Tuned and Balanced Redistributed Charge Scheme for Combined Quantum Mechanical and Molecular Mechanical (QM/MM) Methods and Fragment Methods: Tuning Based on the CM5 Charge Model

Tuned and balanced redistributed charge schemes have been developed for modeling the electrostatic fields of bonds that are cut by a quantum mechanical-molecular mechanical boundary in combined quantum mechanical and molecular mechanical (QM/MM) methods. First, the charge is balanced by adjusting the charge on the MM boundary atom to conserve the total charge of the entire QM/MM system. In the balanced smeared redistributed charge (BSRC) scheme, the adjusted MM boundary charge is smeared with a smearing width of 1.0 Å and is distributed in equal portions to the midpoints of the bonds between the MM boundary atom and the MM atoms bonded to it; in the balanced redistributed charge-2 (BRC2) scheme, the adjusted MM boundary charge is distributed as point charges in equal portions to the MM atoms that are bonded to the MM boundary atom. The QM subsystem is capped by a fluorine atom that is tuned to reproduce the sum of partial atomic charges of the uncapped portion of the QM subsystem. The new aspect of the present study is a new way to carry out the tuning process; in particular, the CM5 charge model, rather than the Mulliken population analysis applied in previous studies, is used for tuning the capping atom that terminates the dangling bond of the QM region. The mean unsigned error (MUE) of the QM/MM deprotonation energy for a 15-system test suite of deprotonation reactions is 2.3 kcal/mol for the tuned BSRC scheme (TBSRC) and 2.4 kcal/mol for the tuned BRC2 scheme (TBRC2). As was the case for the original tuning method based on Mulliken charges, the new tuning method performs much better than using conventional hydrogen link atoms, which have an MUE on this test set of about 7 kcal/mol. However, the new scheme eliminates the need to use small basis sets, which can be problematic, and it allows one to be more consistent by tuning the parameters with whatever basis set is appropriate for applications. (Alternatively, since the tuning parameters and partial charges obtained by the new method do not depend strongly on basis set, one can continue to use available CM5-tuned parameters even when one changes the basis set.) Furthermore, we found that, as compared to Mulliken charges, the CM5 charges describe the charge distributions in test molecules better, and they reproduce the dipole moments of full quantum mechanical calculations better; therefore the new tuning procedure is more physical and should be more reliable and robust.