The water-clustered tautomers including WCs, 1–5, 8 and 9, and the keto form (K) of acetone, Kn, show one hydrogen bond between its oxygen atom and the WCs. But, in two other assemblies including 6 and 7, the acetone molecule enters into the structure of WC and forms a new mixed cluster. In all assemblies, the oxygen atom of one water molecule is slightly pointed to the hydrogen atom of the methyl group (α-proton) of the acetone. This interaction may facilitate the formation of enol through proton abstraction by the nearby water molecule, Fig. 2. The length of the hydrogen bond between K and WC (d1) and the distance between the water molecule and the α-proton of acetone (d2) are presented in Table 2.
In the water-clustered tautomers including enol form (E) of acetone, En, the hydroxyl group actively participate, mainly through two hydrogen bonds, to merge two structures into a new WC-like structure, Fig. 3. The length of two hydrogen bonds between E and WC (d3, d4) are presented in Table 2.
Table 2
The length of hydrogen bonds between K or E and WCs in Kn or En assemblies in the gas phase and solution at the M06/6–31 + G** level of theory
Kn
|
|
En
|
|
d1-d2* (Å)
|
d3-d4 (Å)
|
Gas
|
Acetone
|
DMSO
|
Gas
|
Acetone
|
DMSO
|
K1
|
1.90–2.36
|
1.85–2.76
|
1.84–3.02
|
E1
|
1.87- -
|
1.83- -
|
1.84- -
|
K2
|
1.82–2.27
|
1.78–2.86
|
1.78–2.87
|
E2
|
1.82–1.98
|
1.82–2.03
|
1.83–2.02
|
K3
|
1.77–2.46
|
1.75–2.40
|
1.75–2.41
|
E3
|
1.76–1.84
|
1.73–1.84
|
1.74–1.84
|
K4
|
1.89–2.43
|
1.83–2.69
|
1.83–2.69
|
E4
|
1.72–1.79
|
1.71–1.82
|
1.73–1.83
|
K5
|
1.94–2.50
|
1.84–2.57
|
1.84–2.54
|
E5
|
1.75-2.00
|
1.73–1.98
|
1.74–1.98
|
K6
|
1.93–2.51
|
1.76–3.33
|
1.75–3.32
|
E6
|
1.72–1.85
|
1.71–1.87
|
1.72–1.88
|
K7
|
1.86–2.48
|
1.83–2.62
|
1.82–2.64
|
E7
|
1.66–1.92
|
1.68–1.93
|
1.70–1.93
|
K8
|
2.00-2.79
|
1.78–3.02
|
1.77–3.03
|
E8
|
1.68–1.73
|
1.68–1.76
|
1.69–1.75
|
K9
|
1.85–2.54
|
1.82–3.01
|
1.82–3.05
|
E9
|
1.65–1.89
|
1.66–1.90
|
1.67–1.90
|
* Distance between the water molecule and the α-proton of K |
According to Table 1, the K3 assembly is geometrically much more prone to convert into the corresponding enol form, E3, in the solution phase. Because, it has the shortest distance between the α-proton of acetone and the oxygen atom of water molecule (d2).
The enol content of acetone in the presence of different WCs and in the gas phase or polar solvents were calculated based-on the Gibbs free energy of both assemblies, Kn and En, Table 3. It is expected that the increase in the water content leads to the rise of the enol content, pKe, of acetone because of the formation of hydrogen-bonded assemblies, Kn and En, that stabilize both tautomeric forms of acetone. But the results showed that the number of water molecules of WCs and the solvent polarity have different effects on the enol content of acetone. The pKe decreases with the increasing of solvent polarity. Therefore, the gas phase and non-polar solvents are more suitable condition for the enolization of acetone.
