Big Data Meets Quantum Chemistry Approximations: The Δ-Machine Learning Approach

TLDR

Quantum‑chemical exploration of all possible molecules is limited by the high computational cost of accurate methods. The authors propose a composite approach that augments inexpensive legacy quantum methods with machine‑learning corrections. After training, the ML‑corrected model predicts enthalpies, free energies, entropies, and electron‑correlation energies for much larger molecular sets than the training data. The method attains chemical accuracy for thermochemical properties of up to 16,000 C₇H₁₀O₂ isomers, predicts post‑Hartree–Fock correlation energies at Hartree–Fock cost, links entropy to correlation, and transfers to semi‑empirical QM with 1–10 % training data to reproduce DFT‑level enthalpies for the remaining 134,000 molecules.

Abstract

Chemically accurate and comprehensive studies of the virtual space of all possible molecules are severely limited by the computational cost of quantum chemistry. We introduce a composite strategy that adds machine learning corrections to computationally inexpensive approximate legacy quantum methods. After training, highly accurate predictions of enthalpies, free energies, entropies, and electron correlation energies are possible, for significantly larger molecular sets than used for training. For thermochemical properties of up to 16k constitutional isomers of C$_7$H$_{10}$O$_2$ we present numerical evidence that chemical accuracy can be reached. We also predict electron correlation energy in post Hartree-Fock methods, at the computational cost of Hartree-Fock, and we establish a qualitative relationship between molecular entropy and electron correlation. The transferability of our approach is demonstrated, using semi-empirical quantum chemistry and machine learning models trained on 1 and 10\% of 134k organic molecules, to reproduce enthalpies of all remaining molecules at density functional theory level of accuracy.