Making many-body interactions nearly pairwise additive: The polarized many-body expansion approach

Abstract

The Many-Body Expansion (MBE) is a useful tool to simulate condensed phase chemical systems, often avoiding the steep computational cost of usual electronic structure methods. However, it often requires higher than 2-body terms to achieve quantitative accuracy. In this work, we propose the Polarized MBE (PolBE) method where each MBE energy contribution is treated as an embedding problem. In each energy term, a smaller fragment is embedded into a larger, polarized environment and only a small region is treated at the high-level of theory using embedded mean-field theory. The role of polarized environment was found to be crucial in providing quantitative accuracy at the 2-body level. PolBE accurately predicts non-covalent interaction energies for a number of systems, including CO 2 , water, and hydrated ion clusters, with a variety of interaction mechanisms, from weak dispersion to strong electrostatics considered in this work. We further demonstrate that the PolBE interaction energy is predominantly pairwise unlike the usual vacuum MBE which requires higher-order terms to achieve similar accuracy. We numerically show that PolBE often performs better than other widely used embedded MBE methods such as the electrostatically embedded MBE.Owing to the lack of expensive diagonalization of Fock matrices and its embarrassingly parallel nature, PolBE is a promising way to access condensed phase systems with hybrid density functionals that are difficult to treat with currently available methods.

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

“…Ideally, the truncation error of any MBE scheme should be below chemical accuracy already for a two-body approximation (pairwise additive approximation), which is rarely achieved if an energy-based MBE is employed, 29 even in combination with sophisticated embedding schemes. 33 Previously, 34 we successfully applied the density-based MBE to selected clusters of water and aspirin extracted from the respective crystal structures, but did not systematically assess its accuracy. Here, we set out to close this gap by thoroughly benchmarking the density-based MBE using water clusters as a challenging test case.…”

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

“…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.…”

“…While the calculations presented in the previous section allow us to judge the absolute error in the total interaction energy, for many applications relative errors across a set of similar molecular systems are more relevant, and present another challenging test case for MBEs. 33 Therefore, in this section we assess the ability of MBEs to accurately predict the interaction energies of different isomers of water clusters of the same size. We consider the low-energy 81 The relative energies of the different isomers depend on the structure of the respective hydrogenbonding networks as well as the strengths of the intermolecular hydrogen bonds.…”

Frozen-Density Embedding Based Many-Body Expansions

“…Exceptions are the use of the XPol approach in the variational many-body method [50] as well as different variants of the fragment-molecular orbital method [51][52][53]. Recently, Head-Gordon and coworkers [54] have assessed the use of a quantum embedding scheme within the MBE by applying the embedded mean-field theory of Manby and Miller [55] for the subsystem calculations.…”