The nominal computational cost of these methods varies significantly. DFT is generally efficient, scaling with the number of electrons N as O(N 3 ), primarily due to the diagonalization of the Kohn-Sham eigenvalue problem. In contrast, wave-functionbased methods such as configuration interaction (CI), density matrix renormalization group (DMRG), and coupled-cluster (CC) methods demand considerably more computational resources, with scaling complexities that increase steeply depending on the method's sophistication. For example, the computational cost of the "gold standard" in quantum chemistry, coupled-cluster singles and doubles with perturbative triples (CCSD(T)), scales as O(N 7 ). QMC methods, particularly in their commonly used realspace variants, occupy an intermediate position in terms of computational cost, with a scaling of O(N 3 ) per Monte Carlo step, largely governed by the repeated evaluation of the Slater determinant.