Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution

TL;DR

This paper investigates how isotope substitution affects vibrational modes in complex solids, revealing that eigenvectors can undergo significant reorganization, which impacts spectral interpretation and requires advanced tracking methods.

Contribution

It introduces an adiabatic eigenvector-continuation framework to accurately track vibrational mode changes under isotope substitution in dense phonon systems.

Findings

Eigenvector reorganization occurs in congested spectral regions.

Spectral congestion indicates susceptibility to eigenvector changes.

The framework enables reliable mode correspondence under isotope variation.

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 protiated 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 renormalisation or susceptibility to qualitative eigenvector reorganisation 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 analysing isotope-induced spectral flow in dense phonon systems.