Efficient, direct self-consistent-field method in density-functional theory

We have developed a direct self-consistent-field (SCF) molecular-orbital (MO) method based on the density-functional linear combinations of atomic-orbital methods, which is efficient for obtaining total energies of large molecules. In this method, we introduce the Schwartz inequality and efficiently reduce the number of atomic-orbital pairs, which must be considered for calculating the matrix elements and electron density. The MO calculations for ${\mathrm{C}}_{60}$ confirm that the total number of calculation steps for obtaining the matrix elements and electron density becomes 1/6 of that for an ordinary SCF-MO method, keeping an eight-digit accuracy in total energy. © 1996 The American Physical Society.