Acidity and basicity interplay in amide and imide self-association

Simple acid–base properties explain the differences in amide and imide dimerisation, and represent an alternative to the secondary interactions hypothesis.


Experimental section
Compounds A1, A2, A4-A7, I1, I2, I4, I5 and I8 are commercially available and only I3 was synthesised according to the procedure reported by Fun et al. 1 2-pyrrolidone (A1) was further purified by distillation to remove water and other impurities. The dimerisation constants for the rest of systems in Table 3 and all of the molecules in Figure 7 were obtained from the literature.

General procedure for 1 H-NMR titrations
NMR spectra were recorded in a range of 0.002 to 1.0 M at 25 °C in CDCl3. Only compounds A6 and A7 were studied in a range of 8.0‧10 -4 M to 0.08 M because of their low solubility in CDCl3.
All experiments were performed on a 300 MHz spectrometer and N-H chemical shifts are reported in ppm downfield from TMS. 1 H-NMR spectra were processed using the MestReNova NMR software. 2 The association constants were calculated from the downfield shifting of the N-H proton using the online tool supramolecular.org. 3 The self-association constants of the investigated compounds are shown in Table 3. Heterodimerisation constants were calculated with the HypNMR 2008 program. 4  Table 1 in the main body of the paper. The percentage errors are: (CDCl3) ± 0.4% and (Acetonitrile-d3) ± 0.6%. The values of Kdimer in DMSO-d6 could not be determined with good accuracy in virtue of its small value.

Heterodimerisation of A5 and I1 in CDCl3
Saturation of the HB-1 signal Saturation of the HB-2 signal

Heterodimerisation of A1 and I2 in CDCl3
Saturation of the HB-1 signal Saturation of the HB-2 signal  Table 2 in the body of the paper.  Table 2 in the body of the paper.

Computational details
All geometries of monomers, dimers and the species involved in the calculation of proton affinities were optimized using the M06-2x 5 functional with the 6-311++G(2d,2p) basis set as implemented in the Gaussian 09 package. 6 We chose this approximation because it yields a good description of the energetics of protonation and deprotonation processes and most importantly of intermolecular interactions such as hydrogen bonds. 5,7 Each stationary structure was characterised as a minimum via the calculation of the corresponding harmonic frequencies. The inclusion of nonspecific solvent effects in the calculations was made by using the SMD method. 8 Some earlier experimental and theoretical studies about the dimerisation of 2-pyridone, 9 2-pyrrolidone, 10 δ-valerolactam 11 and maleimide 12,13 were taken as a starting point for this work.
These studies conclude that the keto form is the most stable arrangement for the dimer formation. We studied the topology of the electron distribution under the formalism of the Quantum Theory of Atoms in Molecules (QTAIM) to get further insights about the chemical bonding scenario of the investigated dimers. This analysis was complemented with DFT electronic energy partitions in accordance with the Interacting Quantum Atoms (IQA) approach. 14 In particular, we examined the steric repulsion of the carbonyl groups (spectators and those involved in the HB) with both methods with the aid of the AIMAll 15 program. We also calculated QTAIM electron Delocalisation Indices DIs (Ω, Ω′), which are chemical bonding indicators that have been successfully used for the characterisation of non-covalent interactions like hydrogen bonds. 16

QTAIM molecular graphs for the examined amide and imide dimers and heterodimers
We determined the molecular graphs for the considered amide and imide homo-and heterodimers. The bond and ring critical points are displayed respectively with green and red colour. The examined electron densities were computed with the (SMD-CHCl3)-M06-2x//6-311++G(2d,2p) approximation.

Use of the interacting quantum atoms approach for the study of bimolecular clusters
The Interacting Quantum Atoms (IQA) method is an electronic energy partition, E, in one (Enet) and two-atoms (Eint) terms 18 wherein the sums run over atomic regions which divide exhaustively the three-dimensional space. The terms and are referred as (i) the IQA net energy of atom A and (ii) the IQA interaction energy of the pair of atoms A and B respectively. 19 The IQA interaction energy, can be further split in classical (coulombic) and exchange-correlation contributions, The components and are related to the covalency and ionicity of the interaction between atoms A and B respectively.
The IQA method is entirely based on the first order reduced density matrix 1 ( , ′ ) and the pair density 2 ( , ). Neither of these scalar fields are defined in conventional density functional theory. It is possible, nevertheless, to scale one and two atom terms of the Kohn-Sham exchange-correlation energy in a similar fashion to QTAIM. 20 This procedure allows us to obtain the total DFT electronic energy in accordance with equation (1).
The IQA approach has been successfully used to study molecular clusters. 21 Because the formalism of IQA is invariant with respect to the grouping of several QTAIM basins in functional groups or molecules, the electronic energy of a bimolecular cluster ••• can be written as in which comprises the net energies of the atoms within G, along with their corresponding (4) A similar definition holds for while the quantity , is defined as (5) The change in energy associated with the formation of the molecular cluster ••• , , can be written as the sum of the IQA deformation energies of the monomers and its corresponding interaction defined in equation (5), The deformation energy of monomer I is defined as is associated with the changes of the electron density and the nuclear geometry associated with the interaction of monomer I with other species. Finally, we indicate that the analysis presented in this work was performed at the DFT electron density computed with gas-phase single-point calculations at M06-2x/6-311++G(2d,2p) level of theory.  1 IQA analysis of I1-A5 and I2-A1 heterodimers as well as I1 and I2   homodimers   Table S3. Complete set of intermolecular Eint(IQA) values within the I1-I1 homodimer. ǂ The data are reported in kcal/mol.      Figure S29. Correlation of experimental pKa with |E(A)| for the compounds indicated in Table S7.   Table S8.  Figure 5 of the paper for all species studied in this work.  Figure S33. Changes in the electron delocalisation indices as a consequence of the dimerisation of the imides studied in this work. The corresponding data for I1and I2 are reported in Figure 3 in the body of the paper. The DIs whose change is negative (in red) indicate interactions with a decreased covalent character due to the formation of the molecular cluster. A positive value for a change in a DI (in green) evidences an increased covalent bond character as a result of the formation of the HB. Table S10. Changes in bond lengths (ldimer -lmonomer) involved in the resonance-assisted hydrogen bond within the imide homodimers examined in this study, i. e. N-H, (C=O)HB and (N-C)HB, and the spectator chemical bonds (N-C)S and (C=O,S)S. The data are reported in angstroms.