Study of the Stability and Chemical Reactivity of a Series of Tetrazole Pyrimidine Hybrids by the Density Functional Theory Method (DFT)

Introduction

An infection, defined as an invasion of the organism by a foreign agent, namely a bacterium or a virus that can cause a pathological condition by injury to local cells. Among them, we have the invasive fungal infections (IFI), which can be caused by a variety of fungi such as yeasts, molds (Aspergillusspp) and dimorphic fungi (Histoplasmacapsulatum) that are very common in some immunocompromised patients ^1,2. We have more than 300 million people suffering from these diseases causing 1.35 million deaths each year in the world, which poses a real problem to the global health system ^2,3. In the face of this scourge, clinically available antifungal agents have been proposed for the treatment of these IFIs but they are quite limited ^4,5 and most of them are not effective due to high resistance to toxicity and some adverse side effects ^6,7. Therefore, the development of new antifungal agents with low toxicity that will be effective in the control of these fungi are in order. As a result, tetrazole hybrids have been synthesized and tested for their antifungal activities by Sheng-Qiang Wang et al ⁸,

some of which have shown promising activity against drug-sensitive and drug-resistant fungi. Among these hybrids, we distinguish the pyrimidine associated with tetrazole which will give rise to a new series of molecules, namely Pyrimidine-Tetrazole Hybrids. This study will allow us to consider which of them are the most likely to act as antifungal.

Materials and Methods

This study was performed on six (06) molecules of the Pyrimidine Tetrazole Hybrid series presented in Table 1 below:

Table 1: Structure of the studied Pyrimidine Tetrazole Hybrid derivatives. Click here to View table

Software and theory level

The theoretical study of stability and chemical reactivity was carried out based on three theoretical approaches. The first approach relates to global descriptors deriving from frontier molecular orbitals and then the second approach is concerned with local indices of reactivity. The geometries of the molecules were optimized at the DFT calculation level with the B3LYP functional ^9-11 in the 6-311 G (d, p) base using the Gaussian 09 software ¹². This Hybrid functional gives better energies and is in agreement with high level ab initio methods ^13-14.

As for the split-valence and triple-dzeta base (6-311G (d, p)), it is sufficiently extensive and the consideration of polarization functions is important for the explanation of free doublets of heteroatoms. The geometries are kept constant for cationic and anionic systems. The global reactivity indices were obtained from the conceptual DFT model ^15-17.

Standard thermodynamic quantities of formation

The thermodynamic quantities of the molecules were performed from optimization and calculation of frequencies at the B3LYP / 6-311G (d, p) level. The quantities such as entropy, enthalpy and free enthalpy of formation were determined using the following formulas proposed by Otchersky et al. ¹¹.

∑D₀ : Atomization energy

ε₀ (M) : Total energy of the molecule

ε_ZPE : Zero point energy of the molecule

Enthalpy corrections of atomic elements. These values ​​are included in the Janaf table ¹⁹.

Molecule enthalpy correction

H_corr : Enthalpy of thermal correction

x : Number of  atoms in the Molecule.

Reactivity descriptors

Global descriptors

To predict chemical reactivity, some theoretical descriptors related to conceptual DFT have been determined. In particular, the energy of the Lowest Unoccupied Molecular Orbital (E_LUMO), the energy of the Highest Occupied Molecular Orbital (E_HOMO), electronegativity (χ), softness global (σ) and the global electrophilicity index (ω). These descriptors are all determined from the optimized molecules. It should be noted that the descriptors related to the frontier molecular orbitals have been calculated in a very simple way within the framework of the Koopmans approximation ¹⁸. LUMO energy characterizes the sensitivity of the molecule to nucleophilic attack, and HOMO energy characterizes the susceptibility of a molecule to electrophilic attack. Electronegativity (χ) is the parameter that reflects the ability of a molecule not to let its electrons escape. The overall softness (σ) expresses the resistance of a system to a change in its number of electrons. The overall electrophilicity index characterizes the electrophilicity of the molecule. These different parameters are calculated from equations (6):

Local Fukui indices

The local responsiveness study was also conducted by determining the local Fukui indices. Two indices were used:

The electrophilic Fukui function f⁺ which characterizes the electron density response to electron gain and gives information on the most electrophilic site towardnucleophilic attack and the function of nucleophilic Fukui f^– characterizing the electron density response to electron loss and provides information on the most nucleophilic site toward an electrophilic attack.

It has been shown [19], for reactions controlled by frontier orbitals, that a high value of the Fukui index means high reactivity of the site. The condensed form of these two functions in the case of a molecule with N electrons has been proposed by Yang and Mortier ²⁰.

