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). A 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 ε = 4.2) were considered in the DFT calculations. With the correction, the root mean square errors of all DFT calculations were improved by at least 70 %. 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 0.33 kcal/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 R 2, the predictive squared correlation coefficient q 2 and $$q_{cv}^{2}$$ from cross-validation) were >0.92, which suggests that the correction model has good stability, robustness and predictive power. The 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.

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 full-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.

A DFT-SOFM-RBFNN method is proposed to improve the accuracy of DFT calculations on Y-NO (Y = C, N, O, S) homolysis bond dissociation energies (BDE) by combining density functional theory (DFT) and artificial intelligence/machine learning methods, which consist of self-organizing feature mapping neural networks (SOFMNN) and radial basis function neural networks (RBFNN). A descriptor refinement step including SOFMNN clustering analysis and correlation analysis is implemented. The SOFMNN clustering analysis is applied to classify descriptors, and the representative descriptors in the groups are selected as neural network inputs according to their closeness to the experimental values through correlation analysis. Redundant descriptors and intuitively biased choices of descriptors can be avoided by this newly introduced step. Using RBFNN calculation with the selected descriptors, chemical accuracy (≤1 kcal·mol⁻¹) is achieved for all 92 calculated organic Y-NO homolysis BDE calculated by DFT-B3LYP, and the mean absolute deviations (MADs) of the B3LYP/6-31G(d) and B3LYP/STO-3G methods are reduced from 4.45 and 10.53 kcal·mol⁻¹ to 0.15 and 0.18 kcal·mol⁻¹, respectively. The improved results for the minimal basis set STO-3G reach the same accuracy as those of 6-31G(d), and thus B3LYP calculation with the minimal basis set is recommended to be used for minimizing the computational cost and to expand the applications to large molecular systems. Further extrapolation tests are performed with six molecules (two containing Si-NO bonds and two containing fluorine), and the accuracy of the tests was within 1 kcal·mol⁻¹. This study shows that DFT-SOFM-RBFNN is an efficient and highly accurate method for Y-NO homolysis BDE. The method may be used as a tool to design new NO carrier molecules.

Alpha-helical transmembrane proteins (αTMPs) play essential roles in drug targeting and disease treatments. Due to the challenges of using experimental methods to determine their structure, αTMPs have far fewer known structures than soluble proteins. The topology of transmembrane proteins (TMPs) can determine the spatial conformation relative to the membrane, while the secondary structure helps to identify their functional domain. They are highly correlated on αTMPs sequences, and achieving a merge prediction is instructive for further understanding the structure and function of αTMPs. In this study, we implemented a hybrid model combining Deep Learning Neural Networks (DNNs) with a Class Hidden Markov Model (CHMM), namely HDNNtopss. DNNs extract rich contextual features through stacked attention-enhanced Bidirectional Long Short-Term Memory (BiLSTM) networks and Convolutional Neural Networks (CNNs), and CHMM captures state-associative temporal features. The hybrid model not only reasonably considers the probability of the state path but also has a fitting and feature-extraction capability for deep learning, which enables flexible prediction and makes the resulting sequence more biologically meaningful. It outperforms current advanced merge-prediction methods with a Q4 of 0.779 and an MCC of 0.673 on the independent test dataset, which have practical, solid significance. In comparison to advanced prediction methods for topological and secondary structures, it achieves the highest topology prediction with a Q2 of 0.884, which has a strong comprehensive performance. At the same time, we implemented a joint training method, Co-HDNNtopss, and achieved a good performance to provide an important reference for similar hybrid-model training.