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Abstract An accurate treatment of electronic spectra in large systems with a technique such as time-dependent density functional theory is computationally challenging. Due to the Nyquist sampling theorem, direct real-time simulations must be prohibitively long to achieve suitably sharp resolution in frequency space. Super-resolution techniques such as compressed sensing and MUSIC assume only a small number of excitations contribute to the spectrum, which fails in large molecular systems where the number of excitations is typically very large. We present an approach that combines exact short-time dynamics with approximate frequency space methods to capture large narrow features embedded in a dense manifold of smaller nearby peaks. We show that our approach can accurately capture narrow features and a broad quasi-continuum of states simultaneously, even when the features overlap in frequency. Our approach is able to reduce the required simulation time to achieve reasonable accuracy by a factor of 20-40 with respect to standard Fourier analysis and shows promise for accurately predicting the whole spectrum of large molecules and materials. 

Abstract Polymer membranes with ultrahigh CO₂permeabilities and high selectivities are needed to address some of the critical separation challenges related to energy and the environment, especially in natural gas purification and postcombustion carbon capture. However, very few solution‐processable, linear polymers are known today that access these types of characteristics, and all of the known structures achieve their separation performance through the design of rigid backbone chemistries that concomitantly increase chain stiffness and interchain spacing, thereby resulting in ultramicroporosity in solid‐state chain‐entangled films. Herein, the separation performance of a porous polymer obtained via ring‐opening metathesis polymerization is reported, which possesses a flexible backbone with rigid, fluorinated side chains. This polymer exhibits ultrahigh CO₂permeability (>21 000 Barrer) and exceptional plasticization resistance (CO₂plasticization pressure > 51 bar). Compared to traditional polymers of intrinsic microporosity, the rate of physical aging is slower, especially for gases with small effective diameters (i.e., He, H₂, and O₂). This structural design strategy, coupled with studies on fluorination, demonstrates a generalizable approach to create new polymers with flexible backbones and pore‐forming side chains that have unexplored promise for small‐molecule separations.