Spherical harmonic molecular surfaces

Abstract

Starlike surfaces can be defined in spherical coordinates by a function r( theta , phi ) on the unit sphere, which can be expanded in spherical harmonics to give a consequence of smooth approximations to the surface. This method has been used to approximate the solvent-accessible surface of a molecule. The coefficients in the expansion provide a small collection of numbers that characterize the molecular shape. The resulting smooth surfaces can be rendered with random dots or smooth shading. These spherical harmonic surfaces have advantages for modeling overall molecular shape, particularly time-averaged shapes relevant to electrostatic and other intermolecular interactions.