^{1,a)}

### Abstract

The collision-induced (CI) dipole moment, CI polarizability, and CI hyperpolarizability are considered for three –rare gas (Rg) pairs (Rg = He, Ne, Ar). In this study, the symmetry-adapted (SA) components, the projection of the CI dipole, polarizability, and hyperpolarizability on an appropriately tailored set of spherical harmonics are calculated. A set of equations for the respective SA components is derived. The Cartesian components of the CI properties calculated by quantum chemistry methods for three intermolecular geometries are used in our calculations as input data. The analytical, multipolar long-range behavior of the CI properties studied is considered within a multipole-induced multipole model. Taking the SA components at large distances, the *ab initio* SA numerical results and the model semianalytical data were compared. In general, a good agreement has been found. The results of our study are expected to be of value in spectral line shape analysis and in modeling of processes in the Earth's and planetary atmospheres.

This work has been supported by the research Project No. N N202 069939 sponsored by The Government of the Republic of Poland.

I would like to express my thanks to George Maroulis, Jean-Luc Godet, and Waldemar Głaz for many illuminating discussions.

I. INTRODUCTION

II. GENERAL CONSIDERATIONS

III. COLLISION-INDUCED DIPOLE MOMENT

IV. COLLISION-INDUCED POLARIZABILITY

A. The isotropic part

B. The anisotropic part

V. COLLISION-INDUCED HYPERPOLARIZABILITY

VI. CONCLUSION

### Key Topics

- Polarizability
- 30.0
- Ab initio calculations
- 13.0
- Tensor methods
- 13.0
- Electric dipole moments
- 10.0
- Light scattering
- 10.0

## Figures

The *R*-dependence of the symmetry-adapted components of the collision-induced dipole moment for –Ar. All SA components are indicated by their λ *L* indices. The long-range analytical classical multipolar components (dashed lines) are also shown. The component resulting from the quadrupole moment of is denoted by *Q* and the component emerging from the hexadecapole moment of by Φ. The collision diameter σ of the –Ar pair is given as well.

The *R*-dependence of the symmetry-adapted components of the collision-induced dipole moment for –Ar. All SA components are indicated by their λ *L* indices. The long-range analytical classical multipolar components (dashed lines) are also shown. The component resulting from the quadrupole moment of is denoted by *Q* and the component emerging from the hexadecapole moment of by Φ. The collision diameter σ of the –Ar pair is given as well.

The *R*-dependence of the irreducible spherical rotationally adapted components of the isotropic part the CI –He pair polarizability versus intermolecular distance *R*, given in atomic units. The long-range first order DID ^{(DID)} polarizability is also shown. All SA components are indicated by their λ *L* indices.

The *R*-dependence of the irreducible spherical rotationally adapted components of the isotropic part the CI –He pair polarizability versus intermolecular distance *R*, given in atomic units. The long-range first order DID ^{(DID)} polarizability is also shown. All SA components are indicated by their λ *L* indices.

The SA components of the anisotropic (deviator) part of the CI polarizability for –He pair. The radial behavior of the irreducible spherical symmetry adapted components is displayed. The long-range first order DID components and ^{(DID)} and ^{(DID)} are also plotted. All SA components are indicated by their λ *L* indices. The collision diameter σ of the -He pair is given as well.

The SA components of the anisotropic (deviator) part of the CI polarizability for –He pair. The radial behavior of the irreducible spherical symmetry adapted components is displayed. The long-range first order DID components and ^{(DID)} and ^{(DID)} are also plotted. All SA components are indicated by their λ *L* indices. The collision diameter σ of the -He pair is given as well.

The radial dependence of the irreducible spherical symmetry adapted *ab initio* component of the isotropic part the CI –He pair polarizability. The long-range analytical MIM, dipole–octopole component ^{(MIM)} is also presented.

The radial dependence of the irreducible spherical symmetry adapted *ab initio* component of the isotropic part the CI –He pair polarizability. The long-range analytical MIM, dipole–octopole component ^{(MIM)} is also presented.

The *R*-dependence of the irreducible spherical symmetry-adapted *ab initio* component of the isotropic part of the CI –Ne pair polarizability vs intermolecular distance *R*, given in atomic units. Long-range analytical MIM, dipole–octopole component ^{(MIM)} is also shown. The collision diameter σ for a –Ne pair varies from 5.40 to 5.66 bohr for the data taken from various sources (see Ref. 49).

The *R*-dependence of the irreducible spherical symmetry-adapted *ab initio* component of the isotropic part of the CI –Ne pair polarizability vs intermolecular distance *R*, given in atomic units. Long-range analytical MIM, dipole–octopole component ^{(MIM)} is also shown. The collision diameter σ for a –Ne pair varies from 5.40 to 5.66 bohr for the data taken from various sources (see Ref. 49).

The radial behavior of the irreducible spherical symmetry-adapted *ab initio* component of the anisotropic part of the CI –He pair polarizability vs intermolecular distance *R*. All data are given in atomic units. Long-range analytical MIM, dipole–octopole component ^{(MIM)} is also given.

The radial behavior of the irreducible spherical symmetry-adapted *ab initio* component of the anisotropic part of the CI –He pair polarizability vs intermolecular distance *R*. All data are given in atomic units. Long-range analytical MIM, dipole–octopole component ^{(MIM)} is also given.

The *R*-dependence of the irreducible spherical symmetry-adapted *ab initio* component of the anisotropic part of the CI –Ne pair polarizability vs intermolecular distance *R*, given in atomic units. Long-range analytical MIM, dipole–octopole component ^{(MIM)} is also shown.

The *R*-dependence of the irreducible spherical symmetry-adapted *ab initio* component of the anisotropic part of the CI –Ne pair polarizability vs intermolecular distance *R*, given in atomic units. Long-range analytical MIM, dipole–octopole component ^{(MIM)} is also shown.

The *R*-dependence of the *ab initio* and irreducible spherical symmetry-adapted components of the anisotropic part of the –He pair polarizability vs intermolecular distance *R*. All data are given in atomic units. The long range analytical MIM, dipole–octopole origin components are also given.

The *R*-dependence of the *ab initio* and irreducible spherical symmetry-adapted components of the anisotropic part of the –He pair polarizability vs intermolecular distance *R*. All data are given in atomic units. The long range analytical MIM, dipole–octopole origin components are also given.

The radial behavior of the divergence between the model data [Eq. (12)] and the *ab initio* ones for the hyperpolarizability component of –He. All data are given in atomic units.

The radial behavior of the divergence between the model data [Eq. (12)] and the *ab initio* ones for the hyperpolarizability component of –He. All data are given in atomic units.

## Tables

Values of the dipole^{2}–quadrupole hyperpolarizability (*B*), dipole polarizability (α), dipole–octopole polarizability (*E*), and quadrupole moment (*Q*) used in our calculations. All values are in atomic units [a.u.].

Values of the dipole^{2}–quadrupole hyperpolarizability (*B*), dipole polarizability (α), dipole–octopole polarizability (*E*), and quadrupole moment (*Q*) used in our calculations. All values are in atomic units [a.u.].

Article metrics loading...

Full text loading...

Commenting has been disabled for this content