The theoretical calculations of the electronic structure of the BZ, ANI, and NA molecules have shown the effect of double ionization on the chemical bonds of -CC-, -NH2, and -NO2 groups when are removed two electrons from the neutral molecules. The different isomeric conformations lead to the stabilization of the system in the molecular ion doubly ionized (BZ2+, ANI2+, oNA2+, mNA2+, and pNA2+), which each molecular ion needs to find a new conformation of lower energy to compensate the loss of two electrons from the system.
Only the neutral or dicationic molecules of oNA (Figs. 1(c) and 1(h), respectively) do not present any atoms outside of the molecular plane. According to the natural orbital (NBO) [22], there is a formation of hydrogen bonding between the hydrogen of the -NH2 group and the oxygen of the -NO2 group.
3.1. Analysis of the Wiberg bond indices and Bader's topology
It was analyzed the chemical bonds between C-C, C-N, and N-O of neutral and dicationic molecules using Wiberg bond indices and the quantum theory of atoms in molecules (QTAIM) [10],[11], in the search for the weakest bonds and most likely to break to form a possible stable fragments. Molecular ions (M+) show a smaller percentage reduction in bond order and electron density in some bond pairs. This reduction in electron density is evident when molecular structures are studied by computational methods.
Table 1 shows the values of the bond length (L), bond order (BO), electronic density \(\rho \left(r\right)\), Laplacian of the electronic density, \({\nabla }^{2}\rho \left(r\right)\), and the differences for the bond order (∆BO) and electron density (∆ρ) for both, neutral and dicationic states of the benzene molecule. The values for the benzene, aniline, and the nitroanilines, in conformations ortho-, meta- and para-, for the neutral and doubly ionized molecules are shown in the supplementary material. Also, it is calculated the percentage of reduction (PR %) in the electronic density of pairs of atoms, when identifying a reduction in electronic density. The Calculation of percentage reduction is performed using Eq. (1) given below:
Table 1
Comparison of bond length (L (Å); bond order (BO); QTAIM properties at the bond critical points (BCP); bond order difference (∆BO); electron density difference (∆ρ) of benzene molecule neutral and dicationic; and percentage reduction (PR) in the electronic density
|
Exp.[38]
|
Neutral
|
Dicationic
|
|
|
|
Bond
|
L (Å)
|
L (Å)
|
BO
|
\(\rho\)(1/𝑎03)
|
\({\nabla }^{2}\rho\)(1/𝑎05)
|
L (Å)
|
BO
|
\(\rho\)(1/𝑎03)
|
\({\nabla }^{2}\rho\)(1/𝑎05)
|
∆BO
|
∆ρ
|
PR%
|
r(C1-C2)
|
1.3971
|
1.399
|
1.456
|
0.304
|
-0.740
|
1.464
|
0.813
|
0.280
|
-0.688
|
0.643
|
0.025
|
-7.895
|
r(C2-C3)
|
1.3971
|
1.399
|
1.455
|
0.305
|
-0.740
|
1.397
|
1.209
|
0.301
|
-0.725
|
0.246
|
0.003
|
-1.311
|
r(C3-C4)
|
1.3971
|
1.399
|
1.457
|
0.304
|
-0.740
|
1.397
|
1.209
|
0.301
|
-0.725
|
0.248
|
0.003
|
-0.987
|
r(C4-C5)
|
1.3971
|
1.399
|
1.456
|
0.304
|
-0.740
|
1.464
|
0.813
|
0.280
|
-0.688
|
0.643
|
0.025
|
-7.895
|
r(C5-C6)
|
1.3971
|
1.399
|
1.455
|
0.305
|
-0.740
|
1.397
|
1.209
|
0.301
|
-0.725
|
0.246
|
0.003
|
-1.311
|
r(C6-C1)
|
1.3971
|
1.399
|
1.457
|
0.304
|
-0.740
|
1.397
|
1.209
|
0.301
|
-0.725
|
0.248
|
0.003
|
-0.987
|
CCC (o)
|
120
|
119.9
|
123.2-107.2
|
|
|
|
$$PR\text{%}=\left(\frac{{\rho }_{Dication}}{{\rho }_{Neutral}}-1\right)\times 100$$
1
Table 1 shows the pairs of atoms r(C1-C2) and r(C4-C5) of the BZ2+ molecule, which have lower bond order, lower electronic density, and also a percentage of reduction of -7.895%, concerning the neutral molecule. In addition, it is possible to form two types of fragments C2H2+, and C3H3+ of mass-to-charge ratio m/e = 26, and m/e = 39, respectively. They are potentially favorable fragments, and sufficient to maintain consistency with the experimental results of mass spectrometry of benzene molecule [39–43].
