We study inversion-symmetry (IS) breaking in impurity dimers coupled to topological multi-Weyl systems in the low-energy dispersion domain. In the IS-preserved multi-Weyl semimetal phase, Hubbard bands split into symmetric and antisymmetric molecularlike subbands. Breaking IS induces a transition to a multi-Weyl metal, lifting the degeneracy of the Weyl node and closing the pseudogap. This causes opposite energy shifts: valence-band symmetric (antisymmetric) subbands red (blue) shift, reversing in the conduction band until a degeneracy point. Beyond this threshold, symmetric bands flatten near band cutoffs, whereas antisymmetric bands form quasizero energy modes asymptotically approaching—yet never crossing—the Fermi level. Crucially, identical molecular symmetries maintain nondegeneracy even as energy separation vanishes with stronger IS breaking. Our results demonstrate symmetry-selective mechanisms for topological molecular states in multi-Weyl systems.

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• Topological materials
• Weyl semimetal
• Anderson impurity model
• Green's function methods