Transition-intensity analysis

In order to consider the inversion of Qx(0,0) and Qy(0,0) electronic transition intensities in NH-tautomers of non-symmetrical free-base porphyrins we calculated the ground-state orbital energies of the investigated molecules by a CNDO/2 method using the symmetrized crystal geometry of porphyrin molecule (37,38). On the basis of the above experimental results we must introduce a motionless system of molecular X and Y axes, identically fixed in both tautomers. Then using theoretical MO calculations and the analysis... 

It is well known that ferromagnetism favors reentrant behaviour (see subsection 1.3). The formation of such secondary phases is supported by nonstoichiometry. Therefore the chemical characterization of the sample is of prime importance. However, due to the presence of the two light elements B and C the various classical characterization techniques as chemical analysis, intensity analysis of x-ray or neutron diffraction, transition electron... 

The simplest model consists of two centres, one donor (D) and one acceptor (A), separated by a distance I and contains two electrons. Here we consider this simple system to illustrate some general relations between charge transfer, transition intensities and linear as well as non-linear optical polarizabilities. We will show below that the electro-optic parameters and the molecular polarizabilities may be described in terms of a single parameter, c, that is a measure of the extent of coupling between donor and acceptor. Conceptually, this approach is related to early computations on the behaviour of inorganic intervalence complexes (Robin and Day, 1967 Denning, 1995), Mulliken s model for molecular CT complexes (Mulliken and Pearson, 1969) and a two-form/two-state analysis of push-pull molecules (Blanchard-Desce and Barzoukas, 1998). 

The allowed dipole transitions between the states of the complex can be deduced from an analysis of the expression for the transition intensity, and it follows easily that the observed dipole transitions must obey the following rigorous selection rules AJ = 1, Aa = 0 or AJ = 0, Aquantum number is nearly conserved, an additional approximate selection rule should hold AK = 0,1. 

The observed shakedown is analogous to the satellites observed in photoelectron spectroscopy and can be treated in a similar manner [25]. This analysis enables us to quantify the intensity of the Is —> 4p + LMCT shakedown feature as a percentage of the total Is > 4p transition intensity. Comparison of the shakedown intensity to that of the Is > 3d(+4p) pre-edge transition (at 8,979 eV) then allows for quantitation of the amount of 4pz mixing into the 3d orbital. Within the sudden approximation [28-30], the creation of the core hole occurs rapidly, before the electron adjusts to the new potential. Here, the intensity /j of a given transition corresponding to either the main (Is —> 4p ) or shake down (Is —> 4p + LMCT) final state can then be given by the Sudden approximation... 

We studied the XANES spectra of an over exchanged Cu-ZSM-5-164 and an underexchanged Cu-ZSM-5-59. Both catalysts were treated in He flow at 773 K, 30 minutes for 164% and 45 minutes for 59% exchanged samples, before He was replaced by 1% NO/Nj. Their corresponding XANES spectra are shown in Fig. 4 and Fig 7. The most profound feature in these spectra is the difference in Cu(I) ls 4p transition intensity before and after the admission of NO. For Cu-ZSM-5-164, about 70% of the copper ions were reduced to cuprous ions in He flow, using the aforementioned spectral analysis method. The Cu(I) percentage concentration decreases rapidly to 35% after the gas switch and maintains at this level during 60 minutes of NO decomposition catalysis at 773 K. For Cu-ZSM-5-59, virtually all the copper ions were auto-reduced to Cu(I) in He flow. The static... 

The primary result of an AES depth profile analysis is an Auger transition intensity versus sputter time presentation. Quantification leading to atomic concentrations is possible when RSFs or reference materials are available. A measurement of sputter rates which depend on the sputtered material enables... 

We also proposed a novel light scattering intensity analysis mefood, which is, valid up to about 50% hydrated micellar volume fraction. The new light scattering intensity analysis method significantly extends the concentration range of the traditional Zimm Plot (24). Its simplicity makes it useful also as a fingerprint to detect phase transitions. 

Malinowski, J., 2013. A method of computing the interstate transition intensities for multi-state series-parallel systems. Safety, Reliability and Risk Analysis Beyond the Horizon. Proceedings of the European Safety and Reliability Conference, ESREL2013 l i- l 9. 

The matrix element in eq. (143) is valid for transitions between two crystal-field levels. Because of the radial integrals, the calculation of the matrix element is very tedious and can in fact only be done if some approximations are made. Axe (1963) treated the quantities Aiaj3(k,X) in eq. (143) as adjustable parameters. In this expression, X is equal to 2, 4 or 6, and k is restricted to values of Ail. The values of q are determined by crystal-field symmetry constraints and lie between 0 and k. This parametrization scheme was used by Axe for the intensity analysis of the fluorescence spectrum of Eu(C2H5S04)3 9H20. Porcher and Caro (1978) introduced the notation Bxki for the intensity parameters ... 

Over the years, the Judd-Ofelt theory has been proved to be quite successful for the intensity analysis of the trivalent lanthanide ions. A lot of pioneering work concerning the determination of experimental intensities of the f-f transitions over the lanthanide series and the systematic intensity parametrization has been done by Camall and coworkers (Carnall et al. 1965, 1968a, see also Camall 1979). They studied the spectra of the trivalent lanthanide ions in aqueous solution (diluted HCIO4). In order to extend the range of measurements to the near-infrared, spectra were also recorded in diluted DCIO4. The intensity of the transitions between J-multiplets in the spectrum can be rationalized in terms of only three parameters Qx- One can make predictions about the intensity of transitions which cannot be observed experimentally (e.g. infrared 4f-4f transitions in aqueous solution). The parameter sets are a useful tool to compare the f-f intensity properties of different lanthanide systems. They may be used to derive relationships between spectral and stractural properties for different kinds of lanthanide complexes. 

By die transformation (3.3) a substantial step is made in die transition from experimental intensities into quantities characterizing molecular structure. At die first place, a natural separation between dipole derivatives associated with bond stretchings and angle deformations is achieved. In some cases the dp/dSj derivatives can be associated with vibrations localized within certain atomic groupings. Such distortions may be described by local group symmetry coordinates. Snyder [27] first applied dipole moment derivatives with respect to group symmetry coordinates as basic parameters in infrared intensity analysis on a series of crystalline n-alkanes. The procedure described in his work will be discussed later in this section. 

Another possible assignment for peak 1 at highest binding energy would be a tt > ir 7 eV shake-up transition originating from photoelectron peak 6 at 287.3 eV. That supposes that part or all of the electrons of type 6 are in fact CF vinyl radicals with a double bond. The intensity analysis of the 8 carbon components (see Table VI below) completely rules out that interpretation peak 6 is not intense enough to be accompanied by such an intense satellite (peak 1). 

---