A Universal Density Matrix Functional from Molecular Orbital-Based Machine Learning: Transferability across Organic Molecules

Lixue Cheng, Matthew Welborn, Anders S. Christensen, and Thomas F. Miller III

Highlighted by Jan Jensen

Figure 3c from the paper, showing results for MP2 correlation energies

Some years ago I wrote about the ∆-ML approach where ML is used to estimate the energy difference between expensive and cheap methods based on the molecular structure. I remember wondering at the time whether additional information could be extracted from the cheap method and used as descriptors. 

This has now been tested for correlation energies and it does indeed lead to a significant improvement in accuracy. The method uses Fock, Coulomb, and exchange matrix elements in an LMO basis (which makes me wonder why it's called a density matrix functional) and Gaussian process regression (GPR) to machine learn the LMO contributions to MP2, CCSD, and CCSD(T) correlation energies.

Using just 140 molecules with 7 heavy atoms the MOB-ML method can be trained to give reasonably accurate results for molecules with 13 heavy atoms (see figure above), and offer a significant improvement over the ∆-ML approach. An MAE of 0.25 mH/heavy atom translates into an MAE of roughly 2 kcal/mol for a molecule with 13 heavy atoms, which can translate into 4 kcal/mol ∆E-errors depending on the sign, so the method may not be quite accurate enough for many purposes yet. Unfortunately, it doesn't look like training on more molecules leads to additional improvements for transferability to larger molecules, but this is definitely a promising step in the right direction.

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