Theoretical Study of Some Benzene Derivatives in Water

Using the HyperChem programme , the influence of water on the properties of some monosubstituted aromatic compounds was studied from the point of view of the intermolecular interactions. There have been estimated some physico-chemical parameters of the benzene, fluorobenzene, chlorobenzene, bromobenzene, iodobenzene, nitrobenzene, phenol and aniline when solved in water, surrounded by one or two solvation spheres. The boundary lengths, total energies, border levels energy, dipole moments, polarizabilities, wavelengths and the probabilities of the electronic transitions have been obtained.

The intermolecular interactions between the solvent and the solvate are important factors influencing the micromolecular processes; they have been intensely studied in the last years due to their multiple applications in chemistry, biochemistry and technology [1][2][3][4][5][6].
Water has a very high dielectric constant, ε = 78,5 la 25 0 C, so it is a good dielectric and a good solvent for the polar molecules or ionic compounds [1].
A lot of hemi-classical methods of tratment of the solvent effect on the molecular structure use in their calculation different molecular properties which are not accesible by usual physical measurements [10][11][12].These data can be obtained by means of cuantic chemistry calculation, for systems formed of a spectrally active molecule surrounded by many layers of solvent molecules.The hemi-empirical approximations are based on the assumption that the solvent and solvate molecules are distant enough to neglect the cover of the electronic distributions of the molecules in the system.The methods of the cuantum chemistry follow two main directions in modelling the solvent: explicit and implicit.The explicit modellation takes into account all the particularities of the molecules and their interactions, but takes into account a large number of mollecules and it is practically impossible to be used for the complex methods of the cuantum chemistry or for very big molecules.In implicit modelling, were the solvent is considered a "continuum" characterized only by its macroscopic properties (dielectric constant, refraction index, polarizability, dipole moment, ionization potential or density), we do not take into account the specific interactions between the molecules (hydrogen boundaries or donor-acceptor interactions), but we permit a more accesible mathematical approach.For the investigation of the physico-chemical parameters of some spectrally active molecules we have chosen the explicit modelling by using the hemi-empirical calculation method PM3, for systems formed of a molecule surrounded by a given number of solvent molecules, which form 1-2 solvation spheres.
When a molecule is placed in a solvent, there appear interactions between the solvite molecule and the * email: ela_dim@yahoo.com;Tel.: 0741204549 surrounding solvent.Due to intermolecular interactions, the solvated molecules can disturb the local order in the solvent, so the macroscopic properties of the solvent may change.

Bases of the method
The HyperChem programme [13] offers different methods to analyse the molecules in the free space and in different solvents.The method chosen [13][14][15][16] is very important for the obtained results.
For the molecules studied in this paper the following properties have been determined: dipole moments, polarizabilities, total energy value, of the HOMO (Highest Occupied Molecular Orbital) and LUMO (Lowest Unoccupied Molecular Orbital) levels, and the boundary lengths.
In the model of the simple liquid.Abe [10], the solvent molecules, assumed to be spherical, are set around the solvate molecule in spherical layers concentric with the sphere representing the solved molecule [11,12].
Considering that the distance between the centre of the spectrally active molecule , u, and the centre of the solvent molecule v(p) in the solvation layer p is R uv(p) , [10] has shown that the molecules of a layer p have the centres on the radius sphere: (1) The number of the solvent molecules on the solvation layer p (p = 1, 2...) are approximated as being given by the function: (2) The radii of the solvate and the solvent molecules can be calculated using the relation (3): (3) where i = u or v Using the hemi-empirical method PM3 [17] the influence of water as a solvent on some structural parameters of the benzene molecule and its monohalogenate derivatives C 6 H 5 -X : X= F, Cl, Br, I, and also nitrobenzene, phenol and aniline was investigated.This choice was determined by the low water solubility of these molecules [1,18].The theoretical results obtained in the Abe model [10 -12] have been the starting point for the calculation of the interaction energy of the above mentioned structures with the first or the first two solvation spheres.
To analyse the interactions between the solvate molecule and the first or the first two solvation spheres, we have simulated a cube of certain dimensions full of solvent molecules, and we have introduced in its centre the molecule whose properties we want to evaluate.In this "solvent box" the water molecules, which are the solvent, have a random distribution.To simulate the first two solvation spheres, according to Abe's model, we have introduced the studied molecule into the cube and we have also introduced a number of water molecules calculated according to (2), for the first and, respectively, for the first two solvation spheres, the results being given in table 1.
Molecular systems have been optimized using the PM3 method, in the HyperChem pack.After the chosen convergence criterion is fulfilled, the molecule has been "extracted" and "frozen" and on this structure a "single point" calculation has been done.The obtained results have been compared with those obtained in the case in which the molecular structure has been optimized in free space.
Figure 1 shows the chlorobenzene molecule surrounded by the first solvation sphere (a), and, respectively, the first two solvation spheres (b).

