Hartree–Fock and Kohn–Sham atomic-orbital based time-dependent response theory

A reformulation of general time-dependent Hartree–Fock and Kohn–Sham response theories that refers strictly to the atomic-orbital basis is presented. It is based on a recently proposed exponential parametrization of the one-electron atomic-orbital density matrix. In the presented formulation, only matrix multiplications and additions of sparse matrices are needed to compute the response functions and linear scaling with system size may, therefore, be obtained. Thus, this formalism is well suited to the computation of dynamic and static properties for large molecules at the Hartree–Fock and Kohn–Sham density-functional levels of theory.