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  • Open Access

Collective phonon mixing and eigenvector transport under isotope substitution

Jeff Armstrong1,2,*, Hamish Cavaye1, Pankaj Sharma3, and Matthew E. Potter2

  • *Contact author: jeff.armstrong@stfc.ac.uk
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Phys. Rev. B 113, 214325 – Published 24 June, 2026

DOI: https://doi.org/10.1103/pz75-kvfy

Abstract

Isotopic substitution modifies nuclear masses without altering the electronic potential-energy surface to first order and is therefore often interpreted as a simple rescaling of vibrational frequencies. In solids with dense phonon manifolds, however, mass substitution acts as a parametric Hermitian deformation of the mass-weighted dynamical matrix, generating a continuous family of eigenproblems whose eigenvectors can undergo substantial rotation within coupled subspaces. Here, we investigate hydrogenated and deuterated ZIF-8 using inelastic neutron scattering and density-functional theory lattice-dynamics calculations. While many vibrational modes exhibit near-ideal mass scaling and preserve their character across isotopic endpoints, modes embedded in spectrally congested regions display pronounced redistribution of vibrational character that cannot be inferred from frequency shifts alone. Because inelastic neutron-scattering intensity is directly weighted by hydrogen displacement amplitude, spectral sparsity and congestion provide experimental indicators of predictable frequency renormalization or susceptibility to qualitative eigenvector reorganization under deuteration. To establish physically meaningful mode correspondence, we develop an adiabatic eigenvector-continuation framework with overlap-based tracking and explicit stability diagnostics. These results show that vibrational identity in complex framework materials is best understood as a continuous trajectory in eigenvector space and provide a general framework for analyzing isotope-induced spectral flow in dense phonon systems.

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Phys. Rev. B 113, 214325– Published 24 June, 2026
  • Received 24 February 2026
  • Revised 28 April 2026
  • Accepted 3 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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