High resolution NMR of free radicals: 13 C magic angle spinning of two solid organic free radicals derived from 4,5-dihydro-1 H - imidazol-3-oxide-1-oxyl and theoretical calculation of their NMR properties

The 13 C CPMAS NMR spectra of two 4,4,5,5-tetramethyl-2-(1 H-and 2 H -pyrazol-3-yl)-2- imidazoline-1-oxyl-3-oxides have been recorded and their signals assigned, through unrestricted density functional theory (UDFT) calculations of their absolute shieldings, with satisfactory results.


Introduction
In recent years, interest in creation of new classes of magnetically active materials has developed enormously.Syntheses of polyfunctional stable organic radicals and studies of their magnetostructural correlations have become an essential part of this research.Polyfunctional nitroxides are highly effective in design of n-dimensional heterospin systems capable of magnetic ordering. 1The α-nitronyl nitroxides derived from azoles (imidazoles, triazoles) exhibit extremely strong ferro-and antiferro-magnetic interactions, for organic radicals in which the hydrogen bonds have been involved. 2he purpose of the present paper is twofold.On one hand to record in the solid state the 13 C CPMAS NMR spectra of two nitronylnitroxide radicals 3 and 4, and on the other, to evaluate the utility of unrestricted DFT calculations to obtain absolute shieldings of these radicals and those of 4,4,5,5-tetramethyl-2-methyl-imidazoline-1-oxyl-3-oxide 1 and of 4,4,5,5-tetramethyl-2-(4'hydroxyphenyl)-2-imidazoline-1-oxyl-3-oxide 2. Scheme 1.The four studied compounds, including both tautomers of 3.
4][5][6][7][8][9] The X-ray structure of tautomer 3b was described in 2006. 10,11Another important contribution to pyrazolyl-nitronylnitroxides is that of Catala, Feher, Amabilino, Wurst and Veciana who prepared compound 4. 2 Note that we published in 1995 a 13 C NMR study in solution of paramagnetic Co(II) complexes. 12The present paper is one of the rare publications where experimental and theoretically calculated NMR chemical shifts of radicals are reported.

C CPMAS NMR of compounds (3) and (4)
We have represented in Figure 1 the 13 C CPMAS NMR spectra of compounds 3 (it corresponds to tautomer 3b) 10,11 and 4. The spectra have been recorded in two halves and we checked there were no signals in the central missing part; they cover approximately a range of +1010 to -750 ppm.

GIAO calculations of compounds (1, 2, 3a, 3b and 4)
We have carried out GIAO/B3LYP/6-311++G(d,p)//B3LYP/6-311++G(d,p) calculations as implemented in the Gaussian 03 program (see computational details).This level is comparable to that used by Rastelli and Bagno [GIAO/cc-pVTZ//B3LYP/6-31G(d,p)] in their recent study on the use of DFT calculations to predict the NMR spectra of paramagnetic molecules, including free radicals. 13These theoretical calculations correspond to isolated molecules, so consequently the optimized geometries could not agree with the structures found in the corresponding crystals.However, as the studied compounds have rather rigid geometries, we are confident that the calculated geometries are close to the experimental ones.This has been tested with compound 3b whose geometry has been determined by X-ray crystallography: 10,11 the calculated and the experimental geometries are nearly identical, the most important difference concerns the torsion angle between both rings that amount to 8.6º (crystal) and to 0.8º (calculation).[16]

Relative stability of tautomers (3a) and (3b)
We have reported in Table 1 the energetic results of the calculations.Tautomer 3b is 31.3kJ mol -1 more stable than tautomer 3a, therefore, in the discussion of the CPMAS NMR chemical shifts only tautomer 3b will be considered.Remember that only the latter was found in the crystal structure. 10,11Usually, in NH-pyrazoles, 3-substituted tautomers are more stable than 5substituted ones, 17 but in this case an intramolecular hydrogen bond stabilizes 3b.These systems should present in solution a pseudorotation mechanism of the imidazoline ring with very low barriers that we have calculated at the B3LYP/6-31G(d) level to be in the range between 3 and 5 kJ mol -1 .

