Band Structure Theory for Extended Systems

The electronic structure of infinite periodic systems (crystals) is treated with band structure theory, replacing molecular orbitals by crystal orbitals. The chapter starts out by introducing the electron gas and definitions of the Fermi momentum, the Fermi energy, and the density of states (DOS). A periodic linear combination of atomic orbitals (LCAO) type treatment of an infinite periodic system is facilitated by the construction of Bloch functions. The notions of energy band and band gap are discussed with band structure concepts, using the approximations made in Huckel theory (chapter 12). One, two, and three-dimensional crystal lattices and the associated reciprocal lattices are introduced. The band structures of sodium metal, boron nitride, silicon, and graphite, are discussed as examples of metals, insulators, semi-conductors, and semi-metals, respectively. The chapter concludes with a brief discussion of the projected DOS and measures to determine bonding or antibonding interactions between atoms in a crystal.

Ligand Engineering in Cu(II) Paddle Wheel Metal-Organic Frameworks for Enhanced Electrical Conductivity

We report the electronic structure of two metal-organic frameworks (MOFs) with copper paddle wheel nodes connected by a N₂(C₂H₄)₃ (DABCO) ligand with accessible nitrogen lone pairs. The coordination is predicted, from first-principles density functional theory, to enable electronic pathways that could facilitate charge carrier mobility. Calculated frontier crystal orbitals indicate extended electronic communication in DMOF-1, but not in MOF-649. This feature is confirmed by bandstructure calculations and effective masses of the valence band egde. We explain the origin of the frontier orbitals of both MOFs based on the energy and symmetry alignment of the underlying building blocks. The effects of doping on the bandstructure of MOF-649 are considered. Our findings highlight DMOF-1 as a potential semiconductor with 1D charge carrier mobility along the framework

Ligand Engineering in Cu(II) Paddle Wheel Metal-Organic Frameworks for Enhanced Electrical Conductivity

We report the electronic structure of two metal-organic frameworks (MOFs) with copper paddle wheel nodes connected by a N₂(C₂H₄)₃ (DABCO) ligand with accessible nitrogen lone pairs. The coordination is predicted, from first-principles density functional theory, to enable electronic pathways that could facilitate charge carrier mobility. Calculated frontier crystal orbitals indicate extended electronic communication in DMOF-1, but not in MOF-649. This feature is confirmed by bandstructure calculations and effective masses of the valence band egde. We explain the origin of the frontier orbitals of both MOFs based on the energy and symmetry alignment of the underlying building blocks. The effects of doping on the bandstructure of MOF-649 are considered. Our findings highlight DMOF-1 as a potential semiconductor with 1D charge carrier mobility along the framework