We introduce a solid harmonic wavelet scattering representation, which is invariant to rigid movements and stable to deformations, for regression and classification of 2D and 3D images. Solid harmonic wavelets are computed by multiplying solid harmonic functions with Gaussian windows dilated to different scales. Invariant scattering coefficients are obtained by cascading such wavelet transforms with the complex modulus nonlinearity. We study an application of solid harmonic scattering invariants to the estimation of quantum molecular energies, which are also invariant to rigid movements and stable with respect to deformations. We introduce a neural network with a multiplicative non-linearity for regression over scattering invariants to provide close to state of the art results over a database of organic molecules.