Genetic Algorithm Optimization of Point Charges in Force Field Development: Challenges and Insights

Abstract

Evolutionary methods, such as genetic algorithms (GAs), provide powerful tools for optimization of the force field parameters, especially in the case of simultaneous fitting of the force field terms against extensive reference data. However, GA fitting of the nonbonded interaction parameters that includes point charges has not been explored in the literature, likely due to numerous difficulties with even a simpler problem of the least-squares fitting of the atomic point charges against a reference molecular electrostatic potential (MEP), which often demonstrates an unusually high variation of the fitted charges on buried atoms. Here, we examine the performance of the GA approach for the least-squares MEP point charge fitting, and show that the GA optimizations suffer from a magnified version of the classical buried atom effect, producing highly scattered yet correlated solutions. This effect can be understood in terms of the linearly independent, natural coordinates of the MEP fitting problem defined by the eigenvectors of the least-squares sum Hessian matrix, which are also equivalent to the eigenvectors of the covariance matrix evaluated for the scattered GA solutions. GAs quickly converge with respect to the high-curvature coordinates defined by the eigenvectors related to the leading terms of the multipole expansion, but have difficulty converging with respect to the low-curvature coordinates that mostly depend on the buried atom charges. The performance of the evolutionary techniques dramatically improves when the point charge optimization is performed using the Hessian or covariance matrix eigenvectors, an approach with a significant potential for the evolutionary optimization of the fixed-charge biomolecular force fields.

Electrostatic point charge fitting as an inverse problem: Revealing the underlying ill-conditioning

“…The corresponding largecurvature-or "stiff" 32,33 -Hessian eigenvectors u i can still be related to the corresponding multipoles Q l m . This explains previously observed correspondence between the highestcurvature Hessian eigenvectors and the total charge and the dipole moment components; 38,40 this correspondence quickly breaks down for the higher multipole moments.…”

“…4), which is reproduced with only a slight numerical deviation (<0.01), a consequence of the molecular charge density spillover beyond the solvent-accessible surface defining the vdW grid. 38,40 Although the other singular vectors do not exactly match the corresponding spherical harmonics, the u 2 -u 4 vectors can . (50)) and the totalcharge constraint on the values of atom-centered PCs of methanol and the RMSD (kcal/mol).…”

“…38,39 Because of the 2-3 order of magnitude variation of the κ i values, different sets of PCs can produce essentially the same MEP, as these solutions have the same positions along the high-curvature directions, although the positions along the low-curvature directions could be quite different. 38 Importantly, the eigenvectors with the largest curvatures usually correspond to the total charge and dipole moment components of the molecule, while the lowercurvature eigenvectors do not seem to be associated with particular multipole moments. 38,40 However, the exact physical origin of the correspondence between the large curvature eigenvectors and the first terms of the multipole expansion is unclear, along with the nature of the low-curvature eigenvectors.…”

Topochemical Transformations of CaX2 (X=C, Si, Ge) to Form Free‐Standing Two‐Dimensional Materials

“…[9] Similar loweringo f symmetry has also been reported forl arger two-dimensional fragments of s-triazenes. [37] Nevertheless, intercalation of Ca II within the silicene layers is shown to quench the PJT distortion in the B(h) phase, therebym aking the Si 6 rings perfectly planar (Figure 2a,b).…”

Transferable Atomic Multipole Machine Learning Models for Small Organic Molecules

“…With ML we refer to statistical algorithms that extract correlations by training on input/output data, and that improve in predictive power as more training data is added [18]. While ML models for the fitting of potential energies have been in use for decades [19], the possibility to infer point charges, MTPs and polarizabilities has been investigated only recently [20][21][22][23]. These approaches interpolate between a large number of conformations to accurately describe the effects of changes in the geometry.…”