title: Convergence of the Many-Body Expansion for Energy and Forces for Classical Polarizable Models in the Condensed Phase.
abstract: We analyze convergence of energies and forces for the AMOEBA classical polarizable model when evaluated as a many-body expansion (MBE) against the corresponding N-body parent potential in the context of a condensed-phase water simulation. This is in contrast to most MBE formulations based on quantum mechanics, which focus only on convergence of energies for gas-phase clusters. Using a single water molecule as a definition of a body, we find that truncation of the MBE at third order, 3-AMOEBA, captures direct polarization exactly and yields apparent good convergence of the mutual polarization energy. However, it renders large errors in the magnitude of polarization forces and requires at least fourth-order terms in the MBE to converge toward the parent potential gradient values. We can improve the convergence of polarization forces for 3-AMOEBA by embedding the polarization response of dimers and trimers within a complete representation of the fixed electrostatics of the entire system. We show that the electrostatic embedding formalism helps identify the specific configurations involving linear hydrogen-bonding arrangements that are poorly convergent at the 3-body level. By extending the definition of a body to be a large water cluster, we can reduce errors in forces to yield an approximate polarization model that is up to 10 times faster than the parent potential. The 3-AMOEBA model offers new ways to investigate how the properties of bulk water depend on the degree of connectivity in the liquid.
authors.affiliation: Department of Chemistry, ‡Department of Bioengineering, §Department of Chemical and Biomolecular Engineering, ∥Chemical Sciences Division, Lawrence Berkeley National Laboratory, University of California , Berkeley, California 94720, United States.
authors.forename: Omar
authors.initials: O
authors.lastname: Demerdash
authors.affiliation: Department of Chemistry, ‡Department of Bioengineering, §Department of Chemical and Biomolecular Engineering, ∥Chemical Sciences Division, Lawrence Berkeley National Laboratory, University of California , Berkeley, California 94720, United States.
authors.forename: Teresa
authors.initials: T
authors.lastname: Head-Gordon