Recently, manganese-oxide compounds have attracted considerable attention, in particular, as candidate materials for photochemical water-splitting reactions. Here, we investigate electronic states of pristine manganese dioxides (MnO₂) in different crystal phases using spin-polarized density functional theory (DFT) with Hubbard U correction. Geometrical structures and band dispersions of α-, β-, δ-, and λ-MnO₂ crystals with collinear magnetic [ferromagnetic (FM) and antiferromagnetic (AFM)] orders are discussed in detail. We reveal that penalty energies that arise by violating the Goodenough–Kanamori rule are important and the origin of the magnetic interactions of the MnO₂ crystals is governed by the superexchange interactions of Mn–O–Mn groups. In addition, it is found that momentum-dependent band spin splitting occurs in the AFM α-, β-, and δ-MnO₂ crystals while no spin splitting occurs in the AFM λ-MnO₂ crystal. Our results show that spin-split band dispersions stem from the different orientations of Mn-centred oxygen octahedra. Such interesting electronic states of the MnO₂ crystals are unraveled by our discussion on the relationship between the effective (spin-dependent) single-electron potentials and the space-group symmetry operations that map up-spin Mn atoms onto down-spin Mn atoms. This work provides a basis to understand the relationship between the spin-dependent electronic states and the crystallography of manganese oxides. Another relationship to the recent experimental observations of the photochemical oxygen evolution of MnO₂ crystals is also discussed.

The structure of ${\mathrm{C}}_{60}$ molecules adsorbed on the Cu(111)-(1×1) surface has been investigated by scanning tunneling microscopy (STM). Bias voltage dependent STM images of individual ${\mathrm{C}}_{60}$ molecules in the monolayer film showed unique intramolecular structures with a threefold symmetry. The observed images agree well with those calculated using the local density approximation. With charge transfer from the Cu(111) substrate to the monolayer film, the ${\mathrm{C}}_{60}$ molecule ratchets to threefold hollow sites.

The rush to synthesize novel two-dimensional (2D) materials has excited the research community studying ternary-layered carbide and nitride compounds, known as MAX phases, for the past two decades in the quest to develop new 2D material precursors.

Radioactive endohedral ${}^7\mathrm{Be}@{\mathrm{C}}_{60}$ can be detected using radiochemical and radiochromatographic techniques in the final solvent. Such a ${}^7\mathrm{Be}$ atom can penetrate into the ${\mathrm{C}}_{60}$ cage to produce ${}^7\mathrm{Be}@{\mathrm{C}}_{60}$ by a recoil process of the nuclear reactions. An ab initio molecular dynamics simulation was carried out to demonstrate that a direct insertion process is really possible. Both the experimental and the theoretical results were consistent with each other.

Length-dependent charge redistribution in dangling-bond (DB) linear chains fabricated on a hydrogen-terminated $\mathrm{Si}\left(100\right)-(2\times 1)$ surface is analyzed by using scanning tunneling microscopy and first-principles calculations. The second-layer Si atoms are displaced alternately to form pairs with charge redistribution, which is explained by the Jahn-Teller distortion in an artificial pseudomolecule. In a short even-numbered (DB) structure, an unpaired second-layer Si atom exists and behaves as a soliton accompanied by the flip-flop motion of the structure. We point out that the odd-even problem, the edge effect, and the finite length of the DB structures are indispensable to understand the relaxation in the structures.

We investigate the spin-dependent electronic states of antiferromagnetic (AFM) lanthanum chromite (LaCrO ₃ ), lanthanum manganite (LaMnO ₃ ), and lanthanum ferrite (LaFeO ₃ ) using spin-polarized first-principles density functional theory with Hubbard U correction. The band structures are calculated for 15 types of their different AFM structures. It is verified for these structures that there is a very simple rule to identify which wave number k exhibits spin splitting or degeneracy in the band structure. This rule uses the symmetry operations that map the up-spin atoms onto the down-spin atoms. The resulting spin splitting is very small for the most stable spin configuration of the most stable experimental structure. We discuss a plausible benefit of this characteristic, i.e. the direction-independence of the spin current, in electrode applications.