The influence of exocyclic lone pairs on the bonding and geometry of type A mesoionic rings

Based on structures determined by X-ray crystallography, ab initio MP2 calculations on type A mesoionic rings give geometries in good agreement with observed values. A study of four mesoionic ring systems, each with exocyclic oxygen, nitrogen or carbon groups, shows that the presence and configuration of exocyclic lone pairs significantly influences the geometry and configurational preference. Using a localised bond model and NBO analysis, these effects are rationalised in terms of an anomeric interaction of lone pairs with the antibonding orbitals of adjacent σ bonds. In agreement with experiment, similar effects are calculated for pyran-2-imines.


Introduction
To investigate the influence of exocyclic lone pairs on the geometries, bonding and relative energies of type A mesoionic rings, we have studied four ring systems, each with exocyclic C=O, (E) and (Z) C=NPh and C=C(CN) 2 groups, using ab initio Moller-Plesset MP2 calculations. Early studies of the sydnones 1 did not support a polarised structure 1a in which the ring is associated with an aromatic sextet. The C-O stretching frequencies (1768 cm -1 ) and the exocyclic C-O bond lengths (1.20 and 1.215 Å) from X-ray studies are more consistent with the structure 1b [1][2][3]. Another notable feature is the deformation of the bond angles C-C-O (135.7 and 135.5 o ) and O-C-O (119.2 and 121.2 o ). Thiessen and Hope in a study of 4,4'-dichloro-3,3'-ethylenebissydnone pointed out that the ring C-O bond (1.407 Å) is significantly longer than that in furan (1.362 Å) [2,3]. This led these authors to suggest that the resonance structure 1c contributes to the unusual bond lengths and bond angles. They also implied a participation of the carbonyl oxygen lone pairs leading to a contribution from structures 1d resulting in shortening of one C-O bond and lengthening of the other [2].
Type A mesoionic heterocycles are five-membered rings that can only be represented by dipolar structures and in which the ring heteroatoms formally contributing two electrons to the π-system have a 1,3 relationship; those with a 1,2 relationship are type B [4,5]. The unusual bond lengths and angles in the sydnones 1 are recurring features of the geometries of type A mesoionic rings with an exocyclic oxygen. This is illustrated by comparing the crystal structures 2-5 ( Fig. 1) [1,[6][7][8].
Similar bond angle distortions are seen in the crystal structure of the well-known analytical reagent nitron 6 ( Fig. 2), which is a type A mesoionic ring with an exocyclic imine function [9]. During a casual examination of the crystal structure of the azasydnone imine 7 [10], we noticed two significant differences. In structure 7 the exocyclic angles are almost equal and, in contrast to nitron 6, the imine 7 has the opposite configuration. Steric effects probably force nitron to adopt the observed configuration. Since there are no obvious steric interactions in imine 7, we presumed this adopts the most stable configuration and that this preference may be attributable to the orientation of the exocyclic nitrogen lone pair. Three other crystal structures of mesoionic imines have been reported [11][12][13]. In two 1,3-diazol-4-imines, of which structure 8 is typical, steric effects also control the configuration. However, the 1,2,3-thiadiazol-5-imine 9 [13], in which steric effects are minimal (as in imine 7), also has the opposite configuration to nitron 6. We now report calculations that demonstrate the influence of the configuration of lone pairs on structural properties. Table 1 shows calculated bond lengths and angles for the mesoionic 1,2,3-oxadiazole and 1,2,3,4-oxatriazole derivatives 10a-d and 11a-d. The configurations of the imines are defined as cis or trans by the relationship of the nitrogen lone pair to the ring C-O or C-NR bond; the use of Cahn-Ingold-Prelog (CIP) E and Z nomenclature to define configuration varies with the ring system under consideration and is not a consistent terminology for comparing a series of hetero-rings.

