The Many-Body Expansion: A powerful tool for analyzing intermolecular interactions and driving molecular dynamics

Abstract

The many-body expansion (MBE) is a method of decomposing any molecular propertyinto contributions from the sub-systems of some total system. We focus on applying the MBE to detailed studies of the energy and forces of molecular clusters. In particular, we carry out the MBE up to full order for (H2O)7 and (H2O)10 with increasingly complete basis sets. In doing this, we determine that the convergence of higher-order terms in the MBE depends sensitively on the presence of basis set superposition error (BSSE). Namely, the MBE for 3-body and higher terms in the energy is converged with an aug-cc-pVDZ basis set as long as a BSSE correction is included. If BSSE is ignored, however, the MBE oscillates from term to term and converges very slowly. We carry out a similar analysis of ion-water clusters, Z+/–(H2O)9, where Z+/–= Li+, Na+, K+, Rb+, Cs+, F–, Cl–, Br–, and I–. We verify the same conclusions about convergence of the MBE as for pure water clusters. Additionally, we find a remarkable linear anti-correlation between the total 2-body ion-water and 2-body and 3-body water-water interactions. This provides a quantitative measure of the extent to which hydrogen bond networks are disrupted by the presence of monoatomic ions. For both neutral and ion-water clusters, we find that the correlation energy makes less than 0.1% total contribution to the energy at the 3-body and higher levels. That is, electron correlation only needs to be included at the 1- and 2-body levels to capture 99.9% of the energy. Additionally, we use the MBE as a tool for analyzing molecular interactions in clathrate cages of varying sizes: (H2O)20, (H2O)24, and (H2O)28. These systems are dominated by subtle cooperative hydrogen bonding effects. That is, for (H2O)20 there are 30,026 unique configurations with the least stable of these lying ~30 kcal/mol higher in energy than the most stable one. We show that many of the possible hydrogen bond configurations of these cages are actually not stable local minima, but instead collapse to lower energy families of networks. We use the MBE to understand how many-body effects contribute to the stability of these clathrates cages. It turns out, for these systems, that the 2- and 3-body energies decrease at nearly identical rates as the total energy increases. This means these systems are particularly sensitive to hydrogen bond cooperativity because the 3-body energy is a smaller component of the total energy than the 2-body part. This work provides a good illustration of how the MBE can be used to tease apart complex details of molecular interactions with relative ease. These detailed analyses lay the groundwork for a scheme in which high levels of electronic structure theory, such as MP2 and CCSD(T), can be used to drive the molecular dynamics of medium-sized systems without a major loss of accuracy. We first demonstrate that one can use the MBE to drive dynamics simulations with the MB-Pol water potential. These simulations result in the observation that the MBE is fairly slow to converge the forces and, in certain circumstances, a 5-body description of the force may be needed. We discuss the extension of MBE-MD to ab initio molecular dynamics simulations, emphasizing the algorithmic and software improvements which could be used to make ab initio MBE-MD a practical method.