Copper-based chalcogenide semiconductors are particularly attractive materials for photovoltaic and nonlinear optical applications. Unfortunately, accurate theoretical understanding of the optical responses of these materials is hindered by the presence of strongly localized Cu 3d electrons. To assess the validity of calculation schemes for determining the optical properties of Cu-based chalcogenides, different density functional theory (DFT) approaches including the conventional Perdew−Burke−Ernzerhof (PBE) method and the modified Becke–Johnson (mBJ) potential with and without Hubbard U correction, and the hybrid HSE06 methods are employed to evaluate the linear and nonlinear optical performances of 16 typical Cu-based chalcogenides. We calculate band gaps, dielectric functions, refractive indices, absorption coefficients, and the second harmonic generation susceptibilities of these compounds and compare the results with available experimental measurements. It is clear that the mBJ + U approach yields band gaps close to those predicted using the HSE06 method, which is consistent with the experimental values. More importantly, the fundamental optical properties in the infrared–visible light region calculated within the mBJ + U method agree better with experiments compared with the HSE06 functional. In addition to the linear optical responses, the mBJ potential with on-site Coulomb U correction to the Cu-3d state is also capable of describing the optical nonlinearity of copper chalcogenides reasonably.

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To explain the huge difference in the second harmonic generation (SHG) response of two novel interpenetrated metal−organic frameworks (MOFs) that consist of Zn 2+ ions coordinated to the trans-2-(4-pyridyl)-4-vinylbenzoate (pvb) ligand, eightfold interpenetrated Zn(pvb) 2 (M1) and sevenfold interpenetrated [Zn(pvb) 2 ]•DMF (M2), first-principles calculations were performed to study the geometries, band structures, and various linear and second-order nonlinear optical properties of M1 and M2 and two other hypothetical Zn-MOFs. Our results indicate that the structural transformation from M2 to M1 by the loss of the DMF guest is energetically favorable, and the M1 compound with the most tightly packed structure has the largest dielectric constant. For MOFs with the same order of interpenetration, the presence of the DMF guest has a small effect on the optical anisotropy of the system. Due to the different coordination environments of two kinds of Zn atoms, eightfold interpenetrated M1 shows more significant optical anisotropy than M2, and correspondingly, the range of phase matchability of M1 (>863 nm) is wider than that of M2 (>1126 nm). This means that at an experimental wavelength of 950 nm, M1 has a favorable phase-matching feature and displays strong SHG response, while the phase-mismatched behavior of M2 with sevenfold interpenetration leads to a weak SHG signal. Therefore, the difference in the interpenetrated structure induced by the guest DMF solvent is the main reason for the giant deviation in SHG intensity between M1 and M2 compounds. The present work provides new insights into how the phase-matching ability can be tuned by switching of the degree of interpenetration to enhance SHG response of MOFs.

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