Electron magnetogyric ratio

In Eqs. (4)-(7) S is the electron spin quantum number, jh the proton nuclear magnetogyric ratio, g and p the electronic g factor and Bohr magneton, respectively. r//is the distance between the metal ion and the protons of the coordinated water molecules, (Oh and cos the proton and electron Larmor frequencies, respectively, and Xr is the reorientational correlation time. The longitudinal and transverse electron spin relaxation times, Tig and T2g, are frequency dependent according to Eqs. (6) and (7), and characterized by the correlation time of the modulation of the zero-field splitting (x ) and the mean-square zero-field-splitting energy (A. The limits and the approximations inherent to the equations above are discussed in detail in the previous two chapters. 

All terms contributing to either JM N or Jm,n are proportional to the magnetogyric ratio of both coupled nuclei, M and N. Since this is a nuclear property not associated with the molecular electronic structure, the reduced coupling constants, Km,n or Km,n are often quoted instead of Jm,n or Jm,n, respectively. They are related by... 

Electron spin quantum component Electron spin quantum number Hyperhne coupling constant Larmor angular frequency Larmor frequency Magnetogyric ratio Nuclear magneton Nuclear spin quantum component Nuclear spin quantum number Orbital quantum number Orbital quantum number component Principal quantum number Quadrupole moment Relaxation time longitudinal transverse Shielding constant... 

Whereas JAB involves the nuclear magnetogyric ratios, the reduced coupling constant KAB represents only the electronic contribution and is thus approximately isotope independent and may exhibit chemical trends. 

The magnetogyric ratio of a free electron is approximately 657 times that of a proton. Modem EPR spectrometers use a microwave generator (klystron) as the source of electromagnetic radiation (i.e., the oscillating magnetic field), with operating frequencies in the range 1-100 GHz (1 GHz = 103 MHz = 109 Hz) 9.5 GHz (the so-called A-band) is perhaps the most common. 

An unpaired electron, like a proton, can adopt either of two spin orientations when immersed in a magnetic field. An electron in either orientation will precess at a frequency given by Eq. (11.1). The g factor is similar in some respects to the magnetogyric ratio (y) used in NMR spectroscopy. The value of g, used as the position parameter in EPR spectroscopy, depends on the exact structure of the free radical possessing the unpaired electron. 

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