Acidity and basicity interplay in amide and imide self-association † ChemicalScience EDGE

Amides dimerise more strongly than imides despite their lower acidity. Such an unexpected result has been rationalised in terms of the Jorgensen Secondary Interactions Hypothesis (JSIH) that involves the spectator (C ] O S ) and H-bonded (C ] O HB ) carbonyl groups in imides. Notwithstanding the considerable body of experimental and theoretical evidence supporting the JSIH, there are some computational studies which suggest that there might be other relevant intermolecular interactions than those considered in this model. We conjectured that the spectator carbonyl moieties could disrupt the resonance-assisted hydrogen bonds in imide dimers, but our results showed that this was not the case. Intrigued by this phenomenon, we studied the self-association of a set of amides and imides via 1 H-NMR, 1 H-DOSY experiments, DFT calculations, QTAIM topological analyses of the electron density and IQA partitions of the electronic energy. These analyses revealed that there are indeed repulsions of the type O S / O HB in accordance with the JSIH but our data also indicate that the C ] O S group has an overall attraction with the interacting molecule. Instead, we found correlations between self-association strength and simple Brønsted – Lowry acid/base properties, namely, N – H acidities and C ] O basicities. The results in CDCl 3 and CCl 4 indicate that imides dimerise less strongly than structurally related amides because of the lower basicity of their carbonyl fragments, a frequently overlooked aspect in the study of H-bonding. Overall, the model proposed herein could provide important insights in diverse areas of supramolecular chemistry such as the study of multiple hydrogen-bonded adducts which involve amide or imide functional groups.


Introduction
Hydrogen bonds (HBs) in amides and imides are ubiquitous directional forces in nature. HBs in these functional groups are responsible for the secondary interactions, along with other interactions of the tertiary and quaternary structures of proteins. 1,2 Other molecules in which hydrogen bonding is relevant are nucleic acids. The recognition among nitrogenous bases such as uracil and thymine is crucial in the DNA, RNA and other related systems. 3 Besides HBs, base stacking, steric and electrostatic effects can be important in the stabilisation of nucleic acids. 4 Additionally, the dimerisation of amides and imides is of interest in several elds such as supramolecular chemistry in which the self-recognition of these functional groups is relevant. 5,6 The formation of amide and imide dimers is frequently studied by NMR or IR spectroscopy to determine selfassociation constants in solution. 7,8 Rebek and co-workers 9 examined the intramolecular imide-imide and amide-amide association through NMR measurements. The corresponding results indicate that despite their lower acidity, amides exhibit stronger self-associations than imides. Electronic structure calculations made by Jorgensen and co-workers are consistent with these unexpected experimental observations. 10 We consider herein a rationalisation of the surprising stronger selfassociation of amides as compared with imides based on three different criteria.

(i) Repulsions involving the spectator carbonyls of imides
The Jorgensen Secondary Interactions Hypothesis (JSIH), 11 is usually invoked to explain the larger K dimer of amides as compared to imides in spite of their lower acidic character. 9,10 The JSIH considers that amides and imides have a similar kind of primary (hydrogen-bonded) interactions, namely O HB /H contacts as shown in Fig. 1-i. On the other hand, secondary electrostatic interactions (attractions or repulsions between 2.3 and 3.7 A) 11 among atoms in the neighbourhoods of HBs are different in amide and imide dimers. In both cases the molecular clusters present secondary repulsive interactions of the carbonyl oxygens (O HB /O HB ) and hydrogens (H/H) involved in HBs between the monomers (black double arrows in the above-mentioned gure). Nevertheless, the imide dimers present two additional repulsive interactions O HB /O S (green arrows), wherein O S denotes the oxygen atom in a spectator carbonyl group. The repulsions O HB /O S are also consistent with the notion of two nearly parallel repulsive C]O electric dipoles in the imide dimers (purple arrows). There is a considerable body of theoretical and experimental work which is concordant with the JSIH. For example, crystallographic data of some imides such as maleimide, trans-3,4-diphenylsuccinimide, and 1-methyl-hydantoin show that the separation between O S and O HB is very long (>4 A) 12 in agreement with the proposed repulsive character of the interaction of these atoms. Additionally, the JSIH has also been successfully used to study tetrapeptide analogues, 13 stabilisation of base-pairs (A-T and G-C), 14 and triply hydrogen bonded complexes. 15 (ii) Disruption of the resonance-assisted hydrogen bond (RAHB) in imide dimers As schematised by the black arrows in Fig. 1-ii, the hydrogen bonds in both amide and imide dimers can be regarded as resonance-assisted hydrogen bonds. Electron withdrawing groups adjacent to these RAHBs 16,17 could impair the electron ux across these interactions (magenta arrows shown at the bottom of Fig. 1-ii).

