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

Abstract

<div>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.</div>

A simple and consistent quantum-chemical fragmentation scheme for proteins that includes two-body contributions

“…To further increase the accuracy of quantum-chemical fragmentation methods for proteins, we will consider the inclusion of higher-order many-body corrections as well as the use of suitable embedding schemes in the fragment calculations [34] in our future work. Moreover, an extension of the MFCC-MBE(2) scheme to the electron density and its use within our recently developed formalism for a density-based many-body expansion [77,78] can be expected to further increase the accuracy.…”

“…In this case, it will become possible to simplify the expansions significantly by deleting terms that appear for both the protein and protein-ligand complex. Here, the combination of MFCC-MBE(2) with a density-based MBE [77,78] seems particularly promising.…”

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

“…For the isolated db-MBEs, the errors are reduced compared to the isolated eb-MBE(2), but remain rather large. Thus, while for water clusters already the isolated db-MBE (2) could reduce the error per fragment below the threshold of chemical accuracy [45], for ion-water clusters the use of a suitable embedding potential is essential. As soon as some embedding potential is included, the accuracy of the db-MBE improves.…”

Massively Parallel Fragment-Based Quantum Chemistry for Large Molecular Systems: The Serestipy Software

“…In particular, we will employ subsystem time-dependent densityfunctional theory [32][33][34][35] (subsystem TDDFT) with parallel FDE calculations as a reference [36,37] to efficiently obtain excited states. Besides the presented example, this massively-parallel framework could be employed to efficiently perform tasks such as embarrassingly-parallel potential-energy surface constructions [38][39][40][41][42][43], parallel mode-and intensity-tracking or general semi-numerical frequency calculations [44][45][46][47], or many-body expansion calculations [48][49][50][51][52].…”