Hyperfine coupling energy

Figure 3 UMP2/6-311G potential energy profile (a) and hyperfine coupling constants (b) of CH3 versus s. Vibrational wave functions are normalized to 5.

Table 2 Restricted Hartree-Fock energies (Hartrees) for Ceo and C70 and their muon adducts. AE is the difference in energy between the carbon allotrope and its adduct. In all cases, except where indicated by f, only the six carbon atoms in the immediate vicinity of the muon have had there positions optimised, f means that a full geometry optimisation has been carried out. The type specifies the defect and for C70 is identified in Table 1. is the spin density at the muon in atomic units (and the hyperfine coupling constant in MHz). JMuon constrained to lie in equatorial plane. indicates geometry not fully optimized.

Quotations of the hyperfine coupling in terms of energy (or frequency) are not unique for Mossbauer spectra, unless the values are explicitly referenced to the nuclear ground or the excited state. Therefore, it is common to introduce the... 

Because of the different properties of the nuclear ground and excited states, the hyperfine coupling constants (A-values) for Mossbauer nuclei are often quoted in units of the internal field, where /I represents an energy and is the... 

The eigenfunctions corresponding the E+ and E are mixtures of f —i) and -1 i). If the hyperfine coupling is sufficiently small, A < < gp B, the second term in brackets in eqns (1.8C) and (1.8D) are negligible, which corresponds to first-order in perturbation theory, and the energies become ... 

Recently the spectrum of O- has been observed on MgO by Lunsford and co-workers (50, 51). The species was formed by adsorption of N20 at low temperatures onto MgO which contained trapped electrons. By using N2170 it was shown that the species was indeed 0 The spectrum shown in Fig. 21 is characterized by gx = 2.042 and g = 2.0013 with = 19.5 and an = 103 G. From the hyperfine coupling it may be shown that the unpaired electron is localized mainly in one 2p orbital. Both the g values and the hyperfine coupling constants are consistent with the energy level diagram of Fig. 20a. The results are also consistent with the spectrum of... 

The method presented here for evaluating energy levels from the spin Hamiltonian and then determining the allowed transitions is quite general and can be applied to more complex systems by using the appropriate spin Hamiltonian. Of particular interest in surface studies are molecules for which the g values, as well as the hyperfine coupling constants, are not isotropic. These cases will be discussed in the next two sections. 

The resonance expression relating the magnetic field and energy (frequency) as seen in equation 3.16, AE = hv = g B R, has its analog for hyperfine interactions written as equation 3.19, where A is the hyperfine coupling constant in Hz ... 

The ozonide ion has widely spaced energy levels, and to first order the g values are not influenced by the host lattice or the surface. Thus, the absolute values of the g values are useful in the identification of the ion. These g values, along with the hyperfine coupling constants, are given in Table I. The three sets of hyperfine constants indicate that the oxygen atoms are not equivalent, at least when the ozonide ion is formed according to reaction 2. The geometry of the ion on MgO is believed to be... 

Mossbauer spectroscopy The Mossbauer effect is resonance absorption of 7 radiation of a precisely defined energy, by specific nuclei. It is the basis of a form of spectroscopy used for studying coordinated metal ions. The principal application in bioinorganic chemistry is Fe. The source for the 7 rays is Co, and the frequency is shifted by the Doppler effect, moving it at defined velocities (in mm/s) relative to the sample. The parameters derived from the Mossbauer spectrum (isomer shift, quadrupole splitting, and the hyperfine coupling) provide information about the oxidation, spin and coordination state of the iron. 

Figure 3. INDO open shell hypersurface calculations for the hydrazine radical cation (23,24) contracted to 3 angular coordinates of freedom (cf. text) (A) INDO total energies vs. the B/w coordinate pair, and hypersurface maps for the dependence of the ESR hyperfine coupling constants, ajj (B and C) and ajj (D and E) on the dihedral angle w and the HNH bond angle a (B and D) or the out-of-plane bending angle B (C and E).

In general, fluctuations in any electron Hamiltonian terms, due to Brownian motions, can induce relaxation. Fluctuations of anisotropic g, ZFS, or anisotropic A tensors may provide relaxation mechanisms. The g tensor is in fact introduced to describe the interaction energy between the magnetic field and the electron spin, in the presence of spin orbit coupling, which also causes static ZFS in S > 1/2 systems. The A tensor describes the hyperfine coupling of the unpaired electron(s) with the metal nuclear-spin. Stochastic fluctuations can arise from molecular reorientation (with correlation time Tji) and/or from molecular distortions, e.g., due to collisions (with correlation time t ) (18), the latter mechanism being usually dominant. The electron relaxation time is obtained (15) as a function of the squared anisotropies of the tensors and of the correlation time, with a field dependence due to the term x /(l + x ). 

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