^{1,a)}, Zong-Chao Yan

^{2,3}, Ting-Yun Shi

^{1}, James F. Babb

^{4}and J. Mitroy

^{5}

### Abstract

The long-range non-additive three-body dispersion interaction coefficients *Z* _{111}, *Z* _{112}, *Z* _{113}, and *Z* _{122} are computed for many atomic combinations using standard expressions. The atoms considered include hydrogen, the rare gases, the alkali atoms (up to Rb), and the alkaline-earth atoms (up to Sr). The term *Z* _{111} arising from three mutual dipole interactions is known as the Axilrod-Teller-Muto coefficient or the DDD (dipole-dipole-dipole) coefficient. Similarly, the terms *Z* _{112}, *Z* _{113}, and *Z* _{122} arise from the mutual combinations of dipole (1), quadrupole (2), and octupole (3) interactions between atoms and they are sometimes known, respectively, as dipole-dipole-quadrupole, dipole-dipole-octupole, and dipole-quadrupole-quadrupole coefficients. Results for the four *Z* coefficients are given for the homonuclear trimers, for the trimers involving two like-rare-gas atoms, and for the trimers with all combinations of the H, He, and Li atoms. An exhaustive compilation of all coefficients between all possible atomic combinations is presented as supplementary data.

This work was supported by the National Natural Science Foundation (NNSF) of China under Grant Nos. 11104323 and 11034009, and by the National Basic Research Program of China under Grant No. 2012CB821305. Z.-C.Y. was supported by NSERC of Canada and by the computing facilities of ACEnet, SHARCnet, WestGrid, and in part by the Chinese Academy of Sciences (CAS)/SAFEA International Partnership Program for Creative Research Teams. J.M. would like to thank the Wuhan Institute of Physics and Mathematics for its hospitality during his visits. The work of J.M was supported in part by the Australian Research Council Discovery Project DP-1092620. ITAMP is partially supported by a grant from the US National Science Foundation (NSF) to Harvard University and the Smithsonian Astrophysical Observatory.

I. INTRODUCTION

II. DEFINITIONS OF THE DISPERSION COEFFICIENTS

A. Expressions using oscillator strength sum rules

B. Combination rules

III. UNDERLYING DESCRIPTION OF ATOMIC STRUCTURES

A. Hydrogen

B. Hylleraas descriptions for He and Li

C. Pseudo-oscillator strength distributions for heavier rare gases

D. Semi-empirical description of structure for alkali and alkaline-earth atoms

IV. NUMERICAL RESULTS

A. H, He, and Li

B. Homonuclear trimers

C. Impurity atoms embedded in the rare gases

D. Other systems

E. The Midzuno-Kihara approximation

V. CONCLUSIONS

### Key Topics

- Dispersion
- 14.0
- Disperse systems
- 10.0
- Oscillators
- 10.0
- Polarizability
- 10.0
- Quadrupoles
- 6.0

## Tables

The dispersion constants (in a.u.) for homonuclear trimers consisting of either hydrogen, helium, or lithium. All other dispersion coefficients are given by the symmetry conditions as described in the text. The numbers in parentheses are the computational uncertainties arising from incomplete convergence of the basis set. Values for hydrogen are correct to all quoted digits. The numbers in the square brackets denote powers of ten.

The dispersion constants (in a.u.) for homonuclear trimers consisting of either hydrogen, helium, or lithium. All other dispersion coefficients are given by the symmetry conditions as described in the text. The numbers in parentheses are the computational uncertainties arising from incomplete convergence of the basis set. Values for hydrogen are correct to all quoted digits. The numbers in the square brackets denote powers of ten.

The three atom dispersion constants for combinations of H, He, and Li with two like atoms. The other dispersion constants are given by the symmetry relations =, =, and = (in a.u.). The numbers in parentheses are the computational uncertainties arising from the finite basis set size.

The three atom dispersion constants for combinations of H, He, and Li with two like atoms. The other dispersion constants are given by the symmetry relations =, =, and = (in a.u.). The numbers in parentheses are the computational uncertainties arising from the finite basis set size.

The dispersion coefficients for the heteronuclear H–He–Li trimer (in a.u.). The numbers in parentheses are the computational uncertainties arising from incomplete convergence of the basis set.

The dispersion coefficients for the heteronuclear H–He–Li trimer (in a.u.). The numbers in parentheses are the computational uncertainties arising from incomplete convergence of the basis set.

