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The reaction force F( ξ) is the negative gradient of the potential energy of a chemical process along the intrinsic reaction coordinate ξ. We extend the rigorous concept of F( ξ) to the 'activation strain model' of Bickelhaupt et al., to formulate the 'strain' force F( ξ) that retards a reaction and the 'interaction' force F( ξ) that drives it. These are investigated for a group of Diels-Alder cycloadditions. The results fully support the interpretation of the minimum of F( ξ) as defining the beginning of the transition from deformed reactants to eventual products. [ABSTRACT FROM AUTHOR]

A synchronous, concerted chemical process is rigorously divided by the reaction force F( R), the negative gradient of V( R), into 'reactant' and 'product' regions which are dominated by structural changes and an intervening 'transition' region which is electronically intensive. The reaction force constant κ( R), the second derivative of V( R), is negative throughout the transition region, not just at the nominal transition state, at which κ( R) has a minimum. This is consistent with experimental evidence that there is a transition region, not simply a specific point. We show graphically that significant nonsynchronicity in the process is associated with the development of a maximum of κ( R) in the transition region, which increases as the process becomes more nonsynchronous. (We speculate that for a nonconcerted process this maximum is actually positive.) Thus, κ( R) can serve as an indicator of the level of nonsynchronicity. [Figure not available: see fulltext.] [ABSTRACT FROM AUTHOR]

We have analyzed the variation of the reaction force F( ξ) and the reaction force constant κ( ξ) along the intrinsic reaction coordinates ξ of the water-assisted proton transfer reactions of HX-N = Y (X,Y = O,S). The profile of the force constant of the vibration associated with the reactive mode, k( ξ), was also determined. We compare our results to the corresponding intramolecular proton transfers in the absence of a water molecule. The presence of water promotes the proton transfers, decreasing the energy barriers by about 12 - 15 kcal mol. This is due in part to much smaller bond angle changes being needed than when water is absent. The κ( ξ) profiles along the intrinsic reaction coordinates for the water-assisted processes show striking and intriguing differences in the transition regions. For the HS-N = S and HO-N = S systems, two κ( ξ) minima are obtained, whereas for HO-N = O only one minimum is found. The k( ξ) show similar behavior in the transition regions. We propose that this fine structure reflects the degree of synchronicity of the two proton migrations in each case. [Figure not available: see fulltext.] [ABSTRACT FROM AUTHOR]

The concept of the reaction force is presented and discussed in detail. For typical processes with energy barriers, it has a universal form which defines three key points along an intrinsic reaction coordinate: the force minimum, zero and maximum. We suggest that the resulting four zones be interpreted as involving preparation of reactants in the first, transition to products in the second and third, and relaxation in the fourth. This general picture is supported by the distinctive patterns of the variations in relevant electronic properties. Two important points that are brought out by the reaction force are that (a) the traditional activation energy comprises two separate contributions, and (b) the transition state corresponds to a balance between the driving and the retarding forces. [ABSTRACT FROM AUTHOR]