2.1 Determination of the reactive forms of the reagents under the experimental conditions used.
Before starting the theoretical study to ensure the possibility of carrying out this reaction at the synthetic laboratory level or not, it is very important to know the reactive forms of the reagents under the experimental conditions used. Indeed, the distribution diagram of the different species distribution of the reagents as a function of the pH obtained by the MARVINSKETCH software makes it possible to achieve this objective.
In an acidic medium, the carbazole acts as a nucleophile through the nitrogen atom of the NH group. At pH = 14, the base eliminate the hydrogen from the NH group of the carbazole to give the carbazol-9-ide (anionic form). The pH value also remains an important parameter to find the reactive form of carbazole. The distribution diagram obtained using the MARVINSKETCH software, indicating the relative fraction (or the percentage) of the neutral and ionic of carbazole in the pH range between 0 and 14, indicate that in the interval 12-14 (figure 1), we find the unique presence of the anionic form, on the other hand, there is absence of the form neutral carbazole, which explains why the mechanism of this reaction will go first through the tearing of the proton of the carbazole followed by a nucleophilic attack on 3-bromopropyne.
Likewise, the different species of 3-bromopropargyl as a function of the pH determined by the MARVINSKETCH program shows that the neutral form is the only form which exists in the pH range 0-14 (figure 2). The absence of the anionic form makes it possible to conclude that 3-bromopropargyl cannot play the role of a nucleophile in this zone in any reaction. This remark is surprising since the terminal alkyne contains an acidic proton. This result can be explained by the existence of a strong attractor group Br. Indeed the same result is observed in the distribution diagram of the different forms of 3-chloropropargyl, 3-fluoropropargyl and 3-iodopropargyl as a function of the pH.
To increase the percentage of the anionic form of this reagent, it is necessary to work at a high temperature. This hypothesis was verified by the Marvinsketch software, which proved that at a temperature of 573K the anionic form becomes the majority. In our experimental part, we have no interest in working with the anionic form of this reagent, so we don't need heating.
2.2 The geometry parameters of the reagents.
The geometry parameters related to the reagents molecules, such as: Charges densities, interatomic distances and angles ... the calculations were investigated using DFT method at B3LYP With the base 6-31G (d, p), the values of the charge densities are gathered in Table 1. The optimized geometries of the reagents are respectively represented in Figures 3 and 4.
Table 1. The charges densities of reagents
Carbazol-9-ide (R1)
|
3-Bromoprop-1-yne (R2)
|
C1 ; C9
|
0.143
|
C1
|
-0.964
|
C2 ; C11
|
-0.250
|
C2
|
0.941
|
C3 ; C7
|
-0.137
|
C3
|
-0.492
|
C4 ; C12
|
-0.238
|
Br4
|
-0.140
|
C5 ; C8
|
-0.190
|
|
|
C6 ; C10
|
-0.283
|
|
|
N13
|
-0.649
|
|
|
2.3 Computational study of the reaction between carbazol-9-ide (R1) and 3-bromoprop-1-yne (R2).
2.3.1 Thermodynamic parameters
We calculate some thermodynamic parameters characterizing the reaction between R1 and R2 in Table 2.
Table 2. Thermodynamic of the synthesis reaction calculated using output files of Gaussian calculations using DFT/B3LYP 6-31G (d, p)
Thermodynamic parameters of the reaction
|
ΔHr (Kcal/mol)
|
-21.173
|
ΔSr (Kcal/mol.K)
|
-50.854 10-3
|
ΔGr (Kcal/mol)
|
-36.335
|
The negative value of enthalpy ΔHr indicates the exothermic nature of this reaction. Then, The free enthalpy variation ΔGr<0 show the possibility of this reaction with thermodynamic view.
2.3.2 Prediction of electrophile/nucleophilic proprieties of reagents
In order to predict the electrophilic/nucleophilic characters of the reagents we calculated various parameters among them we found: The HOMO/LUMO energy, The gap energies ΔE, the electronic chemical potentials μ, the chemical hardness η, the global electrophilic indices ω and the global nucleophilic indices N, using the following equations [19]:
ΔE(I) = EHOMO (Carb) − ELUMO (3-Bromoprop-1-yne)
ΔE(II) = EHOMO (3-Bromoprop-1-yne) − ELUMO (Carb)
ω = μ2/2*η
μ = (EHOMO +ELUMO)/2
η = ELUMO – EHOMO
N=EHOMO–EHOMO (TCE)
S(I)=1/ η
With EHOMO (TCE) = -9.3686eV calculated by DFT/B3LYP 6-31G (d, p).
In table 3 are grouped the calculated energy values of the frontier orbitals and the energy gap. These results are illustrated in figure 5.