AIM analysis
An AIM analysis (see computational details) was carried out on all the radicals.The topological analysis of the electron density (Figure 2) shows the presence of bond critical points between the oxo groups of the imidazole moiety with the groups in ortho of the additional ring.In all cases they correspond to O•••H interactions with the exception of an O•••N contact in the 3a structure.Interactions between electronegative atoms have been described in the literature, [18][19][20] and in some cases were considered to explain the extra stability of those systems in which they are present. 21,22However, in this case, tautomer 3b shows an O•••H interaction that appears to be more stabilizing than the O•••N one.The ortho-ortho' interactions observed in these molecules show small values of the electron density and positive values of the Laplacian, similar to those found in hydrogen bond interactions. 23The seven O•••H interactions found range between 2.1 and 2.6 Å, showing exponential relationships between the interatomic distances and the values of the electron density and Laplacian at the bond critical point. 23,24he analysis of the spin density shows that it is concentrated over the atoms 1, 2, 3 and the two oxygen atoms attached to 1 and 3. We have reported these calculations for compound 3b (Figure 3).  2 summarizes all the information available on the five compounds of Scheme 1.A simple regression of these data led to the following equation: This equation is very similar to Eq. 2 we obtained using the data of a large set of diamagnetic compounds in solution:   The assignment 29 of the signal at -367 ppm to the C4 of 2 could be an error.b Note the nonequivalence of carbons C3' and C5' of 4 due to the absence of proton transfer in the solid state.
However, the residuals do not appear to be at random.Thus, we tried a model including four dummy variables (1 if present, 0 if absent): C4,5 of the imidazoline ring (C2 carries too much spin and it is not observed), 29 Cipso, Cortho and Cmeta of the substituent at position 2 (for pyrazoles, Cortho and Cmeta are C4' and C3' in 3b and Cortho is C3' and C5' in 4).Rastrelli and Bagno 13 have calculated several types of paramagnetic molecules, including the four radicals depicted in Scheme 2. In most cases, they averaged the calculated absolute shieldings since the observed experimental chemical shifts, due to conformational freedom, correspond to average signals.
From their data, calculated at the GIAO/BPW91-30HF//cc-pVTZ//B3LYP/6-31G(d,p) level, the following trendline can be calculated (Equation 4) which is similar to that found in Equation 1.In summary, for free radicals it becomes possible to measure chemical shifts in the solid state as well as to calculate absolute shieldings in the gas phase, but with some snags.7][28] It is expected that this type of research will considerably develop in the future, both in what experimental measurements and theoretical calculations are concerned.

Computational details
The optimization of the geometries of the structures were first carried out at the B3LYP/6-31G(d) and then reoptimized at the B3LYP/6-311++G(d,p) computational level, [33][34][35][36][37][38] within the Gaussian-03 package. 39Frequency calculations at the B3LYP/6-31G(d) level were carried out to confirm that the obtained structures correspond to energy minima. 40The GIAO approximation 41,42 has been used at the B3LYP/6-311++G(d,p) computational level to calculate the orbital absolute chemical shielding, the hyperfine coupling constant and the electron g tensor.5][46] The electron density molecular graphs have been represented with the MORPHY3 program. 47n the NMR spectroscopy of paramagnetic systems several nonvanishing interactions between the nuclear and electron magnetic moments should be considered.They can be divided in Fermi orbital, contact and dipolar terms, see Equation 5: 13,48 δ = δ o + δ FC + δ PC (5)   The orbital term δ o is similar to the shielding of diamagnetic molecules and thus it can be approximated to that value.The Fermi contact term δ FC is due to the interaction of the magnetic moment of the resonant nucleus and the effective local field generated by the unpaired electron density.In the simpler form, it can be calculated from Equation 6: where γ I is the magnetogyric ratio of the nucleus I, g e the electron g factor, µ B the Bohr magneton, A the isotropic hyperfine coupling constant, S is the total spin quantum number and kT the thermal energy.
The dipolar term δ PC is in general negligible in organic radical systems and has not been considered in the present calculations.

Figure 3 . 13 C
Figure 3. Analysis of the spin density for compound 3b.