Machine learning based approaches for describing the electronic properties of molecules and materials have been recently approached by several pioneering reports in the literature. Pereira et al. used various nonlinear regression models including neural network (NN) method to predict the orbital energies of 111k molecules consisted of several main group elements. Ramakrishnan and Lilienfeld introduced a property-invariant kernel for the machine learning models in predicting the various electronic and thermodynamic properties, including E H , E L , and ΔE HL , out of 110k organic molecules. Both Coulomb matrix 1 and bag-of-bonds 2 descriptors, being in conjunction with supplying three dimensional molecular structures, were adopted to represent the chemical space, and the results were close to the level of chemical accuracy at 1 kcal/mol (~0.043 eV). Huan et al. developed a class of hierarchal motif-based fingerprints to represent the molecular structures, and the fingerprints were classified as the zeroth-to thirdorder expressions, as being described in the format of multi-dimensional vectors. The average predicted error of ΔE HL was reported to be about 0.2 eV. Browning et al. introduced the generic algorithm optimization of training set approach, in which the training set was categorized as 10 classes subject to the targeted property, and the average predicted error was improved as 0.173, 0.243, 0.317 eV for the energies of E H , E L , and ΔE HL , respectively. Faber et al. reported a comprehensive comparison using the various combination of regressor/representation/property, and the predicted results were shown to outperform the hybrid functional of Density Functional Theory (DFT) for describing the electronic ground-state properties of organic molecules in QM9 dataset. Among their predicted 13 electronic properties, the mean absolute error (MAE) of E H , E L , and ΔE HL were up to 0.228, 0.373, 0.441 eV, respectively, using linear model with elastic net regularization (0.221/0.367/0.430 eV with linear Bayesian ridge regression model). It should be noted that MAE of E H , E L , and ΔE HL can be generally reduced to half in respect to the linear results if the non-linear models (Kernel ridge regression or random forest) were adopted while the use of NN approach was shown to go well beyond the accuracy of hybrid DFT. Gilmer et al. reported the message passing neural network (MPNN) models for the predictions of quantum chemistry properties. Schütt et al. introduced a deep learning model (SchNET) and provided the predictions of E H , E L , and ΔE HL to satisfy the level of chemical accuracy. Such an apparent improvement required the use of three dimensional Cartesian coordinates of molecules for generating atom embedding, and these atomistic coordinates were calculated at Density Functional Theorya computational demanding theory level for constructing a dataset of thousands molecules.