Non-bonded force field model with advanced restrained electrostatic potential charges (RESP2)

Abstract

The restrained electrostatic potential (RESP) approach is a highly regarded and widely used method of assigning partial charges to molecules for simulations. RESP uses a quantum-mechanical method that yields fortuitous overpolarization and thereby accounts only approximately for self-polarization of molecules in the condensed phase. Here we present RESP2, a next generation of this approach, where the polarity of the charges is tuned by a parameter, δ, which scales the contributions from gas- and aqueous-phase calculations. When the complete non-bonded force field model, including Lennard-Jones parameters, is optimized to liquid properties, improved accuracy is achieved, even with this reduced set of five Lennard-Jones types. We argue that RESP2 with δ≈0.6 (60% aqueous, 40% gas-phase charges) is an accurate and robust method of generating partial charges, and that a small set of Lennard-Jones types is good starting point for a systematic re-optimization of this important non-bonded term.

Fig. 1. Mean errors in electrostatic properties.

Mean errors in molecular dipole moments a and electrostatic potentials b across 71 test compounds, relative to reference double-hybrid calculations, for various QM methods. Compute time requirements, normalized to the duration of the corresponding HF/6–31G* calculations, are provided as well c.

Fig. 2. MUE with SMIRNOFF LJ parameters.

Comparison of theoretical and experimental results (MUE) as a function of the charge mixing parameter δ with SMIRNOFF LJ parameters. No parameters are optimized for these results. Separation of training and test set is kept to facilitate comparison with Fig. 3. Mean error for densities and HOV for the training set a, b and test set c, d. Mean error for the dielectric constants e of the test set, and HFE error for all molecules in the FreeSolv database and either in the test or training set f. The red line are results obtained with RESP1 charges and is used as a reference.

Fig. 3. MUE with reoptimized LJ parameters.

Comparison of theoretical and experimental results as a function of the RESP2 charge mixing parameter δ with reoptimized LJ parameters. Mean error for densities and HOV for the training set a, b and test set c, d. Mean error for the dielectric constants e for the test set, and HFE error for all molecules in the FreeSolv database and either in the test or training set f. The red lines are results obtained with RESP1 charges and smirnoff99Frosstv1.0.7 LJ parameters. The green lines are results with RESP1 charges and reoptimized LJ parameters.

Fig. 4. Average error as function of the mixing parameter δ.

Average unsigned error, relative to baseline RESP1/SMIRNOFF (red), of test set predictions as a function of the RESP2 charge mixing parameter δ with reoptimized LJ parameters (blue).

Fig. 5. Comparison of molecular dipole moments from partial charges with those obtained directly from QM calculations.

Scatter plots of molecular dipole moments based on RESP1 and RESP2_0.6 point charges against molecular dipole moments based on electron density from QM (PW6B95/aug-cc-pV(D + d)Z) calculations in gas phase a and aqueous phase b. Black line: slope of unity.

Fig. 6. Comparison of partial atomic charges generated by various methods.

Charge comparisons between RESP1 charges and RESP2 charges with a mixing parameter of 0.6 a; RESP2 gas phase and RESP2 implicit solvent charges b, and AM1-BCC and RESP1 charges c.

Fig. 7. Flow chart to generate RESP2 charges from SMILES strings.

Conformers are generated using Openeye’s Omega. QM calculations are done with psi4. Respyte is used for the ESP point selection and the charge fitting stage.

Fig. 8. Molecules used in this study.

Molecules in a were used to train new LJ models, whereas the molecules in b were used to test the new parameters. The SMILES string for each molecule is given under the chemical structure.