Resonant field positions, calculation Resonator

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.

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. 

The quadrupole perturbed NMR spectriun of Rb (I = 312) consists of the central hne and two satelUte Unes. In D-RADP-x the nuclear quadrupole couphng constant decreases linearly with x from 9.6 MHz (x = 0) to 6.6 MHz (x = 0.95) [10], whereas the Larmor frequency amounts to 98.163 MHz in a Bo field of 7 T. Due to the substitutional disorder, and the corresponding loss of the translational invariance, the satelHte transitions are inhomogeneously broadened that much, that only the central transition can be directly observed. The position of the corresponding resonance line can be calculated using standard NMR-NQR theory [16], where the second order shift is given by ... 

Empirically determined chemical shift additivity parameters have been determined- for diene-type polymers. The shift contribution of a quaternary carbon which is fllto the carbon in question was not determined by those authors. However, using their additivity parameters and the shift positions of the ( carbons in Figure 8, a value of +15.4 ppm can be estimated for the contribution of a neighboring (0() quaternary carbon. Using this value, the shift positions of the carbons in structures VII and VIII are calculated as shown. If the first 1,2 unit were on the chain in a 2,1 manner, the methylene carbon resonance would be at a considerably higher field, but it would be difficult to estimate its position with any certainty because the quaternary effect... 

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