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Abstract Self‐sorting is commonly observed in complex reaction systems, which has been utilized to guide the formation of single major by‐design molecules. However, most studies have been focused on non‐covalent systems, and using self‐sorting to achieve covalently bonded architectures is still relatively less explored. Herein, we first demonstrated the dynamic nature of spiroborate linkage and systematically studied the self‐sorting behavior observed in the transformation between spiroborate‐linked well‐defined polymeric and molecular architectures, which is enabled by spiroborate bond exchange. The scrambling between a macrocycle and a 1D helical covalent polymer led to the formation of a molecular cage, whose structures are all unambiguously elucidated by single‐crystal X‐ray diffraction. The results indicate that the molecular cage is the thermodynamically favored product in this multi‐component reaction system. This work represents the first example of a 1D polymeric architecture transforming into a shape‐persistent molecular cage, driven by dynamic covalent self‐sorting. This study will further guide the design of spiroborate‐based materials and open the possibilities for the development of novel complex yet responsive dynamic covalent molecular or polymeric systems. 

Abstract Herein, the synthesis of Cu₃(HAB)_x(TATHB)_2‐x(HAB: hexaaminobenzene, TATHB: triaminotrihydroxybenzene) is reported. Synthetic improvement of Cu₃(TATHB)₂leads to a more crystalline framework with higher electrical conductivity value than previously reported. The improved crystallinity and analogous structure between TATHB and HAB enable the synthesis of Cu₃(HAB)_x(TATHB)_2‐xwith ligand compositions precisely controlled by precursor ratios. The electrical conductivity is tuned from 4.2 × 10⁻⁸to 2.9 × 10⁻⁵ S cm⁻¹by simply increasing the nitrogen content in the crystal lattice. Furthermore, computational calculation supports that the solid solution facilitates the band structure tuning. It is envisioned that the findings not only shed light on the ligand‐dependent structure–property relationship but create new prospects in synthesizing multicomponent electrically conductive metal‐organic frameworks (MOFs) for tailoring optoelectronic device applications. 

We present a method for calculating first-order response properties in phaseless auxiliary field quantum Monte Carlo by applying automatic differentiation (AD). Biases and statistical efficiency of the resulting estimators are discussed. Our approach demonstrates that AD enables the calculation of reduced density matrices with the same computational cost scaling per sample as energy calculations, accompanied by a cost prefactor of less than four in our numerical calculations. We investigate the role of self-consistency and trial orbital choice in property calculations. We find that orbitals obtained using density functional theory perform well for the dipole moments of selected molecules compared to those optimized self-consistently.