2.1. Crystal growth and structural motifs of the XRD structures
Diisocyanides 1 and 2 and dinitrile 3 were co-crystallized with 1,3,5-FIB (1:1 molar ratio between the components) on slow evaporation of their solutions at 20–23 °C. This procedure gave three cocrystals, 1·1,3,5-FIB, 2·2(1,3,5-FIB), and 3·2(1,3,5-FIB), which were studied by XRD. The homogeneity of the samples was confirmed in powder diffraction X-ray experiments (the Supporting
Materials).
The structures exhibit different molar ratios between the coformers, namely 1:2 for 2·2(1,3,5-FIB) and 3·2(1,3,5-FIB), and 1:1 for 1·1,3,5-FIB; for TG characterization see the Supporting Materials. In all structures, 1,3,5-FIB acts as a trifunctional 120°-orienting HaB donor, whereas the diisocyanides (1 and 2) and the dinitrile (3) function as homoditopic 180°-orienting HaB acceptors. In the structures of 1·1,3,5-FIB and 2·2(1,3,5-FIB), we observed several types of HaBs, namely I···C, σ-(I)-hole···iodine electron-belt, and I···F. In 3·2(1,3,5-FIB), I···N and σ-(I)-hole···iodine electron-belt contacts.
Although the crystal structures exhibit different supramolecular architectures, their common feature is the presence of I···C
isocyanide or I···N
nitrile HaBs occurred between an iodine σ-hole and the isocyanide C- (or the nitrile N-) atom (
Table 1). These HaBs are characterized by rather short interatomic distances. For the diisocyanide cocrystals, the I···N distances are comparable with those previously observed in cocrystals of iodo(perfluoro)arenes with CNMes[
36] or with
1 and
2.[
38] For the dinitrile cocrystal, the I···N distance is similar to those found in C
6F
5I·NCMes (3.092(4) Å, EBIHEF)[
40] and (2,3,5,6-tetramethyl-1,4-dicyanobenzene)·1,4-I
2C
6F
4 (3.061(3) Å, HUMLOQ).[
41] In addition, weak σ-(I)-hole···iodine electron-belt HaB was observed in the structures of
2·2(1,3,5-FIB) and
3·2(1,3,5-FIB) and σ-(I)-hole···fluorine, I···F HaB in
1·1,3,5-FIB (
Table 1).
The diisocyanide and dinitrile cocrystals,
2·2(1,3,5-FIB) and
3·2(1,3,5-FIB), are isostructural, they exhibit similar cell parameters, and display the same supramolecular organization. In these structures, the I-atoms of the I···C contact (in
2·2(1,3,5-FIB)) or the I···N contact (in
3·2(1,3,5-FIB)) function as HaB acceptor site and are involved in two additional I···I HaBs (
Figure 3). In these two cases, two relatively short contacts, which are different in
2·2(1,3,5-FIB) and
3·2(1,3,5-FIB), namely I···C and I···N, exist in a very similar environment; this provide a basis for an accurate comparison between the isocyanide and the isomeric nitrile groups. For this comparison, we performed appropriate quantum chemical calculations detailed in section 2.2.
In the structure of
1·1,3,5-FIB, a rather strong HaB is formed apparently because of an enhanced σ-hole acceptor ability of the isocyano C-atom in
1 due to the combined effect of four electron-donating methyl groups (
Figure 4); tri(poly)-center HaBs were not observed.
We measured FTIR-ATR spectra for pure
1–
3 and their cocrystals (see the Supporting Materials for details). The isocyanide-based cocrystals
1·1,3,5-FIB and
2·2(1,3,5-FIB) demonstrate high-frequency shift of ν(NC) band (18 and 13 cm
–1) relatively to
1 and
2, while the difference between the dinitrile-involving structures,
3·2(1,3,5-FIB) and
3, is small (1 cm
–1). This trend in experimental ν(NC) band shifts is in a good agreement with theoretical data (
Table S4). Small changes in ν(NC) frequency for dinitrile-based system may indicate a weakening of the charge transfer (CT) for dinitrile as compared to isocyanides; this correlates well with the calculation of the CT by NBO method (section 2.2.4).
