Response calculations in the framework of time-dependent density-functional theory (TDDFT) have by now been shown to surpass time-dependent Hartree-Fock (TDHF) calculations in both accuracy and efficiency. This makes TDDFT an important tool for the calculation of frequency-dependent (hyper)polarizabilities, excitation energies, and related properties of medium-sized and large molecules. Two separate approximations are made in the linear DFT response calculations. The first approximation concerns the exchange-correlation (xc) potential, which determines the form of the Kohn-Sham orbitals and their one-electron energies, while the second approximation involves the so-called xc kernel fxc, which determines the xc contribution to the frequency-dependent screening. By performing calculations on small systems with accurate xc potentials, constructed from ab initio densities, we can test the relative importance of the two approximations for different properties and systems, thus showing what kind of improvement can be expected from future, more refined, approximations to these xc functionals. We find that in most, but not all, cases, improvements to vxc seem more desirable than improvements to fxc.
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