Improving The Accuracy Of Density-Functional Theory Calculation For Absorption Energies: Neural Network And Genetic Algorithm

Absorption energy is a significant physical property for a molecule, which impliesinherent structure information and electronic properties. In this regard, the accurate predictionof the absorption energy is of great significance in computational chemistry. Quantumchemical methods have been developed beyond the level of just reproducing experimentaldata and can now accurately predict the absorption energies which are unknown or uncertainexperimentally. However, the calculation results are not accurate enough for all systems,especially for large systems. This is caused by the inherent approximations adopted infirst-principles methods. To resolve this, simple yet efficient way to correct such errors isdesired.In the present work, genetic algorithm, neural network, neural network ensemble andk-nearest-neighbors approaches have been applied to improve the calculation accuracy ofquantum chemical methods for absorption energies of 150 small organic molecules. Thesecombined methods can greatly eliminate the systemic errors of theoretical calculation andimprove the calculation accuracy of density functional theory (DFT) for absorption energies,which provide a novel tool for predicting the properties of the molecules.Our work has been focus on following aspects:1. The combination of genetic algorithm and neural network correction approach(GANN) has successfully improved the calculation accuracy of the absorption energies afterquantum chemical methods calculated UV-visible absorption spectra. The raw calculatedabsorption energies are evaluated by TDDFT/B3LYP method. In this GANN approach, GA isadopted in searching the optimal initial synaptic weights for neural networks of pre-specifiedtopology, while BP is employed in further training the neural networks to find the optimalfinal synaptic weights. It is employed to reduce the errors of calculated absorption energy of150 molecules. Upon the traditional BP neural networks correction approach, the RMSdeviation of the calculated absorption energies of 150 organic molecules is reduced from 0.47eV to 0.22 eV for the TDDFT/B3LYP/6-31G(d) calculation. With the GANN correction, theRMS deviation is reduced from 0.47 eV to 0.16 eV. This combined GANN correctionapproach avoids being trapped at local minima of the traditional BPN approach, thus leads toimproved DFT calculation results as compared to those of BPN.2. The generalization ability of NN can be substantially improved by using an averagingtechnique with a neural network ensemble (NNE). We use bagging on the training set togenerate six individual base BP networks. The NNE with simple averaging method (NNEA)and weighted averaging method (NNEW) is adopted as for combining the predictions ofcomponent NNs. The experimental data of 150 organic molecules are randomly divided into atraining set with 120 molecules and a testing set with 30 molecules. The BPN, NNEA andNNEW approaches reduce the RMS deviations from 0.48 to 0.20 and both 0.22 eV for the120 absorption energies, respectively. For the 30 absorption energies, they are from 0.41 to0.26, 0.20 and 0.18 eV. Statistical tests show that generalization errors of the NNE approach is significantly lower than that of the TDDFT/B3LYP method, and they attain still lower errors than BPN.3. In this paper, we propose an ensemble of NNs and the KNN approach (NNEKNN) to improve the calculation accuracy of DFT. The traditional artificial feed-forward NN is a memoryless approach. This means that after training is complete all information about the input patterns is stored in the NN weights and the input data is no longer needed. Contrary to that, the k-nearest-neighbors (KNN) approach represents the memory-based approach. The approach keep in memory the entire database of examples, and their predictions are based on some local approximation of the stored examples. The approach is applied to predict the optical absorption energies of 150 organic molecules. This method uses the distance between ensemble responses and the neighbors in the training set as a measure amid the analyzed cases for the nearest neighbor technique. The NNEKNNA and NNEKNNW approach improved DFT calculation results and reduced the RMS deviations from 0.48 to both 0.16 eV for the training set of 120 organic molecules, respectively, while for the testing set of 30 organic molecules, they are from 0.41 to 0.14 and 0.10 eV. Simulation results and comparison of the BPN and NNE corrected values demonstrates the feasibility and effectiveness of the NNEKNN approach to reduce the calculation errors of DFT and it could indeed predict the absorption energies with higher accuracy.