(iii) Intrinsic acid/base properties of amides and imides
An analysis of the inductive and resonance effects in these compounds suggests not only a higher acidity of the protons in imides but also a smaller basicity of their oxygens, because of the distribution of the negative charge of the zwitterionic structure across two carbonyl groups as illustrated in Fig. 1-iii. The hydrogen bond strength relates to the acid/base properties of the hydrogen donor and the acceptor groups involved in the interaction. Nonetheless, the basicity of the carbonyl is oen overlooked when addressing HBs involving this moiety. We conjectured that the acidity of the N-H fragment together with the basicity of the carbonyl group could be responsible for the differences in the self-association of imides and amides.
Given this background, we performed a combined experimental and theoretical study to elucidate the factors governing the self-association of amides and imides. We analysed hypotheses (i)-(iii) through 1 H-NMR titrations, 1 H-DOSY experiments, electronic structure calculations as well as quantum chemical topology tools, namely, the Quantum Theory of Atoms in Molecules (QTAIM) 18 and the Interacting Quantum Atoms (IQA) energy partition. 19 Our results indicate the existence of repulsions between O HB and O S , but these interactions are more than compensated by other intermolecular attractions. Moreover, we found that criterion (iii) is the most suitable to explain the experimental tendencies of the self-association of imides and amides through an interplay of the respective basicity and acidity of the C]O and N-H groups. In other words, a weak HB acceptor carbonyl (as it is the case in many of the examined imides) can signicantly weaken the investigated self-association processes despite a strong acidity of the imidic hydrogen and vice versa. Our results not only explain the studied phenomenon but also provide a model which could be exploited in diverse areas of supramolecular chemistry, such as the study of multiple hydrogen-bonding complexes which entail the amide and imide functional groups.

Results and discussion
Self-association of amides and imides: 1 H-NMR and 1 H-DOSY First, we studied the dimerisation of 2-pyrrolidone (A1), an archetype for the study of the self-association of the functional groups concerned in this investigation, 7b,20 in different Fig. 1 Hypotheses (i)-(iii) considered in this work to explain the larger self-association of amides as compared with that of imides. deuterated solvents such as chloroform-d, acetonitrile-d 3 and DMSO-d 6 , and also considered the reported value in CCl 4 in order to select the most suitable solvent for this research. Another feature of 2-pyrrolidone which makes it particularly suitable for this purpose is the fact that it is liquid at room temperature and thereby its self-association is easier to study in deuterated solvents which cover a broad range of polarity. As expected, K dimer diminishes with the polarity of the medium (Table 1), to the point that it is very complicated to reliably determine the self-association constant of A1 in solvents as polar as DMSO. Additionally, common imides are usually found as crystalline solids and therefore they are rather insoluble in apolar environments. Hence, we decided to carry out the measurements of K dimer in chloroform-d due to its optimal compromise between the solubility of the investigated systems and the possibility to accurately determine their self-association constants. The attainment of this compromise prevented the analysis of a larger collection of amides and imides than that considered in this paper.
Next, we employed 1 H-DOSY experiments to evaluate if imide and amide dimers are indeed the predominant supramolecular aggregates in CDCl 3 . This circumstance is particularly relevant in the case of imides for which it has been suggested that larger clusters might be formed in solution 21 while polymeric structures can occur in the solid state. 22 More specically, we used this technique to determine the hydrodynamic radii (r H ) of the studied amide and imide dimers as reported in Table 2 (the structures of the referred compounds are displayed in Table 3). In addition, we also computed the theoretical hydrodynamic radii from electronic structure calculations (r calc ). As expected, structurally similar compounds have close values for r H and r calc , e.g., the radii of amides A1, A2 and imide I4 are alike because all of them are unsubstituted ve-membered rings. A4, A5 and I1 are likewise six-membered heterocycles with closely related structures as reected in their values of r calc and r H . Nevertheless, the cyclic chains in the uracil derivatives I5 and I8 and the benzoderivatives A6, A7 and I3 introduce discrepancies between r H and r calc . This condition occurs because the spherical particle model employed in the estimation of r H does not represent the oblate spheroid character of these dimers. Despite these differences, the experimental r H values are always smaller than the computed r calc data (apart from I8 for which r calc and r H are similar). These results indicate that the investigated amides and imides do not form trimers or larger clusters to an appreciable extent.
