Yinghua Lu

An accurate density functional theory calculation for electronic excitation energies: The least-squares support vector machine

Support vector machines (SVMs), as a novel type of learning machine, has been very successful in pattern recognition and function estimation problems. In this paper we introduce least-squares (LS) SVMs to improve the calculation accuracy of density functional theory. As a demonstration, this combined quantum mechanical calculation with LS-SVM correction approach has been applied to evaluate the electronic excitation energies of 160 organic molecules. The newly introduced LS-SVM approach reduces the root-mean-square deviation of the calculated electronic excitation energies of 160 organic molecules from 0.32 to 0.11 eV for the B3LYP/6-31G(d) calculation. Thus, the LS-SVM correction on top of B3LYP/6-31G(d) is a better method to correct electronic excitation energies and can be used as the approximation of experimental results which are impossible to obtain experimentally.

Improving the Accuracy of Density Functional Theory (DFT) Calculation for Homolysis Bond Dissociation Energies of Y-NO Bond: Generalized Regression Neural Network Based on Grey Relational Analysis and Principal Component Analysis

We propose a generalized regression neural network (GRNN) approach based on grey relational analysis (GRA) and principal component analysis (PCA) (GP-GRNN) to improve the accuracy of density functional theory (DFT) calculation for homolysis bond dissociation energies (BDE) of Y-NO bond. As a demonstration, this combined quantum chemistry calculation with the GP-GRNN approach has been applied to evaluate the homolysis BDE of 92 Y-NO organic molecules. The results show that the ull-descriptor GRNN without GRA and PCA (F-GRNN) and with GRA (G-GRNN) approaches reduce the root-mean-square (RMS) of the calculated homolysis BDE of 92 organic molecules from 5.31 to 0.49 and 0.39 kcal mol−1 for the B3LYP/6-31G (d) calculation. Then the newly developed GP-GRNN approach further reduces the RMS to 0.31 kcal mol−1. Thus, the GP-GRNN correction on top of B3LYP/6-31G (d) can improve the accuracy of calculating the homolysis BDE in quantum chemistry and can predict homolysis BDE which cannot be obtained experimentally.

An accurate and efficient method to predict the electronic excitation energies of BODIPY fluorescent dyes.

Recently, the extreme learning machine neural network (ELMNN) as a valid computing method has been proposed to predict the nonlinear optical property successfully (Wang et al., J. Comput. Chem. 2012, 33, 231). In this work, first, we follow this line of work to predict the electronic excitation energies using the ELMNN method. Significantly, the root mean square deviation of the predicted electronic excitation energies of 90 4,4‐difluoro‐4‐bora‐3a,4a‐diaza‐s‐indacene (BODIPY) derivatives between the predicted and experimental values has been reduced to 0.13 eV. Second, four groups of molecule descriptors are considered when building the computing models. The results show that the quantum chemical descriptions have the closest intrinsic relation with the electronic excitation energy values. Finally, a user‐friendly web server (EEEBPre: Prediction of electronic excitation energies for BODIPY dyes), which is freely accessible to public at the web site: http://202.198.129.218, has been built for prediction. This web server can return the predicted electronic excitation energy values of BODIPY dyes that are high consistent with the experimental values. We hope that this web server would be helpful to theoretical and experimental chemists in related research.

A machine learning correction for DFT non-covalent interactions based on the S22, S66 and X40 benchmark databases

Background Non-covalent interactions (NCIs) play critical roles in supramolecular chemistries; however, they are difficult to measure. Currently, reliable computational methods are being pursued to meet this challenge, but the accuracy of calculations based on low levels of theory is not satisfactory and calculations based on high levels of theory are often too costly. Accordingly, to reduce the cost and increase the accuracy of low-level theoretical calculations to describe NCIs, an efficient approach is proposed to correct NCI calculations based on the benchmark databases S22, S66 and X40 (Hobza in Acc Chem Rev 45: 663–672, 2012; Řezáč et al. in J Chem Theory Comput 8:4285, 2012).ResultsA novel type of NCI correction is presented for density functional theory (DFT) methods. In this approach, the general regression neural network machine learning method is used to perform the correction for DFT methods on the basis of DFT calculations. Various DFT methods, including M06-2X, B3LYP, B3LYP-D3, PBE, PBE-D3 and ωB97XD, with two small basis sets (i.e., 6-31G* and 6-31+G*) were investigated. Moreover, the conductor-like polarizable continuum model with two types of solvents (i.e., water and pentylamine, which mimics a protein environment with εxa0=xa04.2) were considered in the DFT calculations. With the correction, the root mean square errors of all DFT calculations were improved by at least 70xa0%. Relative to CCSD(T)/CBS benchmark values (used as experimental NCI values because of its high accuracy), the mean absolute error of the best result was 0.33xa0kcal/mol, which is comparable to high-level ab initio methods or DFT methods with fairly large basis sets. Notably, this level of accuracy is achieved within a fraction of the time required by other methods. For all of the correction models based on various DFT approaches, the validation parameters according to OECD principles (i.e., the correlation coefficient R2, the predictive squared correlation coefficient q2 and