Table 2 shows r(C2-C3), r(C4-C5), r(C5-C6), and r(C7-C2) bond lengths of the ANI and ANI2+ molecules, which have lower bond order and lower electronic. However, r(C2-C3) and r(C7-C2) bond lengths have a significant percentage of reduction with values around − 11.3%. This percentage is a strong indication of the break bond position with the possibility of formation of the C5H5+ and C5H6+ fragments of the mass-to-charge ratio of m/e = 65 and m/e = 66, respectively. The fragments show consistency with the result found in the literature [44–46].
Table 2
Comparison of bond length (L (Å); bond order (BO); QTAIM properties at the bond critical points (BCP); bond order difference (∆BO); electron density difference (∆ρ) of aniline molecule neutral and dicationic; and percentage reduction (PR) in the electronic density
| Exp.[39] | Neutral | Dicationic | | | |
Bond | L (Å) | L (Å) | BO | \(\rho\)(1/𝑎03) | \({\nabla }^{2}\rho\)(1/𝑎05) | L (Å) | BO | \(\rho\)(1/𝑎03) | \({\nabla }^{2}\rho\)(1/𝑎05) | ∆BO | ∆ρ | PR% |
r(N1-C2) | 1.402 | 1.400 | 0.962 | 0.296 | -0.908 | 1.295 | 1.542 | 0.360 | -0.703 | -0.580 | -0.064 | 21.622 |
r(C2-C3) | 1.397 | 1.407 | 0.931 | 0.301 | -0.728 | 1.485 | 0.630 | 0.267 | -0.637 | 0.301 | 0.035 | -11.296 |
r(C3-C4) | 1.394 | 1.396 | 1.434 | 0.305 | -0.736 | 1.361 | 1.955 | 0.329 | -0.849 | -0.521 | -0.024 | 7.869 |
r(C4-C5) | 1.396 | 1.399 | 1.439 | 0.304 | -0.736 | 1.441 | 1.021 | 0.288 | -0.707 | 0.418 | 0.016 | -5.263 |
r(C5-C6) | - | 1.399 | 1.439 | 0.304 | -0.736 | 1.441 | 1.021 | 0.288 | -0.707 | 0.418 | 0.016 | -5.263 |
r(C6-C7) | - | 1.396 | 1.434 | 0.305 | -0.736 | 1.361 | 1.955 | 0.329 | -0.849 | -0.521 | -0.024 | 7.869 |
r(C7-C2) | - | 1.407 | 0.931 | 0.301 | -0.728 | 1.485 | 0.630 | 0.267 | -0.637 | 0.301 | 0.035 | -11.296 |
HNH (º) | 113.10 | 111.9 | 115.5 | | | |
HNC (º) | 115.94 | 115.5 | 122.2 | | | |
Table 3. Comparison of bond length (L (Å); bond order (BO); QTAIM properties at the bond critical points (BCP); bond order difference (∆BO); electron density difference (∆ρ) of o-nitroaniline molecule neutral and dicationic; and percentage reduction (PR) in the electronic density. |
| Exp[40],[41] | Neutral | Dicationic | | | |
Bond | L (Å) | L (Å) | BO | \(\rho\)(1/𝑎03) | \({\nabla }^{2}\rho\)(1/𝑎05) | L (Å) | BO | \(\rho\)(1/𝑎03) | \({\nabla }^{2}\rho\)(1/𝑎05) | ∆BO | ∆ρ | PR% |
