Gaussian analysis

Dr. Langford and I decided to look at these spectra again. We remeasured the spectrum of Co(NH3)5Ff2 because this is the one in which to resolve the fourth d-d band. The band comes out nicely and we didn t even need a Gaussian analysis. A Gaussian analysis checked out Lenhart and Weigel s first three bands very nicely and thus we have resolved in one case, outside of octahedral and tetrahedral symmetry, all of the spin-allowed bands. The band from xy to should have the... 

In the single crystal absorption spectra of CrF2 and CrCl2 the pattern of spin-allowed (quintet-quintet) bands for the ammines and hydrates is repeated. Gaussian analysis of the higher wavenumber bands has allowed assignments of all three transitions and calculation of... 

Figure 48 Gaussian analysis of the electronic spectra of [Cu(acac)2] in different donor solvents (a) Cu(acac)2 (b)...

One approach to address the nonstationary nature of sine-wave parameters over a constrained analysis window relies on a time-varying amplitude and frequency model. A specific model assumes a linear evolution of frequency over the analysis window13. With a Gaussian analysis window (this selection includes constant and exponential as special cases), Marques and Almeida [Marques and Almeida, 1989] has shown that... 

In principle, Gaussian analysis can resolve the bands with some assumptions about the shape, number and intensity of ligand-field bands. The analysis of the fine structure of the bands is limited (i.e.) bands which are split into the minimum number of ligand-field components. Such bands are listed in the literature [188]. 

Co(EDTA)]- has been said (to yield, on Gaussian analysis, (69) more components than are given in reference (68). However, the validity of such analyses of circular dichroism spectra is questionable (70). The ORD spectra of (—)s46-[Co(- -CHXTA)]- also compared (67) with those of the derivatives of EDTA and (+)PDTA giving a further assignment to the S(C2) series. A similar conformation assignment on complexes of L-(—)-... 

The exponential factor of FC dominates equation (15). This feature simplifies much of the discussion. This exponential function is in Gaussian form, and it is the basis for a Gaussian analysis of absorption or emission spectra. Equations (15-18) provide the basis for analyzing the absorption or emission spectral envelope by considering some range of values of light frequencies (vobsd), but the nomadiative rate constant corresponds to the zero-photon limit. 

Bands for the anion were resolved by Gaussian analysis. Spectrum in CH2CI2 was identical to [CoL5][CoL(N03)2] except for the yellow band due to [CoLs] ... 

Cis-cis- TOoCl (NH3) (en) ]+ — The absorption and CD spectra in DMSO for the isomer derived from (+)5---[Co(C03)-(NH3)2(en)]+ are shown in Figure 2, where the vertical lines represents the results of the Gaussian analysis of the absorption spectrum, with labels specifying the excited states of the tetragonal components. The CD spectrum shows dominant negative peak at 16,230 cm- , which corresponds closely to the position of the... 

The electronic spectrum of Cu(II) in aqueous solution was investigated by Bjerrum et al. H954) and interpreted in terms of a tetragonally-distorted Cu(H20)e ion. It was recognised that the broad band around 12 kK contained at least two d—d bands which were resolved by gaussian analysis. 

This view is borne out by the spectroscopic study of Allen and Warren (103). For a high-spin d system the ground state is a Aij level, and all d—d transitions would be spin-forbidden, but the intensities of the bands observed below about 25 kK. are comparable with those found for the spin-allowed bands of low-spin NiFe . Whilst it is not possible to place too much rehance on intensity values obtained by reflectance (s. Sect. 1 (iv)), it is usually easy to distinguish between spin-allowed and spin-forbidden transitions, and on this basis the bands lying between 17 and 25 kK.. (Table 3 (iv)) are assigned as spin-allowed doublet-doublet excitations, whilst the much weaker absorptions at 6.4 and 10.3 AK. represent transitions to quartet states. Resolution of the absorption r on above 15 kK., by Gaussian analysis, yields the peak positions shoAvn in the Table, and the bands may be fitted by the parameters Dy=2030 cm. i. 

It is now the question whether it is possible in a case where an overlapping band (even after the mixing) has a pronounced narrowness to make an estimation of its intensity through a gaussian analysis, and thus to make possible an estimation of the matrix elements of spin-orbit coupling. 

We have used a regression analysis digital computer program (5) to preliminary investigate such a gaussian analysis. This program works iteratively from an input of initial parameters and minimizes the mean square deviation through successive linear approximations. 

The use of the inverse Langevin function, as for example to derive eqn (3.20) overcomes the objection that the Gaussian analysis does not take into account the finite extensibility of the network chains. However in order to make the Langevin statistics reasonably mathematically tractable assumptions have to be introduced which strictly make the statistics invalid under non-Gaussian conditions. Their justification must lie in the fact that the resultant expressions give far better fits to the experimental data than the Gaussian statistics. 

Absorption, fluorescence emission spectra at -196°C and Gaussian analysis were previously described (Berkaloff et. di, 1981). 

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