Extension of the Many-Body Expansion (MBE) to Periodic Systems: Developing Tools to Analyze and Improve Models of Intermolecular Interactions

Abstract

Intermolecular interactions govern the structure and dynamics of molecular systems, which collectively give rise to their physical properties across scales from the nano- to the meso- and the macro-scale. These collective properties are often sensitive to the level of theoretical description manifested either by the accuracy of a classical interaction potential or the level of electronic structure theory used to describe the fundamental interactions at the molecular level. Due to the prohibitive scaling of electronic structure calculations with the system size (oftentimes O(N^6) - O(N^7) for the “gold-standard” coupled cluster methods, where N is the number of basis functions), we must seek alternative ways of evaluating the properties of these complex molecular systems without compromising accuracy. The many-body expansion (MBE), a fragmentation approach, partitions the full system into a set of smaller subsystems and combinatorically represents the properties of the full system (i.e., binding energy, forces, dipole moment, etc.). This approach offers a powerful alternative to address the “scaling curse” of accurate electronic structure methods with system size. The following will highlight efforts to unravel the nature of many-body effects in aqueous ionic systems, develop transferable classical models to accurately describe those intermolecular interactions at a reduced cost, and extend the many-body expansion (MBE) formalism to periodic systems. The MBE was applied to investigate the influence of “structure-making” and “structure-breaking” ions in the Hofmeister series on the energetics of aqueous cations and anions (SO_4^{2-}, ClO_4^-, Ca^{2+}, NH_4^+). Significant differences in the many-body terms were identified for the structure-making ions, which exhibit the strongest ion-water and the weakest water-water interactions. Conversely, the structure-breaking ions exhibit weaker ion-water interactions and stronger water-water interactions, demonstrating the intricate balance of interactions governing the energetics of these systems. The trend demonstrating the anti-correlation between the ion-water and water-water interactions persisted across 13 different ion-water systems and further quantified the role of ions (and the identity of said ion) in affecting the water-water interactions. Having established the strong many-body character in ion-water systems, the next step was to develop interaction potentials to describe many-body effects in aqueous ionic systems. A classical induction model using a detailed description of the field due to a charge distribution using distributed multipoles and the response of the charge distribution to an external field using distributed polarizabilities was developed to model 3- and 4-body interactions. The induction energies were benchmarked against 3,120 ab initio 3-body energies for 13 different ion-water-water and water-water-water systems. The induction model was subsequently improved by developing and implementing geometry-dependent distributed multipole and polarizability surfaces. For water, the induction model augmented with 3-body dispersion was compared against results from an existing database of 43,844 3-body and 3,603 4-body CCSD(T) energies. The model was found to reproduce the 3- and 4-body interactions with mean absolute errors of 0.054 and 0.026 kcal/mol, respectively. These findings suggest that the developed classical model with zero adjustable parameters yields an accuracy that is on-par with models fit to tens of tens of thousands of CCSD(T) energies using thousands of adjustable parameters. This physics-based approach provides a simple, fast, and most importantly transferable way of modeling many-body effects in aqueous molecular systems, eliminating the need to perform tens of thousands of expensive electronic structure calculations for each change in solvent or solute identity. A novel approach was developed to extend the MBE to periodic systems and subsequently used to decompose the lattice energies of seven polymorphs of ice into their constituent many-body terms. The sum of the many-body terms (1-body through 4-body) was shown to match the value obtained with periodic boundary conditions using the minimum image convention and an Ewald summation. A resulting three-way relationship was established, demonstrating the correlation between the many-body terms, the local tetrahedral order, and the density of the ice polymorphs. Specifically, ice polymorphs existing at low pressures were shown to have strong cooperative effects, near perfect tetrahedral order, and 5- and 6-membered hydrogen bond cycles. Conversely, high pressure ice polymorphs exhibited weak cooperative effects, low tetrahedral order, and a mixture of hydrogen bond cycle sizes. This lends valuable insight into the structure-energy relationship that governs the complex phase diagram of ice. Besides its utility of gaining insight into the nature of intermolecular interactions, the MBE for periodic systems is currently being used to circumvent the poor scaling of electronic structure methods by computing 2- and 3-body corrections to the correlation energy. This approach is trivially parallelizable and is founded on the preference of performing several CCSD(T) calculations for much smaller systems (dimers and trimers) therefore reducing the size (N) and corresponding cost (N^7) of the requisite CCSD(T) calculations.