Total energy

Combining equations 2.4, 2.9, 2.11 and 2.14 yields the total energy:

$$\mathcal{E} = {1 \over 2}\sum_i\sum_{j\in{\mathcal{N}_i}}\mathcal{E}_{\mathrm{e... ...hrm{Ze}}^{i} + {1 \over 2}\sum_i^N\sum_{j\neq i}\mathcal{E}_{\mathrm{di}}^{i,j}$$ (2.15)

$\mathcal{E}$The total energy in a system

The number of atoms in comparatively small systems is large. Assuming a cubic structure and a lattice spacing of 2.5Å as in iron, cobalt or nickel, a cube of edge length 100nm would contain 6.4$\times$10$^7$ atoms.