Order-N density-matrix electronic-structure method for general potentials

A order-N method for calculating the electronic structure of general (non-tight-binding) potentials is presented. The method uses a combination of the ‘‘purification’’-based approaches used by Li, Nunes, and Vanderbilt, and Daw, and a representaiton of the density matrix based on ‘‘traveling basis orbitals.’’ This method gives a total energy form that has the form of a cubic multicomponent Landau theory. The method is applied to several one-dimensional examples, including the free-electron gas, the ‘‘Morse’’ bound-state potential, a discontinuous potential that mimics an interface, and an oscillatory potential that mimics a semiconductor. The method is found to contain several physical effects that are hard to obtain in real-space total-energy functionals: Friedel oscillations, quantization of charge in bound states, and band-gap formation. Quantitatively accurate agreement with exact results is found in most cases. Possible advantages with regard to treating electron-electron interactions and arbitrary boundary conditions are discussed.