Intrinsic Bond Energies from a Bonds-in-Molecules Neural Network

Intrinsic Bond Energies from a Bonds-in-Molecules Neural Network

Kun YaoOrcid, John E. Herr, Seth N. BrownOrcid, and John Parkhill*

View Author Information
Cite this: J. Phys. Chem. Lett. 2017, 8, 12, 2689–2694
Publication Date:June 2, 2017
https://doi.org/10.1021/acs.jpclett.7b01072
Copyright 2017 American Chemical Society
RIGHTS & PERMISSIONS


Abstract

Neural networks are being used to make new types of empirical chemical models as inexpensive as force fields, but with accuracy similar to the ab initio methods used to build them. In this work, we present a neural network that predicts the energies of molecules as a sum of intrinsic bond energies. The network learns the total energies of the popular GDB9 database to a competitive MAE of 0.94 kcal/mol on molecules outside of its training set, is naturally linearly scaling, and applicable to molecules consisting of thousands of bonds. More importantly, it gives chemical insight into the relative strengths of bonds as a function of their molecular environment, despite only being trained on total energy information. We show that the network makes predictions of relative bond strengths in good agreement with measured trends and human predictions. A Bonds-in-Molecules Neural Network (BIM-NN) learns heuristic relative bond strengths like expert synthetic chemists, and compares well with ab initio bond order measures such as NBO analysis.

Supporting Information
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.7b01072.

More at link: https://pubs.acs.org/doi/suppl/10.1021/acs.jpclett.7b01072/suppl_file/jz7b01072_si_001.pdf
.................


Molecular Geometry Prediction using a Deep Generative Graph Neural Network

Elman Mansimov, Omar Mahmood, Seokho Kang & Kyunghyun Cho
Scientific Reports volume 9, Article number: 20381 (2019) Cite this article



Abstract

A molecule’s geometry, also known as conformation, is one of a molecule’s most important properties, determining the reactions it participates in, the bonds it forms, and the interactions it has with other molecules. Conventional conformation generation methods minimize hand-designed molecular force field energy functions that are often not well correlated with the true energy function of a molecule observed in nature. They generate geometrically diverse sets of conformations, some of which are very similar to the lowest-energy conformations and others of which are very different. In this paper, we propose a conditional deep generative graph neural network that learns an energy function by directly learning to generate molecular conformations that are energetically favorable and more likely to be observed experimentally in data-driven manner. On three large-scale datasets containing small molecules, we show that our method generates a set of conformations that on average is far more likely to be close to the corresponding reference conformations than are those obtained from conventional force field methods. Our method maintains geometrical diversity by generating conformations that are not too similar to each other, and is also computationally faster. We also show that our method can be used to provide initial coordinates for conventional force field methods. On one of the evaluated datasets we show that this combination allows us to combine the best of both methods, yielding generated conformations that are on average close to reference conformations with some very similar to reference conformations.

Introduction

The three-dimensional (3-D) coordinates of atoms in a molecule are commonly referred to as the molecule’s geometry or conformation. The task, known as conformation generation, of predicting possible valid coordinates of a molecule, is important for determining a molecule’s chemical and physical properties1. Conformation generation is also a vital part of applications such as generating 3-D quantitative structure-activity relationships (QSAR), structure-based virtual screening and pharmacophore modeling2. Conformations can be determined in a physical setting using instrumental techniques such as X-ray crystallography as well as using experimental techniques. However, these methods are typically time-consuming and costly.

A number of computational methods have been developed for conformation generation over the past few decades2. Typically this problem is approached by using a force field energy function to calculate a molecule’s energy, and then minimizing this energy with respect to the molecule’s coordinates. This hand-designed energy function yields an approximation of the molecule’s true potential energy observed in nature based on the molecule’s atoms, bonds and coordinates. The minimum of this energy function corresponds to the molecule’s most stable configuration. Although this approach has been commonly used to generate a geometrically diverse set of conformations with certain conformations being similar to the lowest-energy conformations, it has been shown that molecule force field energy functions are often a crude approximation of actual molecular energy3.

In this paper, we propose a deep generative graph neural network that learns the energy function from data in an end-to-end fashion by generating molecular conformations that are energetically favorable and more likely to be observed experimentally4. This is done by maximizing the likelihood of the reference conformations of the molecules in the dataset. We evaluate and compare our method with conventional molecular force field methods on three databases of small molecules by calculating the root-mean-square deviation (RMSD) between generated and reference conformations. We show that conformations generated by our model are on average far more likely to be close to the reference conformation compared to those generated by conventional force field methods i.e. the variance of the RMSD between generated and reference conformations is lower for our method. Despite having lower variance, we show that our method does not generate geometrically similar conformations. We also show that our approach is computationally faster than force field methods.

A disadvantage of our model is that in general for a given molecule, the best conformation generated by our model lies further away from the reference conformation compared to the best conformation generated by force field methods. We show that for the QM9 small molecule dataset, the best of both methods can be combined by using the conformations generated by the deep generative graph neural network as an initialization to the force field method.

Conformation Generation

We consider a molecule as an undirected, complete graph G = (V, E), where V is a set of vertices corresponding to atoms, and E is a set of edges representing the interactions between pairs of atoms from V. Each atom is represented as a vector vi ∈ Rdv of node features, and the edge between the i-th and j-th atoms is represented as a vector eij ∈ Rde of edge features. There are M vertices and M(M − 1)/2 edges. We define a plausible conformation as one that may correspond to a stable configuration of a molecule. Given the graph of a molecule, the task of molecular geometry prediction is the generation of a set of plausible conformations Xa = (xa1,…,xaM), where xai∈R3 is a vector of the 3-D coordinates of the i-th atom in the a-th conformation

More at link: https://www.nature.com/articles/s41598-019-56773-5