Results and Discussion

Study of standard thermodynamic formation parameters

The thermodynamic parameters, namely the enthalpy of formation Δ_fH°, the enthalpy of formation Δ_fS° and the free enthalpy of formation Δ_fG° were also determined. It should be noted that the enthalpy reflects the thermicity of a chemical reaction when entropy provides information on the level of disorder in the system. In addition, the free enthalpy reflects the possibility or not of a chemical reaction. The values ​​of the thermodynamic parameters are given in Table 2.

Table 2: Thermodynamic quantities of PTH formation optimized at the theory level B3LYP / 6-311G (d, p).

Molecule	(kcal/mol)	(cal/mol.K)	(kcal/mol)
PTH_1	-982.1206	-755.3723	-756.9064
PTH_2	-1050.5583	-761.2891	-823.5800
PTH_3	-982.1498	-760.0310	-755.5466
PTH_4	-971.4305	-759.4040	-745.0142
PTH_5	-1131.1434	-871.9923	-871.1589
PTH_6	-1039.4355	-837.8549	-789.6291

 

The results show that all the values ​​of the standard thermodynamic quantities of molecule formation are negative. This means that during the formation of all the PTH compounds occurs spontaneously with a release of heat and a reduction in disorder. At this level, we note that the quantities determined at the level of theory B3LYP / 6-311G (d, p) confirm the formation and existence of the series of Pyrimidine Tetrazole Hybrids explored.

Global reactivity indices

The conceptual DFT descriptors determined have contributed in several ways to understanding the structure of molecules and their reactivity. The reactivity parameters examined in this series of compounds are: chemical potential (µ), hardness (ɳ), softness (S) and electrophilic index (ω). The calculated values ​​of said parameters are reported in table (3).

Table 3: Summary of global reactivity descriptors at the B3LYP / 6-311G theory level (d, p).

Molecule	µ (eV)	η (eV)	S (eV-1)	ω (eV)
PTH_1	5.2518	2.1107	0.4738	6.5338
PTH_2	5.2806	2.0671	0.4838	6.7449
PTH_3	5.3283	2.0304	0.4925	6.9913
PTH_4	5.2838	1.9905	0.5024	7.0127
PTH_5	4.8228	1.8757	0.5331	6.2002
PTH_6	5.0925	2.0401	0.4902	6.3560

 

The chemical potential values ​​recorded for the Pyrimidine Tetrazole Hybrids in Table 3 indicate that PTH_3 is the molecule most likely to retain its electrons due to its fairly high chemical potential value compared to others.

In terms of chemical hardness (η) and overall softness (S), the hardness increases with the stability of the molecule while the softness increases with the reactivity of the molecule. Thus, the harder a molecule, the more stable and less reactive it is. This is the case with PTH_1, which is the hardest molecule, and therefore the least reactive of all, because it has the highest hardness value (η). The PTH_5 molecule, on the other hand, is the softest of all molecules, hence the most reactive. Methoxy therefore contributes to increasing the reactivity of the molecule.

With regard to the electrophilic index (ω), a molecule is all the more electrophilic the higher the value of the overall electrophilic index, the molecule exhibiting the greater value of the electrophilic index is PTH_4 while the compound PTH_5 is the least electrophilic because it has the lowest value. Considering the other values ​​in the table, we deduce that the halogens contribute to the increase in the electrophilic character of our molecules while the electron-donor groups decrease this character.

Local descriptors

Since the dimerization of a biologically active molecule is likely to result in a biologically active molecule, we have therefore found it necessary to search for sites of nucleophilic and electrophilic attacks.

The Fukui indices, the frontier molecular orbitals HOMO and LUMO as well as the coefficients of the atomic orbitals in the frontier orbitals characterize the sites of electrophilic and nucleophilic attacks located for each molecule studied.

Visualization of frontier molecular orbitals

The analysis of the frontier molecular orbitals of PTH_1 is given in figure 1 below

Figure 1: PTH_1 frontier molecular orbitals Click here to View figure

Observation of the frontier molecular orbitals of PTH_1 shows that

The atoms C₁, C₂, C₃, C₆, N₂₃ and C₉ being enclosed in the larger lobes of the HOMO are the atoms most susceptible to electrophilic attacks and those, contained in the larger lobes of the LUMO, to namely C₉ and C₇ are the sites of nucleophilic attacks.

The analysis of the frontier molecular orbitals of PTH_2 is given in Figure 2 below

Figure 2: Frontier molecular orbitals of PTH_2 Click here to View figure

Observation of the frontier molecular orbitals of PTH_2 shows that

The atoms C₁, C₂, C₃, C₄, C₅, C₆ and N₂₃ being enclosed in the larger lobes of HOMO are the atoms most susceptible to electrophilic attacks and those contained in the larger lobes of LUMO, namely C₈, C₇ and N₁₆ are the sites of nucleophilic attacks.

