Exchange Spin Coupling from Gaussian Process Regression

Heisenberg
exchange spin coupling between metal centers is essential
for describing and understanding the electronic structure of many
molecular catalysts, metalloenzymes, and molecular magnets for potential
application in information technology. We explore the machine-learnability
of exchange spin coupling beyond linear regression, which has not
been studied yet. We employ Gaussian process regression, since it
can potentially deal with small training sets (as likely associated
with the rather complex molecular structures required for exploring
spin coupling) and since it provides uncertainty estimates (“error
bars”) along with predicted values. We compare a range of descriptors
and kernels for 257 small dicopper complexes and find that a simple
descriptor based on chemical intuition, consisting only of copper–bridge
angles and copper–copper distances, clearly outperforms several
more sophisticated descriptors when it comes to extrapolating toward
larger experimentally relevant complexes. Exchange spin coupling is
similarly easy to learn as the polarizability, while learning dipole
moments is much harder. The strength of the sophisticated descriptors
lies in their ability to linearize structure–property relationships,
to the point that a simple linear ridge regression performs just as
well as the kernel-based machine-learning model for our small dicopper
data set. The superior extrapolation performance of the simple descriptor
is unique to exchange spin coupling, reinforcing the crucial role
of choosing a suitable descriptor and highlighting the interesting
question of the role of chemical intuition vs systematic or automated
selection of features for machine learning in chemistry and material
science.