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First-principles calculations of electron interactions in materials have seen rapid progress in recent years, with electron-phonon (e-ph) interactions being a prime example. However, these techniques use large matrices encoding the interactions on dense momentum grids, which reduces computational efficiency and obscures interpretability. For e-ph interactions, existing interpolation techniques leverage locality in real space, but the high dimensionality of the data remains a bottleneck to balance cost and accuracy. Here we show an efficient way to compress e-ph interactions based on singular value decomposition (SVD), a widely used matrix and image compression technique. Leveraging (un)constrained SVD methods, we accurately predict material properties related to e-ph interactions—including charge mobility, spin relaxation times, band renormalization, and superconducting critical temperature—while using only a small fraction (1%–2%) of the interaction data. These findings unveil the hidden low-dimensional nature of e-ph interactions. Furthermore, they accelerate state-of-the-art first-principles e-ph calculations by about 2 orders of magnitude without sacrificing accuracy. Our Pareto-optimal parametrization of e-ph interactions can be readily generalized to electron-electron and electron-defect interactions, as well as to other couplings, advancing quantitative studies of condensed matter. 

Abstract CO₂electroreduction (CO₂R) operating in acidic media circumvents the problems of carbonate formation and CO₂crossover in neutral/alkaline electrolyzers. Alkali cations have been universally recognized as indispensable components for acidic CO₂R, while they cause the inevitable issue of salt precipitation. It is therefore desirable to realize alkali‐cation‐free CO₂R in pure acid. However, without alkali cations, stabilizing *CO₂intermediates by catalyst itself at the acidic interface poses as a challenge. Herein, we first demonstrate that a carbon nanotube‐supported molecularly dispersed cobalt phthalocyanine (CoPc@CNT) catalyst provides the Co single‐atom active site with energetically localizeddstates to strengthen the adsorbate‐surface interactions, which stabilizes *CO₂intermediates at the acidic interface (pH=1). As a result, we realize CO₂conversion to CO in pure acid with a faradaic efficiency of 60 % at pH=2 in flow cell. Furthermore, CO₂is successfully converted in cation exchanged membrane‐based electrode assembly with a faradaic efficiency of 73 %. For CoPc@CNT, acidic conditions also promote the intrinsic activity of CO₂R compared to alkaline conditions, since the potential‐limiting step, *CO₂to *COOH, is pH‐dependent. This work provides a new understanding for the stabilization of reaction intermediates and facilitates the designs of catalysts and devices for acidic CO₂R.