r(N1-C2) | 1.455 | 1.358 | 1.148 | 0.322 | -1.056 | 1.290 | 1.457 | 0.368 | -0.795 | -0.309 | -0.047 | 14.286 |
r(C2-C3) | 1.402 | 1.426 | 0.102 | 0.291 | -0.686 | 1.491 | 0.600 | 0.265 | -0.620 | 0.960 | 0.027 | -8.935 |
r(C3-C4) | 1.387 | 1.408 | 0.90 | 0.300 | -0.723 | 1.355 | 0.733 | 0.333 | -0.872 | -0.643 | -0.033 | 11.000 |
r(C4-C5) | 1.374 | 1.383 | 1.961 | 0.312 | -0.768 | 1.449 | 1.305 | 0.283 | -0.687 | 0.656 | 0.029 | -9.295 |
r(C5-C6) | 1.380 | 1.409 | 1.649 | 0.299 | -0.723 | 1.428 | 1.302 | 0.294 | -0.730 | 0.347 | 0.005 | -1.672 |
r(C6-C7) | 1.383 | 1.383 | 1.505 | 0.313 | -0.769 | 1.366 | 1.756 | 0.326 | -0.842 | -0.251 | -0.013 | 4.153 |
r(C7-C2) | 1.379 | 1.421 | 0.477 | 0.294 | -0.706 | 1.488 | 0.366 | 0.266 | -0.631 | 0.111 | 0.029 | -9.524 |
r(C3-N9) | 1.451 | 1.450 | 0.871 | 0.266 | -0.671 | 1.507 | 0.676 | 0.254 | -0.570 | 0.195 | 0.012 | -4.511 |
r(N9-O8) | 1.217 | 1.245 | 0.860 | 0.494 | -1.038 | 1.235 | 0.949 | 0.528 | -1.151 | -0.890 | -0.034 | 6.883 |
r(N9-O10) | 1.226 | 1.230 | 0.914 | 0.476 | -0.976 | 1.203 | 1.102 | 0.488 | -0.995 | -0.188 | -0.011 | 2.521 |
HNH (º) | - | 121.3 | 121.3 | | | |
HNO (º) | 124.7 | 122.4 | 127.4 | | | |
Table 3 shows r(C2-C3) and r(C4-C5) bond lengths with lower bond order, and r(C2-C3), r(C4-C5), and r(C7-C2) bond lengths with lower electronic density for the neutral and dicationic molecules of oNA. However, the results show a percentage of reduction of -8.935% for r(C2-C3), -9.295% for r(C4-C5), and − 9.524% for r(C7-C2). There is possibility of formation of C6H6N+ and C5H6+ fragments of mass-to-charge ratio of m/e = 92 and m/e = 66, respectively. The fragments show consistency with the result found in the literature [23],[24].
Table 4 shows r(C2-C3), r(C5-C6), and r(C7-C2) bond lengths with lower bond order, and r(C2-C3) and r(C7-C2) bond lengths with lower electronic density for the neutral and dicationic molecules of mNA2+. There are two bond lengths with a significant percentage of reduction of -9.603% for r(C2-C3) and − 11.296% for r(C7-C2). There is possibility of formation of C5H5+, C6H6N+, and C5H6N+ fragments of mass-to-charge ratio of m/e = 65, m/e = 80 and m/e = 92, respectively. The fragments show consistency with the result found in the literature [24],[25].
