The article presents a deep learning approach, called Deep Tensor Neural Network (DTNN), that integrates quantum mechanics with machine learning to provide spatially and chemically resolved insights into the quantum-mechanical properties of molecular systems. The DTNN model is designed to be size-extensive and uniformly accurate, achieving an accuracy of 1 kcal mol⁻¹ in predicting molecular energies across compositional and configurational chemical space for molecules of intermediate size. The model's ability to capture complex quantum-chemical phenomena is demonstrated through various applications, including the classification of aromatic rings based on their stability, prediction of atomic energies and local chemical potentials, and reliable isomer energies. The DTNN's performance is validated using large datasets of molecular structures and properties, and it shows promise for advancing the discovery of chemicals with desired properties. The article also discusses the mathematical construction of the DTNN model, which provides a statistically rigorous partitioning of molecular properties into atomic contributions, addressing a long-standing challenge in quantum mechanics.The article presents a deep learning approach, called Deep Tensor Neural Network (DTNN), that integrates quantum mechanics with machine learning to provide spatially and chemically resolved insights into the quantum-mechanical properties of molecular systems. The DTNN model is designed to be size-extensive and uniformly accurate, achieving an accuracy of 1 kcal mol⁻¹ in predicting molecular energies across compositional and configurational chemical space for molecules of intermediate size. The model's ability to capture complex quantum-chemical phenomena is demonstrated through various applications, including the classification of aromatic rings based on their stability, prediction of atomic energies and local chemical potentials, and reliable isomer energies. The DTNN's performance is validated using large datasets of molecular structures and properties, and it shows promise for advancing the discovery of chemicals with desired properties. The article also discusses the mathematical construction of the DTNN model, which provides a statistically rigorous partitioning of molecular properties into atomic contributions, addressing a long-standing challenge in quantum mechanics.