K. L. C. Hunt

Nonlocal polarizability densities and the effects of short‐range interactions on molecular dipoles, quadrupoles, and polarizabilities

Light scattering and absorption processes that are single‐molecule forbidden may be observed in compressed gases and liquids, because of interaction‐induced distortions of molecular charge distributions. In order to extract information about intermolecular dynamics from line shape studies of ‘‘forbidden’’ spectroscopic processes, it is necessary to determine collision‐induced electrical properties as functions of the separations and relative orientations of the interacting molecules. When overlap is not negligible and series expansions valid at long range break down, a model that represents the distribution of polarizable matter in the interacting molecules by means of nonlocal polarizability densities is applicable in computing these properties. In the model the field that induces nonlocal polarization in one molecule is the sum of an external field and the field due to the polarization (permanent, fluctuating, and induced) of the collision partner. With the inclusion of nonlinear response, the model yie...

Effects of van der Waals interactions on the polarizability of atoms, oscillators, and dipolar rotors at long range

Both classical multipolar interactions and the interaction‐induced changes in intrinsic polarizability associated with van der Waals forces contribute to the long‐range pair polarizability of atoms, oscillators, and dipolar rotors. The frequency‐dependent nonlinear polarization of an isotropic system by the field due to the randomly fluctuating multipoles of neighboring systems and by an applied field determines the change in intrinsic polarizability induced in the system by van der Waals interactions. Frequency‐dependent values for the mean‐square fluctuating multipoles are obtained from the fluctuation–dissipation theorem. To lowest order (R−6) the dispersion contribution to the polarizability α(ω) of a pair of atoms A and B is related to an integral over imaginary frequencies iu of the symmetrized product (1+PAB)γA(ω, iu,−iu)αB(iu), where γA(ω, iu,−iu) is a linear combination of the γ‐hyperpolarizability tensor components of atom A and αB(iu) is the polarizability of atom B. By using a mean‐frequency a...

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.

Field‐induced fluctuation correlations and the effects of van der Waals interactions on molecular polarizabilities

New expressions for the van der Waals contribution to the collision‐induced, static polarizability of a molecular pair (ΔαvdW) are derived within a reaction‐field theory. For molecules interacting at long range, multipole expansions are used to determine the reaction field; at shorter range, where overlap is small but nonnegligible, the derivation is based on a nonlocal polarizability density model. In both cases, we obtain ΔαvdW in terms of integrals over imaginary frequencies, each involving the product of a hyperpolarizability for one molecule and a polarizability or hyperpolarizability for the other molecule. In addition, we show that the polarizability changes induced by van der Waals interactions between two molecules stem from two distinct physical effects. First, in an applied field F, each molecule is polarized nonlinearly by the simultaneous action of the field due to the fluctuating charge distribution of its neighbor and the field F. Second, the applied field F alters the correlations between ...

Transient, collision‐induced changes in polarizability for atoms interacting with linear, centrosymmetric molecules at long range

Transient changes in polarizability during collisions between atoms and molecules give rise to interaction‐induced rototranslational Raman scattering: the scalar component of the collision‐induced polarizability Δα00 accounts for isotropic scattering, while the second‐rank component ΔαM2 accounts for collision‐induced depolarized scattering. We have evaluated the changes in electronic polarizability due to interactions between an atom and a molecule of D∞h symmetry in fixed configurations, with nonoverlapping charge distributions. We have cast the resulting expressions into the symmetry‐adapted form used in spectroscopic line shape analyses. Our results are complete to order R−6 in the atom–molecule separation R. To this order, the collision‐induced change in polarizability of an atom and a D∞h molecule reflects not only dipole‐induced–dipole (DID) interactions, but also molecular polarization due to the nonuniformity of the local field, polarization of the atom in the field due to higher multipoles induced in the molecule, hyperpolarization of the atom by the applied field and the quadrupolar field of the molecule, and dispersion. We have analyzed the dispersion contributions to the atom–molecule polarizability within our reaction‐field model, which yields accurate integral expressions for the polarizability coefficients. For numerical work, we have also developed approximations in terms of static polarizabilities, γ hyperpolarizabilities, and dispersion energy coefficients. Estimated polarizability coefficients are tabulated for H, He, Ne, and Ar atoms interacting with H2 or N2 molecules. The mean change in polarizability Δᾱ, averaged over the orientations of the molecular axis and the vector between atomic and molecular centers, is determined by second‐order DID interactions and dispersion. For the lighter pairs, dispersion terms are larger than second‐order DID terms in Δᾱ. In both Δα00 and ΔαM2, first‐order DID interactions dominate at long range; other interaction effects are smaller, but detectable. At long range, the largest deviations from the first‐order DID results for Δα00 areproduced by dispersion terms for lighter species considered here and by second‐order DID terms for the heavier species; in ΔαM2, the largest deviations from first‐order DID results stem from the effects of field nonuniformity and higher multipole induction, for atoms interacting with N2.Transient changes in polarizability during collisions between atoms and molecules give rise to interaction‐induced rototranslational Raman scattering: the scalar component of the collision‐induced polarizability Δα00 accounts for isotropic scattering, while the second‐rank component ΔαM2 accounts for collision‐induced depolarized scattering. We have evaluated the changes in electronic polarizability due to interactions between an atom and a molecule of D∞h symmetry in fixed configurations, with nonoverlapping charge distributions. We have cast the resulting expressions into the symmetry‐adapted form used in spectroscopic line shape analyses. Our results are complete to order R−6 in the atom–molecule separation R. To this order, the collision‐induced change in polarizability of an atom and a D∞h molecule reflects not only dipole‐induced–dipole (DID) interactions, but also molecular polarization due to the nonuniformity of the local field, polarization of the atom in the field due to higher multipoles induc...

