3.2. DFT analysis
3.2.a. Host-guest binding energies
All geometry structures of host-guest species generated by Autodock Tools docking simulations were reoptimized using the BLYP-D3(BJ)/TZP approach. The top and side views of the DFT optimized geometries for the host molecule (EtP5A) in solvated phase (COSMO), are shown in Fig. 3.
The lowest-energy DFT optimized structures of the host-guest complexes in solvated phase (COSMO), are shown in Fig. 4, and their structures optimized with the implicit solvent effects using the ωB97XD/6-311G* and B97D/6-311G* approaches, both side and top views, are given in Figures S1 and S2 (See Supplementary Information). The optimized structures using the different DFT approaches are similar.
The BLYP-D3(BJ)/TZP binding energies reported in Table 2 were computed in both gas and implicit solvent phases. The BLYP-D3(BJ)/TZP results (Table 2) are compared to the ωB97XD/6-311G* and B97D/6-311G* results.
Table 2
Binding energies ΔE (kcal/mol) of the host-guest complexes in the gas and implicit solvent phases.
Complex
|
∆Egas
|
∆Esolv
|
∆Esolv
|
BLYP-D3(BJ)/TZP
|
ωB97XD/6-311G*
|
B97D/6-311G*
|
Complex 1
|
−31.75
|
−29.37
|
−39.11
|
−32.96
|
Complex 2
|
−34.15
|
−30.70
|
−39.49
|
−33.13
|
Complex 3
|
−37.13
|
−35.52
|
−40.68
|
−34.25
|
As compared to the docking simulation results (Table 1), Table 2 shows all DFT binding energies to be negative, corresponding to the bound host-guest complexes, thus indicating that the inclusion phenomenon is stabilized and thermodynamically favored. The computed BLYP-D3(BJ) gas-phase binding energies are higher than those obtained in the solvent phase, by 1.61–3.45 kcal/mol. Notably, the three DFT methods show that the complex 3, associating the EtP5A and 1,7-octadiyne molecule, is found to be the most stable one in comparison to the two others.
Furthermore, our DFT computed binding energies agree well with the experimental trend observed in previous works suggesting that host–guest binding strength increased as follows: alkyne > alkene > alkane. Indeed, as reported by Hu et al. [44], the EtP5A/1,7-octadiyne complex gives the largest association constant (Ka = 82 ± 5 mol− 1 L), compared to the congener EtP5A/1,7-octadiene with the constant 6.8 times lower. In the cases of the unsaturated hydrocarbon (octane), the constant was not accurately measured and was found to be too low (Ka < 2 mol− 1 L) [44].
Indeed, the computed binding energies of the complexes using the ωB97XD/6-311G* and B97D/6-311G* approaches, steadily increase from the complex 1 to complex 3, the latter being the most stable, in good agreement with the BLYP-D3(BJ)/TZP results. One can notice that the ωB97XD/6-311G* binding energies are by ca. 6.25 kcal/mol larger than the B97D/6-311G* values (Table 2). Despite these differences between the three used DFT approaches, the relative stability of the host-guest complexes is predicted to behave in the same way.
Interestingly, the size of guest molecules seems to play an important role in the inclusion process. Indeed, the 1,7-octadiyne has less steric effects due to the sp-hybridization of its terminal carbon, which could favor the inclusion process.
The strain energy as given by the Eq. 2 (see computational details) was computed using the BLYP-D3(BJ)/TZP approach in solvated phase and reported as relative deformation energies ∆Estrain in Table 3 for both the guest and host molecules, both in free and in distorted (complexes 1–3) configurations.
Table 3
BLYP-D3(BJ)/COSMO total bonding energy TBE (eV) and strain energies (∆Estrain) of the host and guest.
Energy (eV)
|
Complex
|
Free
|
∆Estrain (kcal/mol)
|
Host
|
|
|
|
1
|
-783.982
|
-784.049
|
0.067 (1.55)
|
2
|
-783.989
|
-784.049
|
0.059 (1.37)
|
3
|
-784.022
|
-784.049
|
0.026 (0.61)
|
Guest
|
|
|
|
Octane
|
-133.791
|
-133.834
|
0.043 (1.00)
|
Octadiene
|
-100.740
|
-100.775
|
0,035 (0.82)
|
Octadiyne
|
-117.779
|
-117.809
|
0,030 (0.70)
|
From the results of Table 3, it appears that the host (EtP5A), referring to the complex 3 (EtP5A/1,7-octadiyne), exhibits slightly lower strain energy ∆Estrain (0.61 kcal/mol) relatively to the complex 1 and 2, associating the octane and 1,7-octadiene, respectively. Previous studies on similar stable inclusion complexes showed low strain energy for both the guest and host molecule [22, 42, 71].
