Global atomic structure optimization through machine-learning-enabled barrier circumvention in extra dimensions

We introduce and discuss a method for global optimization of atomic structures based on the introduction of additional degrees of freedom describing: 1) the chemical identities of the atoms, 2) the degree of existence of the atoms, and 3) their positions in a higher-dimensional space (4-6 dimensions). The new degrees of freedom are incorporated in a machine-learning model through a vectorial fingerprint trained using density functional theory energies and forces. The method is shown to enhance global optimization of atomic structures by circumvention of energy barriers otherwise encountered in the conventional energy landscape. The method is applied to clusters as well as to periodic systems with simultaneous optimization of atomic coordinates and unit cell vectors. Finally, we use the method to determine the possible structures of a dual atom catalyst consisting of a Fe-Co pair embedded in nitrogen-doped graphene.