Local coordination and migration-network topology shape Li-ion transport and delithiation in the low-energy $\varepsilon$-LiMnO$_2$ polymorph
In rocksalt-derived oxide cathodes, the local Li-migration environment around an O$_4$ tetrahedral intermediate is commonly classified by the number of face-sharing transition-metal (TM) neighbors. In LiMnO$_2$, the TM species is Mn, and 0-TM denotes the absence of face-sharing Mn neighbors. However, migration and delithiation may also depend on higher-shell coordination and tetrahedral connectivity. Using the recently reported low-energy $\varepsilon$-LiMnO$_2$ polymorph as a model, we examine these factors through bond-valence site-energy and bond-valence pathway analyses combined with first-principles calculations. The resulting migration maps and tetrahedral statistics reveal distinct topologies across four LiMnO$_2$ polymorphs. Although the $\varepsilon$ phase and the lithiated-spinel phase Li$_2$Mn$_2$O$_4$ (hereafter spinel) have identical tetrahedral-type fractions, their 0-TM motifs form quasi-one-dimensional chains and a three-dimensional network, respectively. Climbing-image nudged elastic band calculations yield $\varepsilon$-phase barriers of 0.35--0.36~eV, compared with 0.41--0.53~eV in spinel, a difference that may be associated with distinct next-nearest corner-sharing shells. Ab initio molecular dynamics yields an apparent activation energy of 0.32~eV, while direction-resolved mean-squared displacements show preferential Li migration along $c$, supporting low-barrier quasi-one-dimensional diffusion. Delithiation calculations further show that differences in 0-TM connectivity and Li--Li separation between the $\varepsilon$ phase and spinel are associated with Li-site evolution and calculated voltage steps. These results link local environments and the spatial connectivity of 0-TM motifs to Li migration and delithiation, providing a structural perspective for metastable cathode design.