▎ 摘　　要

Geometric structures of carbon networks are key in designing their material properties. In particular, optimization of curved structures through the introduction of topological defects and doping of heteroatoms in the lattice is crucial to the design of carbon-based, non-noble-metal-free catalysts. A simple and practical mathematical model based on discrete geometric analysis is proposed to describe the geometric features of carbon networks and their relationships to their material properties. This model can pre-screen candidates for novel material design, and these candidates can be further examined by the density functional theory (DFT). Inspired by observations regarding the preferential doping of heteroatoms at local curved sites, the important characteristics of the candidate material were experimentally realized, and its enhanced catalytic activity facilitated by chemical dopants was confirmed in the designed carbon network. (c) 2021 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).