Results and discussion
Mesoionic rings with an exocyclic C=C(CN) 2 group are known [14][15][16][17]. We regard the enes 10d and 11d as structures that are not modified by the effects of exocyclic lone pairs and which, therefore, can be used as structural reference points. The effects of lone pairs are measured relative to these geometries. In Tables 1 and 2, φ 15 and φ 45 are the differences between the bond lengths in structures 10a-c and 11a-c and the corresponding bond lengths in 10d and 11d. Similarly, δ 156 and δ 456 measure the differences in the corresponding bond angles. The value Δ exo is the difference between the exocyclic angles 1-5-6 and 4-5-6 for each structure. ΔG rel are the relative free energies of the imine configurational isomers 10b,c and 11b,c.
The calculated gas phase geometries are in satisfactory agreement with the crystal structures 2, 4 and 7 (Figs. 1 and 2). Inspection of Table 1 reveals that lone pairs increase the length of the 1-5 bond (φ 15 ) but the effect of a trans lone pair (10c and 11c) is greater and the effect of two lone pairs (10a and 11a) is greatest. A smaller and opposite effect is seen for the 4-5 bond (φ 45 ); here the larger effect is for the cis lone pair and the effects are not additive. The bond angles are also influenced by the configuration of the lone pair. Trans lone pairs increase angle 1-5-6 (δ 156 ) and decrease angle 4-5-6 (δ 456 ); cis lone pairs have the opposite effect. Inspection of the values of Δ exo indicates that trans-imines have the smallest calculated difference between the exocyclic angles and cisimines have the largest difference. This observation is consistent with the experimentally determined structure 6. It is also significant to note that the trans isomers 10c and 11c are calculated to be the most stable (ΔG rel ) in accord with structure 7.
In a parallel study, we have calculated the properties of the 1,3-diazoles 12 and the 1,3,4-triazoles 13. Relevant structural properties are shown in Table 2. There is good agreement with the observed geometries of aryl analogues of 12a [18], 12b [11,12] and 13b [9]. Comparison with the data in Table 1 reveals similar trends, with notable differences that can be attributed to differences in C-O and C-NMe bonds. Changes in the ring bonds (φ 15 and φ 45 ) show the same trends but the effects are smaller for φ 15 . Trends in bond angle change with exocyclic group (δ 156 and δ 456 ) are comparable in the two series as are the values of Δ exo . However, it is notable that for the imines 12b,c and 13b,c the cis isomers are of lower energy (ΔG rel ). This is in agreement with the crystal structures of rings 6 and 8 (Fig. 2), and can be attributed to steric indicating energetically unfavourable interactions. Although the cis isomer 13b is fully planar, the Ph group is also twisted in the trans isomer 13c indicating steric interaction with C 4 H that is absent when replace by N 4 .
Using the localised bonding model, we rationalise the observed properties in terms of energetically favourable anomeric effects between the exocyclic lone pairs and the antibonding orbitals of the adjacent ring bonds. In the trans configuration 14 the lone pair overlaps with the antibonding orbital of the C-Ẍ bond (n→σ CX *) (Fig. Table 1 MP2 calculated properties of the mesoionic rings 10 and 11. a kcal mol -1 ; b φ = difference in bond length compared to the corresponding bond length in structure d; c δ = difference in bond angle compared to the corresponding bond angle in structure d

