Comparison of Three Efficient Approximate Exact-Exchange Algorithms: The Chain-of-Spheres Algorithm, Pair-Atomic Resolution-of-the-Identity Method, and Auxiliary Density Matrix Method.

We compare the performance of three approximate methods for speeding up evaluation of the exchange contribution in Hartree-Fock and hybrid Kohn-Sham calculations: the chain-of-spheres algorithm (COSX; Neese , F. Chem. Phys.

Wavelet formulation of the polarizable continuum model. II. Use of piecewise bilinear boundary elements.

The simplicity of dielectric continuum models has made them a standard tool in almost any Quantum Chemistry (QC) package. Despite being intuitive from a physical point of view, the actual electrostatic problem at the cavity boundary is challenging: the underlying boundary integral equations depend on singular, long-range operators. The parametrization of the cavity boundary should be molecular-shaped, smooth and differentiable.