Density-Based Many-Body Expansion as an Efficient and Accurate Quantum-Chemical Fragmentation Method: Application to Water Clusters

Fragmentation methods
based on the many-body expansion offer an
attractive approach for the quantum-chemical treatment of large molecular
systems, such as molecular clusters and crystals. Conventionally,
the many-body expansion is performed for the total energy, but such
an energy-based many-body expansion often suffers from a slow convergence
with respect to the expansion order. For systems that show strong
polarization effects such as water clusters, this can render the energy-based
many-body expansion infeasible. Here, we establish a density-based
many-body expansion as a promising alternative approach. By performing
the many-body expansion for the electron density instead of the total
energy and inserting the resulting total electron density into the
total energy functional of density functional theory, one can derive
a density-based energy correction, which in principle accounts for
all higher-order polarization effects. Here, we systematically assess
the accuracy of such a density-based many-body expansion for test
sets of water clusters. We show that already a density-based two-body
expansion is able to reproduce interaction energies per fragment within
chemical accuracy and is able to accurately predict the energetic
ordering as well as the relative interaction energies of different
isomers of water clusters.