Theoretical Study of N-Methyl-3-Phenyl-3-( 4-( Trifluoromethyl ) Phenoxy ) Propan as a Drug and Its Five Derivatives

Quantum chemical calculation was correlated with geometrical structure and total energy of fluoxetine and its five derivatives. Theoretical vibrational frequencies and geometric parameters (bond lengths and bond angles) have been calculated using ab initio (HF), density functional theory (B3LYP), semi-empirical (AM1, PM3) methods with different basis sets to design the fluoxetine drugs and its derivatives by a Gaussian 09 W program. Theoretical optimized geometric parameters and vibrational frequencies of fluoxetine have been compared with the corresponding five derivatives data. The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energies have been determined. The theoretical study includes the calculation of the thermodynamic properties of the drugs and its derivatives like zero-point energy, enthalpy, entropy, ionization energy, electron affinity to make a correlation between the gained results. The results of the four methods were not very clear, but an correlation between the dipole moment (potential character), static distribution (an active site character) and HOMO-LUMO energies (energy for electron transfer) shows that the patent 1.5 was important derivatives as a recommended drug relative to fluoxetine drug.

Fluoxetine is a racemic mixture of the R-and S-enantiomers and are of equivalent pharmacologic activity.Despite distinct structural differences between compounds in this class, SSRIs possess similar pharmacological activity, as with other antidepressant agents [1].The overall clinical effect of increased mood and decreased anxiety is thought to be due to adaptive changes in neuronal function that leads to enhanced serotonergic neurotransmission.Side effects include dry mouth, nausea, dizziness, drowsiness, sexual dysfunction and headache.Side effects generally occur within the first two weeks of therapy and are usually less severe and frequent than those observed with tricyclic antidepressants [1] [2].Employed in the present work, calculations were used to determine the spectroscopic and electronic characters of the drug and its derivatives which are used to make a correlation in bioactivity future of them.It is important to identify the appropriate structures and the detailed electronic charge distribution; dipole moment, total energy and other properties in fluoxetine and its derivatives.Amide bonds are indeed present in a huge array of molecules, including major marketed drugs [3] [4] [5].Hence amides and their derivatives have attracted continuing interest over the years.The five fluoxetine derivatives were prepared previously, but its bioactivity has not been characterized yet.

Materials and Method
The molecular structures of fluoxetine and its derivatives are presented in Table 1 and Figure 2 shows the structural formula, and the atomic position numbers assigned in this work.The program that used in the search.

Gaussian 09
Gaussian 09W (G09) is a computational chemistry program that runs on any modern windows 32 bit PC, or on a 64 bit PC [6].An electronic structure package capable of predicting many properties of atoms, molecules, reactive system, e.g.: -Molecular energies; -Structure; -Vibrational frequencies; -Utilizing an initio, density functional theory, semi-empirical.

Computational Details
In the first step of the calculation, geometrical parameters of these structures were further optimized by using density functional theory DFT (B3LYP)/6-31G, HF, AM1, PM3 methods.On the basis of the lowest energy conformer, the bond length and bond angles were obtained using the four methods.
The electronic properties: HOMO-LUMO energies are calculated by four methods, based on the optimized structure for soluble in water solvent [9] [10].
Thermodynamic properties of the title compound at 310 k temperature have been calculated using four methods.Moreover, the dipole moment and Mulliken atomic charge have also been studied using Gaussian 09 W program package.
The initial atomic coordinates for geometry optimization was taken from Gauss View software database [11].The molecular structure of drug in the ground state (in water) was optimized by HF and DFT/B3LYP with AM1 and PM3 methods for basis set levels.The optimized structure of the molecule was used to calculate the vibrational frequency at four methods.The calculated thermal correction to energy was scaled by 219.57Kcal/mole −1 (AM1), 213.34 Kcal/mole −1 (PM3), 230.67 Kcal/mole −1 (HF), and 216.51 Kcal/mole −1 (DFT) for fluoxetine and compare with the thermal correction energy for five derivatives.

Molecular Structure
The schematic depiction of fluoxetine and optimized structure are shown in Figure 2 and optimized bond lengths, bond angles of fluoxetine molecule which were calculated by using HF, DFT, AM1, PM3 methods with different basis sets are shown in Tables 2-5 compares the calculated geometric parameters with the five derivatives data.Based on this comparison, the bond length, angles for the derivatives showed good agreement with the drugs.From the theoretical values, we can find that most of the optimized bond lengths and bond angles for drug its slightly alike with the derivatives values, comparing bond angles and length of B3LYP with those of H, DFT and AM1, PM3.In spite of the differences, calculated geometric parameters represent a good approximation and they are the best for calculating other parameters, such as vibrational frequencies and thermodynamic properties.

