A coherent derivation of the Ewald summation for arbitrary orders of multipoles: The self-terms

Benjamin Stamm; Louis Lagardere; Etienne Polack; Yvon Maday; Jean-Philip Piquemal

A coherent derivation of the Ewald summation for arbitrary orders of multipoles: The self-terms

Benjamin Stamm ¹ Louis Lagardere ² Etienne Polack ¹ Yvon Maday ¹ Jean-Philip Piquemal ^{2, 3}

1 LJLL - Laboratoire Jacques-Louis Lions

3 IUF - Institut Universitaire de France

Abstract : In this work, we provide the mathematical elements we think essential for a proper understanding of the calculus of the electrostatic energy of point-multipoles of arbitrary order under periodic boundary conditions. The emphasis is put on the expressions of the so-called self parts of the Ewald summation where different expressions can be found in literature. Indeed, such expressions are of prime importance in the context of new generation polarizable force field where the self field appears in the polarization equations. We provide a general framework, where the idea of the Ewald splitting is applied to the electric potential and subsequently, all other quantities such as the electric field, the energy and the forces are derived consistently thereof. Mathematical well-posedness is shown for all these contributions for any order of multipolar distribution.

Document type :

Journal articles

Domain :

Chemical Sciences / Theoretical and/or physical chemistry

Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-01897263
Contributor : Jean-Philip Piquemal <>
Submitted on : Wednesday, October 17, 2018 - 7:28:24 AM
Last modification on : Wednesday, May 15, 2019 - 11:12:09 AM
Long-term archiving on : Friday, January 18, 2019 - 12:56:55 PM

1805.10363 (1).pdf

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A coherent derivation of the Ewald summation for arbitrary orders of multipoles: The self-terms

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