Ab initio linear scaling response theory: electric polarizability by perturbed projection.

A linear scaling method for calculation of the static ab initio response within self-consistent field theory is developed and applied to the calculation of the static electric polarizability. The method is based on the density matrix perturbation theory [Phys. Rev. Lett. 92, 193001 (2004)]], obtaining response functions directly via a perturbative approach to spectral projection. The accuracy and efficiency of the linear scaling method is demonstrated for a series of three-dimensional water clusters at the RHF/6-31G(**) level of theory. The locality of the response under a global electric field perturbation is numerically demonstrated by the approximate exponential decay of derivative density matrix elements.