Quantum chemical studies on acidity-basicity behaviors of some bipyridine derivatives

The protonation of six isomeric forms of bipyridine has been investigated by means of different quantum chemical methods (i.e. semi-empirical (PM5), DFT (B3LYP/6-31G(d)) and ab initio (HF/6-31G(d)). It is concluded that 2,2’-bipyridine exists as transoid isomer, 2,3’-bipyridine as cisoid isomer and 3,3’-bipyridine coexist in equal amount of cisoid and transoid isomeric forms.


Introduction
Many procedures were reported for the synthesis of bipyridine derivatives in the past years.][3][4][5][6][7][8][9] Studies on structure of bipyridine derivatives are also indicate an enormous amount of research affords.A low temperature X-ray structure, 10 the theoretical calculations [11][12][13][14][15] and spectroscopic studies of bipyridine derivatives have been reported in the literature. 16hemical reaction studies of the various bipyridines are numerous.][29][30][31][32][33] Following our previous work on alkyl and halogen substituted pyridines [34][35][36][37][38][39] and bipyrazoles, 40 we now are reporting on the semi empirical (PM5) and ab initio (HF and DFT) calculated structural and thermodynamic parameters of six isomeric bipyridine derivatives (Scheme 1).Any possible parallelism with reported and available experimental data were searched.The parallelism and discrepancies between the experimental and computed data were attempted to be interpreted.

Computational methods
Theoretical calculations were carried out at the restricted Hartre-Fock level (RHF) using PM5, method in the MOPAC 2002 program 41a implemented in an Intel Pentium IV computer.All the structures were optimized to a gradient norm of and 0.1 -1.0 in the aqueous phase , using the eigenvector method following (EF).The initial estimates of the geometry of all the structures were obtained by a molecular mechanics program of CS Chem.Office pro for Windows 42 , followed by full optimization of all geometrical variables (bond lengths, bond angles and dihedral angles), without any symmetry constraint, using the semi-empirical PM5 quantum chemical methods in the MOPAC 2002 program.
Nowadays both microscopic and macroscopic theoretical methods are available for the estimation of solvation free energies.Therefore it is possible, in principle, to determine theoretical relative or absolute acidity constants, pK a values, the thermodynamic cycle using the Equation 1.
Scheme 1 explains the interrelationship between the thermodynamic parameters of gas and solution phases.
Interrelationship between the gas phase and solution thermodynamic parameters.
The acidity constant, pK a , can be computed by using Equation 1 and Equation 2. The Equation 2is an rearranged form of Equation 1.
The ab initio calculation of the absolute pK a values can be made by using Equation 3 in which ∆G g and ∆G a = ∆G s (B) -∆G s (BH) + ∆G s (H + ) are the gas phase and solvation free energies of the ionization and ∆G s 's are solvation free energies respectively. 43,44 a = [∆G g + ∆G a ] / 2.303 RT In the present work ab initio Hartree-Fock (HF) and density functional geometry (DFT) optimizations were performed using the Gaussian 03 program.41b The calculation of solvation free energies was carried out using at HF/6-31G(d) and B3LYP/6-31G(d) respectively.The value of ∆G s (H + ) -271.2 kcal mol -1 was used as suggested in the literature. 44

Result and Discussion
The computed physical and thermodynamic parameters for studied compounds were depicted in Tables 1-3.We have attempted to evaluate the obtained results as follows:

Acidity-basicity
The acidity of a given base, B, for the protonation reaction (Equation 4) can be calculated using the Equation 5, where ∆G is the standard free energy. 45 + AH + = BH + + A ( 4) In Equation 1, 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 pK a values of various species, using Equation 6 in which the δ∆G (BH+) is the standard free energy change for protonation reaction (Equation 4, Table 4 and 5    A more reliable and closer pK a values to experimental values however were found by ab initio calculations (Table 4 and 5) for compound 3.
A perfect correlation was observed between theoretically obtained (i.e.PM5 calculated) and experimental acidity constants [46] with a slope and regression of about unity (i.e.R 2 = 0.99).This high correlation indicates that the first protonation of compounds 1 and 3 occur over the cisoid form (i.e. they are off the line ).Whereas the first protonation of compound 4 occur over both cisoid and transoid form which are exist in equal amounts (Table 6).On the other hand protonation of compounds 2, 5 and 6 occur over transoid form(i.e. they are on the same line) A graph of experimental pK a values against the calculated pK a values using Equation 5 were depicted in Figure 1.

Substituent constants
One of the commonly used method to search for the effect of substituent on an equilibrium processes has been the usage of the Hammett Equation (Equation 7). 45 a (unsubstituted molecule) -pK a (substituted molecule) = ρσ The σ (i.e.substituent constant) values for 2-, 3-and 4-pyridinyl group can be calculated by using Equation 7. The ρ (i.e.equilibrium constant) value for the pyridine protonation was given as 5.77. 46Hence the ionization equilibrium in water for protonated pyridinium molecules can be written as in Scheme 3.The experimental pK a value for unsubstituted pyridine was taken as 5.17   The substituent constants using the experimental and theoretical pK a values were calculated and obtained results were depicted in Table 7.When we take σ values of which calculated using the experimental pK a values into account we observed that all σ values have positive sign indicating the electron -withdrawing effect of the substituted pyridyl ring (B).
We also can predict that this electron-withdrawing effect is not big and it is close to the σ p value of 0.06 for fluorine atom. 47It seems that the obtained calculation results are quite satisfactory and PM5 calculated σ values for all studied molecules were close enough to experimental values to be considered successful.