Table 4
Comparison of bond length (L (Å); bond order (BO); QTAIM properties at the bond critical points (BCP); bond order difference (∆BO); electron density difference (∆ρ) of m-nitroaniline molecule neutral and dicationic; and percentage reduction (PR) in the electronic density
| Exp.[2] | Neutral | Dicationic | | | |
Bond | L (Å) | L (Å) | BO | \(\rho\)(1/𝑎03) | \({\nabla }^{2}\rho\)(1/𝑎05) | L (Å) | BO | \(\rho\)(1/𝑎03) | \({\nabla }^{2}\rho\)(1/𝑎05) | ∆BO | ∆ρ | PR% |
r(N1-C2) | 1.380 | 1.392 | 0.949 | 0.302 | -0.942 | 1.301 | 1.465 | 0.357 | -0.773 | -0.516 | -0.055 | 18.212 |
r(C2-C3) | - | 1.405 | 1.329 | 0.302 | -0.731 | 1.468 | 0.828 | 0.273 | -0.651 | 0.501 | 0.029 | -9.603 |
r(C3-C4) | - | 1.393 | 0.551 | 0.308 | -0.752 | 1.356 | 1.218 | 0.331 | -0.850 | -0.667 | -0.024 | 7.468 |
r(C4-C5) | - | 1.395 | 0.526 | 0.307 | -0.755 | 1.441 | 0.678 | 0.290 | -0.714 | -0.152 | 0.018 | -5.538 |
r(C5-C6) | - | 1.397 | 1.792 | 0.304 | -0.737 | 1.430 | 1.288 | 0.292 | -0.721 | 0.504 | 0.012 | -3.947 |
r(C6-C7) | - | 1.395 | 1.562 | 0.306 | -0.742 | 1.366 | 1.848 | 0.325 | -0.837 | -0.286 | -0.020 | 6.209 |
r(C7-C2) | - | 1.410 | 1.109 | 0.301 | -0.728 | 1.486 | 0.648 | 0.267 | -0.635 | 0.461 | 0.034 | -11.296 |
r(C4-N9) | 1.457 | 1.479 | 0.657 | 0.254 | -0.623 | 1.483 | 0.703 | 0.265 | -0.654 | -0.460 | -0.011 | 4.331 |
r(N9-O8) | 1.222 | 1.230 | 0.869 | 0.496 | -1.051 | 1.203 | 1.125 | 0.490 | -1.019 | -0.256 | 0.006 | -1.210 |
r(N9-O10) | 1.221 | 1.228 | 0.804 | 0.495 | -1.045 | 1.235 | 1.027 | 0.526 | -1.131 | -0.223 | -0.031 | 6.263 |
HNH (o) | 114.6 | 113.0 | 115.5 | | | |
HNO (o) | 122.8 | 124.3 | 128.9 | | | |
Table 5 shows r(C2-C3), r(C3-C4), r(C6-C7), r(C7-C2), and r(C5-N9 ) bond lengths with lower bond order, and r(C2-C3), r(C4-C5), r(C5-C6), r(C7-C2) and r(N9-O10) bond lengths with lower electronic density for the neutral and dicationic molecules of pNA2+. There are five bond lengths with a significant percentage of reduction of -9.030% for r(C2-C3), -7.213% for r(C4-C5), -7.213% for r(C5-C6), -9.030% for r(C7-C2), and 4.684% for r(N9-O10). There is possibility of formation of C5H6N+, C6H6N++, and C6H5NO+ fragments with mass-to-charge ratio of m/e = 80, m/e = 92, and m/e = 107, respectively. The fragments show consistency with the result found in the literature [24],[26],[27].
Table 5
Comparison of bond length (L (Å); bond order (BO); QTAIM properties at the bond critical points (BCP); bond order difference (∆BO); electron density difference (∆ρ) of p-nitroaniline molecule neutral and dicationic; and percentage reduction (PR) in the electronic density
| Exp.[2] | Neutral | Dicationic | | | |
Bond | L (Å) | L (Å) | BO | \(\rho\)(1/𝑎03) | \({\nabla }^{2}\rho\)(1/𝑎05) | L (Å) | BO | \(\rho\)(1/𝑎03) | \({\nabla }^{2}\rho\)(1/𝑎05) | ∆BO | ∆ρ | PR% |
r(N1-C2) | 1.355 | 1.380 | 1.064 | 0.307 | -0.978 | 1.301 | 1.458 | 0.357 | -0.795 | -0.394 | -0.050 | 16.287 |
r(C2-C3) | - | 1.413 | 1.066 | 0.299 | -0.722 | 1.474 | 0.845 | 0.272 | -0.651 | 0.221 | 0.027 | -9.030 |
r(C3-C4) | - | 1.388 | 2.204 | 0.309 | -0.751 | 1.356 | 1.977 | 0.330 | -0.842 | 0.227 | -0.021 | 6.796 |
r(C4-C5) | - | 1.399 | 0.482 | 0.305 | -0.746 | 1.445 | 0.908 | 0.283 | -0.686 | -0.426 | 0.022 | -7.213 |
r(C5-C6) | - | 1.399 | 0.482 | 0.305 | -0.746 | 1.445 | 0.908 | 0.283 | -0.686 | -0.426 | 0.022 | -7.213 |
r(C6-C7) | - | 1.388 | 2.204 | 0.309 | -0.751 | 1.356 | 1.977 | 0.330 | -0.842 | 0.227 | -0.021 | 6.796 |
r(C7-C2) | - | 1.413 | 1.066 | 0.299 | -0.722 | 1.474 | 0.845 | 0.272 | -0.651 | 0.221 | 0.027 | -9.030 |
r(C5-N9) | 1.433 | 1.459 | 0.753 | 0.264 | -0.671 | 1.453 | 0.454 | 0.279 | -0.765 | 0.299 | -0.015 | 5.682 |
r(N9-O8) | 1.244 | 1.233 | 0.861 | 0.491 | -1.027 | 1.181 | 1.413 | 0.550 | -1.233 | -0.552 | -0.059 | 12.016 |
r(N9-O10) | 1.235 | 1.233 | 0.861 | 0.491 | -1.027 | 1.254 | 1.056 | 0.468 | -0.928 | -0.195 | 0.023 | -4.684 |
HNH (o) | 120.9 | 114.9 | 115.6 | | | |
HNO (o) | 122 | 123.9 | 132.9 | | | |
