Spectra calculations spinning

Fig. 12b). Since practically the same spectral shape is obtained at Q-band (35 GHz) (Fig. 12c), the commonly used criterion stating that the shape of an interaction spectrum is frequency-dependent fails to apply in this case. Actually, outer lines arising from the exchange interaction are visible on the spectrum calculated at Q-band (Fig. 12c), but these lines would be hardly detectable in an experimental spectrum, because of their weak intensity and to the small signal-to-noise ratio inherent in Q-band experiments. In these circumstances, spectra recorded at higher frequency would be needed to allow detection and study of the spin-spin interactions. 

Guo, R., Balasubramanian, K., Wang, X. and Andrews, L. (2002) Infrared vibronic absorption spectrum and spin - orbit calculations of the upper spin-orbit component of the AU3 ground state. Journal of Chemical Physics, 117, 1614-1620. 

Fig. 28 Pure rotational spectrum of C>2. Trace (a) is the S3 transition recorded at a pressure of 1.0 atm. Trace (b) is the result of deconvolving the S3 profile with a Voigt profile to remove most of the pressure broadening, Doppler broadening, and instrument effects. Trace (c) was calculated using a 0.035-cm-1 Gaussian profile and calculated spin splittings. The traces are scaled to the same height.

The method used in these calculations is based on the theoretical developments of Sakimoto [42] and is also an extension of our previous work on the Stark spectrum of spin-orbit autoionized Rydberg states of argon [43] and of the vibrationally autoionized states of hydrogen [44, 45], Only the homoge-... 

Line spectrum calculated in the low temperature approximation, valid at both 4 °K and 1.2 °K. There are no free parameters the lack of sharp lines in the observed spectra is attributed to spin relaxation (After Lang and Marshall, Ref. 103))... 

Next we deal with the nature of the correction Awc. The resonance signals in a spectrum may be composed of overlapping, closely spaced components. Usually this is caused by either weak spin-spin couplings (we consider here only those which are included explicitly in the assumed model of an exchanging spin system) or by almost degenerate transitions in the spin multiplets. (81) Such effects should be compensated for by the correction Awc which can be determined from measurement of an apparent line-width, wa, in a theoretical spectrum calculated for a reasonably assumed value of the natural line-width, wtheor The correction (wa — wtheor) is virtually independent of the value... 

To determine these parameters accurately and rigorously, the experimental ESR spectrum should be compared to a computer-simulated spectrum calculated using trial parameters, and a convenient mathematical representation and description of the ESR spectrum should be provided by use of the operator spin Hamiltonian (Wertz and Bolton, 1972). In practice, the g-values and hyperline and superhyperfine constants, A, can be obtained relatively simply, although not rigorously, by direct computation from data derived accurately from the experimental ESR spectrum and from spectrometer setting values used in the measurement, according to conventional equations (Senesi, 1992). 

The ESR experiment by Aasa (27) yields two sets of spin Hamiltonian parameters — one for each iron site. A Mossbauer spectrum calculated from each set of Aasa s parameters has been found to be no different from the calculation assuming identical sites. This indicates that the ESR experiment is much more sensitive to small effects than the Mossbauer technique. 

Neilson and Symons observed a complex spectrum in KN3 powders which were UV irradiated at 77°K [34]. The spectrum was interpreted on the basis of an Nl model and the assumption that the spin-Hamiltonian parameters were essentially the same as those observed for N3" in BaN6 [52]. However, no attempt was made to generate a theoretical powder spectrum by computeraveraging the single-crystal spectrum calculated from these parameters over all possible orientations. Therefore, the assignment must be considered tentative. 

Fig. 6. The optical absorption spectrum and the electronic structure of Mn2". (a) Experimental data, where a photodissociation action spectrum of Mn2 was measured by observing Mn" " photofragment, (b) The spectrum calculated by a hybrid-type density-functional method. The bars show oscillator strengths the solid line a spectral profile, (c) Density-of-states profiles of the majority and the minority spin electrons obtained by the same theoretical calculation. The shadows indicate occupied electronic levels. The manganese dimer ion, Mn2 ", was shown to have a spin multiplicity of twelve with a bond length of 3.01 A. ...

Figure 4 EPR spectrum of the electrogenerated cation [Ru(bpy)(tpm)NO] in MeCN/0.1 MBU4NPF6 at 110 K. Experimental conditions microwave frequency, 9.604 GHz modulation amplitude, 4 G. Bottom computer-simulated spectrum. Top right DFT-calculated spin density of the same species in a vacuum (B3LYP level, LanL2DZ basis set).

For the variational calculations of the vibronic spectrum and the spin-orbit fine structure in the X H state of HCCS the basis sets involving the bending functions up to 0i = 02 = 11 with all possible and I2 values are used. This leads to the vibronic secular equations with dimensions 600 for each of the vibronic species considered. The bases of such dimensions ensure full... 

Another related issue is the computation of the intensities of the peaks in the spectrum. Peak intensities depend on the probability that a particular wavelength photon will be absorbed or Raman-scattered. These probabilities can be computed from the wave function by computing the transition dipole moments. This gives relative peak intensities since the calculation does not include the density of the substance. Some types of transitions turn out to have a zero probability due to the molecules symmetry or the spin of the electrons. This is where spectroscopic selection rules come from. Ah initio methods are the preferred way of computing intensities. Although intensities can be computed using semiempirical methods, they tend to give rather poor accuracy results for many chemical systems. 

In addition to total energy and gradient, HyperChem can use quantum mechanical methods to calculate several other properties. The properties include the dipole moment, total electron density, total spin density, electrostatic potential, heats of formation, orbital energy levels, vibrational normal modes and frequencies, infrared spectrum intensities, and ultraviolet-visible spectrum frequencies and intensities. The HyperChem log file includes energy, gradient, and dipole values, while HIN files store atomic charge values. 

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