Geometry Optimization with Machine Trained Topological Atoms

Abstract

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.

Contributions of IQA electron correlation in understanding the chemical bond and non-covalent interactions

“…The interaction energy, V AB corr , of each atom with itself (A = B) or with one of the other atoms (A ≠ B) is obtained from the 2PDM via a 6D quadrature integration. The 3D ESP [51] approach was more recently developed with the intent of ultimate implementation in our polarizable multipolar [52] topological force field FFLUX [53][54][55][56][57], since 3D ESP is faster and more accurate when compared to the 6D approach. The master equation for the 3D ESP integration is given just below, where any derivation details are not repeated here but can be found in the selfcontained account of ref.…”

“…Three different types of ML techniques, that is, Random Forest (RF), Support Vector Regression (SVR), and Kriging [39,56,[66][67][68][69], were applied to predict correlation energies of three systems: the water monomer, the H 2 -He complex and the water dimer. In the first system, intramolecular-interatomic correlation energies were investigated, while in the last two, the intermolecular correlation energies are in the spotlight, since they are correlated with intermolecular dispersion forces.…”

Atomic Partitioning of the MPn (n= 2, 3, 4) Dynamic Electron Correlation Energy by the Interacting Quantum Atoms Method: A Fast and Accurate Electrostatic Potential Integral Approach

“…This restriction is the price paid for the faster algorithm presented here, and the reason for this price will become clear in the next section. However, such overall interaction between a given atom and its environment is sufficient for the development of our quantum topological based force field, called FFLUX . This force field uses kriging to deliver fully polarizable multipolar electrostatics alongside intra‐ and interatomic nonelectrostatic energies and charge transfer as a function of flexible molecular geometries.…”

“…It is only this sum that is needed. Knowing the individual terms would only be useful if detailed chemical insight were being kept track of, which can be done in principle but this is computationally expensive.…”

Perspective: new insights from loss function landscapes of neural networks

“…The first classification problem that we consider involves predicting the outcome of local minimisation for a triatomic cluster, as in previous reports [13,14,22]. Here we emphasise that we are not using machine learning to perform the optimisation [54][55][56], but instead to predict the outcome from a given starting configuration.…”