Application of Geometric Eigensubspace Framework in The Characterization of Atomic Structure

Abstract

The specific atomic structure of materials plays an important role in solid-state physics and materials science because it is inherently related to many physical properties of materials. Various structural fingerprints have been proposed to identify the configuration of atoms. They do not depend on the coordinate system and the order of atoms, so they are more convenient than traditional atomic coordinates. They are unique, but they cannot fully describe the structure of the atom. Therefore, we hope to have a notation that uniquely identifies the atomic configuration and contains as much structural information as possible. This paper proposes a novel and intrinsic representation of atomic structure. We first proposed an extended distance matrix to describe the atomic structure of the cluster. It is different from the traditional distance matrix in that the zero of the diagonal element is replaced with the characteristic quantity of each atom to distinguish different elements. The extended distance matrix contains all the structural information of the cluster. In addition to the overall chirality, through spectral decomposition, the position information of the atoms can be discussed based on the eigenvector coordinate system and the eigensubspace framework. Studies have shown that due to the difference in the number of bonds, the Λ dec distance between the diamond atom (the number of bonds is 4) and the other two atoms (the number of bonds is 3) is relatively large, about 0.076; graphene atoms and C 60 atoms the Λ dec distance is relatively small, about 0.051.