The Tinker software, currently released as version 8, is a modular molecular mechanics and dynamics package written primarily in a standard, easily portable dialect of Fortran 95 with OpenMP extensions. It supports a wide variety of force fields, including polarizable models such as the Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field. The package runs on Linux, macOS, and Windows systems. In addition to canonical Tinker, there are branches, Tinker-HP and Tinker-OpenMM, designed for use on message passing interface (MPI) parallel distributed memory supercomputers and state-of-the-art graphical processing units (GPUs), respectively. The Tinker suite also includes a tightly integrated Java-based graphical user interface called Force Field Explorer (FFE), which provides molecular visualization capabilities as well as the ability to launch and control Tinker calculations.

Classical molecular mechanics force fields typically model interatomic electrostatic interactions with point charges or multipole expansions, which can fail for atoms in close contact due to the lack of a description of penetration effects between their electron clouds. These short-range penetration effects can be significant and are essential for accurate modeling of intermolecular interactions. In this work we report parametrization of an empirical charge–charge function previously reported (PiquemalJ.-P.26313624J. Phys. Chem. A200310353) to correct for the missing penetration term in standard molecular mechanics force fields. For this purpose, we have developed a database (S101×7) of 101 unique molecular dimers, each at 7 different intermolecular distances. Electrostatic, induction/polarization, repulsion, and dispersion energies, as well as the total interaction energy for each complex in the database are calculated using the SAPT2+ method (ParkerT. M.09410624606352J. Chem. Phys.2014140). This empirical penetration model significantly improves agreement between point multipole and quantum mechanical electrostatic energies across the set of dimers and distances, while using only a limited set of parameters for each chemical element. Given the simplicity and effectiveness of the model, we expect the electrostatic penetration correction will become a standard component of future molecular mechanics force fields.

The principal challenge of using classical physics to model biomolecular interactions is capturing the nature of short-range interactions that drive biological processes from nucleic acid base stacking to protein-ligand binding. In particular most classical force fields suffer from an error in their electrostatic models that arises from an ability to account for the overlap between charge distributions occurring when molecules get close to each other, known as charge penetration. In this work we present a simple, physically motivated model for including charge penetration in the AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications) force field. With a function derived from the charge distribution of a hydrogen-like atom and a limited number of parameters, our charge penetration model dramatically improves the description of electrostatics at short range. On a database of 101 biomolecular dimers, the charge penetration model brings the error in the electrostatic interaction energy relative to the ab initio SAPT electrostatic interaction energy from 13.4 kcal/mol to 1.3 kcal/mol. The model is shown not only to be robust and transferable for the AMOEBA model, but also physically meaningful as it universally improves the description of the electrostatic potential around a given molecule.

Pauli repulsion is a key component of any theory of intermolecular interactions. 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. 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. 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. 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. 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. 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.