Exact lattice summations for Lennard-Jones potentials coupled to a three-body Axilrod-Teller-Muto term applied to cuboidal phase transitions

Simple item page
dc.citation.issue9
dc.citation.volume163
dc.contributor.authorRobles-Navarro A
dc.contributor.authorCooper S
dc.contributor.authorBuchheit AA
dc.contributor.authorBusse JK
dc.contributor.authorBurrows A
dc.contributor.authorSmits O
dc.contributor.authorSchwerdtfeger P
dc.date.accessioned2025-09-24T21:48:05Z
dc.date.available2025-09-24T21:48:05Z
dc.date.issued2025-09-07
dc.description.abstractThree-body interactions have long been conjectured to play a crucial role in the stability of matter. However, rigorous studies have been scarce due to the computational challenge of evaluating small energy differences in high-dimensional lattice sums. This work provides a rigorous analysis of Bain-type cuboidal lattice transformations, which connect the face-centered cubic (fcc), mean-centered cubic (mcc), body-centered cubic (bcc), and axially centered cubic (acc) lattices. Our study incorporates a general (n, m) Lennard-Jones (LJ) two-body potential and a long-range repulsive Axilrod-Teller-Muto (ATM) three-body potential. The two-body lattice sums and their meromorphic continuations are evaluated to full precision using super-exponentially convergent series expansions. Furthermore, we introduce a novel approach to computing three-body lattice sums by converting the multi-dimensional sum into an integral involving products of Epstein zeta functions. This enables us to evaluate three-body lattice sums and their meromorphic continuations to machine precision within minutes on a standard laptop. Using our computational framework, we analyze the stability of cuboidal lattice phases relative to the close-packed fcc structure along a Bain transformation path for varying ATM coupling strengths. We analytically demonstrate that the ATM cohesive energy exhibits an extremum at the bcc phase and show numerically that it corresponds to a minimum for repulsive three-body forces along the Bain path. Our results indicate that strong repulsive three-body interactions can destabilize the fcc phase and render bcc energetically favorable for soft LJ potentials. However, even in this scenario, the bcc phase remains susceptible to further cuboidal distortions. These results suggest that the stability of the bcc phase is, besides vibrational, temperature, and pressure effects, strongly influenced by higher than two-body forces. Because of the wrong short-range behavior of the triple-dipole ATM model, the LJ potential is limited to exponents n > 9 for the repulsive wall, otherwise one observes distortion into a set of linear chains collapsing to the origin.
dc.description.confidentialfalse
dc.identifier.citationRobles-Navarro A, Cooper S, Buchheit AA, Busse JK, Burrows A, Smits O, Schwerdtfeger P. (2025). Exact lattice summations for Lennard-Jones potentials coupled to a three-body Axilrod-Teller-Muto term applied to cuboidal phase transitions. Journal of Chemical Physics. 163. 9.
dc.identifier.doi10.1063/5.0276677
dc.identifier.eissn1089-7690
dc.identifier.elements-typejournal-article
dc.identifier.issn0021-9606
dc.identifier.number094104
dc.identifier.urihttps://mro.massey.ac.nz/handle/10179/73604
dc.languageEnglish
dc.publisherAIP Publishing LLC
dc.publisher.urihttp://pubs.aip.org/aip/jcp/article/163/9/094104/3361137/Exact-lattice-summations-for-Lennard-Jones
dc.relation.isPartOfJournal of Chemical Physics
dc.rights(c) 2025 The Author/s
dc.rightsCC BY-NC-ND 4.0
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.titleExact lattice summations for Lennard-Jones potentials coupled to a three-body Axilrod-Teller-Muto term applied to cuboidal phase transitions
dc.typeJournal article
pubs.elements-id503246
pubs.organisational-groupOther
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
503246 PDF.pdf
Size:
8.36 MB
Format:
Adobe Portable Document Format
Description:
Published version.pdf
Download
License bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
license.txt
Size:
9.22 KB
Format:
Plain Text
Description:
Download
Collections
Journal Articles