Tersoff

Computer-Assisted Proofs for Geometric Optimization: From Crystallization to Carbon Nanotubes

Announce Type: replace Abstract: We present a framework based on computer-assisted proofs that turns geometry optimization simulations for atomistic structures into mathematical proofs. Starting from a numerically computed approximation of a local minimizer or saddle point, we use validated numerical computations to prove the existence of a critical point of the potential energy close to this approximation. We demonstrate this framework in two settings.