We propose a generic method to model polarization in the context of high-rank multipolar electrostatics. This method involves the machine learning technique kriging, here used to capture the response of an atomic multipole moment of a given atom to a change in the positions of the atoms surrounding this atom. The atoms are malleable boxes with sharp boundaries, they do not overlap and exhaust space. The method is applied to histidine where it is able to predict atomic multipole moments (up to hexadecapole) for unseen configurations, after training on 600 geometries distorted using normal modes of each of its 24 local energy minima at B3LYP/apc-1 level. The quality of the predictions is assessed by calculating the Coulomb energy between an atom for which the moments have been predicted and the surrounding atoms (having exact moments). Only interactions between atoms separated by three or more bonds ("1, 4 and higher" interactions) are included in this energy error. This energy is compared with that of a central atom with exact multipole moments interacting with the same environment. The resulting energy discrepancies are summed for 328 atom-atom interactions, for each of the 29 atoms of histidine being a central atom in turn. For 80% of the 539 test configurations (outside the training set), this summed energy deviates by less than 1 kcal mol(-1).

Hydrogels have applications in drug delivery, mechanical actuation, and regenerative medicine. When hydrogels are deformed, load-relaxation arising from fluid flow-poroelasticity-and from rearrangement of the polymer network-viscoelasticity-is observed. The physical mechanisms are different in that poroelastic relaxation varies with experimental length-scale while viscoelastic does not. Here, we show that poroviscoelastic load-relaxation is the product of the two individual responses. The difference in length-scale dependence of the two mechanisms can be exploited to uniquely determine poroviscoelastic properties from simultaneous analysis of multi-scale indentation experiments, providing insight into hydrogel physical behavior. V

The geometry optimization of a water molecule with a novel type of energy function called FFLUX is presented, which bypasses the traditional bonded potentials. Instead, topologically-partitioned atomic energies are trained by the machine learning method kriging to predict their IQA atomic energies for a previously unseen molecular geometry. Proof-of-concept that FFLUX’s architecture is suitable for geometry optimization is rigorously demonstrated. It is found that accurate kriging models can optimize 2000 distorted geometries to within 0.28 kJ mol−1 of the corresponding ab initio energy, and 50% of those to within 0.05 kJ mol−1. Kriging models are robust enough to optimize the molecular geometry to sub-noise accuracy, when two thirds of the geometric inputs are outside the training range of that model. Finally, the individual components of the potential energy are analyzed, and chemical intuition is reflected in the independent behavior of the three energy terms (intra-atomic), (electrostatic) and (exchange), in contrast to standard force fields.

Present computing power enables novel ways of modeling polarization. Here we show that the machine learning method kriging accurately captures the way the electron density of a topological atom responds to a change in the positions of the surrounding atoms. The success of this method is demonstrated on the four aromatic amino acids histidine, phenylalanine, tryptophan, and tyrosine. A new technique of varying training set sizes to vastly reduce training times while maintaining accuracy is described and applied to each amino acid. Each amino acid has its geometry distorted via normal modes of vibration over all local energy minima in the Ramachandran map. These geometries are then used to train the kriging models. Total electrostatic energies predicted by the kriging models for previously unseen geometries are compared to the true energies, yielding mean absolute errors of 2.9, 5.1, 4.2, and 2.8 kJ mol(-1) for histidine, phenylalanine, tryptophan, and tyrosine, respectively.