DFT Comparative Study of the Formamide and Fluoro-FormamideTautomers and Their Corresponding Transition States


 Seventeen tautomers of formamide [NH3CO] and thirty one tautomers of fluoro-formamide [NH2FCO] were examined by density functional theory (DFT) calculations. Five methods of DFT (B3LYP/ 6-311++G, B3LYP/ 6-311++G(2df,2p), B3LYP/cc-pVTZ, wB97X-D/6-311++G(2df,2p) and wB97X-D/ cc-pVTZ) were used to calculate the energies and optimized geometries of formamide tautomers. B3LYP/cc-pVTZ method was determined as the best method and used to calculate relative energies, optimized geometries, mulliken charge distributions, Gibbs free energies and enthalpy of formations of all proposed fluoro-formamide/fluoro-formamidic acid tautomers. Ten transition states of formamide tautomers and nineteen transition states of fluoro-formamide tautomers were determined by vibrational frequency calculations (they have an imaginary value of frequency). Using B3LYP/cc-PVTZ, the relatively small energies of formamide (A1) and formamidic acid (A6) (-446246 and -446193kJ.mol -1 , respectively) participate to it being more stable than other formamide/formamidic acid tautomers, as well as for fluoro-formamide (C1) (-706947 kJ.mol -1 ) and fluoro-formamidic acid (C3) (-706855 kJ.mol -1 ). The stability of fluoro-formamide at carbonyl and at nitrogen was discussed using two thermodynamic calculations: Enthalpy of formation [∆H(298)] and Gibbs free energy (∆G) values, positive ∆G values (59 to 114 kJ mol-1) for fluoro-formamidetautomerism confirms the stability of fluoro-formamide at carbonyl.

We have used the DFT method for calculation studies of a series of tautomersims described in a previous report [16,17,18].In this study, the possible tautomers of formamide and fluoro-formamide and their transition states are elaborated using quantum mechanical density functional theory (DFT). DFT results are used to study the stability of all tautomers and transition states at both the carbonyl carbon and at the nitrogen position, as well as details of their relative energies. A comparative study of the geometrical parameters is made between both the more stable formamide tautomers and the more stable fluoro-formamide tautomers. Mulliken charge distributions, Gibbs free energy and heat of formation of the more stable fluoroformamide tautomers were discussed.

Geometry Parameters
In this research, five conformers of formamide and twelve conformers of formamidic acid were proposed, optimized and applied to frequency calculations. Geometrical  (Table I) are compared with that obtained by several theoretical and experimental methods.
As shown in Table I, the calculated values by the five methods are closed to the observed values. The minimum energies for all tautomers were obtained using the B3LYP/cc-pVTZ method (Table II)  respectively. This result suggests a good agreement between the calculations in this work and experimental studies especially with microwave study. As for the formamidic acid, both bond lengths and angles are close to that obtained theoretically.

Relative Energies
Methods of DFT were used to calculate the energies of all tautomers in order to determine the most stable ones. It is also used to compare the results with previous studies and with fluoro-formamide tautomersim.
Charge distribution shows that the electrostatic attraction between atoms has larger magnitude (0.333) in formamide (A1) while in formamidic acid (A6) is (0.04).

Geometry Parameters
The B3LYP/cc-PVTZ method is the best of the five methods that have been used for formamide tautomerism as shown in previous part. Therefore this method will be  Table III.
Geometry parameters of tautomers C1, C3, A1 and A6 were compared based on B3LYP/cc-PVTZ method. By comparison in (Tables II and III)

Transition States
Vibrational frequency calculations that obtained in this study confirm that nineteen tautomers (Fig. 4)

Gibbs free energy
All possible tautomerisms between the most stable tautomers are summarized in (Table VI). Negative Gibbs free energy values represent the forward direction to form more products (spontaneous process). On the other hand, positive Gibbs free energy represents non-spontaneous process [30]. Fluorine at carbon atom prefers the reverse direction that determines the stability of fluoro-formamide tautomers, while the fluoro-formamide tautomerization at nitrogen represents spontaneity process. This can be noticed by the positive ∆G values (59 to114 kJ mol -1 )which are higher in magnitude. The higher values detect the stability of fluoro-formamide (at carbonyl) whereas the negative values ( ̶ 4 to ̶ 33 kJ mol -1 )of fluoro-formamide at nitrogen represent less stability.

Enthalpy of formation
When Enthalpy of formation is more negative a more stable tautomer is made [27].

CONCLUSION
The B3LYP/cc-pVTZ method is considered a suitable method for the calculation of tautomers is due to the attractive and repulsive forces variation within each conformer ( Fig. 3), discussing the stability of C1 and C3 tautomers (Scheme 2). The more nonspontaneous processes are when C1 is a reactant (∆G = 95 to 114 kJ mol -1 ) that discussingthe stability of C1 tautomer.