Assessment of Basis Set Projection and Many-Body Expansion for Initial Guesses of Self-Consistent Field Calculations

In Self-Consistent Field (SCF) calculations, the choice of initial guess plays a key role in determining the time-to-solution by influencing the number of iterations required for convergence. However, focusing solely on reducing iterations may overlook the computational cost associated with improving the accuracy of initial guesses. This study critically evaluates the effectiveness of two initial guess methods—basis set projection (BSP) and many-body expansion (MBE)—as well as a newly developed hybrid approach on Hartree-Fock and hybrid Density Functional Theory (B3LYP and MN15) methods. Our assessment considers both the number of SCF iterations and the total computational wall-times. The results demonstrate that the non-SAD techniques BSP, MBE, and the hybrid method could significantly outperform the conventional superposition of atomic densities (SAD) technique. With these methods, reductions in total wall-time, including the time spent generating initial guesses, by up to 21.9%, 27.6% and 21.6% could be observed with HF, B3LYP and MN15, respectively, when tested on systems containing up to 14,386 basis functions. Furthermore, we also examine the influence of these initial guess schemes on difficult-to-converge metalloprotein and triplet electronic states.