The high-freqiency shift induced by the HaB, resembles the situation with C-isocyanide/N-nitrile coordination to Lewis acidic centers. Siginficant ν(NC) increase (150 cm
–1) was observed for the H
3B·CNMe associate and this blue shift was rationalized by appropriate increase of CN force constant upon coordination.[
42] High-frequency shift of ν(NC) band in IR and Raman spectra was observed for the homoleptic copper(I) [Cu(CNMe)
4]
+ and [Cu(NCMe)
4]
+ complexes as compared to the corresponding uncomplexed isocyanide and nitrile species.[
43] This shift is greater for the isocyanide ligand (40–60 cm
–1) and smaller for the nitrile (~15 cm
–1).[
43]
2.2. Theoretical calculations
The nature of C–I···C/N contacts occurred between the diisocyanides or the dinitrile and 1,3,5-FIB were studied by a set of computational methods including Molecular electrostatic potential (MEP), Quantum theory of atoms in molecules (QTAIM), Independent gradient model (IGMH), Electron localization function (ELF), Natural Bond Orbital (NBO), The domain based local pair-natural orbital coupled-cluster (DLPNO-CCSD(T)), and Symmetry Adapted Perturbation Theory (SAPT). We also performed a comparative analysis of HaB in the cocrystals to verify common features and differences of these noncovalent interactions.
To study HaB in our systems, geometry optimization was carried out for all bimolecular fragments, [(
1–
3)‧1,3,5-FIB]. The optimized structures are shown in
Figure 5, and the relevant main geometric parameters are collected in
Table S3. In all structures, the geometry optimization led to a reduction of N≡C (isocyanide) or С≡N (nitrile), and С–I distances (
Table S3) and a slight decrease (by ~6°) of ∠(C–I···C/N). The lengths of the I···C/N HaBs increase by 0.03, 0.08, and 0.10 Å, respectively, for the two diisocyanide structures and one dinitrile structure. In general, the obtained optimized structures are consistent with the experimental XRD data.
2.2.1. Nucleophilicity and molecular electrostatic potential.
We determined the global (N
Nu) and local (N
Nuloc) nucleophilicity indexes and found that N
Nu decreases in the following order:
1 (2.35 eV) >
2 (1.80 eV) >
3 (1.40 eV). This order correlates well with Mayr’s experimental nucleophilicity N+ indexes.[
44] At the same time, the analysis of local nucleophilicity showed that the N
Nuloc of the C-atom of the isocyanide group in
1 is approximately equal to the N
Nuloc of the C-atom in
2. This observation suggests that the interaction energy of HaB should be approximately the same for
1 and
2. The N
Nuloc at the N-atom of the nitrile group in
3 is slightly lower than that at any one of the C-atoms of the isocyanide groups (
Table 2); this is in agreement with V
s,min MEP potentials of the HaB acceptors (
Figure 6).
2.2.2. QTAIM-IGMH.
The QTAIM[
45,
46] analysis for all contact types revealed the presence of bond critical points (BCPs) and a bond path through the BCP. This bond path indicates the accumulation of the maximum electron density between the interacting nuclear attractors. The most important topological parameters at BCPs (namely, electron density (ρ
b), Laplacian (∇
2ρ
b), and total energy density (H
b = V
b + G
b), potential and kinetic energy densities (V
b and G
b), and second eigenvalues of the Hessian matrix (λ
2) are listed in
Table 3. The molecular graphs for [(
1–
3)‧1,3,5-FIB] are given in
Figure 7. Low values of ρ
b (0.015–0.019 a.u.), positive values of ∇
2ρ
b (0.047–0.050 a.u.), and virtually zero values of Hb are typical for noncovalent interactions and their consideration confirms the presence of the closed-shell HaB. The ρ
b values for the HaB involving the nitrile are slightly lower than those found for the isocyanides; this indicates a weakening of the interaction energy in the nitrile system. The negative value of λ
2 ranges from –0.012 to –0.010 a.u. showing that these interactions are attractive. Furthermore, the computed value of the electron localization function (ELF) at the BCP is slightly higher for both (diisocyanide)·1,3,5-FIB systems (
Table 3) probably because of a higher contribution of the covalent component in the HaB (for detailed ELF consideration see section 2.2.3).