There was a significant increase in the bond order in the dicationic states in relation to the isomeric positions of the r(N1-C2) bond length, following the order: oNA2+ (26.92%) < pNA2+ (45.8%) < mNA2+ (54.4%). In relation to the isomeric positions of the r(CX-N9; X is the atom number = 3, 4 and 5) bond length, there was a change in the bond length following the order: mNA2+ (-39.7%) > oNA2+ (-22.4%). However, there is an increase in the bond order of pNA2+ (7%) due to charge relocation which can be favorable to the electron transfer by the -NO2 group in the pNA2+. Therefore, the best relocation of charge is an indication of an increase in the bond order[28].
The electron transfer possibility an analysis from this first analysis based on electrostatic potential maps can relate the changes in the bond order, the electronic density, and positive/negative regions. The electrostatic potential map (PES) [29] is a tool used to determine the reactive regions of nucleophilic and electrophilic attacks in a molecular system.
Figure 2 shows the map of the potential energy surface generated by the electron isodensity surface of 0.02/a.u3 for each point on the map for the molecules of BZ, ANI, oNA, mNA, and pNA. Thereby, the increase in bond orders of the -NH2 group, and the reduction of bond orders for the group -NO2 can be analyzed with help of electrostatic potential maps from the electrostatic interactions between species doubly ionized. These areas of electrostatic potentials can be displayed as isocontour surfaces (maps of electron density).
The electrostatic potential maps of neutral and dicationic molecules indicate a lower charge concentration in all dications, mainly in the dark blue regions, justified by the decrease in the -NH2 group bond order. The regions of positive electrostatic potential are concentrated mainly on the nitrogen atoms of the amine group and also on the hydrogen atoms. The dark blue and light blue areas represent a positive potential of atoms -H bond to the nitrogen and ring carbon atoms. However, due to the influence of the -NO2 group, which determines the character of a negative charge, this potential map is changed and these changes are represented in the regions in red, negative potential. The loss of two electrons in the (f), (g), (h), (i), and (j) monomers; leaving the peripheral regions to the center of the ring more positive (surface observed in dark blue and light blue) toward the center of the ring for bonds with lower bond order. The electron-donating groups, such as the -NH2, increase the electron density in the positions ortho-, meta-, and para- in an aromatic of the Kekulé's circuits type[30] (electron-withdrawing groups).
Wiberg's binding indices and Bader's topological analysis satisfactorily describe the weaker connections of molecular systems in the studies. In the comparison of the results found by both theories, it was necessary to define the connections with lower charge concentrations, with greater possibilities of breaking chemical bonds. In order to do this, electronic density maps and the Laplacian electronic density (topological analysis), show curves, and regions of higher concentrations of charge on the bonds in the layer of valence [31].
The electronic densities are located in pairs of atoms showing higher and lower concentrations of charge, especially in the regions probable to break bonds at the dications. The pairs of atoms that have connected regions have higher concentrations of load on the bonds and are less likely to break the bond in these regions [32].
From Fig. 3, it is possible to observe the different concentrations of charge. The BZ molecule (a) shows concentrations of uniform charges throughout its structure, but the BZ2+ molecule (C) shows a low concentration of charge (or lower electronic density) in the r(C1-C2), and r(C4-C5) bond lengths. The ANI molecule (b) removes the uniformity of density in the aromatic ring due to group -NH2. The change in the electronic density of ANI2+ molecule (d) shows a difference between the electronic densities in the r(C2-C3), r(C4-C5), r(C5-C6), and r(C7-C2) bond lengths.