Once we chose a suitable solvent and veried that the dimeric species are indeed predominantly formed in solution, we consider now the compounds shown in Table 3. This collection of systems contains a good variety of structures and even some previously reported derivatives of nitrogenous bases found in RNA. 3 In agreement with previous studies, 9 the selfassociation of amides is stronger than that of imides for molecules with the same ring size and unsaturation patterns, e.g., A5 vs. I1, A1 vs. I2, A6 vs. I3 and A4 vs. I6-I13. These results point out that an increase in acidity does not necessarily lead to a stronger self-association. For example, the decreasing orders of acidity of the structurally related imides (I7-I11) are I7 z I10 > I11 > I8 > I9, while those of dimerisation are backwards. We found, however, also exceptions to this behaviour, for instance A5 vs. A4 and I5 vs. I8 in which acidity and self-association increase in the same direction. Based on the above experimental results, now we proceed to examine the three considered hypotheses concerning the comparison of the self-association between amides and imides.
(i) Repulsions involving the spectator carbonyls of imides. We test here the hypothesis that repulsions involving the spectator carbonyl groups are responsible for the smaller degree of dimerisation of imides as compared with that of amides. For this purpose, we used electron density topology analyses in accordance with the QTAIM theory and the IQA approach. The results shown in Fig. 2 indicate that the intermolecular interactions present in the amide A5 and the imide I1 dimers are only HBs. QTAIM shows no repulsion of either kind O HB /O HB , H/H or O HB /O S . In particular, we did not detect either attractive or repulsive interactions involving the spectator carbonyl moieties in the analysed imide dimers (Table S1 in the ESI † shows the QTAIM results for the complete set of investigated systems). Nevertheless, QTAIM can be too restrictive in the identication of relevant non-covalent interactions, as it is the case of the weak HB in ethylene glycol. 40 Therefore, we decided to use the IQA energy partition to determine the attractive or repulsive character of the intermolecular interactions that involve the spectator carbonyls in imide dimers. The le part of Table 4 shows the IQA interaction energies of a spectator oxygen (O13 in the I1 molecule displayed in green) with the atoms of another I1 monomer (shown in orange). We  Fig. S1 in the ESI).  a The values of K dimer were determined with errors lower than 2% (see Fig. S2-S13 in the ESI). b Statistical factor applied to imides with equivalent (or nearly equivalent) carbonyls and value of the corresponding corrected self-association constant (K corr ). c pK a of the compound without alkyl substituents. d pK a of the species without alcohol protecting groups. e Data for molecules with a methyl instead of a cyclohexyl substituent.
note that the interaction between O HB and O S is indeed strongly repulsive (pair O13/O25 in Table 4) because of the electrostatic repulsion between oxygens in accordance with the JSIH. The same atom O S presents however other pairwise interactions which contribute to the attraction between the two monomers (e.g., pairs O13/C14 and O13/C15). Aer considering all the atoms of the neighbouring molecule, the atom O S has an overall repulsion with the interacting monomer (+10.7 kcal mol À1 ). The nearly parallel C]O HB and C]O S dipoles also present a slight repulsive interaction between them (1.1 kcal mol À1 in each case).
The same analysis can also be carried out for every atom in one monomer (say those diplayed in green in Table 4, with the corresponding results shown in the right of the same chart) to obtain the complete IQA interaction energy of the system. The results indicate that not only the atoms considered in the JSIH contribute signicantly to the formation of the molecular cluster.
