3.2. Effect of Hydrogen Bonding on EPR spectral parameters
Experimental results suggest that EPR spectra are more sensitive to the HFCC of the nitrogen atom and of the hydrogen atoms of the amino- and methyl-groups in acidic solution. In addition, EPR spectra are more sensitive to HFCC of the nitrogen atom, the -hydrogen atom, and the hydrogen atoms of methyl group in alkali solution. Figs. 4 and 5 show the average of the g -tensor and the HFCC of the atoms considering 200 snapshots along the trajectory and optimization structure in the gas phase radicals, respectively. The solvent induces an increase ingxx (435 ppm) and in gyy(199 ppm) for the radicals but does not have a similarly significant effect on their gzz (-84 ppm). Meanwhile, solvation decreases the HFCCs [N (-9.84 MHz), Havg.(amino) (-28.50 MHz) and Havg.(methyl) (-12.27 MHz)].
For radicals, on the other hand, solvation decreasesgxx (-163 ppm) and gyy(-116 ppm) and have no significant effects on neithergzz (+13 ppm) nor on the HFCC of N (-2.55 MHz), of Havg.(amino) (+0.76 MHz), and of Hα(+0.67 MHz)]. According to previous studies [18-25] and consistent with Eqns. (2) and (3), the values of gxx ,gyy , and of atomic HFCC are strongly dependent on the geometric parameters and on spin density.
<Fig. 4 >
<Fig. 5 >
As can be seen from Eq. (2), the main contribution of g -tensor components is spin-orbit coupling. Considering the directions of theg -tensor components (Fig. 1) and the shape of the spin density iso-surface, we observe significant contributions fromgxx and gyy but a negligible contribution from gzz , yielding the following order: gxx > gyy > gzz (negligible). The greater value of the spin density iso-surface of radical in comparison with that for the and radicals (Fig. 1) we can argue that the values of the g -tensor components of the radical are greater. It may be concluded from the results displayed in Fig. 5 and listed in Table 2 that the transfer from the gas to the solution phase is accompanied by a decrease in the HFCC of atoms for radical since it exhibits a lower spin density than the gas phase. In contrast, the radical exhibits a spin density that remains quasi-constant on passing from the gas to the solution phase and this is accompanied by the constancy of the HFCC of the atoms of this radical. In the radicals, the oxygens of carboxyl groups have more spin-orbit coupling due to the highest spin-density on the oxygen atoms. This leads to an increase ing values in radical compared to their values for and , in agreement with previous work such as in Ref. [30].
Variations of the spin density distribution on the oxygen atoms (which have the most spin-orbital coupling) results in substantial variation of the gxx and gyycomponents. Fig. 6 shows variation of g -tensor components versus the magnetic moment of the oxygen atoms of the carboxylic groups in the , and radicals. From the figure, the gxx(gyy ) components have a linear dependence with Pearson correlation coefficients of 0.86 (0.76), 0.85 (0.43) and 0.80 (0.73) on the magnetic moment of the oxygen atom for the , and radicals, respectively. In contrast, it is found that thegzz component is not linearly correlated with the magnetic moment of the oxygen atoms of the carboxyl group as the data exhibit a marked scatter. The little change of thegzz component is probably due to some spin-orbital coupling of the oxygen atoms of the water molecules (since these oxygen atoms form hydrogen bonds with the radicals toward direction of the magnetic moment).
Therefore, in the case of radical, the transfer from the gas to the solution phases results in an increase in the spin density of the oxygen atoms of the carboxyl groups (Table 2) and, consequently, a concomitant increase in the gxx andgyy components. On the contrary, the radical this inter-phase transfer results in the reduction of thegxx and the gyy components due to a decrease in the spin density on the oxygen atoms (Table 2).
<Fig. 6 >
The HFCCs is known to depend on the spin density at the nuclei of the atom and is a direct measure of unpaired electron delocalization through the Fermi contact term, dominant for s -electrons (the only orbitals with a maximum rather than a node at the nucleus) - (see discussions in Refs. [49-50]). Fig. 7 shows the correlation of the HFCC of the methyl group and its magnetic moment for , and radicals with a linear Pearson correlation coefficient of 0.97.
<Fig. 7 >
<Table 4 >
Table 4 collects the MD-averaged calculated isotropic HFCC andg -tensors for radicals along with their experimental counterparts in acidic and alkaline solutions [27-28]. In the case of the alkaline pH (11-13.5), the calculated HFCC for the N atom and for the methyl group are in good agreement with experiment. A similarly good agreement also exists between the calculated and experimental HFCC of amino group and the isotropic giso .
At acidic pH (2.5-5), the calculated HFCC of the N atom and of the methyl group for the have better agreement with the experiment compared to the results obtained for the radical. On the other hand, the calculation giso and the HFCC for the Hα atom of is in better agreement with the experimental results. Therefore, both radicals can exist in acid solution.