Counterintuitive bond paths: An intriguing case of the $\mathrm{C}{({\mathrm{NO}}_2)}_3^{-}$ ion

Highlights

• The O⋯O contacts in $\mathrm{C}{({\mathrm{NO}}_2)}_3^{-}$ are destabilizing.

• A bond path does not mean stabilizing nor attractive interaction.

• The benefit of the rotation of the nitro groups is in the C–N bonds.

Abstract

Based on the finding that, like the planar form, also the relaxed form of the $\mathrm{C}{({\mathrm{NO}}_2)}_3^{-}$ ion features O$\cdots$O bond paths between adjacent nitro groups, Luaña et al. [J. Phys. Chem. B 107 (2003) 4912] have announced that these interactions are stabilizing. However, it will be shown that the presence of a bond path strongly depends on the computational model used and that these interactions are destabilizing. Thus the presence of a bond path between a pair of atoms is not evidence of attractive interaction between these atoms. The benefit of the partial rotation of the nitro groups during relaxation of the planar form is also given.

Introduction

Despite the solid mathematical and physical foundations, the Quantum Theory of Atoms in Molecules (QTAIM) [1] proposed by Bader caused a lot of confusion in theories of chemical bond and intermolecular interactions, which seems to occasionally also manifest itself nowadays. This confusion was basically caused by one sentence resulting from this theory, which states that, for any pair of atoms, the simultaneous presence of a bond path and a bond critical point is a necessary and, moreover, sufficient condition to declare that these atoms are bonded to one another [1]. The significance of this statement is revealed in obtaining the ability to easily find chemical bonds using molecular graphs, i.e. diagrams displaying spatial distribution of bond paths and their critical points. The fact that in many simple cases the molecular graph is a mapping of a molecular structural formula [2] has strengthened the belief that a bond path can indeed be indentified with an appropriate chemical bond [3]. This belief has given great popularity and almost uncritical confidence in QTAIM. Much later, however, Bader, in a rather subtle way based on English terminology, tried to significantly loosen the described alignment of a chemical bond with a bond path [4], [5].

Since a chemical bond should be a stabilizing, i.e. binding, interaction, it might have seemed obvious that the presence of a bond path between any pair of atoms means their local stabilization. Nevertheless, Cioslowski, Mixon and Edwards [6], [7], [8] have initiated a long-lasting [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35] discussion on whether equating a bond path with a stabilizing, i.e. attractive, interaction is actually correct. Namely, they have shown that the simultaneous presence of a bond path and a corresponding bond critical point is not necessarily equivalent to a stabilizing effect, and quite the opposite, this presence may result from a repulsive interaction between atoms [6], [7], [8].

In addition to somewhat exotic but very important endohedral systems [10], [11], [12], [13], bond paths for X$\cdots$Y interactions, which are likely to be destabilizing, also occur between a whole lot of combinations of X and Y atom pairs (where X and Y are e.g. H, O, S, F, Cl, Br, I, etc.) in many smaller or larger molecular systems [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35]. Moreover, which may seem strange at first, most of these interactions relate to closely spaced highly electronegative atoms with the same signs (especially negative) of atomic charges, where strong interatomic repulsion would rather be expected [9], [10], [11], [12], [13], [14], [15], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36]. For this reason, this type of bond path may be called counterintuitive [35]. Importantly, it has been shown that many such X$\cdots$Y counterintuitive interactions are indeed destabilizing [7], [8], [9], [10], [11], [19], [20], [23], [24], [25], [26], [27], [28], [33], [34], [35].

There are certainly a lot of examples with a counterintuitive bond path. For a more comprehensive analysis of various cases, see Refs. [34], [35] . In this article, I will discuss the O$\cdots$O bond paths in the $\mathrm{C}{({\mathrm{NO}}_2)}_3^{-}$ anion. Topology of the electron density distribution of the $\mathrm{C}{({\mathrm{NO}}_2)}_3^{-}$ ion was first studied by Cioslowski et al. [6] and then by Luaña et al. [17]. Intriguingly, while the former group of authors have reported that the O$\cdots$O bond paths between adjacent nitro groups are result of repulsion between close atoms, the latter one has considered this interaction as stabilizing. Moreover, as the argument against the idea of locally repulsive O$\cdots$O interactions in this ion suggested by Cioslowski et al. [6], Luaña et al. have argued that “the “steric crowding” is eliminated in the nonplanar optimal geometry of $\mathrm{C}{({\mathrm{NO}}_2)}_3^{-}$ by the rotation of the NO₂ groups around the C-N axes, but the fact is that the OO bonds do not disappear by this relaxation of the symmetry.” [17].

The purpose of this article is to show that for twisted, i.e. fully optimized ion, the O$\cdots$O bond paths between adjacent nitro groups disappear in fact if only a better computational model (i.e. the level of theory) is used. Then I will show that these O$\cdots$O interactions are actually destabilizing and the cause of twisting of the nitro groups during relaxation of geometry of the planar form of the $\mathrm{C}{({\mathrm{NO}}_2)}_3^{-}$ ion will be given. I will also discuss the most reliable molecular graphs of $\mathrm{C}{({\mathrm{NO}}_2)}_3^{-}$ in the context of the Poincaré-Hopf relationship.