Moreover, regarding the strain energies ∆Estrain of the three guest molecules, the alkyne molecule shows the lowest deformation energy (0.70 kcal/mol) relative to the alkane and alkene, thus resulting in a better guest molecule inclusion in the cavity of the host. These results are in line with the higher association constant (Ka) between the alkyne (guest) and EtP5A (host) within the complex 3, which was observed to be 6.8 times larger than the association constant measured for alkene in the complex 2, while for the alkane-EtP5A complex 1, the association constant is much weaker [44].
3.2.b. Frontier molecular orbital analysis
It was established that for a macromolecule to act as a controlled delivery system, it should reversibly adsorb and release a ligand (e.g., a drug), via a kinetically controllable process [9, 22, 66]. To understand the kinetic stability of these inclusion complexes, the Egap, the energy difference between the HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) was computed using the ADF/BLYP-D3BJ method. The computed HOMO and LUMO energies (eV), Egap (eV), and the global dipole moment µ (Debye) for all the species in the solvent phase are provided in Table 4.
Table 4
BLYP-D3(BJ)/TZP calculated HOMO, LUMO, and HOMO-LUMO gap energies (eV) as well as global dipole moment µ (Debye) for the free and distorted* host, guests, and their complexes in the implicit solvent phase.
|
EtP5A
|
octane
|
1,7-octadiene
|
1,7-octadiyne
|
Complex 1
|
Complex 2
|
Complex 3
|
HOMO
|
−4.119
|
−7.071
|
−6.056
|
−6.421
|
−4.302
|
−4.342
|
−4.378
|
LUMO
|
−0.957
|
+ 0.126
|
−0.706
|
−0.284
|
−1.116
|
−1.160
|
−1.245
|
Egap (eV)
|
3.162
|
7.197
|
5.350
|
6.137
|
3.186
|
3.182
|
3.133
|
µ (D)
|
0.059
|
0.055
|
0.887
|
1.636
|
3.236
|
3.092
|
1.600
|
µ (D) Host*
|
|
|
|
|
2.999
|
3.341
|
1.637
|
µ (D) Guest*
|
|
|
|
|
0.094
|
0.521
|
0.142
|
As shown in Table 4, the HOMO-LUMO gap for the inclusion complexes is significantly smaller than for the hydrocarbons (guests), which indicates that complexes formation can be kinetically controllable, in good agreement with previous studies [9, 22, 66]. Moreover, complexes 1, 2, and 3 show similar energy gaps, ca. 3.15 eV, close to the host EtP5A (3.16 eV). The same trend is obtained using the ωB97XD and B97D functionals (see Tables S1 and S2), showing that all complexes have the HOMO−LUMO gaps noticeably smaller than the guest hydrocarbons, again in well agreement with the BLYP/D3(BJ) results. HOMO and LUMO of the complexes are mainly those of the host molecule as it can be seen in Fig. 5.
Moreover, it appears that the computed global dipole moment (µ) of the free guest decreases with the change of the terminal carbon atom hybridization, sp > sp2 > sp3. Indeed, the relatively higher electronegativity of the sp-hybridized terminal carbons on 1,7-octadiyne was reported, that resulting in stronger binding between alkyne and EtP5A compared to the other guests [44]. For the saturated hydrocarbon (octane), very weak binding is observed as can be seen from the lower value of the association constant [44]. Interestingly, the dipole moment trend is inverted for the inclusion complexes leading to the highest dipole moment (3.236 D) for the octane-containing (sp3) complex 1. It can be seen from Table 4 that the dipole moment of the host in its distorted geometry (within complexes 1–3) exhibit the same trend as the dipole moment of the complexes, increasing from 0.059 to 1.637 D when passing from the free to the inclusion structure (complex 3).
