The ground state geometry optimization of the pyrene molecule and its monochlorinated derivatives: 1-chloropyrene, 2-chloropyrene, and 4-chloropyrene were performed by using the DFT/B3LYP/6-311G** method and shown in Figure 1. All the optimized geometries of pyrene and its derivatives kept good planarity. Details of the resulted calculated structural parameters for all four molecules are presented in Table 1.

The calculated bond lengths and bond angles of pyrene are in good agreement with the experimental values obtained by X-ray crystal diffraction [12] . This result is a good indication for the validity of the computational method. The similarity of the derivatives to the parent molecule explains the similarity in bond lengths and bond angles in all the molecules especially as we move farther away from the substituent (Cl). The carbon-chlorine bond length values average at around 1.763 Å and this is very close to the mean Caromatic-Cl bond length of 1.76 Å.

The computed dipole moments are in the order of 4-chloropyrene (2.04) < 1-chloropyrene (2.11) < 2-chloropyrene (2.49). This predicts that 4-chloropyrene is the most stable compound in organic chlorination reaction media due to its lowest dipole moment value followed by 1-chloropyrene. On the other hand, the computed minimum energy (a.u.) is in the order of 2-chloropyrene (−1075.53213120) < 1-chloropyrene (−1075.53096880) < 4-chloropyrene (−1075.53084833). This result assumes that 2-chloropyrene exhibits the

lowest thermodynamic heat of formation. Since 2-chloropyrene is very polar, the conditions of the chlorination reaction will dictate the stability of the product. Experimentally, when pyrene is chlorinated with NCS, the main product was monochloropyrene [8] . Therefore, it can be concluded that the product is a mixture of the three derivatives: 1-chloro, 2-chloro and 4-chloropyrene. A study by Jensen and Berg [13] suggested that the 1-chloropyrene and the 2-chloropyrene have good reactivity in the organic medium ether. Moreover, 1-chloropyrene was one of the main products of the chlorination of pyrene in aqueous solution [14] .

The appropriateness of the DFT method in predicting the geometrical values was tested by applying different levels of the DFT theory. They include: B3PW91, MPW1PW91, and PBE1PBE in addition to B3LYP. The same methods were also used in the vibrational frequency calculations.

The energies of frontier orbitals: the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) were computed. Figure 2 illustrates the energies (in hartrees) of frontier molecular orbitals and their gaps (ΔE) at the B3LYP/6-311G** level. It can be seen that the values of EHOMO increase in the order pyrene < 1-chloropyrene < 4-chloropyrene < 2-chloropyrene. The same trend is seen for the ELUMO. We notice that ΔE values are very similar within the monosubstituted derivatives. The trend indicates that 1-chloropyrene is less involved in chemical or photochemical processes with electron transfer and hence it is the least reactive in agreement with previous results. Our calculated value for ΔE for pyrene (3.84 eV = 0.141 a.u.) is in excellent agreement with the experimental value of 3.85 eV [15] .

The energies of frontier orbitals: the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are used to determine several chemical reactivity parameters as a measure of relative stability and reactivity. These include total energy (E₀), chemical hardness (η), electronic chemical potentials (μ) and electrophilicity (ω). The energies of the HOMO and LUMO obtained by the B3LYP/6-311G** method (Figure 2) are listed in Table 2.

Chemical hardness is linked to the stability and reactivity of a chemical system. It measures the resistance of a compound to changes in the electron density distribution or to electron charge transfer. According to the frontier molecular orbital approach, chemical hardness is directly proportional to the energy gap between the HOMO and the LUMO and is estimated as. The larger the HOMO-LUMO energy gap, the harder and more stable (less reactive) the compound [16] .

The smaller the electronic chemical potential value (μ), the more stable is the compound. Table 2 lists the calculated electronic chemical potential (μ) values for the four studied compounds. It is clear that since 1-chloropyrene has the lowest μ value (0.141 a.u.), it is expected to be the most stable while 2-chloropyrene with the highest μ value (0.1445 a.u.) is the least stable. The results for the electronic chemical potential (μ) agree well with the experimental chlorination of pyrene [8] .

The electrophilicity parameter (ω), is calculated using the electronic chemical potential (μ) and the chemical hardness (η) using the equation. In a chemical process, it measures the capacity of a species to accept electrons and therefore measures the stabilization in energy after a system accepts additional electronic charge.

The electrophilicity values (ω) for the studied compounds are listed in Table 2. They are 0.1481 for 2-chloro, 0.1461 eV for 4-chloro and 0.1441 for 1-chloro. Among the compounds, and having the lowest ω value, 1-chlo- ro is the strongest nucleophile while 2-chloro is the strongest electrophile with the lowest ω value. The result suggests some sort of selectivity in the mechanistic chemistry of pyrene chlorination. Experimentally, more stable compounds correspond to smaller electrophilicity values and this is the case with 1-chloropyrene.

Standard Heat of formation () is a basic thermodynamic property of a chemical compound. Computational methods are increasingly being used for predicting and verifying the heat of formation of gas-phase systems at 298 K. Many studies focused on computing using DFT methods (such as B3LYP, MPW1PW91, PBE1PBE) for a large number of organic or inorganic compounds [18] .

To our knowledge, the literature contains no attempts to calculate for chlorinated pyrene compounds. Here, we apply DFT calculations in predicting the gas phase heat of formation for pyrene and its three mono- chlorinated derivatives at 298 K.

The calculations for the heat of formation were performed using the methodology of computing the total electronic energy of molecules and their individual atomic constituents. Utilizing the properties of isodesmic reactions and the high similarity between reactants and products, of the studied compounds is evaluated [16] .

Table 5Table 3

. Electronic energy, and calculated heats of formation for pyrene and its three monochlorinated derivatives. Experimental value was taken from reference [21]

Compound	E0 (B3LYP/6-311G**) (a.u.)	Calculated (kJ/mol)	Experimental (kJ/mol)
Pyrene	−615.910480870	227.80	225.5
1-chloropyrene	−1075.53096880	103.13	NA
2-chloropyrene	−1075.53213120	106.95	NA
4-chloropyrene	−1075.53084833	102.78	NA

indicating that the 4-chloropyrene derivative is the most stable thermodynamically. This result is in agreement with a study conducted by Nilsson et al. that found 1-chloro and 4-chloropyrene to be the most abundant molecule upon continuous heating of a mixture of pyrene derivatives [20] .