Magnetic field effects calculation

Conventional EPR techniques have been successfully used to measure the D and E values of matrix-isolated carbenes in the ground triplet state because the steady-state concentration of triplet species is sufficiently high in the system. The technique cannot be used, however, for excited species having triplet hfetimes of the order of 10-100 ns, since their steady-state concentration is too low. The D parameters are estimated from the external magnetic field effect on the T—T fluorescence decay in a hydrocarbon matrix at low temperamre. The method is based on the effect of the Zeeman mixing on the radiative and nonradiative decay rates of the T -Tq transition in the presence of a weak field. The D values are estimated by fitting the decay curve with that calculated for different D values. The D T ) values estimated for nonplanar DPC (ci symmetry) is 0.20... 

Fig. 10-3. Relative magnetic field effect AR (cf. Eq. (10-9)) as a function of magnetic field for the triplet exciplex thionine/p-iodoaniline. Circles with error bars represent the experimental results obtained in Ref. [3]. Lines are calculated with an equation similar to Eq. (10-17) and the different values for p indicated in the diagram. (Reproduced from Ref. [4a] by permission from The Royal Society of Chemistry)...

The results thus far obtained agree with the experimental evidence. We cannot say which formulation is more convenient for routine PCM calculations nor to present results about related problems, such as the description of local magnetic field effects or the calculations of other properties of interest for the NMR spectroscopy. 

In this study, the EC method was applied to the H2" molecule in a magnetic field to calculate its highly accurate wave functions. The effects of magnetic fields parallel and perpendicular to the internuclear axis were examined. The EC method was extremely efficient in both cases because the complement functions with suitable forms are automatically generated by the Hamiltonian. The vector potential part of the Hamiltonian was shown to accelerate the convergence of the EC wave... 

However, the theory for the interaction of matter with the electromagnetic field has to be coherent. The finite field method, so gloriously successful in electric field effects, is in the stone age stage for magnetic field effects. The propagator methods look the most promising, these allow for easier calculation of NMR parameters than the sum-over-states methods. 

The effect of an elongational flow field on a nematic solution is according to Panar rather similar to the observed effects of a magnetic field [42]. Calculations by Khokhlov and Semenov, and Maissa et al. show that an external field does... 

As mentioned above, the ESR spectrum is affected by the strength of spin-orbit coupling in molecules. The effect of spin-orbit coupling in ESR is represented by the Elamiltonian, H = SgB, where Pb is the Bohr magneton, S is spin, g is the so-called g-tensor, and B is the external magnetic field. For a free electron g = 2.0023. The shift in g due to the molecular environment and to the external magnetic field was calculated by Engstrom et al. from the product of spin-orbit and orbital Zeeman matrix elements... 

Two main types of theoretical treatment have been used for the calculation of MCD terms of organic -electron systems (see Spectrum Prediction Spectrum Simulation). Both use perturbation theory to treat the effect of the magnetic field. Most calculations use an ordinary atomic basis set and a sum-over-states expansion, and a few use London orbitals and finite perturbation theory. 

The electric and magnetic fields appearing in Sections 2.3.1 and 2.3.2 have been described in terms of the SI system of units. The Gaussian system of cgs units has frequently been employed in the theory of liquid crystals when magnetic fields are discussed. Gaussian units are considered by many to be natural units for the calculation and measurement of magnetic field effects in liquid crystals. Since much of the literature contains results in both Gaussian units and SI units, it seems appropriate at this point to make some comments on the conversion from one system of units to the other. A comprehensive account of the points touched upon here may be found in Jackson [132] or Moskowitz [206]. Readers should also be famihar with derived SI units. 

Fig. 8.9 Semilogarithmic plot of the ratio of fluorescence intensity obtained in the simulation (line) and adjacent average smoothing (circle) using 2 pairs (cyan) 5 pairs (magenta) 10 pairs (green) and 15 pairs (blue). Cations were linearly distributed with a mean spacing of a 40 A c 100 A and e 150 A. In b, d and f the solid red line is the analytically calculated magnetic field effect using the T values in Table 8.8, with T2 5 ns. Anions were distributed using a Gaussian distribution with mean zero and standard deviation of 80 A. A mutual diffusion coefficient (D ) of 0.325 A ps was used for S7 / c-RH+...

In order to calculate the time-resolved magnetic field effect, the simulation commenced by placing the cations and anions according to a particular distribution. 

Reactions which have occurred at zero time are replaced by their reactive products (if applicable). For all surviving species reactions times are generated from a model distribution conditioned on the radical pair separation distance. The fluorescence intensity I (t) (which is the experimentally observable quantity) is detected as D D [reaction (10)] and D [reaction (7)] to allow better statistics to be obtained. The simulation is therefore run twice, one with zero field parameters and one using high field parameters the ratio of I sit)/hit) is then obtained to observe the magnetic field effect. In the simulation, no T or relaxation mechanism was assumed to take place at high fields (unless otherwise stated). For zero field calculations Tq was assumed to be equal to T2 with the spin-spin relaxation time set to a value of 30 and 9 ns for S+ and D+ respectively. These values are based on the analysis by Borovkov on the rate of electron self-exchange [34, 41, 42] for S+ and D+, with... 

Fig. 8.18 TR MFE curves obtained using 4 pairs of S+ / e , with cations distributed inside a sphere of radius of 50 A. [D] = 0.02 M. Blue triangle, circular symbol and solid line represents the TR MFE curves calculated in this work, by Borovkov and experiment respectively. Second curve with a lower magnetic field effect corresponds to pi] = 1 mM. a Spin relaxation treated phenomenologically at high field without allowance for reactions (15), (16) tmd (17). b No paramagnetic spin relaxation was assumed at high field but included reactions (15), (16) and (17)...

The development of Remote Field Eddy Current probes requires experience and expensive experiments. The numerical simulation of electromagnetic fields can be used not only for a better understanding of the Remote Field effect but also for the probe lay out. Geometrical parameters of the prohe can be derived from calculation results as well as inspection parameters. An important requirement for a realistic prediction of the probe performance is the consideration of material properties of the tube for which the probe is designed. The experimental determination of magnetization curves is necessary and can be satisfactory done with a simple experimental setup. 

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