Herein, the first semiconducting and magnetic phosphonate metal–organic framework (MOF), TUB75, is reported, which contains a 1D inorganic building unit composed of a zigzag chain of corner‐sharing copper dimers. The solid‐state UV–vis spectrum of TUB75 reveals the existence of a narrow bandgap of 1.4 eV, which agrees well with the density functional theory (DFT)‐calculated bandgap of 1.77 eV. Single‐crystal conductivity measurements for different orientations of the individual crystals yield a range of conductances from 10⁻³ to 10³ S m⁻¹ at room temperature, pointing to the directional nature of the electrical conductivity in TUB75. Magnetization measurements show that TUB75 is composed of antiferromagnetically coupled copper dimer chains. Due to their rich structural chemistry and exceptionally high thermal/chemical stabilities, phosphonate MOFs like TUB75 may open new vistas in engineerable electrodes for supercapacitors.

A conductive phosphonate metal–organic framework (MOF), [{Cu(H₂O)}(2,6‐NDPA)_0.5] (NDPA = naphthalenediphosphonic acid), which contains a 2D inorganic building unit (IBU) comprised of a continuous edge‐sharing sheet of copper phosphonate polyhedra is reported. The 2D IBUs are connected to each other via polyaromatic 2,6‐NDPA's, forming a 3D pillared‐layered MOF structure. This MOF, known as TUB40, has a narrow band gap of 1.42 eV, a record high average electrical conductance of 2 × 10² S m⁻¹ at room temperature based on single‐crystal conductivity measurements, and an electrical conductance of 142 S m⁻¹ based on a pellet measurement. Density functional theory (DFT) calculations reveal that the conductivity is due to an excitation from the highest occupied molecular orbital on the naphthalene‐building unit to the lowest unoccupied molecular orbital on the copper atoms. Temperature‐dependent magnetization measurements show that the copper atoms are antiferromagnetically coupled at very low temperatures, which is also confirmed by the DFT calculations. Due to its high conductance and thermal/chemical stability, TUB40 may prove useful as an electrode material in supercapacitors.

Many open quantum systems encountered in both natural and synthetic situations are embedded in classical-like baths. Often, the bath degrees of freedom may be represented in terms of canonically conjugate coordinates, but in some cases they may require a non-canonical or non-Hamiltonian representation. Herein, we review an approach to the dynamics and statistical mechanics of quantum subsystems embedded in either non-canonical or non-Hamiltonian classical-like baths which is based on operator-valued quasi-probability functions. These functions typically evolve through the action of quasi-Lie brackets and their associated Quantum-Classical Liouville Equations, or through quasi-Lie brackets augmented by dissipative terms. Quasi-Lie brackets possess the unique feature that, while conserving the energy (which the Noether theorem links to time-translation symmetry), they violate the time-translation symmetry of their algebra. This fact can be heuristically understood in terms of the dynamics of the open quantum subsystem. We then describe an example in which a quantum subsystem is embedded in a bath of classical spins, which are described by non-canonical coordinates. In this case, it has been shown that an off-diagonal open-bath geometric phase enters into the propagation of the quantum-classical dynamics. Next, we discuss how non-Hamiltonian dynamics may be employed to generate the constant-temperature evolution of phase space degrees of freedom coupled to the quantum subsystem. Constant-temperature dynamics may be generated by either a classical Langevin stochastic process or a Nosé–Hoover deterministic thermostat. These two approaches are not equivalent but have different advantages and drawbacks. In all cases, the calculation of the operator-valued quasi-probability function allows one to compute time-dependent statistical averages of observables. This may be accomplished in practice using a hybrid Molecular Dynamics/Monte Carlo algorithms, which we outline herein.