Accurate calculation of many-body energies in water clusters using a classical geometry-dependent induction model

18 April 2023, Version 1
This content is a preprint and has not undergone peer review at the time of posting.


We incorporate geometry-dependent distributed multipole and polarizability surfaces into an induction model that is used to describe the 3- and 4-body terms of the interaction between water molecules. The expansion is carried out up to hexadecapole with the multipoles distributed on the atom sites. Dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole distributed polarizabilities are used to represent the response of the multipoles to an electric field. We compare the model against two large databases consisting of 43,844 3-body terms and 3,603 4-body terms obtained from high level ab initio calculations previously used to fit the MB-pol and q-AQUA interaction potentials. The classical induction model with no adjustable parameters reproduces the ab-initio 3- and 4-body terms contained in these two Databases with a Root-Mean-Square-Error (RMSE) of 0.104/0.058 and a Mean-Absolute-Error (MAE) of 0.054/0.026 kcal/mol, respectively, results that are on a par with those obtained by fitting the same data using tens of thousands of Permutationally Invariant Polynomials (PIPs). This demonstrates the accuracy of this physically motivated model in describing the 3- and 4-body terms in the interactions between water molecules with no adjustable parameters. The triple-dipole-dispersion energy was included in the 3-body energy and was found to be small but not quite negligible. The model represents a practical, efficient and transferable approach for obtaining accurate non-additive interactions for multi-component systems without the need of performing tens of thousands of high level electronic structure calculations and fitting them with tens of thousands of PIPs.


Interaction potential
Force field
Many body expansion
Molecular interactions

Supplementary materials

Supporting Information
Figures motivating the range of the 3D intramolecular scan, tables outlining the ranges of multipoles/polarizabilities, figures and tables demonstrating the success of the linear interpolation, plots showing representations of the multipoles and polarizability surfaces, tables comparing static multipoles and polarizabilities derived from different levels of theory and basis sets, comparisons of the accuracy of the models truncating the multipoles and polarizabilities at different orders, examples of trimers and tetramers removed from the databases


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