An Accurate and Efficient Method to Predict Y-NO Bond Homolysis Bond Dissociation Energies

q_{cv}^{2}

SPXYE: an improved method for partitioning training and validation sets

qcv2 from cross-validation) were >0.92, which suggests that the correction model has good stability, robustness and predictive power.ConclusionsThe correction can be added following DFT calculations. With the obtained molecular descriptors, the NCIs produced by DFT methods can be improved to achieve high-level accuracy. Moreover, only one parameter is introduced into the correction model, which makes it easily applicable. Overall, this work demonstrates that the correction model may be an alternative to the traditional means of correcting for NCIs.Graphical abstractA machine learning correction model efficiently improved the accuracy of non-covalent interactions(NCIs) calculated by DFT methods. The application of the correction model is easy and flexible, so it may be an alternative correction means for NCIs by first-principle calculations.

Correlation and redundancy on machine learning performance for chemical databases

A cascaded model is proposed to establish the quantitative structure–activity relationship (QSAR) between the overall power conversion efficiency (PCE) and quantum chemical molecular descriptors of all‐organic dye sensitizers. The cascaded model is a two‐level network in which the outputs of the first level (JSC, VOC, and FF) are the inputs of the second level, and the ultimate end‐point is the overall PCE of dye‐sensitized solar cells (DSSCs). The model combines quantum chemical methods and machine learning methods, further including quantum chemical calculations, data division, feature selection, regression, and validation steps. To improve the efficiency of the model and reduce the redundancy and noise of the molecular descriptors, six feature selection methods (multiple linear regression, genetic algorithms, mean impact value, forward selection, backward elimination, and +n‐m algorithm) are used with the support vector machine. The best established cascaded model predicts the PCE values of DSSCs with a MAE of 0.57 (%), which is about 10% of the mean value PCE (5.62%). The validation parameters according to the OECD principles are R2(0.75), Q2(0.77), and Qcv2 (0.76), which demonstrate the great goodness‐of‐fit, predictivity, and robustness of the model. Additionally, the applicability domain of the cascaded QSAR model is defined for further application. This study demonstrates that the established cascaded model is able to effectively predict the PCE for organic dye sensitizers with very low cost and relatively high accuracy, providing a useful tool for the design of dye sensitizers with high PCE.

Combined Density Functional Theory and Ensembled Elman Network Correction Approach for Electronic Excitation Energies

The paper suggests a new method that combines the Kennard and Stone algorithm (Kenstone, KS), hierarchical clustering (HC), and ant colony optimization (ACO)-based extreme learning machine (ELM) (KS-HC/ACO-ELM) with the density functional theory (DFT) B3LYP/6-31G(d) method to improve the accuracy of DFT calculations for the Y-NO homolysis bond dissociation energies (BDE). In this method, Kenstone divides the whole data set into two parts, the training set and the test set; HC and ACO are used to perform the cluster analysis on molecular descriptors; correlation analysis is applied for selecting the most correlated molecular descriptors in the classes, and ELM is the nonlinear model for establishing the relationship between DFT calculations and homolysis BDE experimental values. The results show that the standard deviation of homolysis BDE in the molecular test set is reduced from 4.03u2009kcalu2009mol−1 calculated by the DFT B3LYP/6-31G(d) method to 0.30, 0.28, 0.29, and 0.32u2009kcalu2009mol−1 by the KS-ELM, KS-HC-ELM, and KS-ACO-ELM methods and the artificial neural network (ANN) combined with KS-HC, respectively. This method predicts accurate values with much higher efficiency when compared to the larger basis set DFT calculation and may also achieve similarly accurate calculation results for larger molecules.