**1. Introduction**

The hydrogen bond (HB) is one of the the most important non-covalent interactions (NCI) in nature. Since its first appearance in the chemistry parlance, back in the second decade of the twentieth century [1], HB interactions have been recognised as key factors determining the properties and structure of a wide variety of molecules and materials. Indeed, the role of HBs is known to affect countless systems, from simple molecular liquids and solids, such as water or hydrogen fluoride, to complex and intricate biomolecules. Furthermore, in recent years, a renewed interest for HB interactions has arisen within the scientific community owing to the importance of these contacts in emerging technologies such as (i) CO2 capture [2–5], (ii) rechargeable aqueous zinc [6,7] and aprotic Li-O2 batteries [8], (iii) photovoltaic cells [9,10], (iv) asymmetric catalysis [11], or (v) hydrogen production [12], among others.

**Citation:** Gallegos, M.;

Barrena-Espés, D.; Guevara-Vela, J.M.; Rocha-Rinza, T.; Martín Pendás, Á. A QCT View of the Interplay between Hydrogen Bonds and Aromaticity in Small CHON Derivatives. *Molecules* **2022**, *27*, 6039. https://doi.org/10.3390/ molecules27186039

Academic Editor: Miroslaw Jablonski

Received: 6 August 2022 Accepted: 13 September 2022 Published: 16 September 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

As it often happens in the context of inter-molecular bonding scenarios, the complex interplay between different kinds of interactions drives the global properties of supramolecular systems. Therefore, the combination of HB with other similar or drastically different NCIs is of particular importance. We can consider, for instance, the prototypical example of water clusters. The existence of single HB donors and acceptors in H2O clusters has been associated with the mutual strengthening (cooperativity) of HBs (Figure 1a), whereas the occurrence of double HB donors and acceptors has been related with the reciprocal weakening (anticooperativity) of HBs (Figure 1b) [13–17]. Additionally, there are other instances of non-additive effects of hydrogen bonding reported in the literature, e.g., charge assisted HBs [18,19] and ion-dipole contacts [20].

**Figure 1.** (**a**) Homodromic and (**b**) antidromic cycles within the structure of (H2O)6. These two motifs are, respectively, related to cooperative and anticooperative hydrogen bonding effects.

As a general result, the above mentioned cooperative and anticooperative effects are the result of subtle electron fluctuations that accompany the formation of non-covalently bonded systems [21]. Some of these electron redistributions take place through *σ* bonds and, it is thus common to refer to them as *σ*-cooperative or *σ*-anticooperative HB effects. However, such charge transfers might also occur throughout *π* systems particularly those found in conjugated moieties [14,22–27]. Well-known examples of the interplay between H-bonds and conjugated *π* systems are Resonance-Assisted Hydrogen Bonds (RAHB) as originally proposed by Gilli et al. [28,29]. RAHBs are understood usually as the result of *π*-cooperative effects, which considerably strengthen HBs coupled with *π* bonds. On the other hand, conjugated systems and hydrogen bonds can also reveal anticooperative effects as those found, for instance, in the bicyclic fused rings of malondialdehyde [23,30] or in Resonance-Inhibited Hydrogen Bonds (RIHB) [25–27].

Another particularly relevant interplay between H-bonds and *π* systems can be found in the case of the more recently proposed Aromaticity and Antiaromaticity Modulated Hydrogen Bonds (AMHB) [31,32]. The concept of AMHB was first introduced to rationalise the apparent strengthening or weakening of HB interactions modulated by changes in aromaticity and antiaromaticity in the involved systems. Although clearly intuitive and useful, the ideas of aromaticity and antiaromaticity are built upon elusive and ill-defined chemical concepts, which hinder a quantitative and rigorous analysis. Fortunately, state-ofthe-art wave function analysis methods have proved very useful in the study of electron delocalisation, which is a critical aspect in the study of aromaticity and antiaromaticity. In particular, and in the context of Quantum Chemical Topology (QCT), the Quantum Theory of Atoms in Molecules (QTAIM) [33] and the Interacting Quantum Atoms (IQA) [34] methods have been successfully exploited to investigate the mutual influence of HBs and *π* systems [22–25].

In this work, we make usage of the QTAIM and IQA approaches as well as electronic delocalisation indices developed within the conceptual framework of QCT to provide a detailed real-space-based picture of AMHB. For this purpose, we compared the energetics and studied the chemical bonding scenario using QCT in the formation of different AMHB

molecular clusters shown in Figure 2. We emphasize the effects of the formation of different molecular clusters on pairwise inter-atomic interactions. For the sake of convenience, and considering the large computational cost of some QCT analyses, derivatives of the simple, but representative, azete and pyridinde molecules will be used as model systems in this work. It should be noticed that these molecules have already been successfully employed in the literature [31,32] as minimal models to study hydrogen bond driven dimerisation phenomena. The manuscript is organised as follows. First, we provide a brief background of the QTAIM and IQA approaches. Then, we discuss the electronic and energetic changes accompanying the dimerisation of a collection of organic scaffolds. Later, we consider the interplay between the above mentioned changes and the aromatic character of the monomers. Lastly, we examine somewhat atypical systems to finally gather the main conclusions of this work.

**Figure 2.** Systems examined throughout this investigation. (**a**) Dimers with the hydrogen bond acceptor contained within the ring (ACR): azet-2-ol (AZH), 2- hydroxypyridine (2HP), azet-2-amine (AZA) and 2-aminopyridine (2AP). (**b**) Dimers with the hydrogen bond donor contained within the ring (DCR): azet-2(1*H*)-one (AZH), pyridin-2(1*H*)-one (2HP), azet-2-amine (AZA) and pyridin-2(1*H*) imine (2AP). (**c**) Representation of the ACR and DCR dimers of formamide (NCO) and formamidine (NCN), used as reference. In NCN, the ACR and DCR tautomers are indistinguishable.