Table 3. Energetically parameters of the reagents by the DFT/B3LYP method in the base (6-31G) (d, p)
Compound
|
E (eV)
|
HOMO (eV)
|
LUMO (eV)
|
∆E(I) (eV)
|
∆E(II) (eV)
|
Carbazol-9-ide
|
-14071.061
|
-4.339
|
-0.324
|
-2.750
|
-7.575
|
3-Bromoprop-1-yne
|
-73205.091
|
-7.900
|
-1.589
|
The results obtained indicate that the gaps | 𝑬𝑯𝑶𝑴𝑶 (R1) - 𝑬𝑳𝑼𝑴𝑶 (R2) | is small compared to the gaps | 𝑬𝑯𝑶𝑴𝑶 (R2) - 𝑬𝑳𝑼𝑴𝑶 (R1) |. This can be predicting an electrophilic character of 3-bromoprop-1-yne (R2) and the nucleophilic property carbazol-9-ide (R1)[20].
2.3.3 Global descriptors of reagents
In table, 4 gathers the values calculated theoretically by the DFT method of the global parameters.
Table 4. Global parameters calculated by B3LYP DFT/6-31G (d. p)
Compound
|
E (eV)
|
µ (eV)
|
ƞ (eV)
|
S(I) (eV)
|
ω (eV)
|
N (eV)
|
Carbazol-9-ide
|
-14071.06
|
-2.33
|
4.02
|
0.25
|
0.68
|
5.03
|
3-Bromoprop-1-yne
|
-73205.09
|
-4.74
|
6.31
|
0.16
|
1.78
|
1.47
|
From this result we can show that the electronic chemical potential μ of carbazol-9-ide (μ= -2.33 eV) is on a level of energy more interested than that of 3-bromoprop-1-yne (μ= -4.74 eV). Consequently, we can propose that electron transfer takes place from carbazol-9-ide to 3-bromoprop-1-yne. Also, from the global nucleophilicity N values of carbazol-9-ide and 3-bromoprop-1-yne. We can deduce the same result; carbazol-9-ide plays the role of a nucleophile whereas 3-bromoprop-1-yne is an electrophile. The same conclusion can be drawn from the values of the global electrophilicity ω. Chemical hardness of carbazol-9-ide (η = 4.02 eV) is less than that of 3-bromoprop-1-yne (η = 6.31 eV). This means that carbazol-9-ide retains few electrons in its environment. Unlike 3-bromoprop-1-yne which maintains them in its own environment. Therefore, electron transfer takes place from carbazol-9-ide to 3-bromoprop-1-yne. We can conclude, all global indices show the nucleophilic nature of carbazol-9-ide and the electrophilic properties of 3-bromoprop-1-yne.
Prediction of local reactivity of reagents
2.3.4.1. Application of the Domingo polar model using Fukui indices fk+ and fk-
From Domingo's polar model through the local electrophilicity ωk and local nucleophilicity Nk, in order to predict the most favored electrophilic-nucleophilic interaction for the formation of a chemical bond between the most electrophilic site of the electrophilic reagent and the most nucleophilic site of the nucleophilic reagent [21]. The local electrophilic and nucleophilic values (ωk , Nk) for the reactive atoms of the 3-bromoprop-1-yne and carbazol-9-ide are regrouped in Tables 5 and 6.
Table 5. Determination of natural populations (Pk (N-1), Pk (N), Pk (N + 1)) of reagents.
Carbazol-9-ide
|
3-Bromoprop-1-yne
|
Atoms
|
P (N)
|
P (N-1)
|
Atoms
|
P(N)
|
P(N+1)
|
C1
|
5.857
|
5.890
|
C1
|
6.501
|
6.680
|
C2
|
6.250
|
6.156
|
C2
|
6.049
|
6.051
|
C3
|
6.137
|
6.156
|
C3
|
6.229
|
6.432
|
C4
|
6.238
|
6.224
|
|
|
|
C5
|
6.190
|
6.167
|
|
|
|
C6
|
6.283
|
6.174
|
|
|
|
C7
|
6.137
|
6.077
|
|
|
|
C8
|
6.191
|
6.167
|
|
|
|
C9
|
5.857
|
5.890
|
|
|
|
C10
|
6.283
|
6.174
|
|
|
|
C11
|
6.250
|
6.156
|
|
|
|
C12
|
6.238
|
6.224
|
|
|
|
N13
|
7.649
|
7.373
|
|
|
|
Table 6. Fukui indices (fk+, fk-) and local electrophilicity and nucleophilicity values (ωk , Nk) for reagents.
Local indices NPA
|
Carbazol-9-ide
|
3-Bromoprop-1-yne
|
Atoms
|
fk-
|
Nk
|
Atoms
|
fk+
|
ωk
|
C1
|
-0.03
|
-0.17
|
C1
|
0.18
|
0.32
|
C2
|
0.09
|
0.48
|
C2
|
0.01
|
0.01
|
C3
|
-0.02
|
-0.09
|
C3
|
0.20
|
0.36
|
C4
|
0.02
|
0.07
|
|
|
|
C5
|
0.02
|
0.12
|
|
|
|
C6
|
0.11
|
0.55
|
|
|
|
C7
|
0.06
|
0.30
|
|
|
|
C8
|
0.02
|
0.12
|
|
|
|
C9
|
-0.03
|
-0.17
|
|
|
|
C10
|
0.11
|
0.55
|
|
|
|
C11
|
0.09
|
0.47
|
|
|
|
C12
|
0.02
|
0.07
|
|
|
|
N13
|
0.28
|
1.39
|
|
|
|
ωk=ω*fk+ (ω=1.78 eV) and Nk= N*fk- (N=5.03 eV) [21].
fk+=[Pk(N+1)–Pk(N)] show a nucleophilic attack site.
fk-=[Pk(N)–Pk(N-1)] show an electrophilic attack site.