Results and discussions
Optimization by means of the PM3 method, of the HyperChem programme permitted us, for the beginning, the calculation of the volume of the investigated molecules and then, their radii.These radii have been compared to those in (3), using the molecular mass and densities of the investigated substances, as presented in table 2.

Table 2 RADII OF THE INVESTIGATED MOLECULES
As one can see in table 2, there is a proportionality factor between the molecule radii determined by means of HyperChem programme and those obtained from the substance densities.For benzene, fluorobenzene, chlorobenzene, bromobenzene and iodobenzene the medium value of this factor is 1.304, whereas for the other molecules in the table, with stronger interactions, the value of f raises up to ~ 1.333.A lower value can be seen in the case of fluorobenze, which has a higher stabilization energy by conjugation.The highest calculated value is that of water, which can form 4 hydrogen boundaries simultaneously and so the strength of the interactions is much higher than in the case of the molecules with only Van der Waals forces.
In table 3 the lengths of the boundaries C -X (X = F, Cl, Br, I, NO 2 , OH, NH 2 ) for the studied systems are given.From the table, one can see a good concordance between the values calculated by means of the PM3 method, in free space and those determined experimentally [16 -22].
For the fluorobenzene and chlorobenzene molecules, one can see an increase of the length of the boundary length C -X when passing from the gaseous state to solution.In the case of nitrobenzene, phenol and aniline molecules, due to the formation of the hydrogen boundaries with the water molecules, one can see the shortening of the boundaries C -X.The alteration in the value of the C -X boundary determines the variation of the electric dipole moment of the studied molecules.
To evidence the variation of the dipole moment of the studied molecules by the number of water molecules, even when the solvation spheres are incomplete, we have made calculations for the molecules placed in "solvent boxes" containing 12, 24, 60, and respectively 96 water molecules.In figure 2 this dependency is shown..One can see that at  4 contains values of the total energy variation, calculated by means of the PM3 method in all the considered cases: in free space and in solvent.∆E 1 and ∆E 2 represent the difference in total energy obtained when molecules pass from the free space in the first solvation sphere and, respectively, in the first two solvation spheres.One can see that ∆E 2 is always smaller than ∆E 1 , which means that, when passing from the first solvation sphere into the first two solvation spheres, the total energy decreases.
The values of energy obtained for the highest molecular orbital (HOMO -Highest Occupied Molecular Orbital) and the lower vacant molecular orbital (LUMO -Lowest Unoccupied Molecular Orbital) are given in table 5.
The lowest the energy of the last occupied energetic level (HOMO), the more stable the molecule is.One can   5 that the energy values of the HOMO level for the case in which the analyzed molecules are surrounded by the first solvation sphere are greater than in the case in which these molecules are in free space.Quite big differences between the values of the HOMO energy corresponding to the unsolved state and the values obtained for the molecules surrounded by the first two solvation spheres are noticed for the nitrobenzene, phenol and aniline.The polarizability of the molecules in fundamental state has been calculated by means of QSAR (Quantitative Structure-Activity Relationships) [23], a HyperChem module which allows us to calculate a number of physical parameters of the studied systems.In Table 6 one can see a good concordance between the experimental values [24] and those obtained by means of the Hyper Chem programme.

Conclusions
The values of the physical parameters (the distances carbon -substitute and polarizability) are in a good agreement with those in the literature.
The values of the total energy of a molecule in the solvent box show the low solvability in water of benzene and its studied derivatives.

Table 1 Fig. 1
Fig. 1 Chlorobenzene molecule in the water cube, in the first solvation sphere (a), respectively the first two solvation spheres (b)

Table 3 Fig. 2
Fig.2Variation of the dipole moment for the studied molecules in free space and in the solvent box

Table 4
DIFFERENCE IN TOTAL ENERGY (KCAL/MOL) WHEN THE MOLECULES PASS FROM THE FREE SPACE TO THE FIRST SOLVATION SPHERE, AND RESPECTIVELY THE FIRST TWO SOLVATION SPHERES

Table 6 VALUES
OF THE POLARIZABILITIES α(cm 3 ) (• 10 -24 ) FOR THE MOLECULES INVESTIGATED IN THEIR FUNDAMENTAL STATE OBTAINED BY MEANS OF THE QSAR APPLICATION AND BY EXPERIMENT

Table 5
BORDER LEVEL ENERGY VALUES (eV) FOR THE STUDIED MOLECULES, IN FREE SPACE AND IN THE SOLVENT BOX see from table