Thermodynamic Parameters and Molecular Properties
To evaluate the energetic behavior of the title compound in water solvent media theoretical calculations were carried out at 310 k.Total energies and dipole  fluoxetine and its derivatives.Were obtained using (AM1, PM3) methods, showed that the Patent 3, 4 are more stable than the other patents.The prediction of accurate dipole moments is a very important issue because the magnitude of the dipole moment is strongly related to structure activity of drug.The results obtained using (HF, DFT) method predicts the same evaluation.The value of the dipole moment (D.M) for drugs was also calculated in Table 6 and Table 7.The dipole moment is a measure of the molecular charge distribution.Adirection of the (D.M) in a molecule depends on the centers of positive and negative charges.
As a result of calculations, the highest dipole moment was observed for a drug in HF/6-31G (6.121) whereas the smallest one was observed for a drug in PM3 (4.029) the value of dipole moment due to their effect on the charge density of the molecule.The value of the (D.M) for the compounds is a character for the polarity of the compounds mostly, the higher the compound polarity the higher that activity of it.As Table 6, Table 7 shows that Patent 1, 5 is a D.M have a similar D.M to the drug, relatively has the same activity.These parameters may also play an important role in the biological activity of drugs.The vibration entropy and C V are found considerably change by changing the methods.The DFT/B3LYP/6-31G result has been given the biggest value for fluoxetine for vibrational entropy (84.47) (Cal/mole-Kelvin) and the biggest vibrational C V (73.474) (Cal/mole-Kelvin) value whereas the five derivatives have been given the more stability for Patents 3 and 4. Mostly, DFT method is a more professional way to evaluate the methods of characters due to its modern and complex calculations, there its results more reliable than other method.DFT method gives relatively similar results for the energy evaluations but not for the HOMO, LUMO energies and the dipole moment which give relativity different results as

Theoretical Atomic Charge Calculation
Mulliken atomic charge calculation plays an important role in the application of quantum chemical calculation to molecule system [12].Since the charge distribution on the molecule has an important for the vibration spectra.Calculated atomic charges are a different matter.Atomic charges can be defined in various ways.Mulliken atomic charges are commonly used in molecular orbital theory and are used in and G09.They have varying values according to the basis set and the method of calculation [13].Table 8 and Table 9 show effective atomic charge calculations which have an important role in the application of quantum chemical calculation to the molecular system the atomic charge levels to the dipole moment, molecular polarization, electronic structure of drug, and the comparison of the different methods to describe the electron distribution of the drugs with its derivatives.Milliken charge distributions were calculated by determining the electron population of each atom as defined by the four methods.The results in the (AM1, PM3, HF, and DFT) were in Table 8 and Table 9.The charge change with the method, basis set presumably occurs due to polarization.In the atomic charge calculation O 16 , N 5 atoms exhibit a substantial negative charge, which is donor atom.But S and C 8 , C 11 , S 35 atoms exhibit a positive charge, which is an acceptor atom (See Table 8, Table 9).

HOMO and LUMO Molecular Orbital
In principle, there are several ways to calculate the excitation energies.The simplest one involves the difference between the highest occupied molecular orbital (HOMO) of a neutral system, which is a key parameter in determining molecular properties [13].The Eigen values of HOMO (π donor) and LUMO (π acceptor) and their energy gap between HOMO and LUMO characterizes the molecular chemical stability.The energy gap reflects the chemical activity of the molecules [13].The relatively large LUMO-HOMO energy gap of the studied molecule indicates that it can be considered as kinetically stable.In addition, energy of the HOMO is directly related to the ionization potential, while the energy of the LUMO is directly related to the electron affinity.The energy gaps are largely responsible for the chemical and spectroscopic properties of the molecules [13].LUMO-HOMO gap energy of fluoxetine and its derivatives are calculated by four methods and various levels which are given in Table 6, Table 7 and Figure 3.As a result, at the HOMO energies calculated by the (AM1, PM3, HF, DFT) methods by using the Gaussian 09 program by the different basis sets with diffuse function are higher than those of the other basis sets.The HOMO energy value for drug calculated at (AM1, PM3, HF, DFT) (−9.6533, −9.5124, −9.2147, −5.754) eV.The biggest HOMO energy value calculated at DFT/6-31G/B3LYP, whereas the smallest one is calculated at AM1.The biggest LUMO energy value is (3.1066) eV obtained using HF/6031G, band energy gap (E g ) value is (12.3213)eV obtained using HF/6-31G (Table 6, Table 7 and Figure 3).

