Delocalization energy, theory

Such cross-conjugation (where two of the vinyls are conjugated with each other through boron but not simultaneously with the third vinyl35) always lowers the total delocalization energy (DE) of the conjugated atomic set In simple Hiickel MO theory, for example, ( )-l,3,5-hexatriene (37) has a DE of 0.988/3, while 2-vinyl-1,3-butadiene (38) yields a DE of 0.900/3. 

Track theory starts with localized energy loss. On the other hand, attention has been frequently drawn to the role of delocalized energy loss in radiation chemistry. Fano (1960) estimated from the uncertainty relation that an energy... 

However, it may be assumed that the difference between the energy of one Kekule structure and the actual energy as calculated by MO theory will also be the resonance energy except that, in keeping with the basic concept of MO theory, we shall call it the. delocalization energy. 

This molecule provides an interesting and entirely genuine illustration of the predictive power of simple Hfickel MO theory it also serves as a good first example of how to apply symmetry methods in more general cases. The molecule was predicted to have —30 kcal/mol of delocalization energy in 1952 in 1962 it was synthesized and shown to be stable.tt The molecule may oe assumed to be planar, and we shall adopt the numbering scheme shown below. 

Of these, 48ab is predicted to have substantial electron delocalization because of the nearly equivalent VB structures 48a and 48b. By the simple MO theory 48ab should have a delocalization energy of 16 kcal mole-1 (Section 21-5B). The biradical 47 has no comparable electron delocalization and would be expected to be formed much less readily. 

Theory delocalization energy by the atomic orbital method. 

Dalton s atomic theory, overview, 1 De Broglie equation, 23 Delocalization energy, definition, 174 Density functional theory chemical potential, 192 computational chemistry, 189-192 density function determination, 189 exchange-correlation potential and energy relationship, 191-192 Hohenberg-Kohn theorem, 189-190 Kohn-Sham equations, 191 Weizsacker correction, 191 Determinism, concept, 4 DFT, see Density functional theory Dipole moment, molecular symmetry, 212-213... 

The weak reactivity of benzene is in part attributed to this additional stabiliza- j tion. That stabilization energy is often called the delocalization energy or reso- nance energy of benzene and is taken as a measure of the aromaticity of the j molecule. The expression resonance energy comes from the description of] the delocalized tt system in valence-bond theory in terms of the resonant hybrid... 

Since the levels are nearly continuous, this can be done by integration. This energy should be compared with the energy of an electron in the two-atom case, = a- - There is a delocalization energy of 0.27 / /electron. Note that in Huckel theory, there is no repulsion energy term. The Huckel P is one-half of the 3 values in Table 5.2. 

Assuming that the cohesive energy is due to the delocalization energy of partly filled bands, we can conclude that Equations (5.20), (5.22) and (5.23) are valid. We can also assume that the coulombic energy a is the same as for the free metal atoms. This is what is done in the simple Huckel theory used for other covalent bonding. Then we can write... 

Some indication of how theory compares with observation is given in Table II which shows the relative rates at which methyl radicals attack some of the compounds of interest (2). Notice that all rates are ordered inverse to delocalization energies. Values of DE quoted in Table II and hereafter have been nondimensionalized by the Hiickel factor 2/2 this nondimensional DE is also known as the Dewar number. The pattern of Table II is observed for a variety of other aromatic reactions such as nitration and sulfonation (I). Among the molecules considered in this study (Table I), benzene and anthracene represent the extremes of reactivity. 

The experimentally observed activation energy for the decomposition of an aromatic molecule is linearly related to its delocalization energy as calculated from Dewars theory. 

Soon after the appearance of the new view about the driving force for the Dsh structure of benzene, Hiickel theory was reexamined by Kataoka and Nakajima.They concluded that the traditional view, in which the r-electron delocalization energy... 

There has been no lack of investigations aimed at calculating the Q and e values theoretically. The polarity factor is a measure of electron density. Q is a measure of the resonance stability in the transition state and can be correlated with the delocalization energy accessible from electronic theory calculations. The quantity -RT In Q can then be considered as the contribution to the activation energy for the opening of tt bonds at the ultimate C atom of the monomer. 

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