We introduce a solid harmonic wavelet scattering representation, invariant to rigid motion and stable to deformations, for regression and classification of 2D and 3D signals. Solid harmonic wavelets are computed by multiplying solid harmonic functions with Gaussian windows dilated at 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 motion and stable with respect to deformations. A multilinear regression over scattering invariants provides close to state of the art results over small and large databases of organic molecules.