DOI: 10.1002/cphc.200900206 Imidazoline-N-oxyl: A DFT Study of Its Protonation Reaction Sandrine Chenesseau, Nicolas FerrØ, Sylvain R. A. Marque,* and Didier Siri [a] 1. Introduction For decades, nitroxides have been used as probes for biologi- cal, chemical, and physical studies. [1] An interesting property of nitroxides is the high sensitivity of the nitrogen hyperfine cou- pling constant a N towards both the surroundings and the sub- stituents attached to the nitroxyl group. [2] Hence, this property was used to determine intra- and extracell pH. [3] Several fami- lies of nitroxides [4] were developed, and one of the most prom- ising was the imidazoline-N-oxyl family. [5, 6] The pK a values of such nitroxides are strongly dependent on the substituents at- tached to the nitroxyl moiety and can vary between 1 and 11. [7] Interestingly, the pK a of a conventional amine such as pyr- rolidine (11) is about 11, whereas nitroxide analogue 8 has a lower pK a of about four. On the other hand, the pK a of 1/2 is about 8 (Figure 1, Table 1). Moreover, it has been shown that the presence of a nitroxyl group in the imidazoline ring modi- fies dramatically the reactivity at the nitrogen center. [8] It has been proposed that these changes in reactivity are due to the field/inductive electrical effects of the nitroxide group. [9] The electron-withdrawing capacity of the nitroxyl group has been estimated [8] to be as large as that of the nitro (s I = 0.67) [10] or nitroso group [11] (s I = 0.53). Consequently, to gain deeper in- sight into the effects governing these striking changes in pK a , the protonation reaction (Scheme 1) was studied by DFT calcu- lations for compounds 1–16. By combining geometry, natural bond orbital (NBO), frontier molecular orbital (FMO), Mulliken charge (MC), and thermodynamic analyses, we show that the decrease in pK a from 11 to 9 is due to the inductive electron- withdrawing capacity of the nitroxyl moiety, and that the ba- sicity of 1/2 is due to “masked” carbanion character (enamine- type group) as proposed by Volodarski et al. [8] A number of high-level calculations have been performed on nitroxides. [12] However, to the best of our knowledge, only a few calculations have been carried out on the effect of the pH on nitro- xides, [13, 14] and none on the effect of the nitroxyl group on the pK a . Methods It is well known that a five-membered ring can adopt several con- formations (envelop E and twist T conformers, see Figure 2). [15, 16] The most stable conformations were first selected by using GenMol software, [17] and then optimized by using the DFT method (Table 1). DFT calculations (Table 1) were performed by using the PBE1PBE method, reported to be suitable for pK a calculations, [13, 18] and the 6-31 + GACHTUNGTRENNUNG(d,p) basis set. Other levels of theory and basis sets were tested. Natural bond orbital, natural resonance theory, [19– 21 Mulliken charge, and frontier molecular orbital analyses were performed with Gaussian 03 software. [22] The Gibbs energy D r G of the protonation reaction (Scheme 2 and Table 1) in the gas phase were given by Equation (1), in which the Gibbs energies of the protonated base GACHTUNGTRENNUNG(BH + ), of the base G(B), and of the proton G(H + ) [23] were computed with the PBE1PBE model/functional at the 6-31 + GACHTUNGTRENNUNG(d,p) level of theory (T = 298.15 K, P = 1 atm). D r G g ¼ G g BH þ ð Þ G g B ð Þ G g H þ ð Þ ð1Þ The reaction enthalpies D r H g were computed in the same way, and the reaction entropies D r S g were given by Equation (2): D r G g ¼ D r H g  T D r S g ð2Þ A few pK a values were computed in the same way at the same level of theory by applying the Polarizable Continuum Model (PCM) combined with the thermodynamic Born–Haber cycle (Scheme 3). The pK a values are given by Equation (3). The Gibbs re- action energies in aqueous solvent D r G aq were given by Equa- [a] S. Chenesseau, Dr. N. FerrØ, Prof. S. R. A. Marque, Prof. D. Siri UniversitØ de Provence, UMR-6264 Laboratoire Chimie Provence case 521, Avenue Escadrille Normandie Niemen, 13397 Marseille Cedex 20 (France) Fax: (+ 33) 4-91-28-87-58 E-mail : sylvain.marque@univ-provence.fr Supporting information for this article is available on the WWW under http://dx.doi.org/10.1002/cphc.200900206. Imidazoline-based nitroxides are developed as pH probes. Their pK a values vary over a wide range (from 1 to 11), depend- ing on the substituents attached to the five-membered cyclic nitroxide. Density functional calculations using the PBE1PBE method at the 6-31 + GACHTUNGTRENNUNG(d,p) level, combined with natural bond orbital (NBO), frontier molecular orbital (FMO), geometry, Mul- liken charge, and thermodynamic analyses, are carried out to disclose the effects involved in the changes in pK a . The studies show that the decrease of seven pK a units from pyrrolidine (11) to imidazoline-N-oxyl 8 is due to the inductive electron- withdrawing capacity of the nitroxyl group. On the other hand, by combining both the inductive and mesomeric electron- withdrawing capacities of the NO 2 group with delocalization of the lone pair on the amino N atom of the p system of the vinyl linker, the pK a of 4.5 of 8 was increased by around three units to 7.8 for 1/2. ChemPhysChem 2009, 10, 2419 – 2428  2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 2419