At the top of Fig. 4, the neutral states of the oNA (a), mNA (b), and pNA (c) molecules are shown. The oNA (a) molecule presents intramolecular interaction between the oxygen from the nitro group and the hydrogen from the amino group, which indicates that the nuclei support all concentrations of charge (\({\nabla }^{2}\rho \left(r\right)\) > 0). Whilst, oNA2+ molecule (d) shows a significant increase in the electronic density in the region of interaction H⋅⋅⋅O(8)-, and a lower electronic density in the r(C2-C3), r(C4-C5), r(C7-C2), and r(C3-N9) bond lengths. The mNA2+ (e) and pNA2+ (f) molecules show the lower concentrations of charge in r(C2-C3), r(C4-C5), r(C5-C6), r(C7-C2), and r(N9-O8) bond lengths in relation to the neutral molecule. Therefore, with the relaxation of the system, the charge distribution is altered, thus leaving some pairs of atoms weaker than the others and this can be seen in the electronic density maps, represented graphically for neutral and doubly ionized species.
Even though, the possibility to find a route of fragmentation by the reduction of the electronic densities (using Bader’s protocol) of chemical bonds in molecule dicationics, not all pairs of atoms involved in this analysis converge to the result of the analysis in terms of the bond orders. Therefore, the use of both methods to estimate the chemical bonds are necessary.
3.2. Thermodynamic properties
In addition, we approach the thermodynamic properties of each neutral and doubly ionized molecular structure and mix it with other results found in the literature, to assemble Table 6, which was very useful in the construction of Table 7, where the results of the enthalpy calculations are found. formation at temperatures of 0K and 298K, and Gibbs free energy.
Table 6
Standard enthalpy of formation of neutral elements (ΔHo), Standard enthalpy of formation at 0K, and entropy at 298K of the cationic elements (ΔfHo in kcal.mol-1 and ΔSo in kcal.mol-1K-1, respectively)
Neutral | ΔHo [a] | ion | | ΔfHo (X,0K) | ΔSo(X,298K) | |
H | 1.01 | H+ | | 365.20[b] | 26.012 | |
C | 0.25 | C+ | | 429.60[c] | 34.773 | |
N | 1.04 | N+ | | 447.60[d] | 33.856 | |
O | 1.04 | O+ | | 373.04[e] | 35.629 | |
[a] ref.[33]; [b] Ref.[42]; [c] Ref.[34]; [d] Ref.[43]; [e] Ref.[44] |
Table 7
Molecular ions, doubly ionized, atomic mass unit (amu), fragmentation channels, and the enthalpy of formation (0K and 298K) and their Gibbs free energies (kcal.mol − 1).
Neutral | molecule | Mass (amu) | ∆Ho(0k) | ∆Ho(298k) | ∆Go(298k) |
---|
BZ | C6H62+ | 78 | 559.9 | 556.1 | 645.0 |
ANI | C6H5NH2+ | 93 | 423.9 | 418.6 | 592.4 |
ONA | C6H6N2O2 + 2 | 138 | 181.7 | 175.8 | 636.9 |
MNA | C6H6N2O2 + 2 | 138 | 175.0 | 169.3 | 635.0 |
PNA | C6H6N2O2 + 2 | 138 | 168.0 | 162.3 | 630.3 |
In Table 6 we present the ions: hydrogen (H+), carbon (C+), nitrogen (N+), and oxygen (O+), with the combination of thermodynamic properties of enthalpies formation of neutral elements (H298K-H0K) with the enthalpies of formation of the cationic atoms and between the calculated entropies of each ion (So298K), seeking a better approximation of the energy properties of the molecular ions listed in Table 7. But, to generate each value enthalpy of formation (\(\varDelta {H}_{0K}^{o}\) and \(\varDelta {H}_{298K}^{o}\)) and Gibbs free energy (\(\varDelta {G}_{298K}^{o}\)). The Eq. (2) represents the enthalpy of formation in 0K, where x is the number of atoms of X that represents each element of a molecule M, and ∑Do(M) represents the atomization energy of the molecule (M).
