NTBuilder: Commensurate Construction of Nanotubes from Arbitrary Two-Dimensional Crystals and a Catalog of 20 Million Structures
Abstract
Although tens of thousands of two-dimensional (2D) crystals are now known, the nanotubes they can form are usually constructed for individual materials, using procedures derived for graphene. Here, we develop a general theory of the rolling construction for arbitrary 2D crystals and implement it in \ntbuilder{} (NanoTube Builder), an open-source library with desktop and web interfaces. We express the size of the exact unit cell of a tube through the reduced form of a single rational number built from the lattice metric, which explains why triangular and square lattices always close with small cells, whereas rectangular, centered rectangular, and oblique lattices can require cells larger by many orders of magnitude. The optimal approximate cells are the best rational approximations of a second number, so that a cell small enough for first-principles calculations can be chosen with a controlled departure from periodicity, as in the biphenylene network, where such a cell is eight orders of magnitude smaller than the exact one. The 17 plane groups reduce to seven distinct chirality maps once rolling is taken into account, the rolling sense of layers without a horizontal mirror defines distinct tubes, and bonds formed or broken by curvature are detected pair by pair against the flat layer. The same framework assembles multiwalled tubes whose walls share one axial period, periodic bundles, and strained or twisted structures that remain periodic. Applied to 46,403 distinct 2D systems, it produced a public catalog of 20,334,372 nanotubes, of which 57.1\% show no bond change upon rolling. All structures can be exported directly as input for first-principles and molecular dynamics codes.
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BibTeX
@misc{junior2026ntbuilder,
title = {{NTBuilder: Commensurate Construction of Nanotubes from Arbitrary Two-Dimensional Crystals and a Catalog of 20 Million Structures}},
author = {Marcelo Lopes Pereira Junior},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22341},
eprint = {2609.22341},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22341},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - NTBuilder: Commensurate Construction of Nanotubes from Arbitrary Two-Dimensional Crystals and a Catalog of 20 Million Structures
AU - Marcelo Lopes Pereira Junior
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.22341
UR - https://arxiv.org/abs/2609.22341
AB - Although tens of thousands of two-dimensional (2D) crystals are now known, the nanotubes they can form are usually constructed for individual materials, using procedures derived for graphene. Here, we develop a general theory of the rolling construction for arbitrary 2D crystals and implement it in \ntbuilder{} (NanoTube Builder), an open-source library with desktop and web interfaces. We express the size of the exact unit cell of a tube through the reduced form of a single rational number built from the lattice metric, which explains why triangular and square lattices always close with small cells, whereas rectangular, centered rectangular, and oblique lattices can require cells larger by many orders of magnitude. The optimal approximate cells are the best rational approximations of a second number, so that a cell small enough for first-principles calculations can be chosen with a controlled departure from periodicity, as in the biphenylene network, where such a cell is eight orders of magnitude smaller than the exact one. The 17 plane groups reduce to seven distinct chirality maps once rolling is taken into account, the rolling sense of layers without a horizontal mirror defines distinct tubes, and bonds formed or broken by curvature are detected pair by pair against the flat layer. The same framework assembles multiwalled tubes whose walls share one axial period, periodic bundles, and strained or twisted structures that remain periodic. Applied to 46,403 distinct 2D systems, it produced a public catalog of 20,334,372 nanotubes, of which 57.1\% show no bond change upon rolling. All structures can be exported directly as input for first-principles and molecular dynamics codes.
ER -