Transition energies, estimates

Abstract Although aromatic azides are believed not to emit phosphorescence, 2,4,6-tribromophenylazide was found to phosphoresce in EPA at 77°K, and the peak of the spectrum coincides with the tail of the absorption spectrum of its concentrated solution in ethyl iodide. The measurements of the So-)Ti absorption spectra in ethyl iodide with vibrational structures were also succeeded in the cases of ethyl p-azi-dobenzoate and ethyl azidocinnamate. The experimantal values coincided with the )3 transition energies estimated by SCF MO Cl... 

Z values are obtained from Eq. (8-76) for solvents having Z in the approximate range 63-86. In more polar solvents the CT band is obscured by the pyridinium ion ring absorption, and in nonpolar solvents l-ethyl-4-carbomethoxy-pyridinium iodide is insoluble. By using the more soluble pyridine-1-oxide as a secondary standard and obtaining an empirical equation between Z and the transition energy for pyridine-1-oxide, it is possible to measure the Z values of nonpolar solvents. The value for water must be estimated indirectly from correlations with other quantities. Table 8-15 gives Z values for numerous solvents. 

Figure 1 Experimental gas phase Nj Auger spectrum (Siegbahn et al [6]) and estimated transition energies for normal processes (vertical lines) and for the other most important processes (dashed vertical lines).

Kaindl et al. [186] have plotted the isomer shift results for metallic hosts versus the number of outer electrons of the 3d, Ad, and 5d metals and found the transition energy to decrease when proceeding from a to a Ad and further to a 3d host metal in the same column of the periodic table. This systematic behavior is similar to that observed for isomer shifts of y-rays of Fe(14.4 keV) [193], Ru(90 keV), Pm (77 keV), and lr(73 keV) [194]. The changes of A(r ) = (r )e — (r )g for these Mossbauer isotopes are all reasonably well established. Kaindl et al. [186] have used these numbers to estimate, with certain assumptions, the A(r ) value for Ta (6.2 keV) and found a mean value of A(r ) = —5 10 fin with some 50% as an upper limit of error. The negative sign of A(r ) is in agreement with the observed variation of the isomer shift of LiTaOs, NaTaOs, and KTaOs, as well as with the isomer shift found for TaC [186]. 

The active space used for both systems in these calculations is sufficiently large to incorporate important core-core, core-valence, and valence-valence electron correlation, and hence should be capable of providing a reliable estimate of Wj- In addition to the P,T-odd interaction constant Wd, we also compute ground to excited state transition energies, the ionization potential, dipole moment (pe), ground state equilibrium bond length and vibrational frequency (ov) for the YbF and pe for the BaF molecule. 

To illustrate how stratification works in the context of free energy calculations, let us consider the transformation of state 0 into state 1 described by the parameter A. We further assume that these two states are separated by a high-energy barrier that corresponds to a value of A between Ao and Ai. Transitions between 0 and 1 are then rare and the free energy estimated from unstratified computer simulations would converge very slowly to its limiting value, irrespective of the initial conditions. If, however, the full range of A is partitioned into a number of smaller intervals, and... 

Bloch (1933a,b) first pointed out that in the Thomas-Fermi-Dirac statistical model the spectral distribution of atomic oscillator strength has the same shape for all atoms if the transition energy is scaled by Z. Therefore, in this model, I< Z Bloch estimated the constant of proportionality approximately as 10-15 eV. Another calculation using the Thomas-Fermi-Dirac model gives I tZ = a + bZ-2/3 with a = 9.2 and b = 4.5 as best adjusted values (Turner, 1964). This expression agrees rather well with experiments. Figure 2.3 shows the variation of IIZ vs. Z. 

Figure 2. Estimated transition energies of (a) iCTi in isolated MgP-P dimers, (b) the lowest four states in isolated dimers, and (c) ICTi in...

Figure 4. Estimated transition energies of low-lying excited singlet and triplet states in the 5.35A MgP-P dimer. S1-S4 and T1-T9 correspond to localized states on the indicated monomers. 85 and Tio correspond...

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