The band energy differences of solids calculated with screened hybrid density functionals, such as the functional of Heyd–Scuseria–Ernzerhof (HSE), reproduce experimental band gaps with a high degree of accuracy. This unexpected result is here rationalized by observing that band energy differences obtained from generalized Kohn–Sham calculations with screened (short-range) Hartree–Fock–type exchange approach the excitation energies obtained via time-dependent density functional calculations with the corresponding unscreened functional. The latter are expected to be the accurate predictions of the experimental optical absorption spectra. While the optimum screening parameter (ω) is system dependent, the HSE standard value of ω=0.11 bohr−1 represents a reasonable compromise across diverse systems.

The influence of a zeolitic imidazolate framework (ZIF)'s metal identity on its gas separation performance is studied extensively through molecular simulations for a variety of gases. ZIF-8 is used as the original framework for alterations of different metal substitutes of the Zn²⁺ metal. ZIF-8 consists of cages connected by narrow apertures that exhibit flexibility through “swelling”, allowing for relatively large penetrants to diffuse. Replacing the central metal atom in the basic tetrahedral unit of ZIF-8 with Cd, Co or Be results in three different structures with increasing bonding stiffness with their neighboring atoms. The metal modification approach offers a way to control the flexibility and the size of the aperture, which constitutes the main energy barrier of the penetrant's hop-like diffusion between the framework's cages. Newly developed force fields are reported and utilized here; the new frameworks are compared to the original one, in terms of the diffusivity of various gas molecules as a function of their size (from He to n-butane). The correlation of the gas diffusivity with the aperture flexibility–molecular size relation is investigated. The results reveal that the aperture flexibility–molecular size relation governs the diffusivity, which shapes a common trend along all modifications. Furthermore, a new generalized method is employed for the screening of the various modifications for specific gas separations. This method is useful to detect optimum separation performance for the various modifications: CdIF-1 (Cd) for n-butane/iso-butane mixture; ZIF-67 (Co) for propylene/n-propane and ethylene/ethane mixtures; BeIF-1 (Be) for CO₂/C₂H₆, CO₂/CH₄ and CO₂/N₂ mixtures.