After the proposal of single molecular diode by Aviram and Ratner in 1974, it has been attempted to produce an efficient molecular diode in collaboration between synthesis, measurement, and theory. Recently, single molecular diodes have been designed from theoretical models based on tunneling through single or multiple molecular orbitals. The rectification behavior is induced by the energy shift of the molecular orbital, bias-dependent coupling ratio, or resonance between molecular orbitals. We introduce each mechanism in detail and the recent progress on the design principles of molecular diodes.

We present the weak field asymptotic theory of tunneling ionization of atoms and molecules in an external static uniform electric field. The theory for the leading order term in the asymptotic expansion within the single active electron and the frozen nuclei approximations is outlined. The extensions of the theory to higher order terms, many-electron systems, and nuclear motions are presented.

A hybrid molecular model QM/MM can make local electronic structures of gigantic systems accessible by drastically reducing computational cost, compared to quantum mechanical model. Although QM/MM has high affinity with static simulation, when it comes to dynamics simulation of solution system, it faces severe limitations due to solvation diffusion. To avoid the problem, adaptive treatment of solvent molecules has been required, where molecular definitions of solvent molecules are revised between quantum and classical models on-the-fly during simulations according to the distance from a solute molecule. To this end, we propose new adaptive QM/MM method, size-consistent multi-partitioning (SCMP) method. Here, we briefly introduce the basic concept of the SCMP method and demonstrate the performance discussing importance of quantum chemical effect in solvation.

All materials can be classified as metals or insulators. According to the standard textbooks of physics, metals are defined as materials possessing a Fermi surface. An unambiguous signature of the Fermi surface is manifested by the quantum oscillations in transport and thermodynamic quantities at high magnetic fields. In addition, the linear-in-temperature term observed in the specific heat and the non-zero offset found in the thermal conductivity divided by temperature provide compelling evidence of the gapless and itinerant excitations of fermionic quasiparticles. Here we uncovered, however, a profoundly controversial behaviors in so-called Kondo insulators, i.e. quantum oscillations in the insulating state and itinerant and gapless excitations of the fermionic quasiparticles. The present results of Fermi surface of insulators expose a novel dichotomy that characterizes the low-energy physics of this nontrivial quantum state of matter.