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     . 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  . Numerous studies have been done to predict the addition of singlet oxygen e.g. in dyes containing azo moieties    .
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 . We similarly define the LUMO electron state of atoms or bonds, where the molecule undergoes a nucleophilic reaction with . The place of electro- or nucleophilic attack is the atom, where the calculated values are the highest  . The reliability of the results obtained in this way has been confirmed during numerous tests on organic dyes  . The local reactivity indices are useful tools for predicting the most likely reaction sites  .
Superdelocalisability determines the relative propensity of compounds toward electrophilic and nucleophilic attack respectively, on the dye molecule, and are calculated with the following equation:
where is electron density measure in the ground/excited state on the r―atom, EHOMO(LUMO)―energy of HOMO or LUMO orbital. It allows comparing the reactivity of corresponding atoms in different molecules    .
Atoms with small fr values possess high resistance to photochemical reactions, while those with larger fr 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  :
- the site of the electrophilic attack with singlet oxygen 1O2 is the atom with the highest values and . For nucleophilic attack with superoxide anion radical , it is the atom with the highest value of and .
- 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.
- i 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   or superoxide anion radical .
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  et al.    . 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  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 (Qf) for highest occupied molecular orbital HOMO and for lowest unoccupied molecular orbital LUMO  .
where cji are the coefficients of frontier orbital i atom j (HOMO or LUMO), ―frontier charge density.
The 1O2 can add to the double bonds via the ene reaction or cycloaddition, as seen in synthetic dyes  . In such case, a good correlation is obtained between the oxidation rate and the sum of the values of two neighboring atoms, where 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  . However, electrophilic or nucleophilic reaction on the corresponding aliphatic chain or on aromatic ring is more likely  .
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  .
The electron density of the ground HOMO state allows to predict the site of the electrophilic attack, while LUMO―the site of nucleophilic attack   .
Molecular Orbital Calculations
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 Hf, the energies of highest occupied molecular orbital (EHOMO) and lowest unoccupied molecular orbital (ELUMO), the electron densities (dHOMO), the frontier densities ( and ) and the dipole moment (μ) in the gaseous phase, using AM1 and PM3 methods  . ELUMO 1O2 equals −6.51 eV  .
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.
3. Results and Discussion
In our research we have analyzed photochemical decomposition of ester derivatives of p-hydroxybenzoic acid at the formula  :
Figure 1. Graphic presentation of superdelocalisabilities SE and SN for selected derivatives of PHB―P1 and P5 (atoms numbering―see formula and appropriate values―Table 3). The circle diameter are proportional to the size of the delocalisability of valence electrons in the ground state (HOMO) and excited state (LUMO) and determines the probability of electro- (by 1O2) or nucleophilic reaction (by ). Bold circle means the site of the most probable attack of the oxidizing agent.
Table 1. [AM1] Hf-enthalpy of formation (kcal・mol−1), HOMO and LUMO energy, EHOMO, ELUMO,) (eV), dipole moment μ HOMO and LUMO (debye).
Table 2. [PM3] Hf-enthalpy of formation (kcal・mol−1), HOMO and LUMO energy, EHOMO, ELUMO,) (eV), dipole moment μ HOMO and LUMO (debye).
DE = ELUMO (singlet oxygen) − EHOMO (paraben). LUMO energy of singlet oxygen has been taken from Guo (=5.860 eV)1,2 ; DEH-L―energy difference [HOMO-LUMO], *1)used in practice as mixture, *2)unused in practice, Ph―phenyl.
Table 3. Frontier electron density calculation for HOMO and LUMO and superdelocalisability SE and SN for selected atoms by AM1 and PM3 methods.
1ELUMO (1O2) = −6.51 eV  .
2Calculated ELUMO of singlet oxygen 1O2 = 6.294 eV (AM1) or 5.858 V (PM3).
DEH-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 λmax = 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 λmax = 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 SE and SN may explain light resistance of parabens in a satisfactory manner.
Table 1 present SE HOMO and SN LUMO values, which allow to predict the prospective site of attack by singlet oxygen 1O2, or superoxide anion radical . High SE and SN 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 theoretical methods are a significant contribution to understanding the physiochemical properties of compounds. In this paper, we have tried to investigate the photochemical distribution of parabens with quantum-chemical calculations, allowing deeper insight into the process itself. The calculation methods have been previously described. The parameters for theoretical calculations are frontier electron densities of HOMO and LUMO orbitals   .
A theoretical study of photofading processes has been very widely used in the analysis of organic dyes degradation, due to their common practical application; the purpose of the study was the identification and root cause analysis for the toxicity of their degradation products   .
In our analysis, we focused on the determination of prospective attack sites of the oxidizing agent on the molecule of parabens derivative (4-hydroxybenzoic acid), including into considerations the derivatives used as anti-oxidants in the cosmetics industry. Cosmetics and their additives, in result of oxidation, especially with regards to trace amounts of metals, may be oxidized to superoxides. Thin layers of cosmetics applied to the skin are particularly exposed to light, heat and oxygen from the air. The characteristic feature of PHB is their ease of oxidation, greater than the applied compounds have. At the same time, their toxicity is low or none in contact with human skin. Thanks to the ease of oxidation, they limit the possibility of harmful products formation, resulting from photooxidation of cosmetics, where the products are compounds toxic to human skin. Additionally, parabens are used as bacteriostatic ingredient.
To understand the dependence of light fastness of the tested derivatives, one needs first to find the location of the most reactive site and then correlate the calculated values with experimental results which, however, is not always possible  . In turn, the length of the alkyl chain of the ester residue has impact on the changes in electron density and the longer it is the stronger is the nucleophilic nature of the -COO- moiety.
