"Feather" corrections to electron-electron interactions & MOPAC/MOZYME model consistency

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This is not quite a bug, but rather a small numerical inconsistency between how some semiempirical models are implemented between MOPAC and MOZYME calculations.

To enable efficient calculations, MOZYME uses a fast, approximate algorithm for electrostatics. Fast, high-accuracy algorithms such as the fast multipole method (FMM) do exist, but MOZYME uses a simpler, more approximate algorithm that only sums charges within a cutoff radius of each source charge and replaces the omitted charge with a spherical shell of counter charge, effectively equivalent to the method of Wolf et al.. This algorithm requires electron-electron interactions to rapidly approach a point-to-point Coulomb interaction, which is not the case for the Klopman-Ohno form used by all MNDO-family models. During the development of the PM7 model, a "feather" correction was introduced that smoothly transitions between the Klopman-Ohno form and a point-to-point Coulomb interaction at a 7 Angstrom separation. While the Wolf algorithm is accurate enough for charge distributions of typical biomolecules to be numerically interoperable with exact electrostatics, the "feather" correction introduces a small, but more noticeable numerical distortion. As a result, the PM7 and PM6-ORG models were developed for native use with the "feather" correction in both MOPAC and MOZYME calculations, although this correction was not made clear in the literature specification of these models. For all other semiempirical models, the "feather" correction is a necessary approximation that is needed specifically in MOZYME calculations and may cause a heat discrepancy with the corresponding MOPAC calculation. From limited testing, this discrepancy is around 0.1 kcal/mol per atom, and it should not have much effect on the shape of the potential energy surface or heat differences between similar systems.

Without a substantial investment in overhauling the fast electrostatics algorithm of the MOZYME solver, this discrepancy cannot be removed without altering the definition of old, established semiempirical models. To facilitate testing of this numerical issue, a new keyword (FEATHER) will be added to MOPAC in the near future to enable the "feather" correction in MOPAC calculations.