Two-dimensional Free Energy Surface Research Articles

Dynamics of twisted intramolecular charge transfer complexes in polar solvents

Abstract The excited-state electron transfer and time-dependent fluorescence (TDF) for twisted intramolecular charge transfer (TICT) molecules in polar solvents are studied theoretically. This reaction class involves critical solvent stabilization of the charge-separated state with a large dipole moment compared to the less polar, locally-excited state; it is also accompanied by a significant solute geometry distortion compared to vacuum, i.e., from a planar to a twisted configuration. A theoretical framework for TICT dynamics is constructed and illustrated throughout for a model dimethylaminobenzonitrile (DMABN) solute. By employing a model two valence-bond state description for the solute in a dielectric continuum solvent for illustration, we obtain a two-dimensional free energy surface in terms of the solute torsional angle θ and a solvent coordinate s that gauges the nonequilibrium solvent orientational polarization. The TICT rate constant and TDF are analyzed via the minimum free energy solution-phase reaction path (SRP), which is found to be strongly curved on the reactive free energy surface. For slow aprotic solvents, the SRP is mainly along the θ coordinate near the transition state. There is little motion in the solvent coordinate s; the solvent lags the solute twisting motion and there is nonadiabatic nonequilibrium solvation. Near the reactant and product states, however, the SRP is almost completely along s with little solute torsional motion. This indicates that the solvent orientational polarization fluctuation is important in initiating the TICT reaction. By contrast, for faster solvents (on the same surface), the SRP becomes nearly parallel to s at the transition state, while it is almost along θ near the reactant and product states. Thus the reactive mode relevant for electron transfer at the transition state changes markedly with the solvent time scale. The consequences of the SRP curvature on the TICT rate constant and its contrasts with traditional activated electron transfer are also discussed. The SRP analysis also shows that the dynamics relevant for TDF vary during the course of the reaction. In particular, for DMABN in acetonitrile solvent, about the first 70% of the dynamic Stokes shift upon photoexcitation occurs mainly via the solute torsional dynamics with a minor s participation, followed by the remaining relaxation along s with a minimal θ motion near the perpendicular geometry. Thus the TDF dynamics probed via DMABN involve the solute twisting dynamics as well as the solvation dynamics; the former dominates at the early and middle stages of TDF until the latter eventually takes over towards the end. As the solvent becomes faster, the solvent motions begin to participate in the TDF dynamics progressively earlier; as a result, the TDF probes the concomitant motions of both the solute and solvent. This picture provides a theoretical explanation for the recent experimental findings that the dynamic Stokes shift measured with DMABN is much faster than that with coumarin dyes (with no torsional degrees of freedom) for the same solvents. Finally, it is found that the variations of the activation free energy with solvent polarity and overall reaction free energetics correlate well with Hammond postulate behavior and experimentally observed trends for activated TICT reactions.

Bihalide ion combination reactions in solution: electronic structure and solvation aspects

The Kim—Hynes theory for electronic structure for reaction systems in solution is applied to the reaction class of the title, focusing on the I - +I → I 2 - reaction in acetonitrile solvent from a valence bond perspective. The transition between a delocalized electronic structure at small internuclear separations r to localized structures at large r is described in terms of a two-dimensional nonequilibrium free energy surface; the second coordinate is a solvent coordinate gauging the state of the solvent orientational polarization. The reaction path on this surface is described, and is contrasted with an equilibrium solvation perspective. An important focus is the polarization force, defined as the force on the diatomic ion coordinate r due to the solvent, which arises from the charge shifting, or electronic structure change, in the solute system along the reaction coordinate. It is argued that this force should play a significant role in the vibrational relaxation of the I 2 - ion.