Direct minimization of the energy in density functional theory

The minimization of the energy functional of the first-order density matrix γ( r , r ') is achieved using unitary transformations applied to γ. Equivalently, such transformations can be carried out also on one-electron orbitals (natural orbitals) and their occupation (integer or non-integer) numbers. The conventional local density approximation based on the electron density p( r ) is then considered as a special case. The direct minimization of the energy functional of p with respect to the parameters of the unitary transformation leads to stationary conditions that are all equivalent to the Kohn–Sham equations. Preliminary numerical tests show that the proposed algorithms for the direct minimization of the energy work in a satisfactory manner. © John Wiley & Sons, Inc.