Charge sloshing

To solve the KS equations in 0 N) operations the localized, Wannier-like states are used as they are constrained by their own localization region. Each atom / is assigned a number of states equal to mt(Z ° /2 + 1) so that, if doubly occupied, they can contain at least one excess electron (they can also become empty during the minimization of the energy functional). These states are confined to a sphere of radius (common to all states) centered at nuclei I. Irrespective of whether the 0(N) functional or the standard diagonalization is used, an outer self-consistency iteration is required, in which the density matrix is updated. Even when the code is strictly 0 N), the CPU time may increase faster if the number of iterations required to achieve the solution increases with N. In fact, it is a common experience that the required number of self-consistency iterations increases with the size of the system. This is mainly because of the charge-sloshing effect, in which small displacements... 

In Figure 9.2 (below) the electrons in Br—Br have sloshed to the left, leaving a large partial + charge on one Br atom. At this moment, the it electrons of the alkene can act as a nucleophile and make a bond to the electrophilic Br atom. 

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