Assessment of Predicting Frontier Orbital Energies for Small Organic Molecules Using Knowledge-Based and Structural Information

Abstract

A systematic comparison is demonstrated for the predictions of frontier orbital energies�highest occupied molecular orbital (HOMO) (E H ), lowest unoccupied molecular orbital (LUMO) (E L ), and energy gap (ΔE HL ) of the molecules in the QM9 dataset, where it contains 120k-plus three-dimensional organic molecule structures determined by first-principles simulations. The target molecular properties (E H , E L , and ΔE HL ) are predicted using linear regression (LR), machine learning (random forest, RF), and continuous-filter convolutional neural network (SchNET) approaches. LR and RF models built upon various knowledge-based descriptors, being derived from SMILES of the molecules, can provide predictivity of the target properties with the mean absolute errors (MAEs) 4−6 times the chemical accuracy (0.043 eV). The best approach, SchNET, using the graph representation derived from molecular Cartesian coordinates, is confirmed to provide MAEs of E H , E L , and ΔE HL at 0.051, 0.041, and 0.076 eV, respectively. With the introduction of bond-step matrix representation with the SchNET model, the computational cost of dataset preparation can be substantially reduced, and the corresponding MAEs increase moderately to 2−3 times the chemical accuracy. The chemical interpretation of the important descriptors identified in the LR and RF models appears to align with the chemical knowledge of describing these molecular electronic properties but is accompanied with tolerable prediction errors. The combination of bond-step representation and the SchNET model can provide an assessable and balanced option for the highthroughput screening of organic molecules and the development of the data science approach.

Enhanced Predictions for the Experimental Photophysical Data Using the Featurized Schnet-Bondstep Approach

“…Through the recursive interaction refinements, the atom-wise contributions subject to given target molecular properties can be well allocated, and that can consequently lead to the quantitative predictions of molecular properties . The quality of the interatomic distances, the extent of physical meaning contained in these interatomic representations, was found to play an essential role in affecting the accuracy of molecular property predictions by the SchNET model …”

“…The QM9 data set was used for the predictions of E H , E L , and Δ E HL . The partition sizes of the training set, validation set, and testing set were 87000, 1560, and 43620, respectively, and remained identical with the previous Schnet-bs model . The current partitions including the corresponding molecules of each subset remained unchanged for all of the reported models in this study.…”

“…Ye et al reported the use of the bondstep matrix, i.e. a type of low-dimensional bonding information derived directly from SMILES, with the SchNET model (denoted as the Schnet-bs model) to substantially reduce the effort of data preparation . However, the corresponding errors by the Schnet-bs model were sacrificed to marginally lower than 0.1 eV for predicting E H , E L , and Δ E HL .…”

“…a type of low-dimensional bonding information derived directly from SMILES, with the SchNET model (denoted as the Schnet-bs model) to substantially reduce the effort of data preparation . However, the corresponding errors by the Schnet-bs model were sacrificed to marginally lower than 0.1 eV for predicting E H , E L , and Δ E HL . Joung et al integrated the environment effect to their deep learning graph convolution network approach for simultaneously and directly predicting several experimental photophysical properties, including absorption/emission peak position and bandwidth, extinction coefficient, PLQY, and lifetime …”

Machine Learning Frontier Orbital Energies of Nanodiamonds

“…Machine learning frontier orbital energies of molecules and materials has been the subject of previous investigations. A range of studies focused on learning frontier orbital energies and related properties for optimizing solar photovoltaic materials. − Further studies explored the use of different molecular descriptors, ,− investigated structure–property relationships, , compared different DFT functionals, and presented improved learning strategies . Additionally, networks such as SchNOrb and PhiSNet that directly predict electronic wave functions can be used to predict orbital energies as well.…”