This increase of dipole moment from the host and guest to the complexes is also closely related to the enhancement of induced dipole-dipole interactions (van der Waals interactions) between the guest and host molecules which are, in cooperative multiple noncovalent interactions, essential for realizing such strong complexations. Therefore, it is likely that the latter interactions play a significant role in stabilizing the inclusion process. This point will be detailed later in the text.
The FMO plots for the complexes obtained at the BLYP/D3(BJ) level are shown in Fig. 5. For all the complexes, the HOMO density is predominantly located on the host moiety, with no contributions from the guest molecules. This indicates that no electronic charge transfer occurs within such host-guest inclusion complexes, and the encapsulated ligand does not alter the electronic structure of the host significantly. This result suggests that the encapsulation occurs by a pure physical adsorption process [10].
The comparison with the ωB97XD/6-311G* and B97D/6-311G* computed plots of the frontier MOs (cf. Figs. S3 and S4) shows good agreement with the BLYP-D3(BJ)/TZP obtained plots (Fig. 5). Even with larger isosurface value, 0.01 au, it is clearly seen that both HOMO and LUMO of the complexes are dominated by the host moiety contributions, with very small, if any, guest contributions.
The binding energy values (Tables 2 and S1), along with the HOMO and LUMO plots, indicate that the inclusion process is dominated by rather physical adsorption and suggest that the EtP5A can be used as a reversible host for the considered hydrocarbon molecules as reported for delivery systems [72].
3.2.c. Molecular Electrostatic Potential (MEP) analysis
Molecular electrostatic potential (MEP) analysis is a useful tool for studying the charge distribution within the host cavity and orientation of noncovalent bonds in the inclusion complexes [73]. A rationalization of noncovalent intermolecular interactions based on MEP analysis has been carried out using the BLYP-D3(BJ)/COSMO results including the implicit chloroform solvation effects.
Figure 6 displays molecular electron density isosurfaces (0.001 au) of the EtP5A host overlaid, e.g., with MEP of the inclusion complex 2. Similarly, the MEP analysis has been carried out using ωB97XD/6-311G* calculations (Fig. S5).
Figure 6 shows that the electrostatic potential surface of the complexes is typically non-uniform. It reveals combination of electron-rich negative regions (depicted in red) corresponding mainly to the oxygen-containing groups, and electron-deficient positive parts (blue) corresponding to ends of the alkyl groups. Such positive regions can be considered as electrophilic sites, and negative regions surrounding the guest molecules in attractive interactions are considered as nucleophilic sites. Indeed, as reported by previous studies [22, 42, 73, 74], these electrostatic properties shown on the EtP5A macromolecule favor stronger attractive host − guest interactions arising from their binding during the inclusion process (Fig. S5). The polarization of the host upon complexation is significant as it can be seen comparing Figs. 6a and 6b.
3.2.d. Energy decomposition analysis (EDA)
To shed more light on the contributions of the different components of the interaction energy ΔEbind within the considered host-guest complexes, the energy decomposition analysis (EDA) was performed considering the implicit solvent phase (chloroform) using the BLYP-D3(BJ)/TZP COSMO approach. The total binding energies as well as the decomposition terms (kcal/mol) along with their contributions in percentage (%) are reported in Table 5. The different decomposition terms are given by Eq. 3 (see Computational details):
ΔEbind = ΔEPauli + ΔEelst + ΔEorb + ΔEdisp (3)
In Table 5, the percentages (%) are the weights of the different stabilizing terms, Pauli repulsion (ΔEPauli), electrostatic interactions (ΔEelst), orbital interaction (ΔEorb), and dispersion (the London or van der Waals interaction) (ΔEdisp), the components of the total binding energy (ΔEbind).
Table 5
BLYP-D3(BJ)/TZP COSMO EDA (kcal/mol) and percentage (%) of the contributions in the implicit solvent phase (chloroform) in the complexes 1–3.
