Work with the AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications) force field has shown that adding atomic anisotropy via multipoles is an excellent way to make molecular mechanics models more accurate. One of the most important factors to achieving this level of accuracy for atom-based force fields is anisotropy. This is of great practical importance since a factor of 10 variance in a drug’s binding affinity can be the difference between a medicine that hits a specific target and the one that binds non-specifically. Because of the relation ΔG = RT log(K D), at room temperature, every order of magnitude in the binding affinity translates into 1.36 kcal/mol in the free energy of binding. A primary, current use for biomolecular force fields is prediction of drug binding affinities. While this requirement is not universal, and higher accuracy may well be required for many applications in molecular interactions, a particular example will serve to rationalize its importance. For force fields, this standard is referred to as “chemical accuracy,” which we define here as a fidelity in computed energies to within 1 kcal/mol. The level of model accuracy needed is always a function of its intended use. 1–3 This paper intends to show that intermolecular Pauli repulsion is a simple consequence of Coulomb’s law and furthermore that this interpretation leads to an accurate classical model of Pauli repulsion. This could not be farther from the truth. This term, which also goes by the names “steric” or “exchange” repulsion, is too often described as a mysterious “quantum mechanical (QM)” force. In particular, one of the most important parts of any force field is the term responsible for intermolecular Pauli repulsion. These predictions are only as good as the model used to make them, meaning that every part of the force field must contain a sufficient level of accuracy. To solve difficult questions such as drug binding specificity or nanotube formation, fields from biology to materials science have come to rely on molecular mechanics models, or force fields, to generate hypotheses and make predictions. Nowhere is this principle more essential or more often forgotten than in molecular modeling. Good classical models of everyday phenomenon are not just lucky they are the true limiting behavior of fundamental physical laws. A true classical model must also be interpretable that is to say, it must be a derivable approximation from first principles. While it is necessary for physics-based models to be accurate and predictive, these qualities alone are not sufficient. The beauty of classical physics models is not that they work for describing most of our world but rather why they work. Several applications of the multipolar Pauli repulsion model are discussed, including noble gas interactions, analysis of stationary points on the water dimer potential surface, and the directionality of several halogen bonding interactions. Parameters for 26 atom classes encompassing most organic molecules are derived from a fit to Symmetry Adapted Perturbation Theory exchange repulsion energies for the S101 dimer database. Mathematically, the proposed model consists of damped pairwise exponential multipolar repulsion interactions truncated at short range, which are suitable for use in compute-intensive biomolecular force fields and molecular dynamics simulations. We provide a concise anisotropic repulsion formulation using the atomic multipoles from the Atomic Multipole Optimized Energetics for Biomolecular Applications force field to describe the electron density at each atom in a larger system. In fact, closed shell intermolecular repulsion can be explained as a diminution of election density in the internuclear region resulting in decreased screening of nuclear charges and increased nuclear-nuclear repulsion. Although Pauli or exchange repulsion has its origin in the quantum mechanical nature of electrons, it is possible to describe the resulting energetic effects via a classical model in terms of the overlap of electron densities. Pauli repulsion is a key component of any theory of intermolecular interactions.
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