Relative Stabilities
Equation 8 was used to calculate the relative stabilities (RS) using the heat of formation value of the studied molecules.

RS = ∆H
The aqueous phase PM5 calculated relative stabilities were given in values were calculated by utilizing the pK a values).f RS = ∆H f (transoid)-∆H f (cisoid) The negative sign indicates the favorability of cisoid form.

Isomeric Equilibrium Constants
The isomeric equilibrium constants, K is values, of the studied molecules were calculated by two methods as described below; i-Using the equation K is = e (δ∆G f / RT) Where K is is the isomeric equilibrium constant between the cisoid and transoid forms.δ∆G f is the difference in Gibbs free energies of the isomers, δ∆G f = ∆G f (transoid form) -∆G f (cisoid form).The R value is 1.987x10 -3 kcal/mol and T is 298 K.The following equilibrium represents the isomeric equilibrium between isomers cisoid form and transoid form.The K is values obtained by this way suggest the predominance of transoid form over the cisoid forms for compounds 1 and 4.The predominance of cisoid form over the transoid form for compound 2. Whereas for compounds 3,5 and 6 they suggest the presence of the equal amount of cisoid and transoid forms.
Using the equations 6 and 7 pK a (transoid)-pK a (cisoid) = pK is (9)   K is = K a (transoid)/K a (cisoid) (10)   The obtained K is values by using Equations 9-10 were depicted in Table 6.The K is values obtained using Equations 9-10, like the other K is values mentioned above have suggested the predominance of the transoid form over the cisoid form for compound 1.Similarly for compound 2 the predominance of transoid form over the cisoid form for compound 2 was confirmed.For compound 4 supporting to above conclusion it indicates the predominance of the cisoid form over the transoid form.Whereas for compounds 3, 5, 6 it suggest the presence of the equal amount of cisoid and transoid forms.Ab initio calculated K is values are however suggest the predominance of transoid forms with a values of 1.26 and 2.13 respectively (Table 6).

Mole Fractions
The mol fractions of the cisoid and transoid isomers were calculated by using the following equations and the obtained results were depicted in Table 6.
Mole fraction values indicate that the predominance of transoid form over the cisoid form for 1.For 2 however two different mole fraction calculation methods indicates two different conclusions; the first one, N c values, indicates the predominance of cisoid form(with the exception of the B3LYP method).Whereas the second one, N e values, indicates the predominance of transoid form.This discrepancy presumably source out from the difference between two methods of calculations.In the first one, K is b values, the solvation effect is being neglected in the second one, K is d values, the solvation effect has been taken into account.This point had reflected also in the geometry of the neutral and protonated species in calculations of acidity constants, pK a values which were used in calculations of N e values.The change in the dihedral angle of N1-C2-C3-C4 ( i.e. changes from -53.74 to -0.06 for cisoid protonation and from -0.04 to -0.02 for transoid form) for cisoid protonation may explain why compound 2 prefers to exist in the transoid form (Table 8).For compound 4 the calculated mole fraction values leads to two differerent conclusions; N c values, indicates the predominance of transoid form.Whereas the other conclusions, N e values, indicates the predominances of cisoid form.For 3, 5, 6 however they suggest the existence of equal amount of two isomers (Table 6 ).The lower solvation effect on compounds 1, 2 and 4 comparing to compounds 3 and 5 is reflected by decrease in nucleophilicities.It seems that the most solvated molecule among the others is compound 6 which possess two nitrogen atoms which are positioned very suitably for solvation after protonation and form paraquat like stable dication which plays a very important role in electron transport phenomena. 50

N N H H
It seems that the nucleophilicity is more substituent dependant than that of ionization constant, K a value, for these derivatives.This means that the position of substituent is also an important factor and effects the electronic changes on the protonation center.

Table 2 .
Aqueous phase ab initio calculated thermal and solvation free energies, investigated compounds at 298K

Table 3 .
Aqueous phase ab initio calculated thermal and solvation free energies, investigated compounds at 298K

Table 4 .
Aqueous phase PM5 and ab initio calculated pK a values for the investigated molecules

Table 5 .
Aqueous phase PM5 and ab initio calculated pK a values for the investigated molecules pK a (expt.)weretakenfromref.45,PM5 Calculated pK a value for pyridine is 5.10 Possible protonation patterns for the studied molecules were depicted in Scheme 2. The aqueous phase calculated acidity constants, pK a values, were given in Table4and5.From these data the pK a value of compound 5 was found to be the highest (i.e.4.29 by PM5) where as the lowest pK a value of 3.35 was found for compound 2.

Table 6 .
The RS values indicate that the transoid form is predominant over the cisoid form for molecule 1 and 2. RS values for 3, 5 and 6 indicate equal amount of cisoid and transoid forms, as expected, because of the symmetry.On the other hand the PM5 calculated RS values are indicative of equal amount of cisoid and transoid forms for compound 4. Whereas the ab initio calculated RS values suggest the predominance of cisoid forms.

Table 6 .
The aqueous phase PM5, HF and B3LYP calculated isomeric equilibrium constants (K is ) stability constants (RS) and mole fraction (N) values of studied molecules

Table 9 .
Aqueous phase PM5, HF and B3LYP calculated nucleophilicty values for neutral molecules