Different Zeroes of Interaction Energies As the Cause of Opposite Results on the Stabilizing Nature of C−H···O Intramolecular Interactions Miroslaw Jabloń ski* ,† and Guglielmo Monaco* ,‡ † Department of Quantum Chemistry, Nicolaus Copernicus University, 7-Gagarina St., PL-87 100 Toruń, Poland ‡ Dipartimento di Chimica e Biologia, Universita di Salerno, Via Giovanni Paolo II, 132, 84084 Fisciano SA, Italy *S Supporting Information ABSTRACT: The interaction energy of the C−H···O intramolecular interaction is estimated by several methods for a large group of systems possessing a quasi-cyclic six-membered ring. In the case of the geometry corrected method (GCM), the related rotamers method (RRM), and Espinosa’s method (EM), the linear correlations between interaction energies and the electron density at the bond critical point have close slopes. The first and the last two methods yield almost systematically opposite results concerning the stabilizing/destabilizing character of the interaction, and their main difference is their zero of the interaction energy. An investigation on the limitations of reference energies has led to the introduction of the geometry corrected related rotamers method (GCRRM), estimating both stabilizing and destabilizing C−H···O interactions. An extension of EM is proposed. ■ INTRODUCTION In the world of inter- and intramolecular interactions, hydrogen bonds have a firm position due to their influence on a variety of bonding motifs, such as the spatial structure of ice, the secondary structure of proteins, or the DNA double helix. 1−9 Thus, hydrogen bonds are nowadays the object of research in biochemistry, molecular engineering, and many other branches of science. In the majority of cases, hydrogen bonds, which may be labeled by the X−H···Y formula, are formed if X and Y atoms are both much more electronegative than H and, moreover, Y possesses an electron lone-pair. Those systems suggested the development of electrostatic pictures of a hydrogen bond. 10−13 On the other hand, the important role of a partial covalent character of a hydrogen bond was also proved. 14−22 Both these views, rather than being incompatible, have been shown to be coarse-grained pictures within a single more complete theoretical framework. 23 It is accepted at present that the X atom does not need to be much more electronegative than H and, furthermore, Y may in fact be any region of excess of the electron density. Thus, hydrogen bonds as C−H···Y (Y = O, N, S, etc.) and X−H···π are nowadays widely known. 7 The identification of a hydrogen bond can be based on its stabilizing character and thus on the negative contribution to the molecular energy. However, the usual definition of the hydrogen bond energy as the difference of energies of hydrogen bonded and isolated moieties is not straightforwardly extended to intramolecular hydrogen bonds. This results from the lack of a unique reference system devoid of a hydrogen bond. 8,24−28 Lacking any assessment on the stabilizing character of an X− H···Y interaction, the structural analogy with intermolecular hydrogen bonds is often used to consider it as a hydrogen bond. Of course, in the case of standard hydrogen bonds where the hydrogen atom interacts with two highly electronegative atoms as e.g. O−H···O, N−H···O, the stabilizing character is rather certain; however, this is not the case if X is not much more electronegative than H as, for instance, in the case of the C−H···O interaction. Thus, the study of weak intramolecular hydrogen bonds would most benefit from methods to estimate their interaction energy. Several such methods have been proposed, differing for the system(s) chosen as reference to compute the molecular total energy deprived of the contribution of the intramolecular hydrogen bond. 26,27,29−47 Even if applied within their operating limits, 26−28 different methods can give a rather wide range of energy values, which is a source of concern, especially if the interaction is particularly weak. Contrary results obtained by methods differing for their reference system(s) call for a nontrivial assessment of the quality of these reference system(s). This problem formally does not exist in the case of reference- free methods. One of these methods is the quantum theory of atoms in molecules (QTAIM) developed by Bader. 48,49 According to QTAIM, the joint presence of a bond path (BP) and a bond critical point (BCP) is proclaimed to indicate the bonding character of an interaction between any two atoms linked by that bond path. 50,51 Not surprisingly, the appealing Received: February 4, 2013 Published: June 16, 2013 Article pubs.acs.org/jcim © 2013 American Chemical Society 1661 dx.doi.org/10.1021/ci400085t | J. Chem. Inf. Model. 2013, 53, 1661−1675