Multipole polarizabilities of the helium atom and collision‐induced polarizabilities of pairs containing He or H atoms

The transient, collision‐induced changes in electric properties of ion–atom or atom–atom pairs at long range are determined by the polarizabilities and hyperpolarizabilities of each of the interacting species. Induction effects on moments of the charge distribution or static susceptibilities depend on the response at zero frequency, and dispersion effects depend on the polarizabilities (linear and nonlinear) at imaginary frequencies. In this paper, we give numerical results for four static multipole hyperpolarizabilities of the helium atom obtained from large‐basis, ab initio calculations using many‐body perturbation theory and coupled‐cluster methods. We report and analyze the numerical results for the R−6 and R−8 terms in the dispersion contributions to the He–He, He–H, and H–H pair polarizability functions with a corrected formula for the contributions from the P‐hyperpolarizability tensor. For both parallel and perpendicular components of the polarizability, the numerical results at order R−8 have con...

Transient changes in polarizability for centrosymmetric linear molecules interacting at long range: Theory and numerical results for H2...H2, H2...N2, and N2...N2

Transient, collision‐induced changes in polarizability Δα on the subpicosecond time scale affect Rayleigh and rototranslational Raman scattering by diatomic molecules in dense gases and liquids, induced birefringence, impulsive stimulated scattering, and dielectric and refractivity virial coefficients. For pairs of D∞h molecules, this work gives the long‐range contributions to Δα complete through order R−6 in the intermolecular separation R, including the first‐ and second‐order dipole–induced‐dipole (DID) interactions, higher‐multipole induction, effects of the nonuniformity in the local field, hyperpolarization, and dispersion. We have used spherical tensor methods to cast Δα into the symmetry‐adapted form needed for spectroscopic line shape analysis.The polarization mechanisms included here give rise to isotropic rototranslational Raman scattering and to simultaneous rotational transitions on two interacting molecules; both are collision‐induced phenomena. Transitions with ΔJ up to ±4 are produced by t...

Dipoles induced by van der Waals interactions during collisions of atoms with heteroatoms or with centrosymmetric linear molecules

Using a reaction field model, we have derived symmetry‐adapted expressions for the van der Waals dipoles of atom–heteroatom and atom‐D∞h molecule pairs, with nonoverlapping charge distributions.The leading van der Waals contributions vary as R−7 in the intermolecular separation R and depend upon products of the polarizability ααβ(iω) of one molecule with a dipole–quadrupole hyperpolarizability Bαβ,γδ (0,iω) of the other, integrated over imaginary frequencies. We have developed new approximations for these integrals in terms of the static polarizabilities ααβ, the hyperpolarizabilities Bαβ,γδ, and the van der Waals energy coefficients C6 and C8 (both isotropic and anisotropic components for atom–molecule pairs). The approximations agree well with accurate perturbation results for two model systems. Applied to He⋅⋅⋅H2, our approximations give the first direct results for the leading van der Waals contributions to the dipole. In two symmetry components of the He⋅⋅⋅H2 dipole at long range, van der Waals effects are larger than induction effects; both should be included in fitting collision‐induced roto‐translational spectra.Using a reaction field model, we have derived symmetry‐adapted expressions for the van der Waals dipoles of atom–heteroatom and atom‐D∞h molecule pairs, with nonoverlapping charge distributions.The leading van der Waals contributions vary as R−7 in the intermolecular separation R and depend upon products of the polarizability ααβ(iω) of one molecule with a dipole–quadrupole hyperpolarizability Bαβ,γδ (0,iω) of the other, integrated over imaginary frequencies. We have developed new approximations for these integrals in terms of the static polarizabilities ααβ, the hyperpolarizabilities Bαβ,γδ, and the van der Waals energy coefficients C6 and C8 (both isotropic and anisotropic components for atom–molecule pairs). The approximations agree well with accurate perturbation results for two model systems. Applied to He⋅⋅⋅H2, our approximations give the first direct results for the leading van der Waals contributions to the dipole. In two symmetry components of the He⋅⋅⋅H2 dipole at long range, van der Waals effec...

Dipoles induced by long‐range interactions between centrosymmetric linear molecules: Theory and numerical results for H2⋅⋅⋅H2, H2⋅⋅⋅N2, and N2⋅⋅⋅N2

We have derived symmetry‐adapted expressions for the dipole moments of pairs of D∞h molecules interacting at long range, in a form useful for line shape analyses of collision‐induced rototranslational spectra. Our results are complete to order R−7 in the intermolecular separation R. In addition to quadrupolar and hexadecapolar induction effects, results to this order include induction due to nonuniformities in the local field acting on a molecule (E‐tensor induction), back induction, and polarization due to dispersion forces. The dispersion terms are computed within our recently developed reaction field model, from which we have obtained accurate integral expressions for the dipole coefficients, and approximations in terms of static susceptibilities and dispersion energy coefficients. For H2⋅⋅⋅H2, H2⋅⋅⋅N2, and N2⋅⋅⋅N2, numerical results for the dipole coefficients are tabulated. While quadrupolar induction dominates the long‐range dipole, other induction effects are evident in the far‐infrared collision‐i...

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 650u2009cm−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 experime...