Linear scaling exchange gradients for Hartree–Fock and hybrid density functional theory

A new method is introduced which allows to form the exchange part of self-consistent field energy gradients in a way which scales linearly with molecular size for molecules with a non-vanishing HOMO–LUMO gap. This is not only important for Hartree–Fock but as well for the popular hybrid density functional theory methods. The method preserves the optimized integral-driven structure of conventional direct methods. Efficiency and scaling behavior of the new method are illustrated for DNA fragments.