Absolute-energy-minimum principles for linear-scaling electronic-structure calculations

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Two absolute energy minimum principles are developed for first-principle linear-scaling electronic structure calculations. One is with a normalization constraint and the other without any constraint. The density matrix is represented by a set of nonorthogonal localized orbitals and an auxiliary matrix which at the minimum becomes a generalized inverse of the overlap matrix of the localized orbitals. The number of localized orbitals is allowed to exceed the number of occupied orbitals. Comparison with other variational principles is made and numerical tests presented. @S0163-1829~97!01939-5# Most electronic structure calculations are based on a oneelectron Hamiltonian, either within semiempirical approaches such as tight-binding and semiempirical quantum chemical models, or within first-principle approaches such as the density functional and Hartree-Fock-based method. The one-electron Hamiltonian provides building blocks for the construction of the electronic wave function or the electron density. Conventional direct and iterative diagonalization algorithms for obtaining eigenvalues require an overall computational effort which grows as the cubic of the number of atoms. This has been a major limiting factor for the application of the electronic structure methods to large systems. The possibility of obtaining the sum of eigenvalues in electronic structure calculations with effort scaling linearly with the size of the system was first demonstrated in the