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

Abstract

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. File list (3) download file view on ChemRxiv dbMBE_benchmark.pdf (2.72 MiB) download file view on ChemRxiv si.pdf (567.74 KiB) download file view on ChemRxiv si_coords.zip (110.05 KiB)

Accurate quantum-chemical fragmentation calculations for ion–water clusters with the density-based many-body expansion

“…For further details on the evaluation of the different terms in eqn (9), we refer to ref. 44 and 45.…”

“…Therefore, the scaling of the computational effort with cluster size is the same for the eb-MBE( n ) and the db-MBE( n ), even though in the latter case the need for calculating the subsystem electron densities increases the prefactor. 44,45…”

“…We could show that such a db-MBE can capture many-body polarization effects in water clusters already with a two-body expansion and that accurate total and relative energies can be obtained with a density-based two-body expansion. 45 Here, we set out to explore the db-MBE for ion–water clusters, which present an even more challenging test case. We will particularly consider the importance of self-consistent embedding for the fragment calculations, which can be expected to be more important in ion–water clusters.…”

Accelerating the Convergence of Self-Consistent Field Calculations Using the Many-Body Expansion

“…It is worth noting that the fragments generated in this work are disjoint although they need not necessarily be so. The rationale behind the employ of the MBE for the construction of subsystem density matrices is based on the observation that the convergence is faster for electronic density than for the energy values themselves. , …”

Protein Response Effects on Cofactor Excitation Energies from First Principles: Augmenting Subsystem Time-Dependent Density-Functional Theory with Many-Body Expansion Techniques

“…, the fragment molecular orbital method (FMO), , the ONIOM (“our own N-layered integrated molecular orbital + molecular mechanics”) method, , or divide-and-conquer (DC) methods, − to name a few. Within the subsystem density-functional theory (sDFT) context, MBE techniques have so far only been applied to ground-state properties . A crucial aspect in connection with incremental techniques for light-absorption phenomena is the convergence of the many-body expansion (MBE) used to calculate excitation energies.…”