Energy diagrams interpretation

Similar free-energy diagrams, which can be interpreted in exactly the same way, have been constructed for sulphides , carbides and nitrides (Figs. 7.56 to 7.58). 

In 1935, after studying the luminescence of various colorants, Jablonski suggested the electronic energy diagram of the singlet and triplet states to explain the luminescence processes of excitation and emission. The proposed diagram of molecular electronic energy levels formed the basis of the theoretical interpretation of all luminescent phenomena [21],... 

Use and interpret simple atomic and molecular orbital energy diagrams. 

We now turn to the interpretation of the evaporation rate vs. 6 curves. From the potential-energy diagram (Figure 17) one can calculate Ea, the number of atoms that evaporate per square centimeter per second. 

However, in sulphides and related minerals, the effects of covalent bonding predominate and orbital overlap must be taken into account. Thus, concepts of molecular orbital theory are described in chapter 11 and applied to aspects of the sulfide mineralogy of transition elements. Examples of computed energy diagrams for molecular clusters are also presented in chapter 11. There, it is noted that the fundamental 3d orbital energy splitting parameter of crystal field theory, A, receives a similar interpretation in the molecular orbital theory. 

Only the direct self-energy diagrams (e.g. Fig. 9 e) can be interpreted in terms of classical physics. The exchange processes are sometimes important and must be included in actual calculations. However, they do not change the basic physical picture, and in this qualitative discussion we therefore only consider the direct processes. 

The Bronsted relation has proved to be a useful equation for correlating rate and equilibrium results for proton transfer reactions. However, following the analysis by Leffler and Grunwald [73] in 1963 considerable effort has been made to go further than this and understand why the relation should hold, and also to attach some significance to the values of a and 3 in terms of the structure of the transition state for proton transfer. An alternative approach from that to be discussed here interprets the Bronsted relation from molecular potential energy diagrams [74]. 

The discussion above shows that TCV can be reasonably interpreted in the framework of known electronic states. The direct determination of interface states from TCV seems difficult because the dependence of (7° with the tip potential [78, 81] finds no simple explanation within a simple one-dimensional energy diagram. Tip-induced local modifications of the band diagram of the semiconductor may exist (see Sec. 4.2.3) which complicates the determination of energy levels. The experimental dependence of [7° on the pre-history of the electrode [78, 81] stem probably from... 

The energy diagram shown in Fig. 2 gives a possible interpretation of the geometrical and structural isomerization in terms of the biradical mechanism. This... 

Interpretation of the Energy Diagrams, Once the values of zeta potential are determined, eq 9 can be evaluated. The results obtained are summed to those of the van der Waals interaction (eq 8) and plotted as a potential energy of interaction as a function of separation distance between the droplets. The energy is often expressed in terms of kT units, in order to better relate the energy of the interaction to the thermal energy of Brownian... 

We use similar potential energy diagrams to represent the interaction between a pair of objects, such as Earth-moon, Earth-Mars, electron-nucleus, electron-electron, nucleus-nucleus, atom-atom, or molecule-molecule. We construct such diagrams at several points in this textbook and use them to interpret the relative motions of the pair of objects. These methods are extremely important in describing the formation of chemical bonds, the states of matter, and the role of molecular collisions in chemical reactions. 

E2.32 The molecular orbital energy diagram for ammonia is shown in Figure 2.30. The interpretation given in the text was that the 2a) molecular orbital is almost nonbonding, so the electron configuration Iai le 2ai results in only three bonds ((2 + 4)/2 = 3). Since there are three N-H bonds, the average N-H bond order is I (3/3 = 1). 

If the interpretation of the g tensor in planar complexes is quite straightforward once the correct energy diagram has been chosen, the same is not the case for the hyperfine tensor, with the exception of Ax- As several authors have pointed out, a correct interpretation of the A tensor is not possible without considering explicitly low-lying quartet states of the complexes (50,37). 

A detailed analysis shows that the EPR spectra (and the NMR spectra) can be interpreted to a very good approximation by an energy diagram having two doublets and one quartet within 2000 cm above the predominantly yz, ground state. Higher lying states have almost no influence on the EPR parameters. 

Figure 11.1 Representation on the same graph of the absorbance and fluorescence spectra of an ethlyenic compound. The fluorescence spectrum that resembles the mirror image of the absorbance spectrum, as weU as the Stokes shift can be interpreted by considering the energy diagrams (Figure 11.2). In UV/Vis absorption and fluorescence spectra, bandwidths of 25 nm or more are common. This representation is obtained by uniting on the same graph, with a double scale, the spectrum of absorbance with that of emission. Example extracted from Jacobs H. et al, Tetrahedron 1993, 6045.

What information about the reaction mechanism does this correlation provide Interpret the results in terms of a More O Ferrall-Jencks two-dimensional potential energy diagram. 

Schematic potential-energy diagram for the dissociation of HA into H + A, and of DA into D + A. This interpretation of the isotope effect neglects the solvation of the ions in reality there is a difference between the 2ero-point levels for solvated H30 and solvated 030", but the difference is less than that between HA and DA.

The mechanistic reinterpretation of the data that had been considered to support an 8 1 mechanism developed from a generalized interpretation of how minimal-energy reaction pathways are determined. Jencks (1985) has demonstrated the importance of mechanisms involving borderline transition states, where the borderline divides concerted and stepwise mechanisms. These occur where necessary intermediates may be too unstable to exist. In terms of the three-dimensional energy diagram, these mechanisms involve reaction paths that approach the corner occupied by the intermediate but do not reach to the corner. Herschlag and Jencks (1986) analyse the kinetic evidence that has been presented in support of a metaphosphate intermediate in a variety of reactions in solution. They conclude that none establishes the existence of metaphosphate ion as an intermediate but that all are expectedly consistent with an unsymmetrically extended transition state in a concerted mechanism (2). 

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