EDA kcal/mol (%)
|
ΔEbind
|
ΔEPauli
|
ΔEelst
|
ΔEorb
|
ΔEdisp
|
Complex 1
|
−32.97
|
52.96
|
−21.43 (24.93)
|
−12.17 (14.16)
|
−52.34 (60.01)
|
Complex 2
|
−34.95
|
49.22
|
−22.00 (26.13)
|
−12.20 (14,49)
|
−49.97 (59.36)
|
Complex 3
|
−38.20
|
49.53
|
−25.45 (29.01)
|
−13.33 (15.19)
|
−48.94 (55.79)
|
As shown in Table 5, the destabilizing Pauli term (ΔEPauli) is computed to be significantly higher for the complex 1 (52.96 kcal/mol) than for the complexes 2 and 3. This is likely due to the increased steric hindrance caused by the terminal carbon hybridization (sp3) of the guest molecule (octane). The stabilizing electrostatic (ΔEelst) term is computed to be lower for complexes 1 and 2 than for complex 3, in relation with the higher electronegativity of the terminal carbon of the alkyne (sp). Interestingly, one can notice that the dispersion term (ΔEdisp), the dominating effect in the inclusion process, is predicted to be slightly higher in the complex 1 and 2 than in 3. It is noteworthy that regarding the contribution percentage it appears that the dispersion (ΔEdisp) term is the most important factor in stabilisation inclusion process, depending on electronegativity of the terminal atom in this case [41]. Therefore, it appears that the use of dispersion correction is essential in estimating the correct binding energy and to determine the long bonding interactions as stated in the literature [22, 41, 53, 62].
The electrostatic contribution (ΔEelst) for the complex 1–3 is also predicted to be significantly high, contributing to their stability. Furthermore, this electrostatic term seems to increase with the terminal carbon hybridization change (sp > sp2 > sp3), being slightly higher for the complex 3 in comparison to the complexes 1 and 2 (29.0 vs. 24.9 and 26.1) The orbital interaction (ΔEorb) term has low contribution in comparison to the other terms and suggests weak charge transfer and polarization interactions within these host-guest complexes.
It appears that electrostatic and dispersion effects play a crucial role in stabilizing such inclusion complexes corroborating well the experimental and theoretical results [22, 41, 44]. The computed binding energy shows the inclusion complexes to be stable, and thus their formation can occur at room temperature. In order to check this point, Basis Set Superposition Error (BSSE) calculations have been carried out using the Gaussian software at the ωB97XD/6-311G* level in the gas phase. The computed complexation energies with or without the BSSE corrections are reported in Table 6. From Table 6, it follows that taking into account the BSSE somewhat lowers the binding energy as usual, however, the binding trend remains the same as without BSSE. Notably, the BSSE corrections do not change significantly the energies.
Table 6
ωB97XD/6-311G* BSSE calculation results of the complexes 1–3 in gas phase.
kcal/mole
|
Complex 1
|
Complex 2
|
Complex 3
|
Complexation energy
|
−44.34
|
−44.51
|
−46.63
|
+ BSSE correction
|
−38.35
|
−38.35
|
−41.07
|
BSSE energy
|
5.99
|
6.15
|
5.55
|
3.2.e. NCI-RDG analysis on the inclusion complexes
The NCI-RDG analysis was carried out to visualize the nature of interactions between the EtP5A (host) and the three hydrocarbon molecules using the program MultiWfn with larger size grids [56]. Figures 7 and 8 display the NCI-RDG mapping of the EtP5A and the corresponding inclusion complexes 1–3.
Typically, blue and green color regions are used to represent the stabilizing H-bonding and van der Waals interactions while red color region is used for the destabilizing steric interactions [26, 56, 59, 60]. The interaction types are determined by analyzing the sign of λ2 which represents the eigenvalues of the Hessian of the electron density at the BCP (bond critical points). As reported by other authors [75, 76], for the bonding interactions such as H-bonding, the λ2 value will always be less than 0 while for the van der Waals type of interaction, λ2 ≤ 0. The non-bonding interactions like steric repulsions feature λ2 > 0.
As shown by the RDG isosurfaces (Figs. 7 and 8), the strength and type of noncovalent interactions can be assessed from the product sign (λ2)ρ (ranging from − 0.5 to + 0.5 au). For the EtP5A macromolecule (Fig. 7), the NCI results (λ2 < 0) show that the host is stabilized by hydrogen bonds between the oxygen atom of alkoxy group and the methylene hydrogen; the red disk area (λ2 > 0) is also observed indicating a steric repulsion and at the middle of the benzene rings.
