Refinement of Atomic Polarizabilities for a Polarizable Gaussian Multipole Force Field with Simultaneous Considerations of Both Molecular Polarizability Tensors and In-Solution Electrostatic Potentials

Atomic polarizabilities are considered to be fundamental parameters in polarizable molecular mechanical force fields that play pivotal roles in determining model transferability across different electrostatic environments. In an earlier work, the atomic polarizabilities were obtained by fitting them to the B3LYP/aug-cc-pvtz molecular polarizability tensors of mainly small molecules. Taking advantage of the recent PCMRESPPOL method, we refine the atomic polarizabilities for condensed-phase simulations using a polarizable Gaussian Multipole (pGM) force field. Departing from earlier works, in this work, we incorporated polarizability tensors of a large number of dimers and electrostatic potentials (ESPs) in multiple solvents. We calculated 1565 × 4 ESPs of small molecule monomers and dimers of noble gas and small molecules and 4742 × 4 ESPs of small molecule dimers in four solvents (diethyl ether, ε = 4.24, dichloroethane, ε = 10.13, acetone, ε = 20.49, and water, ε = 78.36). For the gas-phase polarizability tensors, we supplemented the molecule set that was used in our earlier work by adding both the 4252 monomer and dimer sets studied by Shaw and co-workers and the 7211 small molecule monomers listed in the QM7b database to a combined total of 13,523 molecular polarizability tensors of monomers and dimers. The QM7b polarizability set was obtained from quantum-machine.org and was calculated at the LR-CCSD/d-aug-cc-pVDZ level of theory. All other polarizability tensors and all ESPs were calculated at the ωB97X-D/aug-cc-pVTZ level of theory. The atomic polarizabilities were developed using all polarizability tensors and the 1565 × 4 ESPs of small molecule monomers and were then assessed by comparing them to the 4742 × 4 ab initio ESPs of small molecule dimers. The predicted dimer ESPs had an average relative root-mean-square error (RRMSE) of 9.30%, which was only slightly larger than the average fitting RRMSE of 9.15% of the monomer ESPs. The transferability of the polarizability set was further evaluated by comparing the ESPs calculated using parameters developed in another dielectric environment for both tetrapeptide and DES monomer data sets. It was observed that the polarizabilities of this work retained or slightly improved the transferability over the one discussed in earlier work even though the number of parameters in the present set is about half of that in the earlier set. Excluding the gas-phase data, for the DES monomer set, the average transfer RRMSEs were 16.25% and 10.83% for pGM-ind and pGM-perm methods, respectively, comparable to the average fitting RRMSEs of 16.03% and 10.54%; for tetrapeptides, the average transfer RRMSEs were 5.62% and 3.95% for pGM-ind and pGM-perm methods, respectively, slightly larger than 5.41% and 3.61% of the fitting RRMSEs. Therefore, we conclude that the pGM methods with updated polarizabilities achieved remarkable transferability from monomer to dimer and from one solvent to another.