Structures, Lipophilicity, Dipole Moments, Acidity and Spectroscopic Properties of Non-Steroidal Anti-Inflammatory Drugs Diclofenac, Bromfenac and Amfenac: A Theoretical Study

This work is a contribution of theoretical chemistry to the classification of some non-steroidal anti-inflammatory drugs (NSAIDs). Indeed, research on the efficacy of NSAIDs has shown that no NSAID is recognized as the most efficient anti-inflammatory drug. We have made a theoretical study of diclofenac, bromfenac and amfenac, in order to compare their efficacy from some physicochemical properties. To do this, we used the DFT and TD-DTF methods at the B3LYP/6-311+G(d, p) level theory. The lipophilicity study shows that diclofenac and bromfenac are very lipophilic. Acidity study shows that diclofenac is more acid than bromfenac and amfenac. The results from molecular orbital and the TD-DFT calculations reveal that for the three NSAIDs, the lowest energy transition is due to the excitation from HOMO to LUMO. The absorption energy corresponding to H→L transition is comparable with the energy gap value. Our findings have shown that bromfenac is more reactive than amfenac, which is more reactive than diclofenac.

inflammatory component such as dental surgery, stomatological surgery, maxillofacial surgery, orthopedic surgery and ocular surgery [3] [4] [5] [6]. Indeed, postoperative inflammation is a common condition that can lead to significant complications and to avoid these complications, ophthalmologists commonly use non-steroidal anti-inflammatory drugs. Particularly, in the processes of angiogenic retinal diseases including age-related macular degeneration (AMD) [7], inflammation plays a substantial role. In the field of the treatment of these diseases, NSAIDs are associated with anti-vascular endothelial growth factor (VEGF).
That combination of NSAIDs with anti-VEGF significantly reduces the treatment burden of anti-VEGF agents.
Bromfenac, diclofenac and amfenac are the commonly used NSAIDs. Bromfenac is 2-amino-3-(4-bromobenzoyl) phenylacetic acid. It is an NSAID that is widely used as an ophthalmic solution for the treatment of ocular inflammation and pain after cataract surgery and inflammatory diseases of external eye segments [8] [9]. Recent studies have shown that bromfenac inhibits laser-induced choroidal neovascularization in rats [10]. Gomi

et al. have reported in humans
that the use of topical bromfenac may reduce the frequency of intravitreal injections of Ranibizumab [11]. Although bromfenac has good intraocular penetration in humans [12], the relationship between its efficacy and pharmacokinetics has not been determined [13]. This led Tetsuo et al to determine the drug levels of bromfenac, diclofenac, and amfenac in the retinochoroidal tissues of rabbits by liquid chromatography-tandem mass spectrometry (LC-MS/MS) [14]. Their studies' findings showed that bromfenac has a stronger inhibitory activity on COX-1 or COX-2 than amfenac or diclofenac. However, there is no theoretical data that can confirm these results.
Verification of these experimental results remains at the center of our team's concerns. The present research aims to investigate the structure, lipophilicity, dipole moment, stability, acidity, and spectroscopic properties of diclofenac, bromfenac and amfenac. This would allow to know their mode of action and to design derivatives with more efficacies. To do this, we use DFT [15] [16] and TD-DFT [17] [18] methods with the B3LYP functional.

Methods of Calculation
Calculations on the ground state geometries are carried out with DFT (B3LYP functional) using 6-311+G(d,p) basis set [15] [16]. The absorption spectrum are calculated using TD-DFT method at B3LYP/6-311+G(d,p) level of theory [17] [18]. The ground state optimization and spectral calculations are carried out in gas and aqueous phases and using Tomasi's conductor-like polarizable continuum model (CPCM) [19]. The Gibbs free energies are obtained from the calculation of the frequencies. Frequency analyses were proceeded to confirm the structure being a minimum or a transition state (i.e. without or with solely an imaginary frequency). These calculations are carried out with the GAUSSIAN-09 program [20]. The freeware ACD/ChemSketch is used for LogP calculation.

Results and Discussions
Generally, the absorption of drugs through the cornea is dependent upon their physicochemical properties. The results concern the lipophilicity, the dipole moment, the acidity, and the spectroscopic properties of diclofenac, bromfenac and amfenac. Previously, they focus on their structures. These results will allow making a comparison of their efficacy.

Structures
The important structural parameters of diclofenac, bromfenac and amfenac are those of the carboxylic group ( Figure 1). The calculated values are in Table 1.
In the gas phase, the length of the O-H bond is 0.970 Å in all the molecules.

