# Higher-order electric multipole contributions to retarded non-additive three-body dispersion interaction energies between atoms: Equilateral triangle and collinear configurations

## Abstract

The theory of molecular quantum electrodynamics (QED) is used to calculate higher electric multipole contributions to the dispersion energy shift between three atoms or molecules arranged in a straight line or in an equilateral triangle configuration. As in two-body potentials, three-body dispersion interactions are viewed in the QED formalism to arise from exchange of virtual photons between coupled pairs of particles. By employing an interaction Hamiltonian that is quadratic in the electric displacement field means that third-order perturbation theory can be used to yield the energy shift for a particular combination of electric multipole polarizable species, with only six time-ordered diagrams needing to be summed over. Specific potentials evaluated include dipole-dipole-quadrupole (DDQ), dipole-quadrupole-quadrupole (DQQ), and dipole-dipole-octupole (DDO) terms. For the geometries of interest, near-zone limiting forms are found to exhibit an R{sup −11} dependence on separation distance for the DDQ interaction, and an R{sup −13} behaviour for DQQ and DDO shifts, agreeing with an earlier semi-classical computation. Retardation weakens the potential in each case by R{sup −1} in the far-zone. It is found that by decomposing the octupole moment into its irreducible components of weights-1 and -3 that the former contribution to the DDO potential may be taken to bemore »

- Authors:

- Department of Chemistry, Wake Forest University, Winston-Salem, North Carolina 27109 (United States)

- Publication Date:

- OSTI Identifier:
- 22253222

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 139; Journal Issue: 24; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; 77 NANOSCIENCE AND NANOTECHNOLOGY; CALCULATION METHODS; DIPOLES; DISPERSIONS; HAMILTONIANS; INTERACTIONS; OCTUPOLES; PARTICLES; PERTURBATION THEORY; QUANTUM ELECTRODYNAMICS

### Citation Formats

```
Salam, A., E-mail: salama@wfu.edu.
```*Higher-order electric multipole contributions to retarded non-additive three-body dispersion interaction energies between atoms: Equilateral triangle and collinear configurations*. United States: N. p., 2013.
Web. doi:10.1063/1.4849757.

```
Salam, A., E-mail: salama@wfu.edu.
```*Higher-order electric multipole contributions to retarded non-additive three-body dispersion interaction energies between atoms: Equilateral triangle and collinear configurations*. United States. https://doi.org/10.1063/1.4849757

```
Salam, A., E-mail: salama@wfu.edu. Sat .
"Higher-order electric multipole contributions to retarded non-additive three-body dispersion interaction energies between atoms: Equilateral triangle and collinear configurations". United States. https://doi.org/10.1063/1.4849757.
```

```
@article{osti_22253222,
```

title = {Higher-order electric multipole contributions to retarded non-additive three-body dispersion interaction energies between atoms: Equilateral triangle and collinear configurations},

author = {Salam, A., E-mail: salama@wfu.edu},

abstractNote = {The theory of molecular quantum electrodynamics (QED) is used to calculate higher electric multipole contributions to the dispersion energy shift between three atoms or molecules arranged in a straight line or in an equilateral triangle configuration. As in two-body potentials, three-body dispersion interactions are viewed in the QED formalism to arise from exchange of virtual photons between coupled pairs of particles. By employing an interaction Hamiltonian that is quadratic in the electric displacement field means that third-order perturbation theory can be used to yield the energy shift for a particular combination of electric multipole polarizable species, with only six time-ordered diagrams needing to be summed over. Specific potentials evaluated include dipole-dipole-quadrupole (DDQ), dipole-quadrupole-quadrupole (DQQ), and dipole-dipole-octupole (DDO) terms. For the geometries of interest, near-zone limiting forms are found to exhibit an R{sup −11} dependence on separation distance for the DDQ interaction, and an R{sup −13} behaviour for DQQ and DDO shifts, agreeing with an earlier semi-classical computation. Retardation weakens the potential in each case by R{sup −1} in the far-zone. It is found that by decomposing the octupole moment into its irreducible components of weights-1 and -3 that the former contribution to the DDO potential may be taken to be a higher-order correction to the leading triple dipole energy shift.},

doi = {10.1063/1.4849757},

url = {https://www.osti.gov/biblio/22253222},
journal = {Journal of Chemical Physics},

issn = {0021-9606},

number = 24,

volume = 139,

place = {United States},

year = {2013},

month = {12}

}