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The Sternheimer approach to all-electron real-space density-functional perturbation theory with atomic basis set

We present an efficient perturbative method to get the response density matrix using localized non-orthogonal basis sets. This scheme is based on the solution of the coupled perturbed self-consistent field equation with the Sternheimer approach, which only requires the occupied states and avoids a sum over unoccupied states. We present a complete derivation of the Sternheimer approach to perturbation theory within the framework of the linear combination of atomic orbitals. To demonstrate the capabilities of this method, we have implemented it in the all-electron Fritz Haber Institute ab initio molecular simulation package and applied it to benchmark molecules. For the response properties with respect to the atomic displacement and to the homogeneous electric field, the results are in excellent agreement with those of the previous traditional method and fully validate this Sternheimer approach.