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Controlling the thermochemistry and kinetics of chemical reactions is a central problem in chemistry. Among factors permitting this control, the substituent effect constitutes a remarkable example. Here, we develop a model accounting for the effect of a substituent on the potential energy surface of the substrate (i.e., substituted molecule). We show that substituents affect the substrate by exerting forces on the nuclei. These substituent-induced forces are able to develop a work when the molecule follows a given reaction path. By applying a simple mechanical model, it becomes possible to quantify this work, which corresponds to the energy variation due to the effect of the substituent along a specific pathway. Our model accounts for the Hammett equation as a particular case, providing the first non-empirical scale for the σ and ρ constants, which, in the developed model, are related to the forces exerted by the substituents (σ) and the reaction path length (ρ), giving their product (σ · ρ) the well-known variation on the reaction energy due to the substituent.

A definition of the triplet-triplet energy transfer reaction coordinate within the very weak electronic coupling limit is proposed, and a novel theoretical formalism is developed for its quantitative determination in terms of internal coordinates The present formalism permits (i) the separation of donor and acceptor contributions to the reaction coordinate, (ii) the identification of the intrinsic role of donor and acceptor in the triplet energy transfer process, and (iii) the quantification of the effect of every internal coordinate on the transfer process. This formalism is general and can be applied to classical as well as to nonvertical triplet energy transfer processes. The utility of the novel formalism is demonstrated here by its application to the paradigm of nonvertical triplet-triplet energy transfer involving cis-stilbene as acceptor molecule. In this way the effect of each internal molecular coordinate in promoting the transfer rate, from triplet donors in the low and high-energy limit, could be analyzed in detail.

The new algorithm presented here allows, for the first time, the determination of the optimal geometrical distortions that an acceptor molecule in the triplet-triplet energy-transfer process undergoes, as well as the dependence of the activation energy of the process on the triplet energy difference of donor and acceptor molecules. This algorithm makes use of the complete potential-energy surfaces (singlet and triplet states), and contrasts with the first-order approximation already published [L. M. Frutos, O. Castano, J. L. Andres, M. Merchan, and A. U. Acuna, J. Chem. Phys. 120, 1208 (2004)] in which an expansion of the potential-energy surfaces was used. This algorithm is gradient based and finds the best trajectory for the acceptor molecule, starting from S(0) ground-state equilibrium geometry, to achieve the maximum variation of the singlet-triplet energy gap with the minimum energy of activation on S(0). Therefore, the algorithm allows the determination of a "reaction path" for the triplet-triplet energy-transfer processes. Also, the algorithm could also serve eventually to find minimum-energy crossing (singlet-triplet) points on the potential-energy surface, which can play an important role in the intersystem crossing process for the acceptor molecules to recover their initial capacity as acceptors. Also addressed is the misleading use of minimum-energy paths in T(1) to describe the energy-transfer process by comparing these results with those obtained using the new algorithm. The implementation of the algorithm is illustrated with different potential-energy surface models and it is discussed in the frame of nonvertical behavior.

Triplet energy transfer (TET) from aromatic donors to 1,3,5,7-cyclooctatetraene (COT) is an extreme case of "nonvertical" behavior, where the transfer rate for low-energy donors is considerably faster than that predicted for a thermally activated (Arrhenius) process. To explain the anomalous TET of COT and other molecules, a new theoretical model based on transition state theory for nonadiabatic processes is proposed here, which makes use of the adiabatic potential energy surfaces (PES) of reactants and products, as computed from high-level quantum mechanical methods, and a nonadiabatic transfer rate constant. It is shown that the rate of transfer depends on a geometrical distortion parameter gamma=(2g(2)/kappa(1))(1/2) in which g stands for the norm of the energy gradient in the PES of the acceptor triplet state and kappa(1) is a combination of vibrational force constants of the ground-state acceptor in the gradient direction. The application of the model to existing experimental data for the triplet energy transfer reaction to COT from a series of pi,pi(*) triplet donors, provides a detailed interpretation of the parameters that determine the transfer rate constant. In addition, the model shows that the observed decrease of the acceptor electronic excitation energy is due to thermal activation of C=C bond stretchings and C-C bond torsions, which collectively change the ground-state COT bent conformation (D(2d)) toward a planar triplet state (D(8h)).