Spectral Displacement Analysis: Mode Reconstruction and Inelastic Scattering Prediction from Molecular Dynamics

Traditional lattice dynamics requires dynamical matrix diagonalization that scales poorly for large systems and assumes the harmonic approximation, neglecting finite-temperature anharmonicity. Machine-learning interatomic potentials, however, enable molecular dynamics (MD) simulations of 10⁵-10⁶ atoms with near-density-functional-theory accuracy, from which anharmonic phonon dispersions can be extracted using spectral energy density (SED). Here we extend SED by taking advantage of the complex spectral amplitudes (q,ω) directly from MD trajectories to reconstruct real-space phonon eigenmodes without diagonalization. The new formulation, spectral displacement analysis (SDA), retains full phase information for visualizing collective motion, polarization patterns, and chirality. With O(N log N) scaling via FFTs, SDA enables phonon analysis of million-atom simulations at finite temperatures. When coherently summed with appropriate coupling factors, SDA directly predicts kinematic momentum-resolved inelastic scattering intensities for quantitative comparison with experiment. We demonstrate identification and visualization of chiral phonon modes, spatially resolved phonon properties across heterointerfaces, and prediction of vibrational electron energy-loss spectra for direct comparison with monochromated STEM-EELS measurements.