The analysis of the frontier molecular orbitals of PTH_3 is given in Figure 3 below

Figure 3: Frontier molecular orbitals of PTH_3. Click here to View figure

Observation of the frontier molecular orbitals of PTH_3 shows that

The atoms C₁, C₂, C₃, C₄, C₅, C₆ and Cl₂₅ being enclosed in the larger lobes of HOMO are the atoms most susceptible to electrophilic attacks and those contained in the larger lobes of LUMO, namely C₈, C₇, N₁₆, N₂₁ and N₂₃ are the sites of nucleophilic attacks.

The analysis of the frontier molecular orbitals of PTH_4 is given in Figure 4 below

Figure 4: Frontier molecular orbitals of PTH_4. Click here to View figure

Observation of the frontier orbital map of PTH_4 shows that

The atoms C₁, C₂, C₃, C₄, C₅, C₆ and Br₂₅ being enclosed in the larger lobes of HOMO are the atoms most susceptible to electrophilic attacks and those contained in the larger lobes of LUMO, namely C₇ and C₉ are the sites of nucleophilic attacks. The analysis of the frontier molecular orbitals of PTH_5 is given

Figure 5: Frontier molecular orbitals of PTH_5. Click here to View figure

Observation of the frontier orbital map of PTH_5 shows that

The atoms C₁, C₃, C₄, C₅ and C₆ being enclosed in the larger lobes of the HOMO are the atoms most likely to undergo electrophilic attacks and those, contained in the larger lobes of the LUMO, namely C₇ , C₈ and C₉ are the sites of nucleophilic attacks.

The analysis of the frontier molecular orbitals of PTH_6 is given by the following figure 6

Figure 6: Frontier molecular orbitals of PTH_6. Click here to View figure

Observation of the frontier orbital map of PTH_6 shows that

The atoms C₁, C₂, C₃, C₄, C₅ and C₆ being enclosed in the larger lobes of the HOMO are the atoms most susceptible to electrophilic attacks and those, contained in the larger lobes of the LUMO, to namely C₇ and C₉ are the sites of nucleophilic attacks.

The visualization of the frontier molecular orbitals indicates for a given molecule, several sites of electrophilic and nucleophilic attacks. However, to be better situated on the most probable electrophilic and nucleophilic site, the calculation of the local Fukui indices was carried out.

Calculation of Fukui indices

The calculation of the Fukui indices of PTH_1 allows us to obtain the values ​​recorded in Table 4.

Table 4: Values ​​of local Fukui indices, calculated at the B3LYP / 6-311G (d, p) level, according to NPA (Natural Population Analysis) for PTH_1

Atome	NPA
	f +	f –
C8	0.0036	0.0044
C9	0.1503	0.0404
C10	-0.017	0.0038
N17	0.1413	0.0843
C18	0.0076	-0.002
F19	0.0264	0.0145
F20	0.0202	0.0129
F21	0.0265	0.0144
N22	0.0235	0.002
N23	0.0443	0.121

 

Analysis of the data in Table 4 indicates that the N₂₃ atom has the highest nucleophilic Fukui index for the population analysis used when C₉ displays the highest electrophilic Fukui index. Therefore, any electrophilic attack will preferentially be on the N₂₃ atom while a nucleophilic attack will be on the C₉ atom.

With regard to the TPH_2 molecule, the calculation of its Fukui indices leads to the values ​​shown in Table 5.

Table 5: Values ​​of local Fukui indices, calculated at the B3LYP / 6-311G (d, p) level, according to NPA (Natural Population Analysis) for TPH_2.

Atome	NPA
	f +	f –
C1	-0.0300	0.1199
C2	0.0064	0.0222
C3	-0.004	0.0587
C4	0.0153	0.1027
C5	-0.006	0.0294
C6	0.0184	0.0365
C7	0.1001	-0.0010
C8	-0.015	0.0041
C9	0.0982	0.0385
C10	-0.1740	0.0033
N16	0.2956	0.0832

 

Analysis of the data in Table 5 indicates that atom C₁ has the highest nucleophilic Fukui index for the population analysis used when N₁₆ displays the highest electrophilic Fukui index. Therefore, any electrophilic attack will preferentially be on the N₁₆ atom when a nucleophilic attack will be on the C₁ atom.

The calculation of the Fukui indices of TPH_3 leads to the values ​​shown in table 6.

Table 6: Values ​​of local Fukui indices, calculated at the B3LYP / 6-311G (d, p) level, according to NPA (Natural Population Analysis) for TPH_3.

