Accuracy in the initial guess is important in self-consistent field (SCF) calculations, not only to accelerate the calculation, but also to avoid oscillation or divergence in the SCF calculation. The many-body expansion (MBE) has recently been used to build high-quality density matrices (DMs) in our group. Such MBE-DM approaches combined with purification and distance-based cutoff schemes provide high-quality DMs as initial guesses to largely reduce the SCF cycles necessary for convergence and perform up to 40% speedup for a wide range of systems as compared with traditional initial guesses including superposition of atomic densities, superposition of atomic potentials, and basis set projection. In addition, MBE-DM can be used to derive energy directly via one Fock build with mean absolute deviation (MAD) per monomer within the so-called "dynamical accuracy" at the three-body expansion. In this work, we move forward one more step to build DMs using the generalized many-body expansion (GMBE) with intersecting fragments. This newly developed GMBE-DM approach shows promising results for the direct energy prediction with MAD per monomer still within the dynamical accuracy but using only the one-body expansion and 2 Angstrom minimum-distance cutoff. The number of subsystem calculations in GMBE1-DM is at least one order of magnitude smaller than MBE3-DM. As compared with the corresponding energy-based GMBE1 approach, the performance of GMBE1-DM is at least one order of magnitude better. Thus, preliminary applications of GMBE-DM to molecular and ionic clusters suggest that this is a route to achieve very high accuracy and low cost in fragment-based calculations.

Building high-quality density matrices via the generalized many-body expansion for the direct energy prediction

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