Determining quantum chemical properties of a molecular system via density functional theory (DFT), although accurate, is computationally expensive and severely limited by the size of the system in question. Machine learning methods are becoming popular as, in certain cases, they maintain state of the art accuracy while offering substantial savings in computer time. However, these methods require extensive data sets of DFT calculations, have difficulty extrapolating beyond training examples, and are difficult to interpret. We present a machine learning model that trains on small molecular systems, and them predicts the quantum chemical energy of larger systems by learning parameters to model the varying electronic interactions and behaviors over a range of length scales. To accomplish this, we create a surrogate electronic density based on atomic positions, while we use to compute multi-scale invariants of the system. These invariants are determined using wavelets inspired by electron orbitals, and they lead to a representation of the system that is unaffected by atom re-indexing and isometric transformations, in addition to varying regularly under system deformations. Performing a multilinear regression on these invariant wavelet scattering coefficients produces an algorithm that is capable of generalizing beyond its training examples in a relatively interpretable manner.