Machine learning the electronic structure of open shell transition metal complexes presents unique challenges, including robust and automated data set generation. Here, we introduce tools that simplify data acquisition from density functional theory (DFT) and validation of trained machine learning models using the molSimplify automatic design (mAD) workflow. We demonstrate this workflow by training and comparing the performance of LASSO, kernel ridge regression (KRR), and artificial neural network (ANN) models using heuristic, topological revised autocorrelation (RAC) descriptors we have recently introduced for machine learning inorganic chemistry. On a series of open shell transition metal complexes, we evaluate set aside test errors of these models for predicting the HOMO level and HOMO-LUMO gap. The best performing models are ANNs, which show 0.15 and 0.25 eV test set mean absolute errors on the HOMO level and HOMO-LUMO gap, respectively. Poor performing KRR models using the full 153-feature RAC set are improved to nearly the same performance as the ANNs when trained on down-selected subsets of 20-30 features. Analysis of the essential descriptors for HOMO and HOMO-LUMO gap prediction as well as comparison to subsets previously obtained for other properties reveals the paramount importance of non-local, steric properties in determining frontier molecular orbital energetics. We demonstrate our model performance on diverse complexes and in the discovery of molecules with target HOMO-LUMO gaps from a large 15,000 molecule design space in minutes rather than days that full DFT evaluation would require.

We employ Gaussian process (GP) regression to adjust for systematic errors in D3-type dispersion corrections. We refer to the associated, statistically improved model as D3-GP. It is trained on differences between interaction energies obtained from PBE-D3(BJ)/ma-def2-QZVPP and DLPNO-CCSD(T)/CBS calculations. We generated a data set containing interaction energies for 1,248 molecular dimers, which resemble the dispersion-dominated systems contained in the S66 data set. Our systems do not only represent equilibrium structures, but also dimers with various relative orientations and conformations at both shorter and longer distances. A reparametrization of the D3(BJ) model based on 66 of these dimers suggests that two of its three empirical parameters, a1 and s8, are zero, whereas a2 = 5.6841 bohr. For the remaining 1,182 dimers, we find that this new set of parameters is superior to all previously published D3(BJ) parameter sets. To train our D3-GP model, we engineered two different vectorial representations of (supra-)molecular systems, both derived from the matrix of atom-pairwise D3(BJ) interaction terms: (a) a distance-resolved interaction energy histogram, histD3(BJ), and (b) eigenvalues of the interaction matrix ordered according to their decreasing absolute value, eigD3(BJ). Hence, the GP learns a mapping from D3(BJ) information only, which renders D3-GP-type dispersion corrections comparable to those obtained with the original D3 approach. They improve systematically if the underlying training set is selected carefully. Here, we harness the prediction variance obtained from GP regression to select optimal training sets in an automated fashion. The larger the variance, the more information the corresponding data point may add to the training set. For a given set of molecular systems, variance-based sampling can approximately determine the smallest subset being subjected to reference calculations such that all dispersion corrections for the remaining systems fall below a predefined accuracy threshold. To render the entire D3-GP workflow as efficient as possible, we present an improvement over our variance-based, sequential active-learning scheme [J. Chem. Theory Comput. 2018, 14, 5238]. Our refined learning algorithm selects multiple (instead of single) systems which can be subjected to reference calculations simultaneously. We refer to the underlying selection strategy as batch-wise variance-based sampling (BVS). BVS-guided active learning is an essential component of our D3-GP workflow, which is implemented in a black-box fashion. Once provided with reference data for new molecular systems, the underlying GP model automatically learns to adapt to these and similar systems. This approach leads overall to a self-improving model (D3-GP) that predicts system-focused and GP-refined D3-type dispersion corrections for any given system of reference data.

Enumerated, de novo transition metal complexes have unique spin state properties and accelerate machine learning model training.