2.1.1. Reference Molecule Structure

The new molecules were designed by substituting hydrogen atoms on the aniline molecule (the reference or parent molecule, sourced from the experimental database) with alkyl groups [2]. The two-dimensional structure of aniline is as follows (Figure 1):

Figure 1. 2D structure of aniline.

2.1.2. Software and Level of Theory Used

GaussView 5.0 [3] software was used to represent the 3D structure and visualize the molecules under study. Subsequently, Gaussian 09 [4] software was used for geometry optimization and frequency calculations at a temperature of 298.15 K and a pressure of 1 atmosphere in the gas phase. The level of theory used to calculate the various molecular descriptors was B3LYP/6-311G (d, p). The 2D structures were generated using ChemSketch [5].

2.2.1. Domain of Applicability of a Model

A QSPR/QSAR (Quantitative Structure-Property Relationship/Quantitative Structure-Activity Relationship) model cannot be considered universal, as it is developed using a limited number of compounds that do not cover the entire chemical space. Consequently, the predicted property or activity of a compound that is chemically dissimilar to the training set cannot automatically be considered reliable [6][7]. The applicability domain (AD) defines the region within which a compound’s properties can be predicted with confidence. The AD thus corresponds to the area of chemical space encompassing the training set compounds and similar compounds located nearby in that same space [8]. Several methods exist for determining the AD of a QSPR/QSAR model; among these is the fragment-based method [8]. This method assesses whether a molecule falls within a model’s AD based on the presence of specific fragments. If a new molecule contains novel fragments, it is deemed to lie outside the model’s AD. Conversely, if the new molecule presents no novel fragments, it is considered to be within the AD, and the prediction is regarded as reliable. The fragment-based method is employed in this study because it is well-suited to our simple molecules, unlike complex ones.

2.2.2. QSPR Model Used to Predict the Octanol/Water Partition Coefficient of New Anilines

The QSPR model used for the design of the new anilines derivatives was developed in our previous work [2]. The equation for this model is presented below, along with some statistical and validation parameters:

with the ionization energy (IE) expressed in electron-volts (eV), the electronic energy (E_T) expressed in expressed in atomic units (a.u.) or Hartrees (Ha), and the dipole moment (µ) expressed in Debyes (D).

2.2.3. Standard Thermodynamic Quantities of Formation

Quantum chemical calculations and the use of experimental data in the form of reference thermodynamic tables [9] allow for the determination of the standard values of the enthalpy of formation ( Δ f H 0 ), entropy of formation ( Δ f S 0 ), and Gibbs free energy of formation ( Δ f G 0 ) for the molecular system at 298.15 K and 1 atm pressure in the gas phase. The enthalpy of formation of a molecular system is calculated using the relationship proposed by J. W. Ochterski [10]:

where the last two terms of this relation are referred to as the enthalpic correction (or increment) for the molecule and the atoms, respectively. For elemental substances, this corresponds to the heat involved in heating the atoms from 0 K to 298 K. These values are obtained experimentally relative to the standard state of the elements. As for the term Δ f H 0 ( M , 0   K ) , it is determined using the following relation:

x defines the number of atoms of species X in molecule M.

Δ f H 0 ( X , 0   K ) is an experimental value corresponding to the heat of formation of atom X at 0 K. The final term, ∑ D 0 ( M ) , corresponds to the atomization energy of molecule M. This energy arises from the decomposition of one mole of the molecule into its constituent atoms. The calculation of ∑ D 0 ( M ) is performed using the electronic energies (ε) of the constituent atoms and the molecule, as well as the internal energy at 0 K known as the Zero-Point Energy (ZPE) of the latter, according to the relation below:

The entropy of formation at 298 K, Δ f S 0 ( 298   K ) , is determined using atomic entropy values ( S 0 ( X , 298   K ) ) from the JANAF Thermochemical Tables [9] and the molecular entropy obtained via quantum mechanical calculation. The relationship proposed by J. W. Ochterski [10] for determining the entropy of formation of a molecular system is:

where S 0 ( M , 298   K ) = H c o r r − G c o r r T is the standard absolute entropy.

Knowing the enthalpy of formation and the entropy of formation, the standard Gibbs free energy of formation is easily calculated using the relationship:

A series of thirty-three (33) molecules was designed by substituting hydrogen atoms of aniline (the parent molecule) with alkyl groups. The molecules were designated AN_i (1 ≤ i ≤ 33). The developed QSPR model was used to predict the octanol/water partition coefficient for this series. The 2D structures, molecular descriptor values, and theoretical octanol/water partition coefficient values are summarized in Table 1.

Table 1. 2D structures of the designed molecules, molecular descriptor values, and theoretical octanol/water partition coefficient values obtained using the QSPR model.

Table 1 shows variations in each determined parameter from one molecule to another. The data indicate that the octanol/water partition coefficient values are all positive, revealing that the designed molecules are lipophilic (hydrophobic). Consequently, these compounds are soluble in fatty substances but insoluble in polar solvents such as water. This lipophilic nature stems from the substitution of hydrogen atoms on the aromatic ring or nitrogen atom with alkyl groups, which are lipophilic moieties. Molecules with a LogP value between 0 and 3 are moderately lipophilic, whereas those with a LogP greater than 3 are highly lipophilic. Furthermore, the hydrophobicity of the molecules increases with the length of the substituent’s carbon chain. For instance, a compound with a methyl group (-CH₃) on the ring is less lipophilic than one with an ethyl group (-C₂H₅); similarly, a compound with an ethyl group is less lipophilic than one with a propyl group (-C₃H₇). Positional isomers exhibit virtually identical octanol/water partition coefficient values, implying they possess essentially the same degree of hydrophobicity. Generally, for a given total number of carbon atoms, a molecule with a branched alkyl group (e.g., isopropyl) shows a slightly lower lipophilicity parameter than one with a linear chain (e.g., propyl) due to differences in steric hindrance. Overall, the hydrophobicity of the molecules varies with the dipole moment. Indeed, as the dipole moment increases, hydrophobic character increases. Conversely, a decrease in hydrophobic character is observed when the dipole moment decreases. For aniline (the parent molecule), the experimental value of the octanol/water partition coefficient is 0.90 (±0.05) [2]. This positive value clearly indicates that aniline is also lipophilic. The lipophilicity of aniline derivatives varies predictably depending on whether the aniline is primary, secondary, or tertiary, as well as on the nature of the substituents attached to the nitrogen atom or the aromatic ring. Overall, lipophilicity increases with the degree of substitution (from primary to tertiary aniline) and with the length or volume of the alkyl groups. However, ideally, experimental octanol/water partition coefficient values for these new molecules should be obtained.

The thermodynamic quantities of formation were determined in order to study the thermodynamic stability and characteristics of the formation reactions of the designed molecules.

Table 2. Structures of the designed molecules and values of formation quantities (in kcal/mol), except for entropy of formation (in cal/mol·K) (T = 298.15 K, P = 1 atm, gas phase).

Variations in the determined thermodynamic quantities are also observed from one molecule to another. The values for the standard thermodynamic quantities of formation for the new anilines are all negative. Negative values for enthalpy and Gibbs free energy indicate an exothermic reaction and a spontaneous reaction, respectively. A negative entropy value indicates a decrease in disorder. Consequently, the formation of all the new anilines occurs spontaneously, accompanied by heat release and a decrease in disorder, at a temperature of 298.15 K and a pressure of 1 atm in the gas phase (Table 2). The negative value of the Gibbs free energy of formation thus reflects the existence and stability of the newly designed molecules.