Density driven self-consistent field method. I. Derivation and basic properties

An explicit Schroedinger-like equation for the Hartree--Fock density amplitude (square root of the electron density) is derived. The potential contains a classical electrostatic part as well as the exclusion potential that arises from the Fermi statistics of the electrons. The exclusion potential is explicitly determined by solving a system of equations for auxiliary functions. Basic features of the new approach are discussed and its equivalence to the standard HF method is demonstrated