Shape similarity between molecules is a concept used by chemists for virtual screening, with the goal of reducing the cost and duration of drug discovery campaigns. This paper reports an entirely novel shape descriptor as an alternative to the previously described descriptors (Hall et al. 2024 Riemannian geometry and molecular similarity I: spectrum of the Laplacian. Proc. R. Soc. A 480 , 20230343. ( doi:10.1098/rspa.2023.0343 )), derived from the theory of Riemannian geometry and Kähler quantization. The treatment of a molecule as a series of intersecting spheres allows us to obtain the explicit Riemannian metric which captures the geometry of the surface. The metric can, in turn, be used to calculate a Hermitian matrix M as a directly comparable surface representation. The potential utility of this method is demonstrated using a series of drug molecules (we consider a type of drug know as a PDE5 inhibitor) considered to have similar shape. The method shows promise in its capability to handle different conformers and compares well to existing shape similarity methods.