### Abstract

The dynamic multipole polarizabilities and thus the second-order van der Waals coefficients C_{2k} of all orders are known exactly for the interaction between two classical spherical conducting shells, each of uniform electron density ρ with outer radius R and thickness t. The result is C _{2k}=-c_{k}(t/R)√4πρ^{[} ^{(}2R^{)}2^{]}k. The c_{k} approach a limiting constant value, so the infinite series for the van der Waals interaction at separation d, -C_{6}/d6-C_{8}/d8-, can be summed analytically, diverging only for d≤2R. This divergence can be removed without changing the asymptotic series. Real quasispherical objects like nanoclusters, fullerenes, and even atoms can be approximated by this spherical-shell model, with R fixed by the true static dipole polarizability. Once t/R is fixed, all the higher coefficients are determined by just C_{6} and C_{8}. Finally, we compare the exact C_{2k} to those from a pair interaction model, which works for solid spheres (t=R) but not for fullerenes.

Original language | English |
---|---|

Article number | 062714 |

Journal | Physical Review A |

Volume | 86 |

Issue number | 6 |

DOIs | |

Publication status | Published - Dec 26 2012 |

### Fingerprint

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A*,

*86*(6), [062714]. https://doi.org/10.1103/PhysRevA.86.062714

**Van der Waals interaction as a summable asymptotic series.** / Perdew, John P.; Ruzsinszky, Adrienn; Sun, Jianwei; Glindmeyer, Stephen; Csonka, G.

Research output: Contribution to journal › Article

*Physical Review A*, vol. 86, no. 6, 062714. https://doi.org/10.1103/PhysRevA.86.062714

}

TY - JOUR

T1 - Van der Waals interaction as a summable asymptotic series

AU - Perdew, John P.

AU - Ruzsinszky, Adrienn

AU - Sun, Jianwei

AU - Glindmeyer, Stephen

AU - Csonka, G.

PY - 2012/12/26

Y1 - 2012/12/26

N2 - The dynamic multipole polarizabilities and thus the second-order van der Waals coefficients C2k of all orders are known exactly for the interaction between two classical spherical conducting shells, each of uniform electron density ρ with outer radius R and thickness t. The result is C 2k=-ck(t/R)√4πρ[ (2R)2]k. The ck approach a limiting constant value, so the infinite series for the van der Waals interaction at separation d, -C6/d6-C8/d8-, can be summed analytically, diverging only for d≤2R. This divergence can be removed without changing the asymptotic series. Real quasispherical objects like nanoclusters, fullerenes, and even atoms can be approximated by this spherical-shell model, with R fixed by the true static dipole polarizability. Once t/R is fixed, all the higher coefficients are determined by just C6 and C8. Finally, we compare the exact C2k to those from a pair interaction model, which works for solid spheres (t=R) but not for fullerenes.

AB - The dynamic multipole polarizabilities and thus the second-order van der Waals coefficients C2k of all orders are known exactly for the interaction between two classical spherical conducting shells, each of uniform electron density ρ with outer radius R and thickness t. The result is C 2k=-ck(t/R)√4πρ[ (2R)2]k. The ck approach a limiting constant value, so the infinite series for the van der Waals interaction at separation d, -C6/d6-C8/d8-, can be summed analytically, diverging only for d≤2R. This divergence can be removed without changing the asymptotic series. Real quasispherical objects like nanoclusters, fullerenes, and even atoms can be approximated by this spherical-shell model, with R fixed by the true static dipole polarizability. Once t/R is fixed, all the higher coefficients are determined by just C6 and C8. Finally, we compare the exact C2k to those from a pair interaction model, which works for solid spheres (t=R) but not for fullerenes.

UR - http://www.scopus.com/inward/record.url?scp=84871731425&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84871731425&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.86.062714

DO - 10.1103/PhysRevA.86.062714

M3 - Article

VL - 86

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 6

M1 - 062714

ER -