Spectroscopic energy

Equation (A2.1.8) turns out to be consistent with die changes of the energy levels measured spectroscopically, so the energy produced by work defined this way is frequently called the spectroscopic energy . Note that the electric and magnetic parts of the equations are now synnnetrical. 

Spectroscopic energy of dissociation of a diatomic molecule in the Morse equation... 

The analysis of spectroscopic data for bound states of diatomic molecules gives accurate potential curves if one follows the semi-classical Rydberg-Klein-Rees method. For a review of this see Ref. 126). It is sufficient to note that this gives the two values of r as a function of potential energy by considering the dependence of the total spectroscopic energy on the vibrational and rotational quantum numbers n and J. A somewhat simpler procedure, and the only one plicable to polyatomic molecule, is to use the Dunham expansion of the potential 127). 

It was pointed out in Section 4-2 that the configuration sp8, which has promotion energy about 200 kcal/mole relative to the ground configuration 2s22p2, is the basis of the quadrivalent state of the carbon atom and is shown by quantum-mechanical calculations for methane to contribute about 49 percent to this valence state. Now let us consider the iron atom, for which spectroscopic energy levels are shown on... 

The redox potentials of an excited state can be estimated from its spectroscopic energy (0-0 transition, E<>0(M/M )) and the oxidation and reduction potentials of the ground state ... 

Fig. 7. Schematic diagram showing the difference in the redox properties of the ground and excited molecule according to Eqs. (12) and (13) c is the one-electron potential corresponding to the zero-zero spectroscopic energy of the excited state...

Analysis of spectra is generally made to obtain (i) crystal field, (B ), (ii) nephelauxetic, (fi) and (iii) intensity parameters for a complex compound. These parameters are used in conjunction with relationships between spectroscopic, energy and geometry factors and deduce information on the structure of the complex. 

Figure 2. Thermodynamic cycles for evaluating the free energy changes AG°et associated with the intramolecular photoinduced electron transfer processes in system 13 in its oxidized (a) and reduced (b) form. The quantity, the spectroscopic energy, is obtained from the emission spectrum the E values, electrode potentials associated with the given redox change, can be determined through voltammetry experiments. The Coulombic term (e /er) has been considered negligible under the present circumstances.

The free energy change, AG°, for the energy transfer reaction can be expressed by the difference between the zero-zero spectroscopic energies of the donor and the acceptor excited states, which can be estimated from the luminescence band maxima of the reference complexes taken at 77 K [57, 64, 65],... 

Thermodynamic properties for the ideal monatomic gas have been computed from the spectroscopic energy levels reported by Moore 241). Vapor pressures reported by Harteck H5) are somewhat lower than the more recent measurements of Speiser and Johnston. Giving the latter workers the most weight we calculate a heat of sublimation at 298 K. of 65,000 cal./gram atom, a normal boiling point of 2510 K., and a heat of vaporization at the normal boiling point of 61,200 cal./gram atom. 

Table 12. Spectroscopic energy shifts vs redox potentials [189]...

An understanding of observable properties is seldom trivial. Spectroscopic energy levels are, in principle, eigenvalues of an infinite matrix representation of H, which is expressed in terms of an infinite number of true de-perturbed molecular constants. In practice, this matrix is truncated and the observed molecular constants are the effective parameters that appear in a finite-dimension effective Hamiltonian. The Van Vleck transformation, so crucial for reducing H to a finite Heff, is described in Section 4.2. 

Caldwell et al. determined the relaxed triplet energies of a series of arylethenes by means of photoacoustic calorimetry (PAC) and compared these with the spectroscopic energies determined by Sq-T, absorption or phosphorescence spectra [37]. In compounds undergoing two-way isomerization with flexible C=C double bonds such as styrenes and stilbene they observed a considerable difierence between the spectroscopic triplet energy [ T(spectroscopic)] and the relaxed triplet energy [Eyfrelaxed)]. For example, T(spectroscopic) is 64.9 and 60.Skcal mol, respectively, for styrene and / -methylstyrene, while r(relaxed) is 51.2 and 53.2 kcal mol respectively. Thus, in the triplet potential energy surface of these ethylenes, not only c, but also t is stabilized by relaxation to p. ... 

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