title: A machine learning correction for DFT non-covalent interactions based on the S22, S66 and X40 benchmark databases.
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).
  
  
  RESULTS
  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 [Formula: see text] from cross-validation) were >0.92, which suggests that the correction model has good stability, robustness and predictive power.
  
  
  CONCLUSIONS
  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.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.
authors.affiliation: School of Computer Science and Information Technology, Northeast Normal University, Changchun, 130117 China.
authors.forename: Ting
authors.initials: T
authors.lastname: Gao
authors.affiliation: School of Computer Science and Information Technology, Northeast Normal University, Changchun, 130117 China.
authors.forename: Hongzhi
authors.initials: H
authors.lastname: Li
authors.affiliation: School of Computer Science and Information Technology, Northeast Normal University, Changchun, 130117 China.
authors.forename: Wenze
authors.initials: W
authors.lastname: Li
authors.affiliation: School of Computer Science and Information Technology, Northeast Normal University, Changchun, 130117 China.
authors.forename: Lin
authors.initials: L
authors.lastname: Li
authors.affiliation: School of Computer Science and Information Technology, Northeast Normal University, Changchun, 130117 China.
authors.forename: Chao
authors.initials: C
authors.lastname: Fang
authors.affiliation: School of Computer Science and Information Technology, Northeast Normal University, Changchun, 130117 China.
authors.forename: Hui
authors.initials: H
authors.lastname: Li
authors.affiliation: School of Computer Science and Information Technology, Northeast Normal University, Changchun, 130117 China.
authors.forename: LiHong
authors.initials: L
authors.lastname: Hu
authors.affiliation: School of Computer Science and Information Technology, Northeast Normal University, Changchun, 130117 China ; Institute of Functional Material Chemistry, Faculty of Chemistry, Northeast Normal University, Changchun, 130024 China.
authors.forename: Yinghua
authors.initials: Y
authors.lastname: Lu
authors.affiliation: Institute of Functional Material Chemistry, Faculty of Chemistry, Northeast Normal University, Changchun, 130024 China.
authors.forename: Zhong-Min
authors.initials: ZM
authors.lastname: Su
keywords: Computational accuracy; Density functional theory; Feature selection; Machine learning correction; Non-covalent interactions