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For analysis of weak  π – π  complexes proton-nuclear magnetic resonance (proton-NMR) simultaneously provides information of stacking configurations and association constants    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$\left( K \right)$$\end{document}    KHowever, an apparent issue for this approach is inconsistent/impossible constant estimation which often leads to unreasonable interpretation for  π – π  complexation. Whether or not this proton-dependent constant variation could be attributed to simple experimental uncertainties or to more sophisticated additional unspecific shielding effects (AUS effects) was addressed by means of hypothesis tests using a robust bootstrap technique in this report. Our analysis shows the significance of AUS effects on such variation in constant estimation. A following study using numeric simulation further reveals the variation patterns induced by AUS effects and concludes that the largest    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$K$$\end{document}   Kamong the obtained    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$K$$\end{document}   Kestimates of a complex is considered as the best estimate of    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$K$$\end{document}   Kdue to minimum deviation from the true value of  K  and the multiple    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$K$$\end{document}   Kestimates of a  π – π  complex could provide preferable inferences for complex geometries.

New insights into prediction of weak π–π complex association through proton-nuclear magnetic resonance analysis