Neural Network Optimization Of Semi-empirical Parameter In Density Functional Approximation

At present, machine learning and data mining have become a hot research area because of the explosive growth of the amount of data and the rapid development of information technology. Machine learning has been applied to not only robotics, pat-tern recognition, translation, and medicine, but also to physics, chemistry and mate-rial science. In this paper, we introduce the application of machine learning to im-prove the computational accuracy of density functional theory (DFT). In the previous studies, GuanHua Chen group and Xin Xu group had combined DFT with machine learning to correct the DFT calculated results. The method gives more accurate results than conventional DFT in the calculation of heat of formations(HOFs), bond dissoci-ation enthalpy, isomerization enthalpies, etc. At present, most of the researchers use the machine learning just to correct energies after the DFT calculation. In 2004, Xi-ao Zheng and co-workers employed a neural network approach to construct the accu-rate exchange-correlation functional of Becke's 3 parameter functional (B3LYP). The method integrates neural network with XC functional and gives more accurate results than conventional B3LYP calculations in atomization energies (AEs), ionization poten-tials (IPs), proton affinities (PAs) and total atomic energies (TAEs). They developed a promising new approach to consruct the accurate DFT exchange correlation functional.In this thesis, we combine machine learning with long-range correction scheme for exchange functionals to B88 exchange + Lee-Yang-Parr correlation exchange func-tional (LC-BLYP). Based on neural network we get the better ? (? is a parameter that determines the ratio of the short-range part and long-range part) for each particle to construct the exchange correlation. We use 362 particles (include molecules, atoms,radicals, etc) and 368 energies (include AEs, HOFs, IPs, etc). It leads to better agree-ment between the first-principles calculations and the accurate energy data. The mean absolute error (MAE) of AEs in training set is reduced from 13.33kcal/mol to 5.49k-cal/mol, and that of HOFs from 26.50kcal/mol to 10.51kcal/mol. The new functional is further tested with 13 HOFs, 19 IPs, 16 EAs and 14 reaction barriers of Diels-Alder re-actions. The MAE of HOFs in test set is reduced from 21.71kcal/mol to 10.68kcal/mol.The calculated IPs, EAs and reaction barriers by our method exhibit good agreements with experimental data.