The IGMH[
47,
48,
49,
50,
51] isosurface (
Figure 7a, b) was also calculated for all types of contacts. This isosurface is represented by a drop-shaped green surface located between the HaB-donating I- and the HaB-accepting C- or N-atoms. Analysis of the calculated intrinsic bond strength index (IBSI,[
52] the local stretching force constant) indices, similar to QTAIM, favors the weakening of HaB between 1,3,5-FIB and the dinitrile than that for diisocyanides. In all adducts, no auxiliary interactions were found and it means that the HaB is the main attractive interaction in the studied systems.
2.2.3. Electron localization function.
To understand the reason why do the isocyanide systems are characterized by a larger contribution of the covalent component, we additionally performed an ELF analysis[
53] for [(
1–
3)‧1,3,5-FIB]. This analysis allows us to measure the excess kinetic energy caused by Pauli repulsion and also to visualize the localization of electrons. The values of the ELF function at high electron localization (the localization can be interpreted either as LPs, or chemical bonds) should exhibit a value close to 1, while for low electron localization the value of the ELF function tends to 0.[
54]
The topological analysis of the gradient field of the ELF function is also very useful because this analysis leads to the division of the molecular space into non-overlapping basins of attractors.[
55] These basins can be classified as basic (C(X), concentrated on atoms) and valence (V(X) or V(X,Y), concentrated between atoms). The basins could have a synaptic order indicating the number of basins linked together.
Figure 8 shows that in all cases, the disynaptic basins between the I-atom of the HaB donor and the C- or N-atoms of the HaB acceptors were not observed; this fact additionally favors the noncovalent nature of the HaB.
Hence, the main attention was paid to the electron population and volume of the monosynaptic V(C) or V(N) and the dinosynaptic V(C,I) basins. The monosynaptic basins can be attributed to LPs on the C- or N- atoms, while the disynaptic basin V(C,I) is related to the localization of the electron density of the C–I bond; these basins are directly involved in the HaBs. The population of the V(C,I) basin for [(
1 and
2)‧1,3,5-FIB], involving in the HaB, is higher (by 0.08
e) than the basins that are not involved in the HaB (
Table 4).
The population of the monosynaptic basin V(C) is reduced by 0.01 e compared to the unbound С-atoms of the isocyanides. We also found that the interaction of the isocyanides with 1,3,5-FIB leads to a decrease in the local volume of the basin V(C) for LP(C) from 280 to 100 Å3 for [1‧1,3,5-FIB], and from 440 to 170 Å3 for [2‧1,3, 5-FIB]. Remarkably, the basin V(C) volume for LP(C) is also decreased from 280 to 100 Å3 for [1‧1,3,5-FIB] and 440 to 170 Å3 for [2‧1,3,5-FIB]. The analysis of the ELF basin for [3‧1,3,5-FIB] also shows an increase in the population of the V(C,I) basin, but the population of the monosynaptic V(N) basin remains unchanged. All these features are coherent with the weakening of the charge transfer (CT) for the dinitrile system in comparison with the diisocyanide systems.
The ELF data clearly indicate that the covalent component is caused by the outflow of electrons as a result of CT from the diisocyanides (or the dinitrile) to 1,3,5-FIB. However, the HaB with the dinitrile, in contrast to those for both diisocyanides, is characterized by a very weak CT.
2.2.4. Natural Bond Orbital approach.
Since the examination of the ELF results revealed the presence of CT, we performed an NBO analysis to characterize orbital interactions between the HaB donors and acceptors; NBO data are collected in
Table 5. We found that two most important donor-acceptor interactions are associated with CT and they are responsible for stabilizing HaB by the HaB acceptors.
The first type is related to the donor-acceptor interaction with LP(C/N) to σ*-orbital (I–C) of 1,3,5-FIB (
Figure 9). The second order perturbation energies E(2) for the transitions LP(C/N)→σ*(I–C) follow the order [
1‧1,3,5-FIB] (9.6) ~ [
2‧1,3,5-FIB] (10.2) > [
3‧1,3,5-FIB] (5.2 kcal/mol). The second interaction type is associated with the LP(I)⟶σ*/π*(C–N)
isocyanide and σ*/π*(N–C)
nitrile bond orbitals. On the whole, the E(2) values also follow the general trend of the first type interaction, but are characterized by smaller E(2) values (
Table 5). To study the directions of the charge flow, we analyzed the occupancy of the σ*(I–C) orbital of 1,3,5-FIB and also the total population of the orbitals associated with the (C–N)
isocyanide or (N–C)
nitrile bonds (
Table 5). As can be inferred from consideration of the data gathered in
Table 5, the population of the σ*(I–C) site increases by 50 me.
