(144h) Toward a New Generation of Reactive and Non-Reactive Force Fields: Charge Equilibration and Electrostatic Energy Improvments

In principle, ab initio quantum mechanics (QM) can provide information about the structure and different properties of the materials but it is far beyond the current QM capabilities to simulate systems with more than several thousand atoms. Instead, molecular mechanics and molecular dynamics (MD) methods are utilized for large systems where force fields (FF) are used. QM and density functional theory (DFT) calculations are among the most relevant methods to develop FFs functions and parameter sets.

However, until recently the properties of materials was a challenge to periodic and non-periodic ab-initio calculations. Non-periodic calculations that are able to predict correctly the non-covalent interaction are too expensive computationally and it is constrained to some tens of atoms. The most popular ab-initio method due to its less expensive requirements is DFT (scaling of N³ or N⁴, with N number of orbitals), but this does not capture the dispersive forces correctly. Many research groups have added empirical parameters to the different DFT functionals to handle the inaccuracy of DFT methods for capturing the non-covalent forces correctly but keeping the scalability. Many popular approaches include: the Grimme corrections, the M05-12 family and PBE-ulg. Our group has proposed the PBE-ulg method which performs DFT calculations in periodic system that correctly captures the non-covalent interaction within 2 kcal/mol, which is in the range of chemical accuracy.

These improvements can be used to improve the quality of available FFs which is of much current interest. As the first step, the non-bond (Coulomb, hydrogen bond, and van der Waals) energy terms are considered. Once they are understood, covalent energy terms can be developed easily. Among non-bond energy terms, the Coulomb energy or, equivalently, charge calculation is of critical importance. Our group proposed charge calculation and equilibration methods (Qeq). In contrast to other charge calculation methods, Qeq allows charges to respond and readjust to match the electrostatic environment. We utilized high quality QM calculations to compute charges using Mulliken population method. Then, a training set was constructed using these reference charges to train Qeq parameters for the first 18 elements of the periodic table. The training set contains more than 500 cases that includes combination of atoms in separate molecules. Large number of test cases were also generated to validate the developed parameters and in all cases good agreement was found between Qeq and QM charges. To further validate the results, several probe molecules were used to scan the attractive and repulsive parts of the energy curve for a wide variety of interest molecules. In all cases, encouraging agreement was found between the computed energy by FF and that of QM. This indicates a promising future in development of the next generation of the FFs.