Assessment of RPA and <i>σ</i>-functional methods for the calculation of dipole moments and static polarizabilities and hyperpolarizabilities

In the present paper, we assess the performance of methods based on the random phase approximation (RPA) and on σ-functionals for predicting static optical properties, i.e., dipole moment, polarizability, and first and second hyperpolarizability, of small- and medium-sized molecules, including chain-like systems. First, we provide accurate reference data by coupled-cluster singles, doubles, with perturbative triples calculations with sufficiently large basis sets. The RPA and σ-functional calculations are carried out post-self-consistently using input orbitals and eigenvalues from the hybrid density-functional calculation. The optimal fraction of exact non-local exchange in these calculations is found to be quite high, around 0.5-0.6 in RPA and around 0.8-1.0 in σ-functional methods. σ-functional methods, however, proved to be less sensitive than RPA methods with respect to the amount of exact non-local exchange used in the generation of their input data. σ-functional methods are shown to outperform in accuracy RPA methods and various other considered density-functional theory methods for static optical properties and, thus, are well-suited for the calculation of linear and non-linear optical properties.