The HSE and CN energy functions only depend on the positions of the Cα atoms in the protein backbone. This allows us to simplify the problem by considering a protein as a chain of connected points representing the positions of the Cα atoms. Furthermore, to reduce and discretize the conformational space of the protein, we require the Cα atoms of the chain to be positioned on a 3D lattice. A lattice can be defined as a set of basis vectors corresponding to the directions to the neighbouring nodes. The basis vectors of the simple cubic lattice (SCC) are the cyclic permutations of [± 1,0,0] ([1,0,0], [-1,0,0], [0,1,0], [0,-1,0], [0,0,1], [0,0,-1]) and the basis vectors of the face centered cubic lattice (FCC) are the cyclic permutations of [± 1, ± 1,0] ([1,1,0], [1,0,1], [1,-1,0], [1,0,-1], [-1,1,0], [-1,0,1], [-1,-1,0], [-1,0,-1], [0,1,1], [0,1,-1], [0,-1,1], [0,-1,-1]). This gives 6 basis vectors for SCC and 12 for FCC as illustrated in Figure 3. The length of an edge between two neighbouring nodes is taken to be 3.8 Å which is the average distance between two consecutive Cα atoms in proteins.