In the gas phase, the WC including 5 water molecules behave differently from most other WCs. But, in the polar solvents, WC with 3 water molecules show such a behavior. For both cases the enolization of acetone is maximum. It seems that the WCs can stabilize the enol form more than the keto form by the formation of an assembly that includes a more stable WC-like segment, E3 and E5, Fig. 3. The significant decrease of enol content in 8 can be attributed to the high stability of its WC, which the cubic structure of it is disrupted by the formation of E8 assembly, Table 3, Fig. 3. (H2O)4 and (H2O)8 among the other small cyclic WCs have distinct stability. Therefore, as is seen in Fig. 2, K4 and K8 show the resistance of the WC against insertion of carbonyl group [43]. Also, the relatively high enol content of 9 can be explained based-on the stabilizing interaction between water molecules and the hydroxyl group of enol form as a part of a stable WC [44].
Table 3
The enol content of acetone, pKe, in the presence of WCs in the gas phase and in acetone and DMSO as a solvent at M06/6–31 + G** levels of theory
pKe
|
|
n
|
Gas
|
Acetone
|
DMSO
|
0
|
10.30
|
12.20
|
12.20
|
1
|
10.20
|
10.80
|
11.50
|
2
|
9.38
|
11.80
|
12.30
|
3
|
9.06
|
9.08
|
9.24
|
4
|
9.39
|
10.40
|
10.10
|
5
|
8.00
|
9.48
|
10.30
|
6
|
8.30
|
10.60
|
10.70
|
7
|
8.34
|
10.40
|
10.60
|
8
|
10.00
|
12.30
|
11.93
|
9
|
8.69
|
9.43
|
9.35
|
The dipole moment of acetone and DMSO |
are 2.62 D and 3.96 D, respectively.
The orientation of orbitals and distance between the hydrogen atom of water and carbon-carbon double bond of the enol form in E5 is such that H-π bonding can form quite easily, Fig. 5 [45]. Therefore, this extra interaction stabilizes more the assembly and increases the Ke.
The energy difference (∆E) and the Gibbs free energy difference (∆G) of Kn and En assemblies in different solvents are plotted against the number of water molecules (n) in the WCs, Fig. 6a and b. It is seen that the value of ∆E for acetone in the gas phase is 13 kcal/mol, which is in good agreement with experimental data, 13.9 kcal/mol [46–48]. The positive value of ∆E indicates that the keto form is more stable than the enol one. Decreasing the ∆E values mean the enolization process is facilitated by the WCs. In other words, the keto form of acetone is easier to convert to the enol form.
As shown in Fig. 6a, the ∆E values for 3, 5 and 9 assemblies in the polar solvents and for 5 and 9 assemblies in the gas phase are all minimum values. The above results are also confirmed by the Gibbs free energy difference (∆G) graphs, Fig. 6b. It is seen that 3 for the solution phase and 5 for the gas phase are global minimum.
To confirm these results, the binding energy for the assemblies was calculated. The binding energy of an assembly (Eb) is defined as:
$${E}_{b}=\left(n\times {E}_{{H}_{2}O}+{E}_{tautomeric form}\right)-{E}_{assembly}$$
, where n is the number of water molecules, \({E}_{{H}_{2}O}\) is the energy of a water molecule, \({E}_{tautomeric form}\) is the energy of enol or keto form of acetone and \({E}_{assembly}\) is the energy of assembly, Kn or En. The binding energy (Eb) of each assembly (Kn and En) was plotted against the number of involved water molecules (n), Fig. 8a. From the graph, it is observed that the binding energy of each assembly is increased by increasing n. Except in some few special cases, the binding energy of En is a little higher than Kn in both the gas phase and in solution, but the Kn assemblies are still more stable than the En ones. The Eb values for the gas phase are higher than the solution phases. This is due to the interaction of water molecules with the solvent, which leads to weakening of the hydrogen bonds in the solution phase and, therefore, decreasing the stability of assemblies.
The binding energy difference (ΔEb) of water-clustered tautomers is calculated by subtracting Eb(Kn) from Eb(En). This quantity is a good and reliable estimate of the overall energy for the enolization reaction of acetone. An energy diagram is created by plotting the -ΔEb values as a function of n, Fig. 8b. The pKe values are also plotted for comparison. As is seen, the enolization reaction of acetone is very favorable in the presence of 5 and 3 water molecules in the gas and solution phases, respectively. As mentioned before, in these cases, the binding energy of enol form of acetone is approaching to the keto form.