Combined quantum mechanical and molecular mechanical methods for calculating potential energy surfaces: Tuned and balanced redistributed-charge algorithm

The combined quantum mechanical and molecular mechanical (QM/MM) method is one of the most powerful approaches for including correlation and polarization effects in simulations of large and complex systems, and the present article is concerned with the systematics of treating a QM/MM boundary that passes through a covalent bond, especially a polar covalent bond. In this study, we develop a new algorithm to treat such boundaries; the new method is called the balanced redistributed charge (balanced RC or BRC) scheme with a tuned fluorine link atom. The MM point charge on the MM boundary atom is modified to conserve the total charge of the entire system, and the modified charge is redistributed to the midpoints of the bonds between an MM boundary atom and its neighboring MM atoms. A pseudopotential is added to the fluorine link atom to reproduce the partial charge of the uncapped portion of the QM subsystem. We select proton affinities as the property used to validate the new method because the energy change associated with the addition of an entire charge (proton) to the QM system is very sensitive to the treatment of electrostatics at the boundary; we apply the new method to calculate proton affinities of 25 molecules with 13 different kinds of bonds being cut. The average proton affinity in the test set is 373 kcal/mol, and the test set provides a more challenging test than those usually used for testing QM/MM methods. For this challenging test set, common unbalanced schemes give a mean unsigned error (MUE) of 15-21 kcal/mol for H link atoms or 16-24 kcal/mol for F link atoms, much larger than the 5 kcal/mol obtained by simply omitting the MM region with either kind of link atom. Balancing the charges reduces the error to 5-7 kcal/mol for H link atoms and 4-6 kcal/mol for F link atoms. Balancing the charges and also tuning an F link atom lowers the MUE to 1.3-4 kcal/mol, with the best result for the balanced RC scheme. We conclude that properly tuning the link atom and correctly treating the point charges near the QM/MM boundary significantly improves the accuracy of the calculated proton affinities.