In particular, the carbon of the spectator carbonyl group (C1) shows an attraction to the adjacent molecule. The attractive interaction of C1 towards the contiguous monomer more than compensates the repulsion of O13 (À12.5 kcal mol À1 + 10.7 kcal mol À1 ¼ À1.8 kcal mol À1 ). We computed the same value for the other spectator carbonyl group. This attraction between the spectator carbonyl moiety and the whole interacting molecule evidences the numerous relevant intermolecular atomic pairwise interactions in the system.
The importance of the intermolecular interactions not considered by the JSIH in hydrogen-bonded dimers had already been pointed out by Popelier and Joubert. 41 Their results were not in accordance with the JSIH in a detailed examination of the relative energetic stability of 27 naturally occurring H-bonded nitrogen base pairs in the gas phase. These researchers considered multipolar expansions of the electrostatic energy (i.e., charge-charge, charge-dipole etc. contacts) which included up to terms which depend on R À6 (e.g. dipole-hexadecapole and quadrupole-octupole interactions), R being the distance between two multipoles. One of the main conclusions of this study concerns the difficulty to explain the relative stability of H-bonded clusters by only considering a subset of atomic pairs located in the boundaries between the interacting monomers as opposed to taking into account the whole set of intermolecular pairs of atoms in the system.
(ii) Disruption of the resonance-assisted hydrogen bonds in imide dimers. QTAIM analyses allowed us to consider the potential disruption of the resonance-assisted hydrogen bonds in imide dimers by virtue of their spectator carbonyl groups (top of Fig. 3). The eventual hindrance of the RAHB in the imide adducts would be accompanied by changes in the QTAIM Delocalisation Indices (DIs) 42 and the IQA exchange-correlation component of the C-N and C]O bonds as schematised in Fig. 1-ii. The DIs, which decrease because of self-association, describe interactions whose covalent character diminishes because of the intermolecular HBs. Conversely, a positive value for DDI evidences a chemical bond with an increased covalent character following the formation of the dimer. The same trend analysis can be applied to the change in the magnitude of the IQA exchange-correlation contribution D|V XC | of these bonds. The results shown in the bottom of Fig. 3 indicate that there is no such disruption of the RAHB in imide dimers due to these spectator carbonyl groups. The lengths ( Table S10 in   increase slightly because of the formation of the RAHB in imide dimers as opposed to the ux of electrons suggested at the top of Fig. 3. Additionally, the changes in the DIs and distances of the bonds involved in this RAHB are substantially larger than those of the neighbouring C-N and C]Os interactions. These data point out that the disruption of the RAHB in imides is not the factor which explains the larger self-association of amides with respect to imides, a condition consistent with the observation that electron delocalisation is not the most stabilizing effect in resonance-assisted hydrogen bonds. 44 (iii) Intrinsic acid/base properties of amides and imides. We test now the hypothesis that the differences for selfassociation between amides and imides are governed by the acidity of the amidic or imidic hydrogen and the basicity of the acceptor carbonyl group. For this purpose, we considered a model which is based on the energies associated with the N-H deprotonation, E(A), and C]O protonation, E(B), as shown in Fig. 4. 45 The acidity of the N-H proton is reduced with the magnitude of |E(A)| while a high value of |E(B)| indicates a strong basicity of the oxygen in the carbonyl group. The deprotonation energies for a wide variety of species which include imides, amides, (thio)ureas, 46 squaramides 47 and carboxylic acids 48 correlate very well with the corresponding experimental pK a values, ditto for |E(B)| and pK BH+ , which indicates the pK a of the conjugate acid of the species under consideration (see Tables S7,  S8 and Fig. S29, S30 in the ESI † for the data of the complete set of compounds). Subsequently, we calculated |E(A)| and |E(B)| for compounds A1-A7 and I1-I13 (Table 5).
As expected, imides are more acidic and less basic than amides as suggested by the resonance structures in Fig. 1-iii.
