Quantum chemical studies on tautomerism, isomerism and deprotonation of some 5(6)-substituted benzimidazole-2-thiones

Acidity constants, pK a values, tautomeric and isomeric equilibrium constants, K T and K eq. values, of some 5(6)-substituted benzimidazole-2-thiones and related fixed models, in which the possibility of proton migration is eliminated by replacing the mobile proton with methyl group, were calculated using semi-empirically computed physical and thermodynamic parameters. Full geometry optimization was carried out using semi-empirical AM1, PM3 and PM5 methods. The theoretically calculated acidity constants were compared with the experimental values and a reasonable correlation was observed.


Introduction
Due to the antagonist effect of benzimidazole derivatives towards purine compounds, the investigation of benzimidazole-2-thiones has been a matter of interest for a long time. 1,2Wolley had observed that benzimidazole inhibits the growth of several kinds of yeasts and bacteria.He also proved that the inhibition could be completely eliminated by the addition of aminopurines. 3[7][8][9][10][11][12][13] An understanding of the tautomeric and isomeric equilibrium of heterocycles, especially thiol-thione, helps in understanding many areas of chemistry and biochemistry, such as rationalization of physical and chemical properties and quantitative reactivity of heterocycles, 14- 20 the variation of intrinsic stabilities, solvent effects, [21][22][23] as a test of aromaticity, [24][25][26] and enzymatic catalysis and receptor interactions. 27Therefore, we believe that 5(6)-substituted benzimidazole-2-thione derivatives deserve a detailed theoretical study and four derivatives of 5(6)-substituted 2-mecapto benzimidazole along with their half model molecules, in which the migration of one proton was eliminated by replacing one of the mobile hydrogen atoms with a methyl group, were investigated in the present work.Since the protonation of these four compounds had been studied already 5,6 we have concentrated now on deprotonation.The nomenclature and formulation of the compounds studied are depicted in Table 1.

Computational methods
Theoretical calculations were carried out at the restricted Hartree-Fock level (RHF) using AM1, PM3 and PM5 semi-empirical SCF-MO methods in the MOPAC 2002 program, 28 implemented on an Intel Pentium IV PC computer, using a relative permittivity of 78.4 corresponding to water.The solvent effect was included in the geometry optimizations following the 'COnductorlike Screening Model' (COSMO) 20 implemented in MOPAC 2002.All the structures were optimized to a gradient norm of <0.1 in the gas phase and 0.1-1.0 in the aqueous phase as commonly accepted, using the eigenvector method (EF).The absolute entropies of all structures were calculated from a complete vibration analysis.Enthalpies were corrected to free energies using calculated entropies.Initial estimates of the geometry of all the structures were obtained by a molecular mechanics program (CS ChemOffice Pro for Windows), 30 followed by full optimization of all geometrical variables (bond lengths, bond angles and dihedral angles), without any symmetry constraint, the semi-empirical AM1, PM3 and PM5 quantum chemical methods in the MOPAC 2002 programs.

H H H
The nomenclature and computed physical and thermodynamic parameters for the studied compounds are depicted in Tables 2-8.We have attempted to evaluate the results obtained as follows.

Relative Stability, Tautomerism and Stereoisomerism
Among the other possible conformers of mercapto bezimidazoles, with the exception of molecule I in which R 1 =R 2 =H and X=H, the syn and anti forms are identical, only the anti (i.e.dihedral angle 1234=180º) and syn (dihedral angle 1234=0º) conformers (Scheme 1) were considered in the present work.
Scheme 1.The anti and syn form for studied molecules.
Using the aqueous phase, AM1, PM3 and PM5 calculated physical and thermodynamic parameters (Table 2) semi-empirical isomerisation and tautomerisation equilibrium constants for 5(6)-substituted benzimidazole-2-thione derivatives along with their fixed models are given Table 3 and Table 4 respectively.
The gas-phase semi-empirical calculated relative stability data for tautomers and isomers along with their fixed models are given Table 5.
As can be seen from Table 3 and Scheme 2, when a potential mercapto group is located at C-2 of benzimidazole and its two half models (i.e. one of the mobile hydrogen atoms replaced by a methyl group) the tautomeric equilibrium constants indicate that thione forms I 1c, I 1cam and I 1cbm are predominant over thiol forms I 2c, I 2cam and I 2cbm with all methods.
When a potential mercapto group is located at C-2 for benzimidazole, the relative stability data indicate that the thione form I 1b predominates over the thiol form I 2c AM1 and PM5 calculations, whereas PM3 data indicate the reverse.PM5 calculation for the model compounds suggest that the predominance of thione form 1bm over the thiol forms 2cam and 2cbm.However the AM1 and PM3 methods suggest the reverse.For 5(6)-substituted benzimidazole derivatives (substituents; CH 3 , NO 2 and Cl) the relative stability data of AM1 and PM5 methods indicate that thione form 1c is predominant over the thiol forms 2c and 3c.However, the PM3 method indicates the reverse.For the model compounds of 5(6)-methylbenzimidazole the relative stability data indicate the predominance of thione forms 1cam and 1cbm over the thiol forms 2cam and 2cbm and 3cam and 3cbm with AM1, PM3 and PM5 methods.Similarly for the model compounds of 5(6)-nitrobenzimidazole and 5(6)-chlorobenzimidazole the relative stability data indicate that the3 thione forms 1cam and 1cbm are predominant over the thiol forms 2cam and 2cbm and 3cam and 3cbm with AM1 and PM5 methods.Whereas with PM3 methods the reverse is true.[33]

