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Precise control over the organic composition is crucial for tailoring the distinctive structures and properties of hybrid metal halides. However, this approach is seldom utilized to develop materials that exhibit stimuli‐responsive circularly polarized luminescence (CPL). Herein, we present the synthesis and characterization of enantiomeric hybrid zinc bromides: biprotonated ((R/S)‐C12H16N2)ZnBr4 ((R/S‐LH2)ZnBr4) and monoprotonated ((R/S)‐C12H15N2)2ZnBr4 ((R/S‐LH1)2ZnBr4), derived from the chiral organic amine (R/S)‐2,3,4,9‐Tetrahydro‐1H‐carbazol‐3‐amine ((R/S)‐C12H14N2). These compounds showcase luminescent properties; the zero‐dimensional biprotonated form emits green light at 505 nm, while the monoprotonated form, with a pseudo‐layered structure, displays red luminescence at 599 and 649 nm. Remarkably, the reversible local protonation‐deprotonation behavior of the organic cations allows for exposure to polar solvents and heating to induce reversible structural and luminescent transformations between the two forms. Theoretical calculations reveal that the lower energy barrier associated with the deprotonation process within the pyrrole ring is responsible for the local protonation‐deprotonation behavior observed. These enantiomorphic hybrid zinc bromides also exhibit switchable circular dichroism (CD) and CPL properties. Furthermore, their chloride counterparts were successfully obtained by adjusting the halogen ions. Importantly, the unique stimuli‐responsive CPL characteristics position these hybrid zinc halides as promising candidates for applications in information storage, anti‐counterfeiting, and information encryption. [ABSTRACT FROM AUTHOR]

DFT calculations of reaction mechanisms in solution have always been a hot topic, especially for transition-metal-catalyzed reactions, in which the traditional DFT-D3 method has been extensively employed. The overestimation of the dispersion from the traditional DFT-D3 method leads to a quite low activation free-energy barrier, so it is worth finding a proper way to deal with the dispersion for solution systems. The solvent–solute dispersion is also important for solution systems, and thus it should be calculated together with the solute dispersion. The newly generated solute–solute dispersion energy should be shared equally with the newly formed cavity between two interacting species; therefore, only half of the solute–solute and solvent–solute dispersion terms belong to the solute molecule. The detailed treatment of dispersion correction for solution systems has been fully addressed, and this method has been confirmed with the examples of ligand exchange reactions and catalytic reactions. [ABSTRACT FROM AUTHOR]

In this paper, we devote ourselves to studying robust error bounds for a convex inequality system in the face of data uncertainty. Under the assumption that uncertain sets are convex compact, we present a sufficient condition for the existence of robust error bounds of the uncertain convex inequality system by means of the associated recession cone and recession functions. When the uncertain sets are only compact, we establish a necessary and sufficient condition for the uncertain convex inequality system to possess a robust error bound by the Ekeland variational principle. As an immediate application, we obtain robust error bounds for the uncertain convex polynomial inequality system. [ABSTRACT FROM AUTHOR]

In this paper, we study the solvability of a nonconvex regular polynomial vector optimization problem on a nonempty closed set. We introduce regularity conditions for the polynomial vector optimization problem and study their properties and characterizations. Under the regularity conditions, we establish the nonemptiness and boundedness of the solution sets of the problem. As a by-product, we infer two Frank–Wolfe type theorems for the nonconvex polynomial vector optimization problem. Finally, we investigate the solution stability of the problem. [ABSTRACT FROM AUTHOR]