Energy benchmarks for water clusters and ice structures from an embedded many-body expansion

TL;DR

This paper introduces an embedded many-body expansion (EMBE) method to accurately compute ab initio energies of water clusters and ice structures, effectively separating correlation and Hartree-Fock energies for improved precision.

Contribution

The paper demonstrates how EMBE can be used with wavefunction methods to accurately calculate energies of water systems, including clusters and ice, with efficient truncation at the 2-body level.

Findings

EMBE reproduces correlation energies within 0.1 mE_h/monomer for MP2.

MP2 energies match experimental values for ice structures.

Coupled-cluster methods are necessary for full many-body correlation description.

Abstract

We show how an embedded many-body expansion (EMBE) can be used to calculate accurate \emph{ab initio} energies of water clusters and ice structures using wavefunction-based methods. We use the EMBE described recently by Bygrave \emph{et al.} (J. Chem. Phys. \textbf{137}, 164102 (2012)), in which the terms in the expansion are obtained from calculations on monomers, dimers, etc. acted on by an approximate representation of the embedding field due to all other molecules in the system, this field being a sum of Coulomb and exchange-repulsion fields. Our strategy is to separate the total energy of the system into Hartree-Fock and correlation parts, using the EMBE only for the correlation energy, with the Hartree-Fock energy calculated using standard molecular quantum chemistry for clusters and plane-wave methods for crystals. Our tests on a range of different water clusters up to the 16-mer show that for the second-order M\o{}ller-Plesset (MP2) method the EMBE truncated at 2-body level reproduces to better than 0.1 m$E_{\rm h}$/monomer the correlation energy from standard methods. The use of EMBE for computing coupled-cluster energies of clusters is also discussed. For the ice structures Ih, II and VIII, we find that MP2 energies near the complete basis-set limit reproduce very well the experimental values of the absolute and relative binding energies, but that the use of coupled-cluster methods for many-body correlation (non-additive dispersion) is essential for a full description. Possible future applications of the EMBE approach are suggested.