Frozen‐density embedding‐based many‐body expansions

Abstract

Fragmentation methods allow for the accurate quantum chemical (QC) treatment of large molecular clusters and materials. Here we explore the combination of two complementary approaches to the development of such fragmentation methods: the many-body expansion (MBE) on the one hand, and subsystem density-functional theory (DFT) or frozen-density embedding (FDE) theory on the other hand. First, we assess potential benefits of using FDE to account for the environment in the subsystem calculations performed within the MBE. Second, we use subsystem DFT to derive a density-based MBE, in which a many-body expansion of the electron density is used to calculate the system's total energy. This provides a correction to the energies calculated with a conventional energy-based MBE that depends only on the subsystem's electron densities. For the test case of clusters of water and of aspirin, we show that such a density-based MBE converges faster than the conventional energybased MBE. For our test cases, truncation errors in the interaction energies are below chemical accuracy already with a two-body expansion. The density-based MBE thus provides a promising avenue for accurate QC calculation of molecular clusters and materials.

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

“…To alleviate this shortcoming, the MBE can be performed for the electron density, which provides a density-based energy correction that accounts for many-body polarization effects already at low expansion orders. 34 In fact, with an exact embedding scheme (e.g., with frozen-density embedding in combination with an exact treatment of the nonadditive kinetic energy 84,85 ), the correct total electron density could in principle already be reproduced at the one-body level, i.e., as the sum of (embedded) monomer densities. While even in this case, the eb-MBE fails to reproduce the supermolecular total energy, the db-MBE becomes exact if the MBE of the electron density agrees with the supermolecular electron density, assuming that exact nonadditive density functional are used.…”

“…Most common is the use of suitable point-charge embedding schemes, 32 but recently the use of more sophisticated quantum embedding schemes has also been explored. 33,34 Second, multilevel composite methods can be constructed based on the MBE, in which a cheaper low-level method (e.g., a polarizable force field) is used to calculate the higher-order many-body contributions that are otherwise neglected in a truncated MBE. 11,[35][36][37] Third, the MBE can be generalized to overlapping fragments [38][39][40] and numerous fragmentation methods have been developed following this strategy.…”

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

“…11, [35][36][37] Third, the MBE can be generalized to overlapping fragments [38][39][40] and numerous fragmentation methods have been developed following this strategy. [41][42][43][44][45][46] Recently, we have proposed a density-based MBE (db-MBE), 34 motivated by the observation that an MBE of the electron density,…”

Quantum embedding electronic structure methods

“…However, MBE is often combined with other embedding methods (such as ONIOM or QM/MM) to incorporate such terms in the energy as electrostatic induction and other many-body effects that would require going much beyond the low MBE orders. [114][115][116][117] In this context, the contribution by Schmitt-Monreal et al [118] explores ways to combine subsystem DFT with MBE to improve convergence. Schmitt-Monreal and Jacob [118] also explore ways to exploit a density-based MBE to achieve faster convergence.…”

“…[114][115][116][117] In this context, the contribution by Schmitt-Monreal et al [118] explores ways to combine subsystem DFT with MBE to improve convergence. Schmitt-Monreal and Jacob [118] also explore ways to exploit a density-based MBE to achieve faster convergence. The crucial aspect is the flexibility provided by the underlying density embedding framework.…”