Optimization of Lennard–Jones Parameters for Induced Dipole Polarizable Gaussian Multipole Force Field

The van der Waals potential is an integral component in molecular mechanics force fields. In this work, we document our effort to develop the parameters for the Lennard-Jones (LJ) 12-6 potential as part of our effort to develop a polarizable Gaussian multipole force field. Starting from the GAFF2 van der Waals parameter set, atom types were assigned using the Antechamber program in the AMBER24 simulation package. Atomic charges and permanent dipoles were calculated via PCMRESP, based on electrostatic potentials computed at the MP2/aug-cc-pVTZ//MP2/6-311++G(d,p) level in four solvents with dielectric constants ranging from 4.24 to 78.36. The optimization of the LJ parameters was conducted in two stages. In the first stage, we employed CCSD(T)/CBS interaction energies of about 4.6 million dimer conformations, including those from Shaw and co-workers, and applied an iterative least-squares fitting procedure. This reduced the Boltzmann factor-weighted root-mean-square error (RMSE) from 2.44 to 0.97 kcal/mol. When tested on 161 neat liquids, the simulated densities yielded an average unsigned percent error of 5.3% from the experimental values. In the second stage, the parameters were further refined by comparing simulated and experimental densities of the same 161-liquid training set using a gradient-guided iterative search based on short molecular dynamics simulations. After 24 iterations, the average unsigned percent error was reduced to 1.71%. Extended 10 ns simulations yielded an average unsigned percent error of 1.69% for the training set densities, which compares favorably with the 2.45% error obtained from GAFF2. The RMSE for heats of vaporization (<i>H</i>_vap) was 1.39 kcal/mol. This result is encouraging, even though it is slightly higher than the 1.23 kcal/mol RMSE from GAFF2 because <i>H</i>_vap was not used in the training, where energetic terms, including <i>H</i>_vap, were part of the training data in GAFF2. Evaluations on a test set further demonstrated that the optimized parameters reproduce experimental densities and <i>H</i>_vap with errors of 1.25% and 1.50 kcal/mol, respectively; both are better than GAFF2, which yielded 1.62% and 2.43 kcal/mol errors, respectively. Given GAFF2's broad adoption and independent validation by the broad community, we consider the accuracy of the optimized pGM LJ parameters to be acceptable.