Numerous applications in computer vision, machine learning, electronic structure computation, system balancing and robot manipulation can be considered as solving optimization problems on manifolds (see [31 34]).
It enables calculations of electronic structure of systems with around 1000 atoms on a single CPU core with computational time of just several hours.
This is an accurate, all-electron electronic structure code that scales efficiently to system sizes up to thousands of atoms, and to computers with (ten thousands of CPU cores.
One is to take the system as a whole, in which case the nanostructures do alter the electronic structure of the system, but it is difficult to calculate the band structure of such large system directly by first principles method due to large number of atoms presented in nanostructures.
In this regard, for many transition-metal systems, the formal oxidation state is an incomplete, and in many cases incorrect description of the electronic structure of the system, because of other important factors, especially metal ligand covalency.
In order to discuss the magnetic ordering and the electronic structure of the system we considered different spin arrangements.
Our result shows that mBJ can significantly improve the electronic structure of the system if a suitable c-factor is used.
To understand the origin of this effect, we analysed the typical vibration frequencies of the proton, the typical O H distances, and the electronic structure of the system under different strain conditions.
To clarify which of the oxygen atoms in the γ-Al2O3 compound are more appropriate for engineering the bandgap, we perform more elaborations on the electronic structure of the system by classifying the O atoms in two different groups.