The methods selected for calculation―AM1 and PM3―belong to the most advanced ones, applied for quantum-chemical analyses and to determine the reactivity of chemical compounds. AM1 makes it possible to explore the geometry of the molecule and correctly predict many physical and chemical properties; while PM3 is used to confirm the accuracy of the AM1 calculations  . Both methods indicate, to varying degrees, the similar sites of electro- (1O2) or nucleophilic ( ) attack. Computational methods allow to predict the fastness of chemical compounds to oxidation, including even those which cannot exist as mixtures of different chemical structures, and help understand the mechanism of photochemical degradation along with the impact of substituents on reaction rates  .
The results obtained in the course of calculations indicate not only the probable sites of reaction for the oxidizing agent in electrophilic and nucleophilic reactions, but also allow for comparison between them. Such analysis helps to find out about the reactivity of a given molecule and select an appropriate compound for required purpose. The applied methods differ in assumptions and results obtained.
3.2. Analysis by AM1 Method
The analysis indicates that the most reactive sites are carbon atoms in position 5- of the aromatic ring (exception of P2) and their reactivity is dependent on the length of the aliphatic chain in ester residue. The reactivity of position 5- in an electrophilic reaction can be ranked as follows:
P2 = P3 > P6 > P4 ≈ P5 > P1 > PPh
The carbon atom C5 has highest value SE as compared to other atoms, where the difference decreases with the length of the aliphatic chain. The longer the chain the lower the value and the higher the probability of reaction in the aliphatic chain than in the PHB phenyl ring. The exception is P2, where the reaction should first should occur on the C11 carbon atom (see formula), of the aliphatic chain. The difference in reactivity to C5 is about 3.7%. What also draws attention is the very low reactivity of the phenyl ring ester residue in PPh, lower even than the on carbon C1 of the paraben. The reaction mechanism of electrophilic oxidation by 1O2 probably takes place via the stadium of superoxide derivative  .
The nucleophilic oxidation reaction by superoxide radical and the nucleophilic oxidation reaction of the susuperoxide radical shows high reactivity of the methyl residue -CH3 of group C11 - C31 (see formula). It may be ranked in the following order:
P2 > P4 > P3 > P5 > P6 > PPh > P1
In nucleophilic oxidation the most important are the alkyl residues of the ester group and the reaction should occur in the first place on the methyl group -CH3, closing the aliphatic chain. The exception is compound P1, where the methyl group is directly linked to ester residue -COO-. This results in a significant reduction in its electron density in the excited state of LUMO.
Exceptions to the above are P1 and P2, where the reaction should occur on the PHB phenyl ring. The sites of the highest SH value are in general carbon positions C11 - C31 (see formula) in an aliphatic chain, and they are methyl residues -CH3, similarly as in the nucleophilic reaction. In the aromatic ring, carbons C1 and C4 are characterized by high reactivity, however it is not high enough for the reaction to occur on these carbon atoms. In P1 and P2 significant SN values are observed on neighboring carbon atoms in the PHB ring (C4, C5 in P1 and C1, C2 in P2) which can lead to the degradation of the aromatic ring by 1,2-addition (Diels-Alder reaction)   . Such reaction mechanism is most probable for P1.
The PPh derivatives are characterized by low reactivity; the reaction should occur on carbon atom C1, whereas similar SN values have carbon atoms C21 and C23, where the differences as compared to C1 are respectively, 5.3% and 6.9% and the reaction should occur through the formation of superoxides.
Similarly to the electrophilic reaction, the reactivity of P1 and PPh derivatives is low; it is difficult to subject them to nucleophilic oxidation reaction with a superoxide radical . In the remaining derivatives, the oxidation reaction would occur or the methyl group on the aliphatic chain of the ester residue.
3.3. Analysis by PM3 Method
The results of calculations made by PM3 indicate a similar electrophilic reaction mechanism SE as described for AM1. High electron density of the basic HOMO state occurs on atoms C1 - C5 in the phenyl ring of the paraben. In all cases, the reaction should occur on carbon atom C5. The reactivity of compounds P1 - P6, PPh can be ranked in the following order:
PPh > P4 ≈ P6 > P3 > P2 > P5 > P1
This method shows yet another possibility for the reaction to occur on C3 atom, where the DSE values differ by about 0.08 - 0.1 from the values calculated for C5. This method confirms the direction of oxidative decay of PHB obtained by AM1. The reaction mechanism probably takes place by the stadium of peroxide derivatives  . In the nucleophilic oxidation by superoxide radical the reaction rate may be ranked in the following order (SN):
PPh > P5 > P2 > P1 > P4 > P3 > P6
However, the conclusions to these calculations are not entirely clear. This reaction may occur in both methyl residues -CH3 (P2, P4) and methylene residues -CH2- (P5, P6) of the aliphatic chain of the ester residue. The reaction mechanism is similar to the one proposed in AM1, i.e. through the superoxide intermediate reaction stage  . The exceptions would be P1 reactions, where one should expect 1,2-addition to the PHB phenyl ring   . High superdelocalisability coefficients are in atoms C1 and C2 and this reaction direction should be privileged. In PPh these coefficients are high for C1, C3 and C5. The characteristic feature of the PM3 calculations for all derivatives are high reactivity coefficients of carbon atoms C1 and C4, which makes them different from AM1 calculations. However they do not determine the direction of reaction, which according to the proposed order is mainly on the alkyl ester residue.
The ease of oxidation is determined by the energy difference DE of the highest occupied molecule orbital (EHOMO) the lowest unoccupied molecule orbital (ELUMO) 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   . They are 3.651 - 3.675 eV (AM1) and 3.829 - 3.638 eV (PM3) when ELUMO 1O2 = 5.860 eV  . 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 SE @ 0.0514 to SE @ 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  . 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   .
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.
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