Entry
Bond   In accord with general bond properties, the size of the antibonding lobe on the C 5 carbon will be related to the polarity of the bond and will increase as the electronegativity of Ẍ increases. This is consistent with the observation of a greater effect in the C=NPh trans structures 10c and 11c (C-O bond) than in 12c and 13c (C-NMe bond) (Tables 1 and 2). A similar analysis (Fig. 3, Structure 15) accounts for the effect of a cis lone pair on bond lengths and angles. In this case the cis lone pair interacts with the antibonding orbital of the C-C or N-C ring 4-5 bond. Again, the greatest effects are on the more polar N-C bonds (11b and 13b). In the cases where the exocyclic atom is oxygen, both lone pairs influence the geometry. For the 1-5 bonds there is an additive effect but for the 4-5 bonds the combined effect is not significant. For the angles 1-5-6 and 4-5-6 there is a compromise between the effects of cis and trans lone pairs and Δ exo has an intermediate value.
The anomeric effects described here are analogous to other hyperconjugative effects between the antibonding orbitals of polar bonds and adjacent lone pairs, which often account for conformational preferences [5]. Anomeric effects are sometimes attributed to dipolar or steric interactions. In the case of type A mesoionic structures these effects seem unlikely; the derivatives 11, which have similar dipolar and steric characteristics regardless of configuration, have a similar profile to the other derivatives 10, 12 and 13. Within the localized bond model, other orbital interactions obviously influence relative energy and geometry. However, we believe that those shown in Fig. 3 dominate. It is also important to recognise that, in addition to lone pairs, other factors influence ring geometries. These include the nature of ring heteroatoms as can be seen from the variation of Δ exo for the dicyano derivatives (10d -12d, Tables 1 and 2). To support the model summarised in Fig. 3, we have carried out a Natural Bond Order (NBO) analysis for the configurational isomers 10b,c and 11b,c. The results for the most significant nitrogen lone pair interactions are shown in Table 3, where the relationships of structures A and B to 10b,c and 11b,c are shown. Inspection of Table 3 reveals that by far the strongest interactions are between the N6 lone pair and the C5-O1 σ* orbital in structures B (Entries 1 and 5). These interactions are much larger (33.24 and 34.53 kcal mol -1 ) than the other lone pair interactions in A or B. This stabilisation energy is sufficient to account for the preferred configurations in structures 7 and 9, in which steric effects are minimal, and are in good agreement with the localised bond model shown in Fig. 3.
It is significant to note that in 11b (A; Y = N) the stabilisation for lone pair interaction with the N4-C5 σ* orbital (21.66 kcal mol -1 ) (Entry 6) is greater than for interaction with the less polar C4-C5 σ* orbital in 10b (A; Y = CH) (15.17 kcal mol -1 ) (Entry 2). However, this is not sufficient to outweight the large interactions with C5-O1 σ*. The stronger lone pair interaction with the σ* orbitals of polar C-O and C-N bonds (Table 3) are also consistent with the calculated variations in bond length (Tables 1 and 2) and the observed bond lengths in Type A mesoionic rings.
We regard the dicyano derivatives as a realistic choice of reference structure. Analogues of this type are known [14-17, 19, 20], and the exocyclic group C=C(CN) 2 is a good lone pair-free electronic analogue of C=O and C=NAr. Unsubstituted derivatives C=CH 2 are of some interest for two reasons: (i) mesoionic examples of this type were prepared and fully characterised (with X-ray structures) in 2020 [21]; (ii) the CH bonds may show some hyperconjugative electron donation, in a manner analogous to lone pairs. Table 4 compares calculated properties of C=C(CN) 2 , cis and trans C=CHCN and C=CH 2 mesoionic 1,3-diazoles 16. The results reveal some evidence of C-H hyperconjugation, especially by the trans CH bond in structure 16c. Although the effects of the CH bonds in structures 16 are less than those of lone pairs, the trends in bond length and bond angle change are similar, and this suggests an analogous but smaller anomeric effect. The isomer 16c is less stable (ΔG rel ) than 16b, and this is attributable to a small steric interaction between Me and CN.
The structure of the CH 2 derivative 16a is of particular interest since, unlike the other mesoionic rings which are planar, the five-membered ring in structure 16a shows distortion from planarity in both the calculated and X-ray structures (torsion angle 1-5-4-3: calc. 4.4 o ; obsd 4.2 o ). This can be attributed to an increased π electron population introducing anti-aromatic character. The index pEDA (pi Electron Donor-Acceptor) is the sum of Fig. 3 Anomeric interactions between trans and cis lone pairs on adjacent ring bonds the populations of the ring p z atomic orbitals minus the aromatic sextet value of six [22]. The pEDA values for the ene structures 16a-d are shown in Table 3. The πelectron ring population of 16a is demonstrably higher than the cyano derivatives 16b-d and also the oxygen and nitrogen derivatives 12a-c (pEDA: 12a 0.230; 12b 0.262; 12c 0.192). Overall the dicyano derivatives have comparable properties to oxygen and nitrogen analogues and are realistic hyperconjugation-free references structures for studying the influence of lone pairs.
To explore whether similar anomeric effects are found in other heterocyclic rings with exocyclic substituents, we have calculated properties of the pyrone derivatives 17a-d. N,4,6-Triphenypyran-2-imines are known [23,24], and Uncuţa and coworkers, in a detailed NMR study, have shown that in equilibrium mixtures, e.g., 17b,c, the trans (Z) configuration prevails [25].
Examination of Table 5 reveals that the structural changes in the series 17a-d are similar to the trends in Tables 1 and 2. It is noteworthy that the angle difference Δ exo is smallest for the trans isomer 17c (+1.8 o ) and largest for the cis isomer 17b (+15.0 o ); this closely parallels the analogous structures 10 and 11 (Table 1). In agreement with experimental data [25], the trans isomer 17c is calculated to be the more stable (ΔG rel -0.23 kcal mol -1 ) ( Table 5). Table 3 Significant NBO stabilisation energies E 2 and orbital energy. Differences E(j)-E(i) for the Configurational Isomers A and B. a kcal mol -1 ; b a.u.  These results provide some insight into the structures of type A mesoionic rings which generally have a short exocyclic bond and a particularly long ring C-Ẍ heterobond (e.g., 1b), rather than a ring associated with an aromatic sextet (e.g., 1a). In agreement with experiment, similar structural effects are seen in pyrone derivatives.

Computational details
Calculations were performed using the Gaussian 16 program [26] at the ab initio Moller-Plesset MP2 level of theory [27]. The correlation consistent aug-cc-pVDZ (ACCD) basis set was used [28,29]. All geometry optimizations were followed by frequency calculations to establish the nature of the stationary point and to calculate the ZPE and thermal corrections to Gibbs free energy. All minima on the Potential Energy Surface have no imaginary frequencies. For the analysis of possible orbital donor→acceptor interactions the Natural Bond Orbital (NBO) analysis was performed [30]. The stabilization energies accompanying the most important delocalizations were estimated via second-order perturbative method.

Code availability Not applicable
Author contribution Not applicable Data availability Additional data (geometric parameters and Gibbs free energies of optimized molecules) are available as Supplementary Information S1

Declarations
Competing interests The authors declare no competing interests.
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