  Crystal material representation is the foundation of crystal material
research. Existing works consider crystal molecules as graph data with
different representation methods and leverage the advantages of techniques in
graph learning. A reasonable crystal representation method should capture the
local and global information. However, existing methods only consider the local
information of crystal molecules by modeling the bond distance and bond angle
of first-order neighbors of atoms, which leads to the issue that different
crystals will have the same representation. To solve this many-to-one issue, we
consider the global information by further considering dihedral angles, which
can guarantee that the proposed representation corresponds one-to-one with the
crystal material. We first propose a periodic complete representation and
calculation algorithm for infinite extended crystal materials. A theoretical
proof for the representation that satisfies the periodic completeness is
provided. Based on the proposed representation, we then propose a network for
predicting crystal material properties, PerCNet, with a specially designed
message passing mechanism. Extensive experiments are conducted on two
real-world material benchmark datasets. The PerCNet achieves the best
performance among baseline methods in terms of MAE. In addition, our results
demonstrate the importance of the periodic scheme and completeness for crystal
representation learning.
