitherto neglected intra-atomic correlation increases the exchange dipole by as much as 30% while the dispersion dipole (which has the opposite polarity of the exchange dipole) is almost 3 times larger than a perturbation estimate of the leading term has indicated. Collision-induced absorption spectra are computed on the basis of the ab initio dipole-moment function, and compared with Bosomworth and Gush's celebrated measurement. We observe close agreement at frequencies where the absorption is strong. Only at the high and low ends of the measured frequency range does the measurement fall below theory by up to 20%, possibly because of the greater experimental uncertainties associated with weak absorption. Other measurements at relatively high densities have resulted in integrated two-body absorption intensities in reasonable agreement with our binary theory.

Van der Waals induced dipoles

Expressions are derived for calculating the induced dipole moment of an arbitrary molecule A interacting with an arbitrary system B through first- and second-order Coulomb interaction. The theory is formulated in terms of linear and quadratic charge-density susceptibilities and takes account of charge penetration but not exchange between the systems. The theory is specialized to the interaction of two nonoverlapping molecules and to a molecule interacting with a nonferroelectric solid, metallic, or crystalline. In the case of two interacting molecules, the induced moment is developed in inverse powers of R, the distance between the centers of the molecules, up to and including R−7; the coefficients of the series are given in terms of the total charges, permanent moments, polarizabilities, and hyperpolarizabilities. In the case of the solid, the results are given in terms of the molecule–solid distance z0, the dielectric function of the solid, and the permanent moments, polarizabilities, and hyperpolarizabilities of the molecule. The expressions for the dispersion and induction dipoles derived here in terms of the charge-density (hyper) susceptibilities are the most general to date in that ionic contributions are included, and the expansion in terms of the (hyper)polarizabilities is the most explicit for nonoverlapping systems. Our results are compared with the work in the literature.

Dipole properties, dispersion energy coefficients, and integrated oscillator strengths for SF6

Dipole oscillator strength distributions (DOSDs) have been constructed for ground SF6 including the IR, UV, and higher energy parts of the absorption spectrum. An adopted DOSD is used to evaluate the dipole oscillator strength sums Sk, k=2,1, 1/2 (− 1/2 )−3,−4,−6,..., mean excitation energies Ik, k=2(−1)−2, dipole–dipole dispersion energies for the interaction of SF6 with itself and with Li, N, O, H2, N2, O2, NO, H2O, NH3, CO2, CO, H, He, Ne Ar, Kr, and Xe, and the triple–dipole dispersion energy for (SF6)3. Pseudo-DOSDs have been constructed for SF6 which facilitate the evaluation of the dispersion energies involving SF6. In most cases uncertainties in our results for the dipole properties and dispersion energy coefficients are ≲1–3%.

Pseudo-spectral dipole oscillator-strength distributions for SO2, CS2 and OCS and values of some related dipole—dipole and triple-dipole dispersion energy constants

Pseudo-spectral dipole oscillator strengths and excitation energies, which are discrete representations of the original continuous dipole oscillator-strength distributions (DOSDs), are presented for the ground-state SO2, CS2 and OCS molecules. These pseudo-DOSDs, together with previously published pseudo-DOSDs, are used to evaluate the dipole—dipole and triple-dipole dispersion-energy coefficients for all the two- and three-body interactions between SO2, CS2 and OCS and between these molecules and H2, N2, O2, NO, N2O, H2O, NH3, CO, CO2, CH4, C2H6, C4H10 and C6H14, with an estimated uncertainty of 1–2%. The importance of results of this type is discussed briefly.

The dispersive collision dipole in a pair of polyatomic molecules

The dipole moment appearing in a pair of polyatomic molecules during a collision, originating from the dynamic correlation of the charges between the two systems, is formulated using two different methods. The first one introduces the electro-optical effect induced in one of the partners by the fluctuating field of the other and by an externally applied field. The second method takes into account the optical rectification processes of one molecule subjected to the fluctuating field of the other. These formalisms may be applied to pairs with any molecular symmetry. An application is made to molecules belonging to the Td group, showing that in such a case the R−7 part of the dispersion polarization may be competitive with inductive effects.

Dipole oscillator strength distributions, sums, and dispersion energy coefficients for CO and CO 2

Globally reliable dipole oscillator strength distributions (DOSDs) have been constructed for ground state CO and CO 2 molecules; the DOSD for CO corresponds to photon energies greater than the electronic absorption threshold while that for CO 2 includes the infrared part of the spectra as well. The recommended DOSDs are used to evaluate the isotropic dipole—dipole dispersion energies for the COCO, COCO2 and CO2CO2 interactions as well as the molar refractivities, as a function of wavelength, and the dipole sums, S k , k = 2(−1) -4, -6, -8, -10, for the two molecules. Pseudo-DOSD representations of the recommended DOSDs are provided which allow the efficient accurate evaluation of the dispersion energy coefficients C 6 for the interaction of CO or CO 2 with a variety of other atoms and molecules. Previous results for C 6 are found to be in disagreement with our recommended results for interactions involving CO 2. The results of this paper are used to give a reasonably general discussion of the difficulties associated with obtaining reliable results for C 6 by using Padé approximant bounding methods.