In the inclusion complexes (Fig. 8a-c), one can observe green areas between the C−H of terminal carbon atom in the hydrocarbon guests and the EtP5A host, indicating the existence of van der Waals forces and electrostatic CH⋯π interactions as pointed out in the literature [26]. The H-bonding is weak as follows from the RDG map (RDG > 0.80). Destabilizing interactions, shown by the red disk area, are also observed indicating steric repulsions and seem to appear at the middle of the benzene rings.
It is noteworthy when passing from Fig. 7 to 8, i.e., after the structural reorganization upon encapsulation of guests, that the steric repulsions (red zone) within the host were slightly reduced by van der Waals stabilizing interactions (green zone). Indeed, one can visualize on NCI isosurfaces the green patches to be evenly distributed inside the EtP5A host molecule in the inclusion complex systems, indicating electrostatic interactions, which are responsible for stabilization of the hydrocarbon molecules inside the EtP5A unit. This phenomenon was also shown by previous studies [21, 42, 56, 59, 60], however, it reveals to be quite similar for the three octane (sp3), 1,7-octadiene (sp2) and 1,7-octadiyne (sp) inclusion complexes, corroborating the EDA results.
3.2.f. NBO (Natural Bonding Orbital) analysis
With the help of NBO analysis, we can gain significant insights into different types of orbital interactions in the compounds of interest [67]. In general, the NBO analysis is performed by considering the possible interactions between the filled (donor) Lewis-type NBOs and the empty (acceptor) non-Lewis type NBOs. Then, their energetic contributions are computed using second-order perturbation theory. These donor-acceptor interactions lead to a decrease in the localized NBOs occupancy in the idealized Lewis structure and an increase in the occupancy of the empty non-Lewis orbitals. Therefore, such interactions are referred to as 'delocalization' corrections to the zero-order natural Lewis-type structures. The stronger donor-acceptor interactions have higher stabilization energies [67]. The second-order stabilization energy E(2) is calculated using Eq. 4:
$${E}^{\left(2\right)}= {q}_{i}\frac{{\left({F}_{i,j}\right)}^{2}}{{\epsilon }_{j}-{\epsilon }_{i}}$$
4
,
In this equation, εi and εj represent off-diagonal elements and Fi.j is the diagonal elements of the NBO Fock matrix, qi is the donor orbital possession, and E(2) is the energy of stabilization.
Table S3 lists the representative values for the host-guest stabilization energies along with energy differences between donor and acceptor i and j NBO orbitals and diagonal NBO Fock matrix elements for the complexes 1–3 (with the stabilization energies threshold 0.1 kcal/mol). In Tables S4-S6 are listed the more significant stabilization energy values for the complexes 1–3, respectively (with the stabilization energies threshold more than 0.2 kcal/mol), all of them computed at the ωB97XD/6-311G* level in the implicit CHCl3 solvent.
Analysis of these stabilization energy values for the complexes 1–3 shows the following. (i) For all three complexes, there exist quite numerous stabilizing intramolecular interactions host→guest and guest→host, with the highest interaction energy 0.99 kcal/mol, for the host→guest LP(O) →σ∗(C−Η) in the complex 2 and 3. (ii) Host→guest interactions are represented by both π(C-C) →σ∗(C−Η) and LP(O)→σ∗(C−Η) type interactions, with the former are due to the relatively highly polarizable π−electrons of the benzene rings and latter due to relatively polarizable (compared to covalent bond electron clouds) lone-pair electrons of the alkoxy groups. In the complexes 1 and 2, generally the LP(O)→σ∗(C−Η) type interactions have somewhat higher energies than the π(C-C)→σ∗(C−Η) type interactions (cf. Tables S4 and S5), whereas in the complex 3 the LP(O)→σ∗(C−Η) type interactions generally have somewhat lower energies than the π(C-C)→σ∗(C−Η) ones (Table S6). (iii) Guest→host interactions are represented by the σ(C-H)→π∗(C−C) and σ(C-H)→σ∗(C−H) type interactions in the complex 1 (see Table S4), by the π(C-C)→σ∗(C−H), σ(C-H)→π∗(C−C) and σ(C-H)→ LP(C) type interactions in the complex 2 containing the alkene (Table S5), and by the π(C-C)→σ∗(C−H) and σ(C-H)→π∗(C−C) type interactions in the complex 3 containing the alkyne (Table S6). The total energy of the guest→host interactions in the complex 3 is higher compared to other two complexes, which can explain higher binding energy in the complex 3.