Unit cell consistency (UCC) means that the physical properties or quantities of solids resulted from electronic structure calculations should not depend on the specific choice of the unit cell. The UCC of maximally localized wannier functions (MLWFs), a family of localized orbitals that are very useful in the theoretical characterization of solids, has scarcely been studied. In this work, we explore both analytically and numerically the UCC of MLWFs, and propose an explicit symmetry constraint on the unitary transformation matrices to ensure the UCC is rigorously preserved. Numerical calculations also demonstrate that without the symmetry constraint the MLWFs constructed in a supercell model may violate the UCC. This work thus provides useful guidance for the use of MLWFs in sophisticated solid-state systems and applications.

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During the ongoing CoVID-19 epidemic, the continuous genomic evolution of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has been generating new variants with enhanced transmissibility and immune escape. Being one key target of antibodies, mutations of the spike glycoprotein play a vital role in the trajectory of virus evasion. Here, we present a time-resolved statistical method, dynamic expedition of leading mutations (deLemus), to analyze the evolution dynamics of the spike protein. Together with analysis on single amino-acid polymorphism (SAP), we proposed one L-index to quantify the mutation strength of each amino acid for unravelling mutation pattern of spike glycoprotein. The sites of interest (SOI) with high L-index hold great promise to detect potential signal of emergent variants.