Geometrical Eigen-subspace Framework Based Atomic Structure Representation

The detailed atomic structure of materials plays an important role in solid state physics and materials science for its intrinsic connection with various physical properties.A reasonable configuration space in which the vectors characterize structures uniquely provides us not only an insight of the intrinsic structure,but also a novel approach to material design,in particular in the age of Big Data.In recent years,material simulation tends to be large-scale and intelligentize,characterized by high-throughput calculations,material genome initiative,global optimization,structure prediction,machine learning and neural network,leading to the high demand of fast structure processing,such as structure recognition,comparison and analysis.More convenient than conventional atomic coordinates,various structural fingerprints have been proposed to characterize atomic configurations,independent of coordinate basis and atomic ordering.They are unique,but not complete.It is thus highly desirable to have a presentation to characterize atomic configurations uniquely and contain as much structural information as possible.We present a novel and intrinsic representation for atomic structure in this disseration.Firstly we propose the extended distance matrix to describe the atomic structure of a cluster.The matrix differs from the conventional distance matrix in the diagonal elements by replacing zeros with the atomic characters,crucial to distinguish elements.Containing all the structural information of a cluster except overall chirality,the extended distance matrix is spectral factorized,with the atomic position information discussed with respect to eigen-vector basis and eigen-subspace framework.The atomic eigen-coordinate and eigen-subspace projection array(EPA)are derived accordingly: the former specifies its position in Euclidean space precisely,while the latter,refined from the former,appears to be a fingerprint of the corresponding atom.Based on EPA,a visual eigen-subspace projection function(EPF)is proposed to serve as atomic fingerprint function,characterizing its surrounding atomic configuration.A complete set of atomic EPFs constitute an intrinsic representation of a cluster,based on which an EPF distance between clusters can be reasonably defined,revealing their difference in structure.By the regulation of extended distance matrix,our approach is easily generalized to crystal structures.In fact,by the construction of different types of extended distance matrices,one can achieve various atomic EPFs revealing its surrounding atomic configuration from different points of view.We introduce two types of EPFs in this disseration,the decreasing EPF,sensitive to atoms nearby,especially the atomic bonding,and the minimum EPF sensitive to the lattice and atoms far away.These two types of EPFs describe the atomic structure complementarily from different perspectives.Several typical cases are presented,including clusters and crystals,which adequately demonstrate the rationality and efficiency of our approach.In particular,the boron sheets within 1-30 supercells are studied by our approach systematically,without repetition and omission,showing the strength of our method in material design.