Curvy steps for density matrix-based energy minimization: Application to large-scale self-consistent-field calculations

A unitary transformation approach to avoiding the diagonalization step in density functional theory calculations is developed into an algorithm that can scale linearly with molecular size. For target accuracy of 10−5 in the rms rotation gradient, the average number of matrix multiples required per self-consistent field iteration is between about 35 (STO-3G) and 50 (6-31G**). This compares favorably to the existing canonical purification method. Crossovers with direct diagonalization are demonstrated for 1D alkane chains and 2D water clusters.