Parabens are the esters of para-hydroxybenzoic acid and they are the most common preservatives in use due to their efficacy and safety; their relatively non-irritating, non-sensitizing characteristics. Parabens are added to cosmetics, foods and pharmaceutical products. They are antifungal and antibacterial; more active against Gram-positive than Gram-negative bacteria. The synergy between esters has been reported and it is very profitable to use their combinations. The mechanism of antibacterial properties of parabens has not been fully explained. Probably, they are inhibitors of the nucleic acid synthesis of DNA and RNA or inhibit enzymes necessary for the proper functioning of bacterial cells such as ATP and phosphotransferase.

The photostability of the chemicals is dependent on many factors, including the chemical structure of the molecules that determined the reactivity of the excited states as a result of the action of light [1] [2] [3] [4] . Till now, there was no research on light fastness of the paraben group of the p-hydroxybenzoic acid (PHB) ester derivatives, used as conservatives for cosmetics. Their protective effect is related to their oxidation, which is quicker than the oxidation of a given chemical compound which it is protecting. The reaction rate depends on the length of the aliphatic chain of the ester residue.

Understanding the effect that substituents have on the parabens lightfastness has a significant meaning or their appropriate applications and skin hazard as regards the products of decomposition of cosmetics.

Molecular orbital calculations can provide an insight into the process of parabens fading in the presence of light depending on their electronic properties [5] . Numerous studies have been done to predict the addition of singlet oxygen e.g. in dyes containing azo moieties [6] [7] [8] .

The frontal orbitals theory suggests that the atoms in the primary HOMO state of high electron density are susceptible to the electrophilic attack of the singlet oxygen atom ¹O₂ and they have high activity coefficients f r E . We similarly define the LUMO f r N electron state of atoms or bonds, where the molecule undergoes a nucleophilic reaction with O 2 • − . The place of electro- or nucleophilic attack is the atom, where the calculated S r E ( N ) values are the highest [1] . The reliability of the results obtained in this way has been confirmed during numerous tests on organic dyes [9] . The local reactivity indices are useful tools for predicting the most likely reaction sites [10] .

Superdelocalisability S r E ( N ) determines the relative propensity of compounds toward electrophilic and nucleophilic attack respectively, on the dye molecule, and are calculated with the following equation:

S r E ( N ) = f r E ( N ) / E H O M O ( L U M O )

where f r E ( N ) is electron density measure in the ground/excited state on the r―atom, E_HOMO(LUMO)―energy of HOMO or LUMO orbital. It allows comparing the reactivity of corresponding atoms in different molecules [8] [11] [12] .

Atoms with small f_r values possess high resistance to photochemical reactions, while those with larger f_r values exhibit poor lightfastness.

The AM1 and PM3 predictive methods allowing to predict electron properties, geometric structure, total energy and formation heat of compounds from period 1 and 2 of the Periodic Table. They are Self-Consistent Fields (SCF) methods. AM1 is an improvement of the MNDO method and is one of the most accurate method, used for organic molecules. PM3 differs from AM1 only in the values of the parameters, which were derived by comparing a larger number and wider variety of experimental versus computed molecular properties.

We based our analysis on the following assumptions [1] :

- the site of the electrophilic attack with singlet oxygen ¹O₂ is the atom with the highest values f r N and S r N . For nucleophilic attack with superoxide anion radical O 2 • − , it is the atom with the highest value of f r N and S r N .

- if the attack is to be effective, the difference in energy of the HOMO state for factors E or N should not be less than ≈6 eV.

- S r E i S r N determine the probability and relative easiness of the electro- or nucleophilic attack on the respective atom of the molecule.

Apart from the above, to understand lightfastness researchers have primarily addressed the reactive site in a particular molecule. The results of MO calculation have been used to propose a possible mode of degradation of parabens when exposed to light.

The chemical reaction occurs at the position where mutual overlap of their frontier orbitals is most effective. The results of the MO calculation have been used to obtain the HOMO and LUMO frontier electron density. This allowed to determine the site of oxidation of parabens by singlet oxygen ¹O₂ [7] [13] or superoxide anion radical O 2 • − .

