Simple and Accurate One-Body Energy and Dipole Moment Surfaces for Water and Beyond

Abstract

Water is often the testing ground for new, advanced force fields. While advanced functional forms for intermolecular interactions have been integral to the development of accurate water models, less attention has been paid to a transferable model for intramolecular valence terms. In this work, we present a one-body energy and dipole moment surface model, named 1B-UCB, that is simple yet accurate and can be feasibly adapted for both standard and advanced potentials. 1B-UCB for water is comparable in accuracy to those with much more complex functional forms, despite having drastically fewer parameters. The parametrization protocol has been implemented as part of the Q-Force automated workflow and requires only a quantum mechanical Hessian calculation as reference data, hence allowing it to be easily extended to a variety of molecular systems beyond water, which we demonstrate on a selection of small molecules with different symmetries.

Figure 1

Accuracy of different coupling models for the 1B MM potential. (a) RMSE to CCSD(T) Hessian and (b) absolute error in vibrational frequencies for no coupling term, various single coupling terms, and any combination of two coupling terms. Using any two coupling terms results in a RMSE smaller than 0.01 kcal mol^–1 Å^–1; thus, these are plotted together. We found that fitting the bonded terms to both the modes and frequencies created errors on the QM Hessian terms as large as 50% compared to fitting directly to Hessian. For panel b, errors smaller than 1 cm^–1 are set to zero with the assumption that this is within numerical error of our Hessian calculation.

Figure 2

Validation of the 1B MM model against the bond and angle CCSD(T) scan data. 1D scan of the (a) bonds and (b) angles for energies below 10 kbT. We obtained MAEs of 0.014 and 0.038 kcal/mol for the bond and angle energies, respectively. The maximum errors at the largest displacements were 0.06 and 0.26 kcal/mol for bond and angle energies, respectively. 2D scan of (c) QM bond–bond, (d) MM bond–bond, (e) QM bond–angle, and (f) MM bond–angle coupling energies (kcal/mol). We obtained MAEs of 0.0005 and 0.015 kcal/mol for the bond–bond and bond–angle couplings, respectively. The maximum errors at 10 kbT displacements were 0.003 and 0.11 kcal/mol for the bond–bond and bond–angle couplings, respectively.

Figure 3

Comparison of 1B potential energies between QM and MM models. (a) 7-, 10-, and 16-mer water cluster 1B energies for DFT, CCSD(T) and PS references and our model on MP2/aug-cc-pVTZ optimized structures taken from Herman and Xantheas. Our simple model has errors of 0.014, 0.026, and 0.036 kcal/mol for CC and 0.002, 0.003, and 0.006 kcal/mol for DFT for the 7-, 10-, and 16-mer water clusters, respectively. (b) Energies of our 1B model derived from DFT plotted against ωB97X-V/def2-qzvppd energies for 1200 snapshots taken from each cluster size, from 2- to 5-mers. We find MAEs of 0.007, 0.009, 0.011, and 0.013 kcal/mol and maximum errors of 0.115, 0.122, 0.113, and 0.115 kcal/mol for the 2-, 3-, 4-, and 5-mers, respectively. (c) Energies of our 1B model derived from CCSD(T) plotted against ωB97X-V/def2-qzvppd energies for 1200 snapshots taken from each cluster size, with MAEs of 0.11067, 0.1456, 0.17435, and 0.19496 kcal/mol for 2-, 3-, 4-, and 5-mers, respectively. The small cluster structures are taken from Wang et al.

Figure 4

Change in the dipole moment over angle and bond distortions. (a) Angle and (b) bond lengths are scanned for QM (DFT), MM (DFT) with and without one of the DMS corrections, and PS model. Both the CF and VS approaches give almost identical results.

Figure 5

Comparison of 1B between QM and MM models for carbon dioxide, ammonia, nitrate, and methane molecules. (a) Potential energies and total dipole moments (b) without and (c) with charge flux. The QM method is ωB97x-V/def2-qzvppd.

Figure 6

Ammonia pyramidal inversion for QM, MM, and 1B-UCB model. (a) Energies and (b) each dipole moment component. (c) Geometry at the minima and saddle point. Y axis is orthogonal to the plane of three hydrogens. X and Z are parallel to the plane of the three hydrogens, with Z pointing toward one of the hydrogens and X being orthogonal to Z.