The change in Brønsted-Lowry acidity or basicity can substantially modify the self-association constants of hydrogen-bonded systems. 21, 52 We found a good correlation of ln K dimer as a function of |E(A)| and |E(B)| whose distribution of points adjusts to a rst-degree polynomial model. The species A2 was not contemplated in the correlation because it is a cyclic carbamate that can form bifurcated hydrogen bonds with CHCl 3 as indicated by DFT geometry optimisations and schematised in   Besides, |C |E(B)| | > |C |E(A)| |, and hence the dimerisation processes of the examined compounds are more sensitive to changes in the basicity of the carbonyl group than to modications of the acidity of the amidic or imidic hydrogen. In general, this model points out that a high acidity or basicity by itself does not ensure a large association constant since there must be a balance between these properties to observe a substantial value of K dimer . In other words, very poor acceptor or donor features of a system can substantially hinder its selfassociation process as it is the case for imides and basic amides A3 and A5 respectively. This analysis indicates that the low basicity of the carbonyl groups in imides allows us to explain why these compounds dimerise less strongly than amides notwithstanding their larger acidic character. The model in Fig. 5 allows us to interpret a series of experimental observations in CDCl 3 . For example, the lowest value of the dimerisation constant corresponds to maleimide I4, a compound with high acidity but the one with the smallest basicity among the analysed systems. On the other hand, A4 undergoes the strongest self-association among the molecules of interest. It has the highest basicity and an acidic character similar to the examined imides. These results point out that the occurrence of an aromatic sextet (top of Fig. 6) might favor zwitterionic structures that lead to a high self-association constant. 49 The relevance of the basicity of the C]O fragments in the self-association of amides and imides is also observed for the uracil analogues I6-I13. These imides are more basic than other compounds with the same functional group and hence dimerise more strongly. Furthermore, the consideration of the basicity of the C]O groups is also useful to rationalise which fragments are involved in the dimerisation. For example, it is well known that uracil derivatives (I6, I8, I9, I12 and I13) form hydrogen bonds with the oxygen at C-4 rather than the one at C-2. 29 This nding is consistent with our results   Table 3 and the first-degree model adjusted for the distribution of points. which indicate that the carbonyl at position four is more basic than its counterpart at position two. The larger basicity of the oxygen bonded to C-4 is associated with the condition that the corresponding carbonyl is conjugated with N-1 via a C-5, C-6 double bond. When this is no longer the case, e.g. I5 and I11, the most basic carbonyl is the one at C-2 as illustrated in the middle and bottom of Fig. 6 (uracil derivatives with and without unsaturations). These observations are supported by the model proposed herein, 2D-NOE analyses 29 and proton affinity calculations for I5 (Table 5). Following the same arguments concerning the relative importance of basicity and acidity of the examined compounds, we can explain why among the studied ve-membered heterocycles, amide A1 associates more strongly than imides I2 and I4. Six-membered rings also follow this trend, as observed when comparing A4 vs. I5-I13. The same occurs with derivatives of benzene A6, A7 vs. I3 as shown in Fig. 7. On the other hand, when two species have a comparable acceptor capacity, the factor which establishes the stronger self-association is the N-H acidity. In this way, we can explain the differences in selfassociation between compounds of the same family, such as amides A3, A5 and A1 or imides I2 vs. I1. Another appealing feature of this model is that it explains the unexpected result that the uracil-containing species dimerise more strongly than amides A5 or A3. Given that all these uracil derivatives have similar acidities, the dimerisation strength is, in this case, based on the variation of the C]O basicities. In addition, there is a good correlation between the experimental values of ln K dimer with those predicted in the model of Fig. 5 as shown in Fig. S32 in the ESI. † Thus, the consideration of the proton acceptor and donor capacities described in this research is a reasonable alternative approach to interpret the differences in the self-association of amides and imides.

Self-association in CCl 4
We considered amide and imide dimerisation constants reported in CCl 4 as well. 21,50 As discussed above, the apolar nature of carbon tetrachloride results in larger dimerisation constants than those obtained in CDCl 3 (ref. 51) (Fig. 8). The set of examined compounds comprises a variety of systems with electron donor and acceptor fragments and hence it allows us to consider the effect of these functional groups on ln K dimer . Similar to the previous discussion of the results in chloroform, there is a correlation between (i) ln K dimer and (ii) the basicity of the carbonyl group together with the acidity of the N-H moiety as shown in Fig. 9. The models of Fig. 5 and 9 are qualitatively similar. In particular, C |E(B)| > 0, C |E(A)| < 0 and |C |E(B)| | > |C |E(A)| |. The last-mentioned condition indicates once again that the dimerisation constant of amides and imides is more sensitive to the basicity of the carbonyl group than to the acidity of the N-H moiety, hence the larger association of amides in comparison to imides.

