| Density functional theory(DFT), with a good computing performance and low computational cost, have become indispensable research tools to understand atoms, molecules, solids and related electronic structure for chemists and physicists. Also, It have become an important tool in chemistry, condensed matter physics, material science and molecular biology. Experimentalists increasingly rely on these methods to interpret their experimental findings. Although DFT achieved great success in practical applications, it is usually not sufficiently accurate enough to predict the experimental measurements. With the increase in the number of atoms in a molecule, the deviations are increasing between the calculated values and experimental values. This is caused by the inherent approximations adopted in the DFT methods.Accuracy of a DFT calculation is mainly determined by exchange-correlation(XC) functional that is employed. But no exact XC functional is known. All DFT calculations employ the approximated XC functionals, which lead to further calculation errors. So it is great significance to look for a more accurate XC functional to improve the accuracy of DFT calculations.This paper have three parts. Firstly, support vector machine (SVM) is adopted to correct 180 free energies of small or medium organic molecules based on DFT calculations. Secondly, new B3LYP functional is constructed combined artificial neural network (ANN) with enlarged training set and the new B3LYP functional is adopted to calculate the molecular energies. Lastly, ANN is adopted to correct the transition state energy for hydroamination reaction.The main results are summarized as follows:1. SVM is adopted to correct the DFT calculation results for 180 free energies of organic molecules. The SVM correction effect is obvious. Upon correction, the root-mean-square (RMS) error for trainging set decreases from 13.0 kcal/mol to 2.7 kcal/mol, the RMS error for testing set decreases from 12.5 kcal/mol to 3.0 kcal/mol, the overall RMS error decreases from 12.9 kcal/mol to 2.8 kcal/mol.2. A neural network approach has been applied to correct three parameters (a0,ax and ac) in B3LYP method successfully, and construct new B3LYP exchange corrlection functional. A three-layer architecture which consists of an input layer, a hidden layer and an output layer, is adopted in our neural network. The total number of electrons, spin multiplicity, dipole moment, kinetic energy, quadrupole moment and zero point energy are choosen as the most important physical descriptors. In this work, 296 energy datas are randomly divided into two subsets, 246 energy datas as the training set to determine the optimized structure of neural network and the optimized synaptic weights, and 50 energy datas as testing set to test the predicting capacity of our neural network. The modified three parameters a~ 0, a~x , a~c , which are got from the output layer, are used to calculate the atomic energy (AE), ionization potential (IP), proton affinity (PA), total atomic energy (TAE) and standard heat of formation (Δf Hθ). The new results based on neural network approach are better than the results calculated by conventional B3LYP/6-311+G(3df,2p) method. Upon the neural network correction, the overall RMS error for 296 species decreases from 9.8 kcal/mol to 3.4 kcal/mol.3. Neural network approach has been successfully applied to correct the transition state energy of hydroamination reaction for 60 transition state moleculars, greatly reducing the deviation of B3LYP/6-31G(d) calculations. The free energy(ΔfGθ,based on B3LYP/6-31G(d) level), the total atom number (Nt), hydrogen atoms (Nh) and the zero point energy (ZPE) are choosen to be the most important physical descriptors to construct the Neural network model. Upon correction, the RMS error for trainging set decreases from 5.1 kcal/mol to 0.8 kcal/mol, the RMS error for testing set decreases from 5.2 kcal/mol to 1.9 kcal/mol, the overall RMS error decreases from 5.1 kcal/mol to 1.0 kcal/mol. |