Acidity
The protonation reaction of a given base can be shown as follows; BH n+ B (n+1)+ + H + (1) (2) in which n can have a negative, positive or zero value.The acidity of a given base, B, for the protonation reaction can be calculated using Eq.2. in which B and BH + are neutral and protonated species of base B, and A and AH + are H 2 O and H 3 O + respectively.The computed thermodynamic data were used in predicting the acidity constants, pK a values, of various species, using Eq. 3, in which the δ∆G (BH+) is the standard free energy change for the protonation reaction (Eq. 1) (Table 6).
pK a(BH+) = δ∆G (BH+) /2.303RT (3) Possible deprotonation patterns for the studied molecules are shown in Schemes 1 and 2. Aqueous phase calculated acidity constant pK a values are given in Table 3. From these data the deprotonation pK a values of 5(6)-methylbenzimidazole-2-thiol was found to be the highest (i.e.13.41 by the AM1method) and the deprotonation pK a values of 5(6)-nitrobenzimidazole-2-thiol was found to be the lowest (i.e.11.71 by the AM1 method).
Experimental pK a : CH  34,35 with calculated pK a values and we observed that the best fit occurred with the AM1 method (Fig. 1).

Nucleophilicity Criteria
The principle of hard and soft bases has been applied to kinetic phenomena for a long time.In this connection, organic chemistry has provided most of the examples, because organic reactions are often slow enough for their rates to be easily measured.In organic chemistry, we are generally interested in the reactions of electrophiles and nucleophiles.These reactions are a particular kind of the general acid-with-base type of reaction, and so the principle of hard and soft acids and bases applies equally to the reactions of electrophiles and nucleophiles.So acidity and basicity can be related to the theoretical interpretation of hard-soft acids and bases stating the following principles: i. Hard acids have high-energy LUMOs and the hard bases have low-energy HOMOs.
ii.The lower the energy of the HOMO of a base the harder it is as a base.
iii.A hard acid bonds strongly to a hard base because the orbitals involved are far apart in energy.iv.A soft acid bonds strongly to a soft base because the orbitals involved are close in energy.Since it was observed that the rates with which nucleophiles attack one kind of electrophile are not necessarily a good guide to the rates with which the same nucleophile will attack other electrophiles, so it is a good idea to categorize nucleophiles as being hard or soft, and electrophiles as being soft or hard.The theoretical interpretation of them are as follows; i. Hard nucleophiles have relatively low-energy HOMOs.
ii. Soft nucleophiles have high-energy HOMOs.
The solvated proton is a hard electrophile and little affected by frontier orbital interactions.For this reason, the pK a of the conjugated acid of a nucleophile is a good measure of the rate at which that a nucleophile will attack another hard electrophile. 36aking all those above mentioned points into account, we have attempted to find possible correlations between the experimental or computed acidity constants, pK a values, and computed nucleophilicity of the studied molecules.
The nucleophilicity, n = E HOMO -E LUMO [37], of the studied molecules was calculated and the aqueous phase calculated n values of the studied neutral molecules are depicted in Table 7.
It seems that the basicity and nucleophilicity of compound IV is reduced as expected from the strong electron-withdrawing effect of the nitro group.Whereas the weaker electronwithdrawing effect of chlorine reduces the basicity and nucleophilicity to a lower extent.On the other hand, the electron-donating methyl group seems to increase the basicity power of molecule II but not its nucleophilicity (Figs.2-3) ARKAT USA, Inc.

Figure 1 .
Figure1.Plot of the aqueous phase AM1 calculated acidity constants, pK a (calc.), and experimental acidity constants, pK a (exp.), for the studied molecules.

Figure 3 .
Figure 3.The plot of the aqueous phase experimental acidity constants, pK a (calc.), and nucleophilicity values n (AM1) , for studied molecules.

Table 1 .
Nomenclature of molecules studied

Table 3 .
Aqueous phase PM3 , PM5 and AM1 calculated tautomeric equilibrium constants K T of studied molecules

Table 4 .
The aqueous phase PM3 ,PM5 and AM1 calculated some isomeric equilibrium constants K is , of studied molecules ©ARKAT USA, Inc.