Pk (N): natural population of the atom k in the neutral form of molecule.
Pk (N + 1): natural population of the k atom in the anionic form of molecule.
Pk (N-1): natural population of the k atom in the cationic form of molecule.
This time, the local Nk nucleophilic indices for the carbazol-9-ide reactive atoms in the basic medium and the local electrophilic indices ωk for the 3-bromoprop-1-yne atoms show that the most favored interaction takes place between C3 the most electrophilic site (ωk=0.36 eV) of the 3-bromoprop-1-yne and N13 the most nucleophilic site (Nk=1.39 eV) of the carbazol-9-ide. Consequently, the Domingo polar model correctly predicts the formation of the N13-C3 bond, experimentally desired.
2.3.4.2. Application of the Gazquez-Mendez rule
The Gazquez-Mendez rule propose that two chemical species have similar softness can form interaction bonds [22]. The Table 7 regrouped the local indices for the reactive atoms of carbazol-9-ide and the reactive atoms of 3-bromoprop-1-yne.
Table 7. Fukui indices (fk+ , fk-) and condensed local softness atoms (Sk+ , Sk-) values for reagents calculated by NPA populations
Local indices NPA
|
Carbazol-9-ide
|
3-Bromoprop-1-yne
|
Atoms
|
fk-
|
Sk-
|
Atoms
|
fk+
|
Sk+
|
C1
|
-0.03
|
-0.01
|
C1
|
0.18
|
0.028
|
C2
|
0.09
|
0.02
|
C2
|
0.01
|
0.001
|
C3
|
-0.02
|
-0.01
|
C3
|
0.20
|
0.032
|
C4
|
0.02
|
0.01
|
|
|
|
C5
|
0.02
|
0.01
|
|
|
|
C6
|
0.11
|
0.03
|
|
|
|
C7
|
0.06
|
0.02
|
|
|
|
C8
|
0.02
|
0.01
|
|
|
|
C9
|
-0.03
|
-0.01
|
|
|
|
C10
|
0.11
|
0.03
|
|
|
|
C11
|
0.09
|
0.02
|
|
|
|
C12
|
0.02
|
0.01
|
|
|
|
N13
|
0.28
|
0.07
|
|
|
|
Sk+ =S*fk+ (S=1/2*η = 0.16 eV-1) ; Sk- =S*fk- (S = 0.25 eV-1).
The interaction as much as possible by this rule was C3- N13 (Table 7): C3 of 3-bromoprop-1-yne and the N13 of carbazol-9-ide. This was the result obtained experimentally.
Study of the substitution effect on optical properties
In order to study the effect of substitution on optical properties, we have found it useful to determine the lmax, Eex and fosc characteristics of the anionic form of carbazole, product 3 and other compounds already synthesized [23]. From the structures optimized in the presence of acetone as solvent, we determined the absorption spectra, the excitation energies (Eex), the wavelength maximums (lmax) and the intensities of the forces d oscillation (fosc) (Figure 6). These calculations (Table 8) were carried out using the theoretical TD-DFT method with the functional B3LYP under the base 6-31 G (d, p).
Table 8. The maximum wavelengths (lmax) and the intensities of the oscillation forces (fosc) as a function of the excitation energies (Eex).
Molecules
|
Eex
|
lmax
|
fosc
|
Carbazol-9-ide
|
3.2170
4.1013
4.7396
|
385.40
302.30
261.59
|
0.0282
0.0094
0.0000
|
9-vinyl-9H-carbazole
|
3.8856
4.4593
4.6548
|
319.09
278.04
266.36
|
0.0476
0.1348
0.2211
|
Product 3
|
4.0066
4.4635
5.0462
|
309.45
277.77
246.51
|
0.0463
0.1786
0.6610
|
N-butylcarbazole
|
3.8939
4.4136
5.0462
|
318.41
280.92
245.97
|
0.0465
0.1311
0.7534
|
N-pentylcarbazole
|
3.8932
4.4134
5.0462
|
318.46
280.93
245.70
|
0.0471
0.1305
0.7509
|
N-decylcarbazole
|
3.9833
4.5022
5.1560
|
311.26
275.38
240.47
|
0.0474
0.1164
0.7676
|
Note: The peaks of the electronic spectra correspond to the highest values of fosc
From the table of results, it can be seen that increasing the excitation decreases the magnitude lmax of the reagent and of the alkylated products. However, it decreases the fosc magnitude of the reagent and it increases it for N-alkylating compounds. The optical properties lmax and fosc of the anionic form of carbazole decrease due to the substitution. As the number of alkyl carbon atoms increases, lmax decreases.