Promotion gaps

The promotion gap is determined by two basic excitations. For -electron pairs, the promotion energy is k-fold singlet—triplet excitation of the A—A dimer, while for mixed-valence cases where the number of electrons exceeds the number of centers (e.g., H3 ) and vice versa, the promotion energy is a charge-transfer excitation, (e.g., from Hr to H2 in H i ). Let us now use the promotion gap quantity to pattern the data concerning delocalized species. 

Maitre, P. Hiberty, P. C. Ohanessian, G. Shaik, S. S. J. Phys. Chem. 1990, 94, 4089. Note that Bo and the curvature of the curves depend also on the promotion gap. In this manner, the gap becomes the organizing quantity. 

FIGURE 6.5 (a) The state correlation for (a) a 2 + 2 cycloaddition reaction, and (b) a Diels—Alder 4 + 2 reaction. The promotion gap expressions are shown beneath the respective diagrams. 

VBSCDs without the VB mixing of the state curves. It is seen that in both cases, the promotion gap is given by the sum of the singlet-to-triplet excitation of the two reactants, while pairing up all the spins into a total singlet spin (see later for a discussion of the meaning of forbiddenness vs. allowedness in the Woodward—Hoffmann sense, in terms of the VB diagram). 

The barriers for a series of radicals have been computed (22), and were found to increase as the R H bond energy D increases the barrier is the largest for R = CF13 and the smallest for R = C(CH3)3. This trend has been interpreted by Pross et al. (23) using the VBSCD model. The promotion gap G that is the origin of the barrier involves the singlet-triplet excitation of the... 

Fig. 6.19 show that, as the promotion gap drops drastically, the avoided crossing state changes from a transition state for H3 to a stable cluster for Li3. Moreover, this transition from a barrier to an intermediate can in fact be predicted quantitatively from the barrier equation, by deriving explicit expressions for G,f, and B (see Exercise 6.6) (16,64,65). 

B. Since AEc can be expressed as a fraction of the promotion gap, we may write the following equation for the barrier ... 

The promotion gap is given by the difference between the vertical ionization energy of X - anions (1 ) and the vertical electron affinity of the cation (A +), leading to the following expression for the barrier ... 

Exercise 6.4 Based on the analysis of the barrier for radical exchange reactions, we can use the relationship G = 2DHx for the promotion gap. If we assume only linear transition states, we can use the relationship B = 0.5DHx given in Equation 6.19 (16). Combining the two expressions and the value f= 1/3, we get the following expression for the barrier (16) ... 

One of key developments of modern VB methods is the ability to compute barriers for elementary reactions (6,7), sometimes with high accuracy (6). Equally important is the current capability to analyze these barriers using the VB diagrams, VBSCD or VBCMD, described in Chapter 6, and to compute reactivity quantities like the promotion gap, G, and the resonance energy of the TS, B. These are multi-layered calculations in which both the adiabatic and diabatic curves are calculated variationally. 

Promotion gap The energy gap between the ground and excited states in the VBSCD (see below). This factor, labeled as G, originates the barrier in chemical reactions. 

Denotes the resonance energy of the transition state in the VBSCD. Denotes the promotion gap in the VBSCD. 

A similar expression can be written for the barrier of the reverse reaction as a function of the gap at the product side and the corresponding quantity/. One then distinguishes between the promotion gaps of the reactants and products, G, and Gp, and the corresponding/factors,/ and/, of the curves that emanate from reactants and products. A general expression for the barrier as a function of the two promotion gaps and... 

To understand the correlation between sulfoxidation barrier height and ionization potential of the substrate, also here a VB curve-crossing diagram was set up (106), which is shown in Fig. 13. In contrast to aliphatic hydroxylation and epoxidation discussed above, the sulfoxidation reaction is concerted without a reaction intermediate. Therefore, the reactants connect with products directly and the promotion gap as a result reflects the excitation energy from the reactant wave function to the product wave fimc-tion in the reactant geometry. The excited wave fimction Fp essentially refers to the one-electron transfer from substrate to oxidant hence it is proportional to the IE of the substrate and the electron affinity of the oxidant. Consequently, the correlation... 

Similar reaction series aboimd. Thus, in a series of Woodward-Hoff-mann forbidden 2 + 2 dimerizations, the promotion gap is proportional to the sum of the AEst (jhi ) quantities of the two reactants. Consequently, the barrier decreases from 42.2 kcal/mol for the dimerization of ethylene, where SAEst nn ) is large ( 200 kcal/mol) down to <10 kcal/mol for the dimerization of disilene for which SAEsr(itit ) is small ( 80 kcal/mol). A similar trend was noted for Woodward-Hoffmann allowed reactions (4 + 2 or 2 + 2 + 2), where the barrier jumps from 22 kcal/mol for the Diels-Alder reaction where SAEsT(7tit ) is small ( 173 kcal/mol) to 62 kcal/mol for the trimerization of acetylene where SAEsrlitit ) is very large ( 297 kcal/mol). 

Chanson M, White NM, Garber SS. cAMP promotes gap junctional coupling in T84 cells. Am J Physiol Cell Physiol 1996 271 C53-C59. 

Figure 1 An SCD for a chemical step R -> P. The excited states are the promoted states and the Cs are corresponding promotion gaps...

To render equation (1) predictive and interactive with both experiment and computations, the destabilization energy must be expressed in terms of the accessible quantities, the promotion gaps. The most compact relationship is equation (2) where the crossing point is given as a fraction (/) of the promotion gap. ... 

These effects can be incorporated into a single expression, equation (3), which shows the dependence of the barrier on all the reactivity factors in the SCD in Figure 2(a) (see also Figure 1) the two different promotion gaps, two independent / factors for the reactant and product curves, the reaction driving force (A rp), and the resonance energy, B, of the TS. Note the / factors now refer to the curvature effect when A rp = 0. For example, in a case where the promotion gaps... 

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