The performance of computational methods for many-body physics and chemistry is strongly dependent on the choice of the basis used to formulate the problem. Hence, the search for similarity transformations that yield better bases is important for progress in the field. So far, tools from theoretical quantum information have not been thoroughly explored for this task. Here we take a step in this direction by presenting efficiently computable Clifford similarity transformations for the molecular electronic structure Hamiltonian, which expose bases with reduced entanglement in the corresponding molecular ground states. These transformations are constructed via block-diagonalization of a hierarchy of truncated molecular Hamiltonians, preserving the full spectrum of the original problem. We show that the bases introduced here allow for more efficient classical and quantum computations of ground-state properties. First, we find a systematic reduction of bipartite entanglement in molecular ground states as compared to standard problem representations. This entanglement reduction has implications in classical numerical methods, such as those based on the density matrix renormalization group. Then, we develop variational quantum algorithms that exploit the structure in the new bases, showing again improved results when the hierarchical Clifford transformations are used.