Analysis of heterodimers
The examination of heterodimers gives further insights about the dimerisation of amides and imides. The determination of K heter indicates that hetero-association between A5 and I1 is stronger than in each homodimer as illustrated in Fig. 10. To rationalise this observation, we consider the relative strength of the individual HBs involved in the heterodimerisation and compared them with those in the homodimers. First, we took into account 1 H-NMR spectroscopy results. The change in the N-H chemical shi due to complexation, Dd N-H , is reported to increase with the strength of the association. 52,53 The change in chemical shi of the imidic hydrogen within the A5-I1 adduct (HB-1 in Fig. 10) is larger than that in the A5 homodimer. Furthermore, the value of Dd N-H in the amidic hydrogen (HB-2 in the same gure) involved in the heterodimer is smaller than the corresponding value for the HB in the imide homodimer. Fig. S15 † shows similar results obtained for A1 and I2 heterodimers. The measurement of K heter was performed with a constant total amount of amide A1 while imide I2 was added to the system. The value of d N-H diminished through the titration, a condition indicative of a weakening of the HB entailing the amidic hydrogen. In the opposite experiment (having a constant total amount of I2 and titrating with A1) the value of d N-H for the imidic proton increased more than in the corresponding homodimers, evidencing the strengthening of the hydrogen bond of the heterodimer which involves this proton. The last-mentioned effect is also observed in the A5-I1 molecular cluster.
Concerning the A5-I1 and A1-I2 heterodimers, the strongest HB-1 is formed between the most acidic proton (the one in the imide) and the most basic carbonyl (found within the amide). On the other hand, the weakest HB takes place in the interaction of the less acidic proton, i.e. N-H of amides A5 and the less basic carbonyl (the one in the imide). The strengths of the HBs in the amide and imide homodimers are between these two extremes. These results along with those of DFT geometry optimisations of the A5-I1 heterodimer show the following trend of descending HB strength: HB-1 > HB in A5 homodimer > HB in I1 homodimer > HB-2 This order is similar to that found by Jorgensen 10 and Leszczynski 54 who studied computationally the hetero-and homodimers of 2-pyrrolidone and succinimide. According to the JSIH, we should expect the hydrogen bond lengths within the heterodimer to be located somewhere between those of the homodimers. Moreover, the shortest hydrogen bond HB-1 is observed next to a presumed electrostatic or dipole-dipole repulsion involving the spectator carbonyl of A5 as opposed to HB-2 which does not present this effect. Despite the aforementioned agreement of the JSIH with structural data, this hypothesis is not completely consistent with the H-bond strength and distance patterns found in the heterodimers. In contrast, the consideration of the acidity and the basicity of the N-H and C]O fragments explains the observed association constants, hydrogen bond distances and chemical shi patterns in these systems. The QTAIM and IQA analysis of the intermolecular interactions within the heterodimers A5-I1 (Table 6) and A1-I2 (Tables S5 and S6 in the ESI †) is consistent   Table S9 in the ESI. † with the previous discussion. The oxygen of the spectator C]O in the imide presents a strong repulsion with the oxygen of the neighbouring carbonyl involved in the HB and with the rest of the molecules of the amide. These repulsions are even stronger than in the case of the I1 homodimer. Still, the hydrogen bond closest to the O S atom in the A5-I1 heterodimer is the strongest of the system. The relative strength of these HBs is revealed by their lengths as previously discussed and other indices used in the study of hydrogen bonds which include (i) Espinosa's empirical formula 55 (Fig. S28 in the ESI †) and (ii) the IQA intermolecular attractions with the interacting molecule (H10 along with O32 on one hand and H31 together with O12 on the other) as reported in the middle and right of Table 6. Despite the repulsion of the oxygen in the spectator carbonyl, this C]O group has an overall attractive interaction with the neighbouring imide or amide in a similar fashion to the corresponding homodimers. These IQA homo-and heterodimer results point out that the O HB /O S repulsions or those between the corresponding dipole carbonyls are not the decisive factor for the energetics of the amide and imide dimerisation.

