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Topology has emerged as a field for describing and controlling order and matter, and thereby the physical properties of materials. There are several largely disparate fields focused on examining and manipulating topology. One of these arenas is in the realm of real space, manipulating systems in terms of their spatial properties, to control the corresponding structural, mechanical, and self- assembling responses. Much of the work in soft matter topology falls within this domain. A second arena is in the domain of momentum or k-space wherein topology controls the features of the electronic band structure of materials, and topologically non-trivial features result in the development of materials with truly unique properties. This work focuses squarely on the realm of condensed matter physics. Here, we review concepts of real- and k-space topology and propose areas for convergence between these two disparate fields. 

Abstract The rational design of molecular electronics remains a grand challenge of materials science. DNA nanotechnology has offered unmatched control over molecular geometry, but direct electronic functionalization is a challenge. Here a generalized method is presented for tuning the local band structure of DNA using transmetalation in metal‐mediated base pairs (mmDNA). A method is developed for time‐resolved X‐ray diffraction using self‐assembling DNA crystals to establish the exchange of Ag⁺ and Hg²⁺ in T:T base pairs driven by pH exchange. Transmetalation is tracked over six reaction phases as crystal pH is changed from pH 8.0 to 11.0, and vice versa. A detailed computational analysis of the electronic configuration and transmission in the ensuing crystal structures is then performed. This findings reveal a high conductance contrast in the lowest unoccupied molecular orbitals (LUMO) as a result of metalation. The ability to exchange single transition metal ions as a result of environmental stimuli heralds a means of modulating the conductance of DNA‐based molecular electronics. In this way, both theoretical and experimental basis are established by which mmDNA can be leveraged to build rewritable memory devices and nanoelectronics. 

The reaction of a pentadentate NHC ligand precursor with Ni(OAc) 2 ·4H 2 O or Pd(OAc) 2 in the presence of a base yields four-coordinate square-planar Ni( ii ) and Pd( ii ) complexes with an unusual ligand generated in situ . A series of experimental studies point to a ring-opening and ring-closing process via novel C–N bond cleavage and formation. 

Four macrocyclic hybrid salts with different numbers of benzimidazolium and amine units, [H 2 L][PF 6 ] 2 (L = L 1 , L 2 , L 3 ) and [H 4 L 4 ][PF 6 ] 4 , have been employed as the heterocyclic carbene (NHC) precursors toward new Ag( i )– and Au( i )–NHC complexes. Three trinuclear and one tetranuclear Ag( i ) complexes 1–4 have been obtained from the reactions of the NHC precursors and Ag 2 O in acetonitrile. Four dinuclear Au( i )–NHC complexes 5–8 have been prepared by reacting the NHC precursors and AuCl(SMe 2 ) in the presence of NaOAc in DMF. The molecular structures of all the complexes are established by single-crystal X-ray diffraction studies. The metal ions in the Ag( i ) complexes 1–3 and the Au( i ) complexes 5–7 are coordinated with two macrocyclic NHC ligands to form a sandwiched structure. In contrast, a trinuclear Ag 3 core is located in the cavity of one macrocyclic ligand in [Ag 3 (L 4 )][PF 6 ] 3 ( 4 ). The photoluminescence properties of Au( i ) complexes 5–8 have also been investigated. 

Abstract DNA double helices containing metal‐mediated DNA (mmDNA) base pairs are constructed from Ag⁺and Hg²⁺ions between pyrimidine:pyrimidine pairs with the promise of nanoelectronics. Rational design of mmDNA nanomaterials is impractical without a complete lexical and structural description. Here, the programmability of structural DNA nanotechnology toward its founding mission of self‐assembling a diffraction platform for biomolecular structure determination is explored. The tensegrity triangle is employed to build a comprehensive structural library of mmDNA pairs via X‐ray diffraction and generalized design rules for mmDNA construction are elucidated. Two binding modes are uncovered: N3‐dominant, centrosymmetric pairs and major groove binders driven by 5‐position ring modifications. Energy gap calculations show additional levels in the lowest unoccupied molecular orbitals (LUMO) of mmDNA structures, rendering them attractive molecular electronic candidates.