Comparison of the *Z* _{111} (in a.u.) parameter for all combinations of the trimers formed by the H, He, and Li with some earlier calculations. The numbers in parentheses are the computational uncertainties arising from incomplete convergence of the basis set.

Comparison of the *Z* _{111} (in a.u.) parameter for all combinations of the trimers formed by the H, He, and Li with some earlier calculations. The numbers in parentheses are the computational uncertainties arising from incomplete convergence of the basis set.

The three-body dispersion coefficients, *Z* _{111}, *Z* _{112}, *Z* _{122}, and *Z* _{113} (in atomic units) for homonuclear trimers. The *f*-value distributions for H, He, and Li use Laguerre type orbitals (H) or Hylleraas basis functions (He and Li) to describe the ground and excited state spectra. Dispersion coefficients for the H, He, and Li trimers are given to additional significant digits in Table I. The heavier gas *f*-value distributions use pseudo-oscillator strength distributions, (Refs. 27,28,44) while those for the other atoms come from CICP calculations. Results in the Midzuno-Kihara (MK) approximation (Refs. 35,36) use the present oscillator strength distributions to compute the underlying α_{ d } and *C* _{6} needed as input. The numbers in the square brackets denote powers of ten.

The three-body dispersion coefficients, *Z* _{111}, *Z* _{112}, *Z* _{122}, and *Z* _{113} (in atomic units) for homonuclear trimers. The *f*-value distributions for H, He, and Li use Laguerre type orbitals (H) or Hylleraas basis functions (He and Li) to describe the ground and excited state spectra. Dispersion coefficients for the H, He, and Li trimers are given to additional significant digits in Table I. The heavier gas *f*-value distributions use pseudo-oscillator strength distributions, (Refs. 27,28,44) while those for the other atoms come from CICP calculations. Results in the Midzuno-Kihara (MK) approximation (Refs. 35,36) use the present oscillator strength distributions to compute the underlying α_{ d } and *C* _{6} needed as input. The numbers in the square brackets denote powers of ten.

The three-body dispersion coefficients (in atomic units), for the X–He–He systems containing two helium atoms. The sources for the *f*-values distributions are the same as those in Table V. The dispersion coefficients involving H and Li are given with additional significant digits in Table II. Results in the MK approximation (Refs. 35,36) use the present oscillator strength distributions to compute the underlying α_{ d } and *C* _{6} needed as input. The numbers in the square brackets denote powers of ten.

The three-body dispersion coefficients (in atomic units), for the X–He–He systems containing two helium atoms. The sources for the *f*-values distributions are the same as those in Table V. The dispersion coefficients involving H and Li are given with additional significant digits in Table II. Results in the MK approximation (Refs. 35,36) use the present oscillator strength distributions to compute the underlying α_{ d } and *C* _{6} needed as input. The numbers in the square brackets denote powers of ten.

The three-body dispersion coefficients (in atomic units) for systems containing two neon atoms and two argon atoms. The sources for the *f*-values distributions are the same as those in Table V. Results in the MK approximation (Refs. 35,36) use the present oscillator strength distributions to compute the underlying α_{ d } and *C* _{6} needed as input. The numbers in the square brackets denote powers of ten.

The three-body dispersion coefficients (in atomic units) for systems containing two neon atoms and two argon atoms. The sources for the *f*-values distributions are the same as those in Table V. Results in the MK approximation (Refs. 35,36) use the present oscillator strength distributions to compute the underlying α_{ d } and *C* _{6} needed as input. The numbers in the square brackets denote powers of ten.

The three-body dispersion coefficients (in atomic units), for systems containing two krypton or two xenon atoms. The sources for the *f*-values distributions are the same as those in Table V. Coefficients in the MK approximation (Refs. 35,36) use the present oscillator strength distributions to compute the underlying α_{ d } and *C* _{6} needed as input. The numbers in the square brackets denote powers of ten.

The three-body dispersion coefficients (in atomic units), for systems containing two krypton or two xenon atoms. The sources for the *f*-values distributions are the same as those in Table V. Coefficients in the MK approximation (Refs. 35,36) use the present oscillator strength distributions to compute the underlying α_{ d } and *C* _{6} needed as input. The numbers in the square brackets denote powers of ten.

Article metrics loading...

Full text loading...

Commenting has been disabled for this content