Chladni-mode selection rules for phonon-driven hydrogen evolution on 2D catalysts

Abstract We develop a symmetry-guided framework for phonon-driven enhancement of the hydrogen evolution reaction on two-dimensional catalysts. Using Chladni patterns and Noether’s theorem as organizing principles, we classify out-of-plane vibrations and map them to zone-center crystal symmetries, then apply site-symmetry projections to obtain a simple selection rule: under uniform coverage, only the fully symmetric breathing branch produces a coherent first-order shift of adsorption energetics of adsorption energetics, whereas other angular patterns cancel or are forbidden. Coupling this symmetry filter to a Brønsted–Evans–Polanyi kinetic description and a driven-oscillator response yields a closed-form rate enhancement and a practical figure of merit that combines linear coupling, modal stiffness, and mechanical quality factor, with microkinetic bandwidth entering as a low-pass constraint. We further introduce Chladni focusing, in which placing active regions along mode-selected annuli suppresses sign cancellations and amplifies the effective coupling. Case studies on hexagonal Mo 2 B 2 , Mo 2 C, and MoS 2 illustrate mode selectivity, dual-site synergy, and clear operando fingerprints-resonant lineshapes, amplitude scaling, and symmetry null tests-that distinguish genuine mechanical acceleration from heating. The framework provides general, quantitative rules for selecting and driving lattice vibrations to surpass static Sabatier limits.