A theoretical formulation for modeling photoinduced nonequilibrium proton-coupled electron transfer (PCET) reactions in solution is presented. In this formulation, the PCET system is described by donor and acceptor electron-proton vibronic free energy surfaces that depend on a single collective solvent coordinate. Dielectric continuum theory is used to obtain a generalized Langevin equation of motion for this collective solvent coordinate. The terms in this equation depend on the solvent properties, such as the dielectric constants, relaxation time, and molecular moment of inertia, as well as the solute properties characterizing the vibronic surfaces. The ultrafast dynamics following photoexcitation is simulated using a surface hopping method in conjunction with the Langevin equation of motion. This methodology is used to examine a series of model photoinduced PCET systems, where the initial nonequilibrium state is prepared by vertical photoexcitation from the ground electronic state to the donor electronic state. Analysis of the dynamical trajectories provides insight into the interplay between the solvent dynamics and the electron-proton transfer for these types of processes. In addition, these model studies illustrate how the coupling between the electron-proton transfer and the solvent dynamics can be tuned by altering the solute and solvent properties.

A new method which we refer to as vertical Franck-Condon is proposed to calculate electronic absorption spectra of polyatomic molecules. In accord with the short-time picture of spectroscopy, the excited-state potential energy surface is expanded at the ground-state equilibrium geometry and the focus of the approach is more on the overall shape of the spectrum and the positions of the band maxima, rather than the precise position of the 0-0 lines. The Born-Oppenheimer approximation and the separability of the excited-state potential energy surface along the excited-state normal mode coordinates are assumed. However, the potential surface is not necessarily approximated as harmonic oscillator potentials along the individual normal modes. Instead, depending upon the nature of the potential surface along a particular normal mode, it is treated either in the harmonic approximation or the full one-dimensional potential is considered along this mode. The vertical Franck-Condon approach is applicable therefore even in cases where the excited state potential energy surface is highly anharmonic and the conventional harmonic Franck-Condon approach is inadequate. As an application of the method, the ultraviolet spectrum of ethylene between 6.2 eV (50,000 cm(-1)) and 8.7 eV (70,000 cm(-1)) is simulated, using the Similarity Transformed Equation of Motion Coupled-Cluster method to describe the required features of the potential energy surfaces. The spectrum is shown to be a result of sharp doublet structures stemming from the pi --> 3s (Rydberg) state superimposed on top of a broad band resulting from the pi --> pi* (valence) state. For the Rydberg state, the symmetric C=C stretch and the torsion mode contribute to the spectrum, while the broad valence band results from excitation into the C=C stretch, CH2 scissors, and the torsion mode. For both states, the potential along the torsion mode is highly anharmonic and the full treatment of the potential along this mode in the vertical Franck-Condon method is required.

ABSTRACT:We present a simple derivation of a recursion formula for calculating harmonic Franck-Condon (FC) overlap integrals for polyatomic molecules. We also provide an efficient algorithm for computer implementation of the recursion formula. The algorithm resolves the problems associated with earlier implementations and has the following features: (1) It allows obtaining convergence of the series of FC overlap integrals to the degree desired (the measure of convergence is the sum of the FC factors, which is unity for the converged series); (2) the maximal number of quanta in the normal modes does not have to be specified a priori; (3) there is no computer memory bottleneck to do large FC calculations with many normal modes; (4) the algorithm uses binary trees to store data, thus making data retrieval fast and the algorithm highly efficient.

Transition metal and reductant free α-C(sp3)-H hydroxylation of carbonyl compounds are reported. This method is promoted by commercially available inexpensive KO-t-Bu and atmospheric air as an oxidant at room temperature. This unified strategy is also very facile for hydroxylation of various carbonyl compound derivatives to obtain quaternary hydroxyl compounds in excellent yield. A preliminary mechanistic investigation, supported by isotope labeling and computational studies, suggests the formation of a peroxide bond and its cleavage by in situ generated enolate.