Through the comprehensive analysis of ab initio and experimental results of a large number of diatomic systems, the systematic deviation of ab initio method in vibrational energies prediction caused by physical/mathematical simplification is located. A joint ab initio and machine learning method based on information across molecules is proposed to deal with the problem. Starting from an ab initio model, and then systematically modifying it through machine learning, the vibrational energies prediction of many diatomic systems (SiC, HBr, NO, PC, N2, SiO, O2, ClF, etc.) have been improved, and significantly surpassed the more complex ab initio model. In addition to the improvement of accuracy, the new method also greatly reduces the computational expense, and is applicable for the systems without experimental data.

By systematically correcting the calculation errors through machine learning, the accuracy of the diatomic vibrational energy prediction based on typical DFT methods has been improved by order of magnitude.

The defect structure, spin Hamiltonian parameters (SHPs: anisotropic g factors g k and g ⊥ and the hyperfine structure constants A k and A ⊥ ), and their compositional dependence of Cu 2þ in xCuO À ð68 À xÞV 2 O 5 À 32TeO 2 (x = 5, 10, 20, 30 mol%) glasses are quantitatively analyzed by using the higher-order perturbation formula of octahedral complex with tetrahedral elongation distortion. Due to the Jahn-Teller effect, the ½CuO 6 10À group is subjected to tetragonal elongation distortion of varying degrees. D q , N, ρ, κ, and H show nonlinear changes with the concentrations of Cu 2þ . When x = 10 mol% CuO, the degree of distortion (ρ ≈ 0:1%) is the smallest; when x = 30 mol% CuO, the degree of distortion (ρ ≈ 15%) is the largest, which indicates that excessive distortion leads to the appearance of Z-axis oxygen vacancies and the coordination number of copper ions from six to four. The increasing tendency of the evaluated N and H reveals decreasing covalency of the whole glass system. Present theoretical studies would be useful to the explore the structural properties and optical applications of glass with different CuO concentrations. K E Y W O R D Selectron paramagnetic resonance, local structure, xCuO À ð68 À xÞV 2 O 5 À 32TeO 2 (x = 5, 10, 20, 30 mol%)

Halides play an important role in atmospheric chemistry, corrosion of steel, and in controlling the abundance of O₃.Moreover high-precision vibrational energy spectra contain a large amount of quantum information of molecular system and is essential basic data for people to understand and manipulate molecules. At present, ab-initio methods have achieved great results in the calculation of the potential energy surfaces and corresponding vibrational energies of molecules, but they still face challenges in terms of accuracy and computational cost. Recently, data-driven machine learning methods have demonstrated a very strong ability to extract high-dimensional functional relationships from massive data and have been widely used in spectroscopy studies. Therefore, a theoretical approach combining ab-initio methods and machine learning algorithms is presented here to predict the vibrational energy of diatomic systems, which improves the accuracy and simultaneously reduces the computational cost. Firstly, the vibrational energy levels of 42 diatomic molecules were obtained with different CCSD(T) method calculation configurations form simple to complex and the corresponding experimental results are also collected. A machine learning algorithm is then used to learn the difference between the calculated CCSD(T) and experimental vibrational results, and a high-dimensional error function is finally constructed to improve the original CCSD(T) computational accuracy. The results for HF, HBr, H³⁵Cl and Na³⁵Cl (they did not appear in the training set) and other halogen molecules show that the current method reduces the prediction error by more than 50% and the computational cost by nearly one order of magnitude compared with the CCSD(T)/cc-pV5Z calculation method alone. It is worth noting that the method proposed in this paper is not only limited to the energy level prediction of diatomic systems, but also can be used in other fields where data can be obtained by ab initio methods and experimental methods simultaneously, such as the energy spectrum properties of macromolecular systems.

Through the comprehensive analysis of ab initio and experimental results of a large number of diatomic systems, the systematic deviation of ab initio method in vibrational energies prediction caused by physical/mathematical simplification is located. A joint ab initio and machine learning method based on information across molecules is proposed to deal with the problem. Starting from an ab initio model, and then systematically modifying it through machine learning, the vibrational energies prediction of many diatomic systems (SiC, HBr, NO, PC, N, SiO, O, ClF, etc.) have been improved, and significantly surpassed the more complex ab initio model. In addition to the improvement of accuracy, the new method also greatly reduces the computational expense, and is applicable for the systems without experimental data.