An energy functional for orbital based $O(N)$ calculations is proposed, whichdepends on a number of non orthogonal, localized orbitals larger than thenumber of occupied states in the system, and on a parameter, the electronicchemical potential, determining the number of electrons. We show that theminimization of the functional with respect to overlapping localized orbitalscan be performed so as to attain directly the ground state energy, withoutbeing trapped at local minima. The present approach overcomes the multipleminima problem present within the original formulation of orbital based $O(N)$methods; it therefore makes it possible to perform $O(N)$ calculations for anarbitrary system, without including any information about the system bondingproperties in the construction of the input wavefunctions. Furthermore, whileretaining the same computational cost as the original approach, our formulationallows one to improve the variational estimate of the ground state energy, andthe energy conservation during a molecular dynamics run. Several numericalexamples for surfaces, bulk systems and clusters are presented and discussed.
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