Lipophilicity and Dipole Moments
Lipophilicity is important in the design of a drug. It allows knowing if the molecule is more likely to be hydrophilic, or more likely to be lipophilic. It has often been used as a criterion for comparing several drugs [

Acidity
It is known that most of the anti-inflammatory drugs are carboxylic acids in which the carboxylic group is available for metal-ligand interactions [24] [25]. Indeed, the carboxylic acid group is ionizable at physiological pH. The anionic charge allows anchoring of the NSAID in the catalytic site by establishing an electrostatic interaction with a positively charged cox enzyme residue. It is important to know their acidic characteristics. The gas phase energy ΔG of the proton abstraction can helps to evaluate the acidity [26]. It may be calculated from the following equations: In gas phase, G g (H + ) = 2.5RT − TΔS = 1.48 − 7.76 = −6.28 kcal/mol [27] [28].

Spectroscopic Properties
In this part, we analyzed the frontier molecular orbitals and absorption properties.

Frontier Molecular Orbitals (FMOs)
Frontier molecular orbitals (FMOs) known as highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) respectively, plays a vital role in chemical reactions of any molecule, as well as absorption spectra [33] [34]. According to Koopman's theorem [35] associated within the framework of HF self-consistent field molecular orbital theory, the ionization energy (I) and electron affinity (A) can be stated through HOMO and LUMO orbital energies as: Higher HOMO energy is corresponds to the more reactive molecule in the reactions with electrophiles, while lower LUMO energy is essential for molecular reactions with nucleophiles [36]. Therefore, hardness of any materials is corresponds to the gap between the HOMO and LUMO orbitals. It clearly indicates that if the HOMO-LUMO energy gap is larger than molecule will be harder [37] [38]. The Hardness (η) of a molecule is calculated by: The calculated values of ΔE and η are presented in Table 4. In gas phase, the energy gap of bromfenac is 3.93 eV followed by amfenac at 4.00 eV and diclofenac at 4.91 eV. Bromfenac is therefore more reactive than amfenac followed by diclofenac. Indeed more ΔE is small more the molecule is reactive.

Absorption Properties
The spectral studies of diclofenac, bromfenac and amfenac have been performed using TD-DFT at B3LYP/6-311+G(d,p) level of theory in gas and aqueous phases. TD-DFT is a reliable method for the excited state computation [40] [41] that provide accurate results. To obtain the nature and energy of the singlet-singlet electronic transition, the prediction of the first 3 excited states are performed.
The calculated absorption energy, corresponding oscillator strength and orbital coefficients are summarized in Table 5. The results show that for all the molecules, the lowest energy transition is due to the excitation of electron from HOMO to the LUMO. The absorption maxima (λ max ) of the three molecules, diclofenac, bromfenac and amfenac correspond to the H→L transition. In gas phase, the absorption maxima (λ max ) of bromfenac is 7 nm greater than that of amfenac. This means that replacing a hydrogen atom with a bromine atom is accompanied by a bathochromic effect that decreases the absorption energy.
Thus for the absorption maxima, the energy of bromfenac (3.36 eV) is smaller than that of amfenac (3.42 eV) which is smaller than that of diclofenac (4.20 eV).
The absorption intensity is directly related with the dimensionless oscillator strength and the dominant absorption bands are the transitions with higher oscillator strength value [36]. Figure

Conclusion
We have studied some physicochemical properties of diclofenac, bromfenac and amfenac using the DFT and TD-DFT methods. The study of the structures of diclofenac, bromfenac and amfenac reveals a slight variation in the values of the geometrical parameters of the carboxylic group. The lipophilicity study shows that, diclofenac and bromfenac are very lipophilic. The evaluation of the polarity through the dipole moment shows that diclofenac is more polar than bromfenac followed by amfenac. The dipole moments increase with the polarity of the medium. In terms of acidity, research establishes that in the gas phase, diclofenac is more acid than bromfenac and amfenac. The energy gap indicates that bromfenac is more reactive than amfenac followed by diclofenac. This result is confirmed by that of TD-DFT calculations. Indeed TD-DFT calculations show that for the three NSAIDs, the lowest energy transition is due to the excitation from HOMO to LUMO. The absorption energy corresponding to H→L transition is comparable with the energy gap value. Moreover, this work opens new perspectives; in particular, its results could help to establish a classification of efficacy of NSAIDs.