Electron paramagnetic resonance spin-orbit coupling

HMO) formalism, because its singly occupied molecular orbital (SOMO) is constrained by symmetry to be on those atoms. More sophisticated molecular orbital analysis finds not only equal, positive spin densities on the end carbons but also a small negative 7T-spin density on the central carbon due to spin polarization. At the UB3LYP/6-31G level, the spin density p ) - p(C3) = +0.700, mostly from 7T-spin contributions, and p(C2) = -0.275.27 The experimental numbers estimated for TT-spin density (not overall spin density) are p(C ) = p(C3) = +0.582 and p(C2) = -0.164 from electron paramagnetic resonance (EPR) studies of 13C hyperfine coupling (hfc).28... 

ENDOR = electron nuclear double resonance EPR = electron-paramagnetic resonance ESR = electron-spin resonance NMR = nuclear magnetic resonance MA = modulation amplitude SOFT = second-order perturbation theory s-o = spin-orbit zfs = zero-field splitting (for S > 1 /2) D = uniaxial zfs E = rhombic zfs g = g-factor with principal components gy, and g ge = free electron g-factor a = hyperfrne splitting constant A = hyperftne coupling constant for a given nucleus N (nuclear spin 7>0). 

For a discussion of spin-orbit coupling off electrons, see, for example A Abragam, B Bleaney. Electron Paramagnetic Resonance of Transition Ions. Oxford Clarendon Press, 1970. 

The electron spin resonance (E.S.R.) spectra of a paramagnetic organic molecule, e.g. free radical, radical cation or radical anion, is directly related to its unpaired electron distribution (spin density). In the region of a magnetic nucleus the hyperfine interaction between the magnetic moments of the nucleus and the electron is a function of the spin density. It has been shown that, for an atom N, a direct correlation exists between its observed hyperfine coupling constant, and [pa—pP), the unpaired electron population of its atomic orbitals 1). 

---