In our research, we focused on the use of AM1 and PM3 MO to calculate the probable site of an electrophilic or nucleophilic attack on a compound molecule. The mechanism of oxidation reaction with singlet oxygen of C=C bonds with MINDO/3 method has been described by Dewar and Thiele [14] et al. [1] [8] [11] . In the most frequently performed MO analysis of dye properties, it is assumed that the molecules are in the gaseous phase. In line with the frontal orbitals theory, only the interactions between the HOMO of the paraben and the LUMO of the oxidant [15] are included in the analysis.

We have calculated electron density of frontal orbitals in the ground HOMO state and excited LUMO state of the oxidant.

The appropriate measure to determine the activity of singlet oxygen in the electrophilic reaction or a radical in a nucleophilic reaction is the frontier charge density (Q_f) for highest occupied molecular orbital HOMO and for lowest unoccupied molecular orbital LUMO [7] .

Q f j = 2 ∑ i − 1 n c j i 2

where c_ji are the coefficients of frontier orbital i atom j (HOMO or LUMO), Q f j ―frontier charge density.

The ¹O₂ can add to the double bonds via the ene reaction or cycloaddition, as seen in synthetic dyes [16] . In such case, a good correlation is obtained between the oxidation rate and the sum S m , n E of the values f r E of two neighboring atoms, where f r E is the frontier electron density of the electrophilic reaction on the r-atom, while m and n are the positions of atoms in the double bond [9] . However, electrophilic or nucleophilic reaction on the corresponding aliphatic chain or on aromatic ring is more likely [16] .

It is believed that the attack of the electrophilic agent occurs when the energy difference DE between the LUMO energy of singlet oxygen and HOMO is less than 6 eV [6] .

The electron density of the ground HOMO state allows to predict the site of the electrophilic attack, while LUMO―the site of nucleophilic attack [7] [11] .

The structure of the tested compounds has been optimized with MM+, DM and AM1 or PM3 (Table 1 and Table 2), to obtain constant energy value. All MO calculations were carried out using HyperChem v.6.0 (Hypercube Inc.). Structure optimization was performed including the standard heats of formation in the gaseous H_f, the energies of highest occupied molecular orbital (E_HOMO) and lowest unoccupied molecular orbital (E_LUMO), the electron densities (d_HOMO), the frontier densities ( f r E and f r N ) and the dipole moment (μ) in the gaseous phase, using AM1 and PM3 methods [2] . E_LUMO ¹O₂ equals −6.51 eV [2] .

The calculated HOMO and LUMO energy values of the singlet state of oxygen ¹O₂ are respectively: −6.294 eV and −5.339 eV (AM1) as well as −5.858 eV i −5.323 eV (PM3).

Formula and Figure 1 was draw in ISIS Draw v.2.04 program.

In our research we have analyzed photochemical decomposition of ester derivatives of p-hydroxybenzoic acid at the formula [17] :

DE = E_LUMO (singlet oxygen) − E_HOMO (paraben). LUMO energy of singlet oxygen has been taken from Guo (=5.860 eV)1^,2 [6]; DE_H-L―energy difference [HOMO-LUMO], ^*1)used in practice as mixture, ^*2)unused in practice, Ph―phenyl.

¹E_LUMO (¹O₂) = −6.51 eV [2] .

²Calculated E_LUMO of singlet oxygen ¹O₂ = 6.294 eV (AM1) or 5.858 V (PM3).

DE_H-L allows to determine range of wavelengths at which the PHB derivatives will be able to occur in the excited LUMO state and react with the electrophilic agent. The HOMO-LUMO energy difference range is approximately 9.51 ÷ 9.54 Ev, corresponding to the calculated absorption range of electromagnetic radiation of wavelength λ_max = 322.9 ÷ 331.6 nm (PPh 266.0 nm) [AM1]. P1 and PPh derivatives are easiest to excite, while it is more difficult with aliphatic chains in ester residue. Similar dependencies are observed for PM3 calculations, respectively 9.16 - 9.69 eV for the calculated absorption range of λ_max = 317.9 - 318.2 nm (PPh 263.1 nm).

The electron density of frontier HOMO and LUMO states has been calculated. Sites with highest electron density and superdelocalisability indicate prospective sites for electrophilic or nucleophilic oxidation reaction.