This increase is associated with the CT from the LP(C or N) orbitals of the diisocyanides (or the dinitrile) to the σ*(I–C) orbital of 1,3,5-FIB. At the same time, the population of the orbitals of the HaB acceptors and σ*(N≡C) and σ*(C≡N) bonds is increased by 16 me. This increase favors the presence of a reverse CT from LP(I)⟶σ*/π*(C≡N)
isocyanide and σ*/π*(N≡C)
nitrile bond orbitals. In these cases, the first effect prevails over the second one and it leads to an increase (by 0.01 Å) of the I–C bond length (
Table S3). This observation indicates that for the isocyanides, the direct CT is 3-fold higher than the reverse CT due to the more pronounced σ-donor properties of the diisocyanides compared to the dinitrile. The direct CT decreases in a series [
1‧1,3,5-FIB] ~ [
2‧1,3,5-FIB] > [
3‧1,3,5-FIB]. The latter trend is consistent with the weakening of the nucleophilicity in the order
1 ~
2 >
3 (section 2.2.1; calculated indices are given in
Table 2). Thus, the diisocyanides and the dinitrile exhibit typical electron-donor and π-acceptor properties with respect to the HaB donor.
2.2.5. Energy.
The interaction (E
intSM) and binding (E
bSM) energy data – obtained using the supramolecular approach and calculated at the DLPNO-CCSD(T))[
56,
57] level – are collected in
Table 6. In general, E
intSM values do not exceed –4 kcal/mol; this energy corresponds to weak noncovalent interactions. The values of E
bSM are comparable to those of E
intSM. This is due to the fact that the deformation energy of the HaB acceptors has a positive sign, while the deformation energy of the HaB donor is negative. Thus, the resultant energy responsible for the deformation of the monomers in the dimer geometry becomes low.
Finally, to closely interrogate the physical nature of the HaBs, we performed the decomposition of the interaction energy by the SAPT[
58,
59,
60,
61,
62] method into electrostatic (E
elec), induction (E
ind), dispersion (E
dis), and exchange (E
exch) components (
Figure 10). In general, the total interaction energies SAPT(0) (E
intSAPT) correlate with the corresponding energies of the supramolecular interaction (
Table 6), although the energies calculated using the DLPNO-CCSD(T) method are by 18% lower in absolute values than those calculated at the SAPT(0) level.
According to the obtained SAPT data (
Table 6), HaBs are characterized by the predominance of electrostatic energy, which comprise approx. 60% of Σ(E
elec, E
ind, and E
dis). The dispersive attractive energy provides a significant contribution (~30%), while the repulsive Pauli energy has a 70% fraction. It has been proved[
63,
64] that the high directionality of HaB is determined by electrostatic and exchange-repulsion interactions and therefore we carefully analyzed the E
exch energy. Ongoing from [
1‧1,3,5-FIB] (66%) to [
2‧1,3,5-FIB] (71%), the contribution of the repulsion Pauli energy increases, and then it decreases in [
3‧1,3,5-FIB] (43%). This trend is in a good agreement with the weakening of orbital interactions on the transition from the diisocyanide to the dinitrile systems. The highest value of E
exch for [
2‧1,3,5-FIB] is probably associated with an increase in the basin volume LP(C) for [
2‧1,3,5-FIB] than that for [
1‧1,3,5-FIB]. As a result of the increase in the LP(C) volume, the E
exch energy also increases (
Table 4). The inductive effect also makes some contribution to the HaB but it does not exceed 15%. In particular, the induction term includes both polarization and CT. However, SAPT method allows the estimate a contribution of CT in the induction energy.[
65] An analysis of the obtained E
ct data shows that the contribution of CT to the HaB interaction energy is relatively small (<30% and 6% of the induction energy for the diisocyanides and the dinitrile, respectively).