Atome	NPA
	f +	f –
C10	-0.0170	0.0030
N16	0.1373	0.0748
C17	0.0066	-0.0020
F18	0.0253	0.0133
F19	0.0193	0.0112
F20	0.0254	0.0132
N21	0.0242	0.0041
N22	0.0439	0.1041
N23	0.0691	0.1022
N24	0.0696	0.0362
Cl25	0.0762	0.1792

 

Analysis of the values ​​in Table 6 shows that the N₁₆ atom has the highest electrophilic Fukui index while the Cl₂₅ atom has the highest nucleophilic Fukui index. All nucleophilic attacks will preferentially go to the N₁₆ atom and all electrophilic attacks will go to the Cl₂₅ atom. The calculation of the Fukui indices of TPH_4 leads to the values ​​shown in table 7.

Table 7: Values ​​of local Fukui indices, calculated at the B3LYP / 6-311G (d, p) level, according to NPA (Natural Population Analysis) for TPH_4.

Atome	NPA
	f +	f –
C9	0.1428	0.0339
C10	-0.0170	0.0023
N16	0.1365	0.0699
C17	0.0065	-0.0011
F18	0,0250	0.0127
F19	0.0192	0.0104
F20	0.0252	0.0126
N21	0.0243	0.0048
N22	0.0436	0.0965
N23	0.0687	0.0943
N24	0.0691	0.0352
Br25	0.0889	0.2414

 

Analysis of the data in Table 7 indicates that the Br₂₅ atom has the highest nucleophilic Fukui index for the population analysis used when C₉ displays the highest electrophilic Fukui index. Therefore, any electrophilic attack will be on the Br₂₅ atom while a nucleophilic attack will be on the C₉ atom.

The calculation of the Fukui indices of TPH_5 leads to the values ​​shown in table 8.

Table 8: Values ​​of local Fukui indices, calculated at the B3LYP / 6-311G (d, p) level, according to NPA (Natural Population Analysis) for TPH_5.

Atome	NPA
	f +	f –
C1	-0.0380	0.1441
C2	0.0265	0.0003
C3	0.0202	0.0816
C4	0.0728	0.0682
C5	0.0091	0.0483
C6	0.0656	0.0251
C7	0.1223	-0.0240
C8	0.0084	0.0028
C9	0.1516	0.0325

 

Analysis of the values ​​in this Table 8 indicates that atom C₁ has the highest nucleophilic Fukui index for the population analysis used when C₉ displays the highest electrophilic Fukui index. Therefore, any electrophilic attack will be on the C₁ atom while a nucleophilic attack will be on the C₉ atom.

Calculation of the Fukui index of TPH_6 leads to the values ​​shown in Table 9.

Table 9: Values ​​of local Fukui indices, calculated at the B3LYP / 6-311G (d, p) level, according to NPA (Natural Population Analysis) for HTP 6.

Atome	NPA
	f +	f –
C1	-0.0330	0.1296
C2	0.0362	0.0213
C3	0.0154	0.0506
C4	0.0836	0.1417
C5	0.0097	0.0193
C6	0.0538	0.0358
C7	0.1248	-0.0090
C8	0.0040	0.0033
C9	0.1489	0.0357

 

Analysis of the data in Table 9 indicates that the highest nucleophilic Fukui index value is obtained with the C₄ atom from which this atom is found to be the preferential center of all electrophilic attacks while the highest electrophilic Fukui index is obtained with the C₉ atom. However, the latter will be the most likely site for nucleophilic attacks.

Conclusion

At the end of our work, we retain that with the level B3LYP / 6-311G (d, p), we proceeded to the characterization of the sites of reactivity of the six (06) molecules of HTP. The values ​​of the local Fukui indices indicated that the sites of reactivity vary depending on the substituent. Molecules with a halogen substituent have revealed that their nucleophilic attack sites are these halogens in question except fluorine whose nucleophilic site is on the C1 atom. Regarding electrophilic sites, the C9 atom is most likely for the molecules of HTP 1, HTP 4, HTP 5 and HTP 6.

The exploitation of the results obtained with the calculation of the global descriptors indicated to us that the HTP 1 molecule is the most stable of all, while the HTP 5 molecule is the most reactive with methoxy as a substituent. The substitution of halogens on the core of the HTP, indicates to us that the stability of our molecules increases with the halogens. Therefore, the more electronegative the halogen, the more stable the HTP molecules. The HTP 1 molecule has the greatest stability with hydrogen (H) as a substituent.

The calculation of the thermodynamic parameters allowed us to know that the formation of our hybrid tetrazole pyrimidine (HTP) molecules occurred spontaneously with the release of heat and reduction of disorder.

In perspective, we can consider to see what influence of temperature and pressure on the stability and reactivity of our series of molecules.

Acknowledgement

We are grateful to Professor ZIAO Nahossé, Director of the Laboratory of Thermodynamics and Physical Chemistry of the Environment, to Dr. BAMBA Kafoumba of the University NANGUI ABROGOUA (Ivory Coast), to Professor NIAMIEN Paulin Marius of the Laboratory of Constitution and Reaction of Matter of the University Félix Houphouët Boigny (Ivory Coast) for their support and motivation.

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