Geometry Orbital of Deep Learning (GOODLE): A Uniform Carbon Potential

This work presents a geometry-driven deep learning framework Geometry Orbital of Deep Learning (GOODLE) that accurately predicts all carbon properties in real space and momenta space. We focus on the hybrid carbon orbitals (sp2 and sp3) geometry to establish their deep learning “potential”. We demonstrate its excellent performance with the properties predictions in dual space, including energy, equation of states, phonon structure, electronic band structure, and optical absorption. Capable of obtaining the carbon orbital geometries from small lattice carbon structures, GOODLE can be used for both inorganic carbon allotropes and organic hydrocarbon molecules, including the magic-angle twisted bilayer graphene, with excellent transferability. GOODLE is also available for the nudged-elastic band calculation. Besides, we proposed an analytic geometry condition criterial for the carbon allotropes stability.