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122] recently carried out a simulation study of the low coverage (∼0:01 ML) in the initial stage of growth of Si=Si(001). Such a study requires the use of a large surface unit cell. This requirement renders ÿrst principles MD schemes not feasible for the simulation study. Liu et al. used the O(N )=NOTB-MD scheme for their study. Slabs of sizes range from 4×4 to 8×8 in the lateral direction and from 12 to 24 layers in the z direction were used in our simulations. The bottom of the slab (2– 4 layers) was ÿxed at their bulk positions while the rest of the system (including adatoms) were fully relaxed.

Since S −1 −1 = (I − (I − S)) = ∞ (I − S)n ; n=0 Mauri et al. 31) n=0 where is an odd number. They proved that the absolute minimum of the functional E[Q; { }] is E0 the Kohn–Sham ground state energy. The set of localized wave functions, { }, is constrained to be nonzero only within appropriately chosen regions of localization. In the calculation of the energy functional E[Q; { }] using the set of localized orbitals { }, the sums entering Eq. 29) and its derivatives extend only to orbitals belonging to overlapping regions of localization.

Y. S. Jayanthi / Physics Reports 358 (2002) 1–74 The Hartree potential in real space can be obtained by another FFT, using Eq. 12). The exchange-correlation energy is determined by Exc = ! 14) i The pseudopotential energy is calculated by Eps = ! 17) Gillan and coworkers have also used an alternative way to represent the support function. B-splines, or blip functions, are piecewise polynomial functions which can be set up to be localized on the points of a grid (blip grid) rigidly attached to each atom [76].

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