An evaluation of spherical designs for molecular-like surfaces

The use of spherical harmonics in the molecular sciences is widespread. They have been employed with success in, for instance, the crystallographic fast rotation function, small-angle scattering particle reconstruction, molecular surface visualisation, protein-protein docking, active site analysis and protein function prediction. The calculation of spherical harmonic expansion coefficients requires integration over the full sphere and can be a computationally cumbersome and also numerically sensitive (with respect to the integration weights) procedure. It is shown here how the use of spherical t-designs and pre-computed near-equal weight integration layouts can significantly reduce the computational effort in the determination of spherical harmonic expansion coefficients for molecular surfaces, thus giving rise to a robust and highly efficient algorithm for the construction of molecular-like objects.