A theoretical relation for the position of the energy barrier between initial and final states of chemical reactions

Performance of the correlation consistent composite approach for transition states: A comparison to G3B theory

“…31 That is, the forward barrier is small, leading to a transition state that strongly resembles the reactants both in energy and in structure. The linear interpolation proposed independently by Agmon 32 and Miller 33 for quantitative application of the Hammond postulate can be used to estimate the degree of completion of a reaction at the transition state using the known forward and reverse reaction barrier heights. While quantitative formulations of the Hammond postulate have been compared to results using Marcus theory, 34 the use of these parameters as an estimation of how well DFT will perform appears to be unique to the current study.…”

“…It is notable that all the transition states for protontransfer reactions were found, despite the small completion estimates for two of them. This leads one to believe that the completion estimates of Agmon 32 and Miller 33 may be a good indicator of when a transition state for nonprotontransfer reactions will be difficult ͑if not impossible͒ to locate using DFT and perhaps whether modification of the geometry optimizations will be necessary.…”

Kinetic Energy Release and Position of the Transition State for С6Н7 + Ions Produced from Isomeric C7H8O Precursors

“…The partitioning energy quotient q= T ß/ e reaction enthalpy AHr and position Xq of the transition state on the reaction coordinate derived from these data are also reported in Table 1. It should be emphasized that the ionization energy and appear ance energy for the different precursors introduced in Table 1 According to Miller's quantification [5] of the Ham mond postulate [6] the position Xq of the transition state of an elementary reaction on the reaction coordi nate can be expressed by the barrier height U*(eb) and potential energy of the reaction Uf(AH£) according to…”

“…According to (5), s* depends on the heat of the reaction, being smallest in case of the most endothermic and largest in case of the most exothermic reac tion (assuming that is constant or varies only slightly). Although the calculated values are not constant and show significant variation, especially for the benzyl alcohol reaction, the calculated e* values follow this rule.…”

Radiationless transitions and photochemical reactivity

“…This parameter corresponds also to the sum of the bond distensions to the transition state. The theory shows that d = n(1AB 1BC) (1) where 1A8 and 1BC are the equilibrium bond lengths of AB and BC and r is the reduced bond distension, a'ln2 + a' (tE)2 (2) n* is the average bond order of the transition state, A is the "configuration entropy" parameter as defined by Agmon and Levine (6), and a' is a constant (a' = 0.156).…”