Resonant field positions, calculation

The simulation of a randomly oriented EPR spectrum involves integration over a unit sphere (Eq. (3)) that is performed numerically by partitioning a unit sphere and calculating the resonant field positions and transition probabilities at all of flie vertex points. 

The basic CW EPR simulation involves the search for the resonant field position, Bi, for each transition, i. The intensity, and linewidth, o) are calculated and with the resonant field define the peak Bj, Ij, crj. The simulated spectrum is then generated by adding each peak to the spectrum using an appropriate lineshape function. 

The shortest possible vector in the parameter space that gives the desired changes in resonant field position and linewidth can then be calculated Irom the normal to the line/plane/etc defined in Eq. (28). 

Figure 4. Variable temperature EPR spectra (calculated using Molecular Sophe, Chap. 4) of a hydroxy-bridged mixed-valent dinuclear Fe -Fe center. Spin-Hamiltonian parameters, Fe g = 2, D = -1 cm EID = 0.3 Fe " = 1.96, g,= 1.85, = 1.75, Z) = 1 cm, EID = 0.3 -2J = -6 cm. (A) Continuous wave spectra and (B) temperature dependence of particular resonant field positions.

EPR spectrometers use radiation in the giga-hertz range (GHz is 109 Hz), and the most common type of spectrometer operates with radiation in the X-band of micro-waves (i.e., a frequency of circa 9-10 GHz). For a resonance frequency of 9.500 GHz (9500 MHz), and a g-value of 2.00232, the resonance field is 0.338987 tesla. The value ge = 2.00232 is a theoretical one calculated for a free unpaired electron in vacuo. Although this esoteric entity may perhaps not strike us as being of high (bio) chemical relevance, it is in fact the reference system of EPR spectroscopy, and thus of comparable importance as the chemical-shift position of the II line of tetra-methylsilane in NMR spectroscopy, or the reduction potential of the normal hydrogen electrode in electrochemistry. 

Tel. 44-223-336384, e-mail cadpac theory.chemistry.cambridge.ac.uk Cambridge Analytical Derivatives Package. General purpose ab initio calculations. Cray and other versions. Spectro for analyzing anharmonic force fields and calculating positions and intensities of lines, including Fermi resonance effects. 

Figure 3. Calculated EPR spectra and (mentation selecti(m on the unit sphere for the observer (Bo field) positions corresp(mding to gi, g, and g. White indicates orientations on-resonance with the m.w. pulse, black shading is off-resonance. The tn.w. pulse for the orientation selection has a width of 25 MHz. (a) Orthorhombic spectrum of MCRreai at X-band (9.8 GHz) with g-values of gi = 2.287, g2 = 2.231, gi = 2.175, and a linewidth of 100 MHz.

---