The quantum Hamiltonian ĤQ in Eq. 50, when represented in the double excited diabatic basis, is very sparse in nature. Although the size of the Hamiltonian increases as O(N 4 ) for N molecules, the sparsity of the Hamiltonian (defined as the ratio between the number of nonzero matrix elements and the total number of matrix elements) scales as 1 -1/N 2 and very quickly converges to 1.