$${\varDelta }_{f}{H}_{0K}^{o}=\sum _{atoms}x{\varDelta }_{f}{H}_{(X;0K)}^{o}-\sum _{atoms}{D}_{o}\left(M\right)$$
2
Equation (3) represents the enthalpy of formation in 298K, where\({H}_{M}^{o}\left(298K\right)-{H}_{M}^{o} \left(0K\right)\) represents the correction of the enthalpy for the molecule M, and\({H}_{X}^{o}\left(298K\right)-{H}_{X}^{o}\left(0K\right)\) is the correction of the enthalpy of atomic elements X.
$${\varDelta H}_{298 K}^{o}={\varDelta H}_{0 K}^{o}+\left[{\varDelta H}_{M}^{o} \left(298K\right)-{\varDelta H}_{M}^{o} \left(0K\right)\right]$$
$$-\sum x\left[{\varDelta H}_{M}^{o} \right(298K)-{\varDelta H}_{M}^{o} (0K\left)\right]$$
3
The Eq. (4) represents the Gibbs free energy in 298K, where\({S}_{(M, 298K)}^{o}\) and\({S}_{(X, 298K)}^{o}\) represent the enthalpy of reaction of the molecule M, the entropy of atoms.
$$\varDelta {G}_{298K}{H}_{0K}^{o}={\varDelta }_{r}{H}_{\left(298K\right)}^{o}-298.15({S}_{(M,298K)}^{o}-\sum {S}_{(x,298K)}^{o})$$
4
The equations (2), (3), and (4) were used to calculate the assemble in Table 7, based on the References [33], [34] and [35]. We present in Table 7 the doubly ionized molecular ions of benzene, aniline, and nitroaniline (ortho, meta, and para), accompanied by their atomic masses of its enthalpies of formation in 0K, and 298K; and their Gibbs free energies.
For positive energies, we have a non-spontaneous process, due to the removal of two electrons of the system requiring a large amount of energy (Ionization Potential - IP) for which the electrons are ejected out of the layer of the valence of the molecule. However, we found a paper that refers to the heat of formation of benzene doubly ionized experimental value of 26.0 eV = 599.57 kcal.mol-1 [36]. From the values of ground state energy of the systems, it was possible to calculate the IP of the structures using Eq. (5) [37].
IP = EN−1 - EN (5)
Where E(N−1) and EN are the total energies of the (N-1) and N electron system, respectively. Table 8 shows the values of electronic energy (E0), dipole moment (µ), and ionization potential (IP), of neutral molecules, and dicationics; and compare them with some experimental results found in the literature. The results show a good approximation of our theoretical calculations with experimental results, revealing that the neutral molecules have theoretical results of the dipole moment of ionization potential, and are very close to the experimental results.
Table 8
Dipole moments (µ) and ionization potential (IP) for neutral and dicationic chemical species at the UB3LYP/aug-cc-pVDZ calculation level, and experimental values found in the literature.
Molecules | Theoretical | Exp. |
---|
| ET (a.u) | µ[D]* | IP (eV) | µ[D]* | IP (eV) |
Neutral | | | | | |
BZ | -232.27460349 | 0.0 | 9.1 | 0.0[a] | 9.24[c] |
ANI | -287.64377206 | 1.6 | 7.5 | 1.5[b] | 7.72[d] |
ONA | -492.18807246 | 4.9 | 8.2 | 4.3[b] | 8.43[e] |
MNA | -492.18374531 | 5.8 | 8.2 | 4.9[b] | 8.60[f] |
PNA | -492.18774648 | 7.4 | 8.3 | 6.2[b] | 8.43[f] |
Dicationic | | | | | |
BZ2+ | -231.37763151 | 0.0 | 21.3 | - | - |
ANI2+ | -286.86572780 | 2.8 | 20.3 | - | - |
ONA2+ | -491.36806291 | 10.1 | 19.8 | - | - |
MNA2+ | -491.36709206 | 12.5 | 19.4 | - | - |
PNA2+ | -491.37881464 | 10.8 | 20.2 | - | - |
[D]* = 1 Debye = 3.33564 x 10–30 C.m |
[a] ref.[45]; [b] Ref.[46]; [c] Ref.[47]; [d] Ref.[48]; [e] Ref.[49]; [f] Ref.[50]. |