Molecular Energies Derived from Deep Learning: Application to the Prediction of Formation Enthalpies Up to High Energy Compounds

Abstract

Total electronic energies and frequencies predicted using the deep learning models ANI‐1x and ANI‐1ccx are converted to gas‐phase formation enthalpies ΔfH0 using an atom equivalent (AE) scheme for a database of CHNO compounds. As expected from the accuracy of those models in predicting reference DFT frequencies and DLPNO‐CCSD(T)/CBS energies, this procedure usually outperforms DFT‐based AE schemes. However, for some compounds, including energetic molecules, significant deviations from experiment are observed, larger than obtained using DFT procedures. A close examination of the GDB‐11 database from which the training data was drawn reveals that many structures of interest in the energetic materials community are excluded from this extensive compilation primarily focused on drug discovery and designed with stability constraints in mind. This points to the urgent need to set up a comparable database including energetic species of interest for the design of energetic materials such as propellants or explosives.

Toward Chemical Accuracy in Predicting Enthalpies of Formation with General-Purpose Data-Driven Methods

“…ANI-1ccx enthalpies of formation for the challenging data sets HEDM-45 and PAH-103 are overall better than enthalpies of formation calculated with the combination of ANI-1x/ANI-1ccx from an independent recent benchmark, especially after removing uncertain predictions as we will investigate below. MAEs of ANI-1ccx are 2.87 and 1.75 kcal/mol before removing outliers and 1.25 and 1.15 kcal/mol after removing outliers for the HEDM-45 and PAH-104 sets, respectively, compared to the respective MAEs of ANI-1x/ANI-1ccx equal to 4.34 and 2.09 kcal/mol before removing outliers and 2.50 and 1.36 kcal/mol after removing the same compounds from statistics as for ANI-1ccx (see individual errors in the SI).…”

“…21 A similar approach was adopted independently in a scheme for calculating ANI enthalpies of formation with a combination of ANI-1x and ANI-1ccx, but using a different data set. 6 The fitted atomic total energies are reported in the SI. Calculation of enthalpies of formation with AIQM1 and ANI-1ccx is implemented in MLatom 59−61 interfaced to TorchANI, 62 MNDO, 63 dftd4, 64 and Gaussian 16 65 programs.…”

“…Knowledge of the thermochemical stability of organic molecules is a central problem of many branches of chemistry and related industries . Hence, accurate thermochemical calculations are used in many applications of chemical kinetics, reaction mechanism elucidation, , materials formulations, combustion reactions, and energetic materials. − For over 50 years a need for accurate thermochemical calculations drives the development of electronic structure theory and the development of ever more sophisticated methods. ,, Reference experimental thermochemical values have served as benchmarks for evaluating new theoretical methods or as correction factors for adjusting computational protocols, − but measurements are usually difficult and costly − and reference enthalpies of formation may have significant errors . However, the availability of measured and properly calibrated uncertainties for principal thermochemical properties, such as enthalpy of formation, is often unappreciated.…”

“…15 This presents a challenge for data-driven approaches too. However, for the HEDM-45 data set previously deemed challenging for ANI, 6 the situation is more complicated, as several factors come into play. First of all, analysis of the errors of AIQM1 and ANI-1ccx for the molecules in the HEDM-45 data set shows that both methods actually do pretty well for many typical organic molecules, but there is a high level of uncertainty for a significant number of molecules, especially where many heteroatoms are in very close proximity, which is a feature of this specific database requiring many heteroatoms to ensure high energy density (Chart 1).…”

“…The potential issues with the reference experimental values may explain why even after removing unconfident predictions, Similarly, G4 and G4MP2 also fail to achieve MAEs lower than 1 kcal/mol for the PAH-103 and HEDM-45, which were previously deemed challenging 6 for AIQM1 and ANI-1ccx. After removal of uncertain predictions, both AIQM1 and ANI-1ccx come close to chemical accuracy (MAEs of 1.0 and 1.3 kcal/mol for HEDM-45 and MAEs of 0.8 and 1.2 kcal/mol for PAH-103, respectively).…”