Signicance in the eld of molecular recognition
Our investigation provides an alternative model to the JSIH to rationalise experimental observations concerning the homoand heterodimerisation of amides and imides, for example, the hydrogen bond distance pattern in amide/imide heterodimers and the relative magnitude of K dimer for these systems. The interplay of acidity and basicity allows us to explain other baffling results e.g. the fact that 2-ethyl-2-methylsuccinimide self-associates much more strongly (by a factor of 15) than tet-rauorosuccinimide. 21 Based on the common consideration of the N-H acidity alone, it is expected that the last-mentioned compound would have a larger K dimer . Likewise and according to the JSIH, the uorinated compound should dimerise to a larger extent because the charges in the carbonyl oxygens are less negative than those in the alkylated succinimide. The alternative explanation that we offer is that the uorine atoms reduce substantially the basicity of the carbonyls, thereby impairing the self-association of this compound.
Additionally, our results can be useful in understanding why amides are much more used in many technologies such as crystal engineering, development of materials and pharmaceuticals than imides. 56 The analysis presented herein indicates that self-association of these functional groups is more sensitive to the basicity of the C]O moiety than it is to the acidity of the N-H group. Hence, the modication of the basicity of this carbonyl represents a good opportunity in the modulation of the strength of the non-covalent interactions established by these groups. For example, the change of a carbonyl in a crucial amide for a more basic imino fragment in vancomycin enhances the association properties with the cell wall of bacteria immune to this antibiotic. 57 This increase of association restores antimicrobial activity and represents a strategy to address vancomycin-resistant infections.
Finally, the results of our investigation suggest a different approach for the analysis of the stability of multiple hydrogenbonded systems such as uracil-diamino purine, cytosineguanine and ADA-DAD systems. 58,59 Generally, these systems are examined by considering only the acidity and basicity of the intermediate hydrogen bond and the JSIH. It would be nevertheless desirable to examine the Brønsted-Lowry acid/base properties for every HB in the system which could lead to valuable insights about the molecular recognition of hydrogenbonded homo-and heterodimers.  Fig. S14 in the ESI †). We also show the hydrogen bond lengths calculated at the SMD-(CHCl 3 )-M06-2x/6-311++G(2d,2p) approximation.
Table 6 E int (IQA) values with the largest magnitudes within the heterodimer. The data are reported in kcal mol À1 . The full set of IQA interaction energies can be found in Table S4 in the ESI a a The IQA deformation energies of the amide and imide are 20.9 and 21.7 kcal mol À1 , so that the IQA formation energy of the molecular cluster is E form ¼ (20.9 + 21.7 À 54.0) ¼ À11.4 kcal mol À1 .

Experimental
General experimental and computational details are given in the ESI. †

Conclusions
We investigated the reasons underlying the stronger selfassociation of amides as compared to imides. Our results indicate that the spectator carbonyl presents indeed repulsions with the oxygens involved in the HB but these repulsive interactions are not the key factor in the energetics of the H-bonded systems examined herein. This statement is based on the relevance of the pairwise interactions which are not accounted for by the JSIH and the experimental and theoretical examination of amide-imide homo-and heterodimers. Our results also reveal that the spectator carbonyl groups in imides do not interfere with the resonance-assisted hydrogen bonds in the dimers of these species. Then, we consider the Brønsted-Lowry acid/base properties of the HB donors and acceptors involved in the interaction within these molecular aggregates. The examination of the basicity of the C]O group, the acidity of the N-H moiety and K dimer resulted in a rst-degree model suggesting that the proton acceptor capacity of the carbonyl group is more important than the acidity of the amidic or imidic hydrogens for the self-association of the investigated compounds. This model also indicates that there must be a balance between the respective acidity and basicity of the N-H and C]O fragments to observe a substantial self-association of these systems. Particularly, amides exhibit larger self-association constants because of their higher basicities in comparison with imides. Similar conclusions were drawn from systems investigated in CCl 4 . Our results also explain the hydrogen bond distance patterns found in amide and imide homo-and heterodimers. The acidity/basicity balance in the dimerisation of amides and imides is an alternative approach to the JSIH in order to explain this phenomenon. Overall, we expect that the application of the insights presented herein will prove valuable to understand and modulate hydrogen bonds between the investigated functional groups which are present in a wide variety of supramolecular systems throughout biology and chemistry.

Conflicts of interest
There are no conicts to declare.