A b i n i t i o study of the electronic structure and hyperfine coupling properties in simple hydrocarbon radicals. II. Short-range and long-range interactions in alkyl free radicals

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Abstract
Nonempirical calculations of the ground−state energy, proton and carbon−13 coupling constants of methyl, ethyl, n−propyl, and cyclopropyl radicals have been performed in the frame of spin−restricted LCAO−SCF open−shell and first−order double−perturbation theories. The rotation barrier is negligible for the ethyl radical. The two barriers of the n−propyl radical are, respectively, 0.3 kcal/mole (0.4 exptl) and 4.7 kcal/mole for the rotations about the Ċ−Cα and Cα−Cβ bonds. The cyclopropyl radical is found to be nonplanar with an out−of−plane angle of 41° and an inversion barrier of 3.80 kcal/mole. For the equilibrium conformations, the computed carbon−13 splittings of the radical carbon of methyl (1), ethyl (2), n−propyl (3), and cyclopropyl (4) are +31.04, +37.90, +37.72, and +138.83 G, respectively; the theoretical α −carbon−13 splittings are −18.14 (2), −17.15 (3), and −8.35 G (4); the β −carbon−13 splitting is +11.8 G for the stable conformation of the n−propyl radical. The calculated coupling constants are negative for α hydrogens, namely −31.03 (1), −33.82 (2), −34.34 (3), and −9.20 G (4); they are found positive for β hydrogens, i.e., +16.8 (2), +23.58 (3), and 12.12 G (4); the γ couplings of the freely rotating hydrogens of the n−propyl radical are negative −0.21 G. The variation of these couplings with conformational and torsional effects has also been investigated. The radical carbon−13 splitting is quite insensitive to rotations of substituents but increases markedly with out−of−plane deviations at the radical site. The coupling constants of α nuclei aHα, aCα are also insensitive to conformational modifications. For β atoms, the contact hyperfine splittings are found to follow the relation aβ=B0+B2 cos2ϑ independently of the chemical nature of the nuclei, B0 being negative if vibronic effects are neglected. Long−range couplings in γ position are generally negative, except in the region depicted by the so−called W−plan arrangement. The role of delocalization and spin polarization is discussed for each kind of coupling. It is shown that intrabond excitations of the CH→CH* type dominate the spin polarization at the proton in all positions, while inner−shell excitations are found to be essential in the case of the radical carbon.