No abstract

No abstract

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 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 R2, the predictive squared correlation coefficient q2 and 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.Electronic supplementary materialThe online version of this article (doi:10.1186/s13321-016-0133-7) contains supplementary material, which is available to authorized users.

Machine learning has exhibited powerful capabilities in many areas. However, machine learning models are mostly database dependent, requiring a new model if the database changes. Therefore, a universal model is highly desired to accommodate the widest variety of databases. Fortunately, this universality may be achieved by ensemble learning, which can integrate multiple learners to meet the demands of diversified databases. Therefore, we propose a general procedure for learning ensemble establishment based on noncovalent interactions (NCIs) databases. Additionally, accurate NCI computation is quite demanding for first-principles methods, for which a competent machine learning model can be an efficient solution to obtain high NCI accuracy with minimal computational resources. In regard to these aspects, multiple schemes of ensemble learning models (Bagging, Boosting, and Stacking frameworks), are explored in this study. The models are based on various low levels of density functional theory (DFT) calculations for the benchmark databases S66, S22, and X40. All NCIs computed by the DFT calculations can be improved to high-level accuracy (root-mean-square error RMSE = 0.22 kcal/mol in contrast to CCSD­(T)/CBS benchmark) by established ensemble learning models. Compared with single machine learning models, ensemble models show better accuracy (RMSE of the best model is further lowered by ∼25%), robustness and goodness-of-fit according to evaluation parameters suggested by the OECD. Among ensemble learning models, heterogeneous Stacking ensemble models show the most valuable application potential. The standardized procedure of constructing learning ensembles has been well utilized on several NCI data sets, and this procedure may also be applicable for other chemical databases.

No abstract

Molecular excited states are important for molecular optical properties, which can be feasibly explored by quantum chemical calculations. However, the computation is highly demanding due to their complicated characteristic features. Therefore, high accuracy and unambiguous descriptions are strongly desired for excited state investigations. This paper proposes accurate, robust, and efficient ensemble correction models for absorption calculations with the most used quantum chemical method, time-dependent density functional theory (TDDFT). Models are built by AdaBoost framework with both weak machine learning: support vector machine (SVM), general regression neural network (GRNN), and an ensemble learning: the random forest (RF) regression method. With the models, the low accuracy calculations, TDDFT calculated absorption energies (λ max ) for 433 organic molecules with the minimum basis set STO-3G, are significantly improved. The mean absolute error (MAE) and the root mean square error (RMSE) of the calculated λ max are reduced from 0.62 and 0.79 eV to 0.11 and 0.14 eV, respectively. The validation parameters of the proposed correction model can reach up to R 2 (0.97), Q 2 (0.98), and Q 2 cv (0.99), which suggests the great goodness-of-fit and predictability. This investigation illustrates that the proposed ensemble correction models by sophisticated algorithms are highly efficient and accurate. Therefore, it may serve as an alternative tool to establish good correction models for TDDFT absorption calculations, which could significantly improve the accuracy of TDDFT calculations and extend machine learning algorithms on other feature calculations of excited states.

A representative dataset is crucial to build a robust and generalized machine learning model, especially for small databases. Correlation is not usually considered in distance‐based set partition methods; therefore, distant yet correlated samples might be incorrectly assigned. An improved sample subset partition method based on joint hybrid correlation and diversity x‐y distances (HSPXY) is proposed in the framework of the sample set partition based on joint x‐y distances (SPXY). Therein, a hybrid distance consisting of both cosine angle distance and Euclidean distance in variable spaces cooperates the correlation of samples in the distance‐based set partition method. To compare with some existing partition methods, partial least squares (PLS) regression models are built on four set partition methods, random sampling (RS), Kennard‐Stone (KS), SPXY, and HSPXY. Upon the applications on small chemical databases, the proposed HSPXY algorithm‐based models achieved smaller root mean square errors and better coefficients of determination than other tested set partition methods, which indicates the training set is well represented. This suggests the proposed algorithm provides a new option to obtain a representative calibration set. Sample subset partition is widely considered in machine learning modeling. An improved sample subset partition method based on a hybrid correlation and diversity x‐y distance (HSPXY) is proposed in the framework of SPXY. Cosine angle distance and Euclidean distance in variable spaces are used to represent the correlation and diversity of samples, respectively. To explore the effectiveness of HSPXY, PLS models are built on four set partition methods, RS, KS, SPXY, and HSPXY. The models based on the proposed HSPXY algorithm carried the overall best result among all regression models, which suggests the proposed algorithm may be taken as an alternative to other existing data partition methods.

No abstract