In the second step, which was performed only with the BP functional, we used pseudopotentials
for the lanthanoids, where the core-shell electrons were sub-stituted by the scalar-relativistic 4f-in-core (substituting 46 (La) to 60 (Lu) inner electrons) pseudopotential
[10,33] and the corresponding (7s6p5d)/[5s4p3d] , (5s5p4d)/[4s4p3d] + 2s1p1d [10,34], and (6s6p5d)/[4s4p4d] + 2s1p1d [10,34,35] basis sets for lanthanoids.
The ordered-disordered phase transition in alloy [Cu.sub.3]Au also is investigated theoretically by applying statistical methods for ordered phenomena such as the Kirkwood method, the pseudopotential
method, and the pseudochemical method [5,6].
For geometric optimization, energy band, density of states, and elastic constants are calculated adopting the plane wave ultrasoft pseudopotential
Finally, in Section 10, some important computational issues are addressed such as a simplification of the electronic interaction with the pseudopotential
, the representation of orbitals in terms of a functional basis, the use of the Fourier and wavelet transform in order to reduce the computational complexity, and the simulation of larger systems with hybrid molecular dynamics.
Difficultly, photocatalytic N[H.sub.3] synthesis from [N.sub.2] also needs to overcome the energy barrier of N [equivalent to] N triple band under the spin-polarized plane-wave pseudopotential
In this calculation with VASP, the projector augmented wave (PAW) pseudopotential
was employed to describe the electron-ion interaction while neutron effects and mass effects were not involved.
Hence, we must find the Born approximation for V(x)-[m.sup.2.sub.L] rather than the one for the pseudopotential
[V.sub.P](x) (see (19)).
which is defined by the pseudopotential
All calculations were performed by CASTEP simulation package , The ion-electron interaction is represented by Vanderbilt ultrasoft pseudopotential
 and exchange-correlation effects were treated within the generalized gradient approximation (GGA) .
 presented the mechanical and electrical properties of twelve III-V semiconductors, under pressure, using Plane wave Pseudopotential
The interaction between ionic cores and valence electrons is modeled with Troullier-Martins nonlocal pseudopotential
. Double-zeta plus polarized basis sets (DZP) are employed for all atoms including C, N, B H, and Fe atoms.