Ionization Energy
The ionization energy associated with a relationship with a higher energy of occupied orbital as follows [14] [15].IE = −EHOMO the high value in the energy of ionization mean the high stability of the molecule and on the other hand, the ionization energy means high effectiveness of the molecule.The calculated ionization energy of the drug fluoxetine and its derivatives have studied theoretically by using G09W program according to the methods (AM1, PM3, HF, and DFT) as in Table 6 and Table 7.The calculated ionization energy for the drug according to DFT and PM3 method was similar to that of Patent 2, 3, on other and was similar to Patent 5 as AM1 and HF indicated.

Electron Affinity
The energy of electron affinity is given by the equation: EA = −ELUMO [15].
The high value of the energy of electronic affinity means high stability and thus leads to less efficiency of the molecule to link; the low energy electronic affinity means high efficiency and less stability of a molecule.The energy of electronic affinity of the drug fluoxetine and its derivatives studied theoretically by using program G09W.The result of the electron affinity shows that Patent 3 was a comparable value with a drug in methods (HF, DFT) showed relatively similar value for the affinity between the drug and Patent 3, 4.

Vibration Analysis
The observed and calculated frequencies using four methods (AM1, PM3, HF/6-31G, DFT/B3LYP/6-31G) with their absolute intensities were shown in Table 10.In order to facilitate assignment of the observed peaks we have analyzed some vibrational frequencies and compared our calculated results of the fluoxetine with their five derivatives shown in Table 10 and Figure 4.  shows IR-spectra of the fluoxetine and its derivatives in four method (AM1, PM3, HF, DFT).The present study, theoretical calculations of vibrational spectra using different methods and different basis sets were compared drugs with the derivatives to obtain the best expectation.The best frequencies calculated by DFT which was in a good agreement with drug frequencies results.

C-H Vibrations
The assignment of carbon-hydrogen stretching mode is straightforward on the basis set of the scaled four methods predicted frequencies as well known group frequencies.The heteroaromatic structure shows the presence of C-H stretching vibrations in the region 3150 -3050 cm −1 [16] [17].
Which is the characteristic region for ready identification of C-H stretching vibration?In this region, the bands are affected appreciably by the nature of the substituents.In the present theoretical study, there are three C-H stretching vibrations observed in the aromatic ring [16] [17].The strong and medium bands observed in IR spectrum at (3190, 3070, 3434, and 3263) in four methods for drugs are assigned to C-H stretching vibrations as reported with the derivatives.

Q. M. A. H. AL-Makhzumi et al.
Table 10.Comparison between experimental and theoretical values of the patterns of seismic movement frequencies drug fluoxetine and its derivatives when the geometry of the equilibrium on according to method of calculation (AM1, PM3, HF, DFT).

Figure 1 .
Figure 1.Structure of fluoxetine drugs and its derivatives.

5 Figure 2 .
Figure 2. 3D structure of fluoxetine and its derivatives using Gaussian 09 program.

Table 1 .
Fluoxetine data with its derivatives.

Table 2 .
Selected bond distances (Å) bond lengths for fluoxetine and its five derivatives.

Table 3 .
Selected bond distances (Å) bond lengths for fluoxetine and its five derivatives.

Table 4 .
Selected bond distances (Å) bond lengths for fluoxetine and its five derivatives.

Table 5 .
Selected bond distances (Å) bond lengths for fluoxetine and its five derivatives.

Table 7
list the calculated values of some thermodynamic parameters (such as zero-point vibrational energy, enthalpy, E HOMO , E LUMO , Gibbs free energy), E HOMO , E LUMO , thermal corrections to (energy, enthalpy, entropy, and Gibbs free energy)

Table 6
and Table7show.Because the study is a correlation study, there the difference in results will not affect the study.Q. M. A. H. AL-Makhzumi et al.DOI: 10.4236/jbm.2018.6800786 Journal of Biosciences and Medicines

Table 6 .
Selected thermodynamic parameters for AM1, PM3 of the drug and its derivativesin G09.

Table 7 .
Selected thermodynamic parameters for HF, DFT of the drug and its derivatives in G09.

Table 8 .
Selected atomic charges of drugs and its derivatives in AM1, PM3 in Gaussian G09.

Table 9 .
Selected atomic charges of drugs and its derivatives in HF, DFT in Gaussian 09.