Supercell simulations

Fig. 32 [92,206,258] one is based on a hexagonal supercell with a = Iuq and the other is based on an orthorhombic supercell with a = aoV and b = luo-Hofmeister and von Platen [92] simulated the XRD powder patterns for a variety of LDHs with different metal ions, stoichiometries and stacking... 

All calculations in this study were implemented with the CASTEP package5, which is capable of simulating electronic structures for metals, insulators, or semiconductors. It is based on a supercell method, whereby all studies must be performed on a periodic system. Study of molecules is also possible by assuming that a molecule is put in a box and treated as a periodic system. Forces acting on atoms and stress on the unit cell can be calculated. These can be used to find the equilibrium structure. 

Use of the plane wave based electronic structure methods introduces two basic parameters the kinetic energy cutoff value, controlling the basis set quality, and the periodic unit-cell (supercell) size, present due to periodic nature of these approaches. Both of these parameters should be large enough to guarantee the convergence in the total energy and in all the physical quantities that are supposed to be determined from the simulation. 

In order to calculate adsorbed SO3 configuration on Pt surface, we used the first-principles calculation code PHASE [9] with a slab model in a periodic boundary condition along the surface plane to simulate the Pt (111) surface. A four-layer slab model was used for main calculations. In these calculations, the atoms at the bottom are fixed at a bond distance d=2.83 A, which is the optimized value in Pt fee crystal with PHASE. A p(4 x 4) lateral supercell was used for the computation of the most energetically stable configuration. The p(4 x 4) surface supercell has 16 Pt atoms per layer with a lateral lattice constant of 11.31 A. 

Adding a single water molecule per supercell, the barrier was reduced by somewhat more than 10 kcal/mol. The simulations showed clearly that the water molecule was active in the proton-transfer process that is needed to change the keto form to the enol form. Thus, the solvent does not only provide an external potential in which the molecule is moving, but takes active part in the transition. Having not only one water molecule per supercell but 28, the barrier was reduced by another 8 kcal/mol. In this case, the hydrogen transfer involves several water molecules and can be described as a Grotthuss like mechanism. 

In their simulations, they use a supercell approach with the cell of Fig. 22 repeated periodically in all three dimensions (with, however, some further layers of Pt atoms). All atoms were treated quantum-mechanically within the density-functional formalism. 

P. L. Silvestrelli (1999) Maximally locahzed Waimier functions for simulations with supercells of general symmetry. Phys. Rev. B 59, p. 9703 G. Berghold, C. J. Mundy, A. H. Romero, J. Butter, and M. ParrineUo (2000) General and Efficient Algorithms for Obtaining Maximally-Locahzed Wannier Functions. Phys. Rev. B 61, p. 10040... 

Figure 2 Nyquist plots of the normalized impedance results of 15 x 8 x 8 supercells obtained from kinetic Monte Carlo (KMC) simulations at 400 K compared with the results from the electrochemical impedance spectroscopy (EIS) measurements on a pulsed layer-deposited polycrystalline thin film YSZ (100 nm in thickness) at 336°C. Reprinted from Reference [115], copyright 2007, with permission from Elsevier.

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