Light fastness can be tested for the possibility of an electrophilic or nucleophilic attack of the oxidizing agent. The analysis of ΔE changes, frontier electron densities HOMO and LUMO, along with respective superdelocalisabilities S^E and S^N may explain light resistance of parabens in a satisfactory manner.

Table 1 present S^E HOMO and S^N LUMO values, which allow to predict the prospective site of attack by singlet oxygen ¹O₂, or superoxide anion radical O 2 • − . High S^E and S^N indicate high likelihood of reaction on a given carbon atom. On Figure 1 a graphical presentation of calculation results of chosen PHB derivatives―P1 and P5 is shown, to illustrate differences in the oxidation mechanism of a photochemical decomposition.

The analysis of superdelocalisability changes in the P1 compound done using AM1 and PM3 suggest the mechanism of electrophilic oxidation reaction according to 5-addition and should lead to the decomposition of the aromatic ring. The side chain of ester group does not take part in this reaction. Nucleophilic reactions should occur primarily in positions 4-, 5-. In AM1 method, positions 2- and 4- have similar reactivity.

The ease of oxidation is determined by the energy difference DE of the highest occupied molecule orbital (E_HOMO) the lowest unoccupied molecule orbital (E_LUMO) of singlet oxygen ¹O₂.

This difference indicates that the tested compounds are easily subject to photofading, since the DE values are lower than the minimal energy value for oxidation which is ca. 6 eV [1] [3] . They are 3.651 - 3.675 eV (AM1) and 3.829 - 3.638 eV (PM3) when E_LUMO ¹O₂ = 5.860 eV [3] . Hence DE are 3.217 ÷ 3.239 eV (AM1) and 3.640 - 3.831 eV (PM3), including values calculated with quantum-chemical methods AM1 and PM3. In each case DE are lower than the reaction energy frontier values = 6 eV.

Among the analyzed compounds, commercial use has been found for P3, P4, P5, PPh. The analysis shows that similar preserving properties may also be found in derivatives of P2 (AM1, electrophilic and nucleophilic reactions) and P6 (AM1, electrophilic reaction), while oxidation should occur also on atom C₅ of the aromatic ring of the P6 derivative, while in P2 the methyl group of ester residue is most reactive. It is also the most reactive of all tested derivatives S^E @ 0.0514 to S^E @ 0.0495 in other derivatives on atom in the PHB aromatic ring. The most probable oxidation mechanism includes the attack of singleton oxygen (¹O₂) on the molecule of the compound and the formation of superoxide derivatives. In the course of the reaction, epoxide derivatives may form [16] . Alicyclic superoxide may form temporarily, which after dehydration gives unsaturated ketone or may be reduced to allyl alcohol.

The reaction mechanism has not yet been thoroughly explained so far. Chemical compounds that generate singlet oxygen ¹O₂ (e.g. sensitizers) in contact with the skin accelerate the destruction nucleic acids and enzymes, and thus can lead to cancer skin changes [21] [22] .

Among the tested PHB derivatives P1 is not recommended for practical use, as its photochemical decomposition may lead to the danger of methyl alcohol formation. Besides, the performed analysis shows that it does not have the highest antioxidant properties (worse is only PPh in the electrophilic reaction) in the tested group of derivatives.

Both AM1 and PM3 methods in many points show similar most probable sites of electrophilic or nucleophilic attack on the PHB molecule. In the electrophilic reaction, it will be the PHB aromatic ring, in the nucleophilic one―the alkyl group in the ester residue.

The results and conclusions of these studies, initiated by a research on organic dyes, may help explain the mechanism of photofading of parabens used as conservatives in cosmetics. Understanding the mechanism of their photodegradation will help to improve the process of their more accurate selection to protect the chemical compounds that remain in direct contact with the skin.

The calculations show that the method of predicting the properties and correlations with calculated values of electron density and energy of ground HOMO and excited LUMO states … etc. has a range of limitations. However, they enable deeper insight into the reaction of photochemical decomposition reaction and can be used to test different compounds.

The authors declare no conflicts of interest regarding the publication of this paper.

Wojciechowski, K. and Szuster, L. (2019) Photofading of Derivatives of Paraben (PHB) by AM1 and PM3 Methods: A Theoretical Study. Computational Chemistry, 7, 39-50. https://doi.org/10.4236/cc.2019.72003