A quantum chemical model for a series of self-assembled nanocages: the origin of stability behind the coordination-driven formation of transition metal complexes up to [M₁₂L₂₄]²⁴⁺

Herein, we present a systematic computational model to study the electronic states and free energies of a self-assembled multi-metal complex series. By combining the previously developed model Hamiltonian approach for transition-metal complexes and the generalized Born model, the thermodynamics, optimized geometries, and electronic states of the [Pd12L24]24+ nanocage are revealed, together with [PdnLm]2n+ complex series. The effective model Hamiltonian is a theoretical method to obtain the d-electron wavefunction and potential energy including interaction energy between the transition-metal and ligands. In the present improvement, the electronic state on each transition-metal center is focused as a building unit and solved under the whole electronic field of the assembling system. We realize a reliable and systematic treatment of multi-transition-metal complexes with different sizes and charges. Consequently, our model could reproduce binding energies of the [PdnLm]2n+ complex series quantitatively as compared to density functional theory (DFT). Regarding free energy, we revealed that the assembling solute becomes unstable due to the electrostatic interaction, and effects of the solvent and counter anions mainly compensated it. Optimized geometries were also analysed. The local square-planar coordination structures around the palladium centres were characterized in the complex series. The relationships between the entire symmetrical geometries and the local coordination structures are also discussed. Finally, electronic structures of the [Pd12L24]24+ nanocage were well characterized as a single-determinant, where only dx2−y2 is unoccupied due to the ligand-field effect. We also found that the solvent polarized the electronic states of the Pd ions, whereas the counter anion suppressed the polarization. The present method realizes size-independent reliable and rapid computations, and therefore can be expected to further application studies on self-assembly dynamics

Hyper-elliptic Nambu flow associated with integrable maps

We study hyper-elliptic Nambu flows associated with some $n$ dimensional maps and show that discrete integrable systems can be reproduced as flows of this class.Comment: 13 page

CHANGE OF DIRECTION MOTION DURING THE DEFENSIVE PHASE IN SOCCER PLAYERS

The purpose of the this study was to the change of direction (COD) movement in the backward direction during the defensive phase. Thirteen male soccer players performed the reactive agility test (RAT) and sprint running. Analysis classified the players to two groups according to the RAT time. There was no significant difference in sprint times, but RAT of the fast group was significantly faster than that of the slow group. Before and after COD of RAT, the fast group had made a deceleration quickly by high-step frequency. In the COD movement, the fast group performed the movement with their body tilted backward while lowering their center of gravity with the hip of the COD foot bent before COD and smaller knee flexion displacement during COD support phase. These findings seem to be a basic knowledge for evaluation and training of COD in soccer

THE THREE-DIMENTIONAL PELVIC MOTION IN THE ACCELERATION AND MAXIMUM PHASES

The purpose of this study was to investigate the mechanism of pelvic motion in the acceleration and maximum velocity phases. Eleven male sprinters performed 30 m and 60 m sprints at maximal effort and captured sprint movement at 15 m and 50 m. The contact time was significantly longer, and the angular displacement of pelvic elevation on the frontal plane was significantly greater in the acceleration phase than in the maximum velocity phase. Additionally, the angular displacement of pelvic elevation on the frontal plane showed a significantly positive correlation with the contact time and the stance length in the acceleration phase. These findings suggest that the greater pelvic frontal plane motion in the acceleration phase could increase the contact time and longer stance length

EFFECTS OF MOVIE OBSERVATION AND MOTOR IMAGERY ON PERFORMANCE AND JOINT KINETICS DURING TAKE-OFF IN DROP JUMP

The aim of this study was to investigate the effects of movie observation and motor imagery intervention during the pre-set phase (prior to jumping off the platform), on drop jump (DJ) performance and the variables of lower leg kinetics. Three male jumpers performed the DJ under three different conditions (Normal, Movie, and Imagery) from a drop height of 0.3 m. The performance variables and joint kinetics were measured. The DJ performance tended to improve with the intervention of movie and imagery condition. Moreover, the negative ankle joint and positive hip joint kinetics variables (power and work) tended to improve with the intervention of movie and imagery condition. Therefore, it was suggested that movie observation and motor imagery intervention could improve DJ performance and the force exerted by lower leg, which affects performance