Density Functional and Density Matrix Method Scaling Linearly with the Number of Atoms

Abstract

A widely applicable ``nearsightedness'' principle is first discussed as the physical basis for the existence of computational methods scaling linearly with the number of atoms. This principle applies to the one particle density matrix $n({r,r}^{\ensuremath{'}})$ but not to individual eigenfunctions. A variational principle for $n({r,r}^{\ensuremath{'}})$ is derived in which, by the use of a penalty functional $P[n({r,r}^{\ensuremath{'}})]$, the (difficult) idempotency of $n({r,r}^{\ensuremath{'}})$ need not be assured in advance but is automatically achieved. The method applies to both insulators and metals.