An earlier time-dependent quantum wave packet propagation study of the photochemistry of Ph-OH [J. Chem. Phys. 2005, 122, 224315] is extended to investigate isotope effects (for Ph-OD) and the dynamics initiated by direct (vibronically induced) excitation to the (1)πσ* state. The isotope effect is significant only when the initially excited state is (1)ππ*, that is, there are noticeable changes not only in the time scale but also in the branching ratio (Ã/X̃) for the electronic states of the product Ph-O radical. In contrast, the isotope effect on the dynamics initiated by direct excitation to the (1)πσ* state is very small. Our most important observation for the dynamics initiated by direct excitation to the (1)πσ* state is that the initial excitation of the O-H stretch mode does not result in a noticeable enhancement of the product Ph-O radical in the à state, which corresponds to a dissociating H atom with low kinetic energy. The initial excitation of the CCOH torsion mode is the main reason for the enhancement of the product Ph-O radical in the à state that was observed in a vibrationally mediated two-photon experiment [J. Chem. Phys.2008, 128, 104307].

A very simple equation, F=[(∂(V-V)/∂Q)/(V-V)]/2, giving a reliable magnitude of non-adiabatic coupling terms (NACTs, F's) based on adiabatic potential energies only (V and V) was discovered, and its reliability was tested for several prototypes of same-symmetry interstate crossings in LiF, C, NHCl, and CHSH molecules. Our theoretical derivation starts from the analysis of the relationship between the Lorentzian dependence of NACTs along a diabatization coordinate and the well-established linear vibronic coupling scheme. This analysis results in a very simple equation, α=2κ/Δ, enabling the evaluation of the Lorentz function α parameter in terms of the coupling constant κ and the energy gap Δ (Δ=|V-V| ) between adiabatic states at the crossing point Q. Subsequently, it was shown that Q corresponds to the point where F exhibit maximum values if we set the coupling parameter as κ=[(V-V)⋅(∂(V-V)/∂Q)]/2. Finally, we conjectured that this relation could give reasonable values of NACTs not only at the crossing point but also at other geometries near Q. In this final approximation, the pre-defined crossing point Q is not required. The results of our test demonstrate that the approximation works much better than initially expected. The present new method does not depend on the selection of an ab initio method for adiabatic electronic states but is currently limited to local non-adiabatic regions where only two electronic states are dominantly involved within a nuclear degree of freedom.

The photodissociation dynamics of thiophenol (PhSH) excited to the 1(1) ππ* state was investigated by time-dependent quantum wavepacket propagation within two-dimensional (2D) space consisting of the S-H bond and -SH torsion. We systematically studied the dependence of the branching ratio (Ã/X(~)) between the two electronic states of the phenylthiyl radical (PhS(.) ) on several factors of the 2D potential energy surfaces (PESs). The effect of a reduced initial barrier to the first ππ*/πσ* conical intersection (CI) was found to be marginal, whereas the effects of a reduced torsional barrier of -SH on the excited ππ* state and the mitigated slope of the πσ* PES between the first (ππ*/πσ*) and the second (πσ*/S0 ) CIs were noticeable. The effect of the slope on the branching ratio has never been previously noticed. It was shown that the branching ratio can be sufficiently above unity without pre-excitation of the torsion mode of -SH, which has been assumed so far.

A fixed relation of α × β = 1.397 between the α- and β-parameters of a Lorentz function and a Laplace function that approximates nonadiabatic coupling terms and maximizes the overlap area between the two functions was found. The mixing angle corresponding to the geometric average between the potential couplings calculated using the individual path-integral of the two functions was then used in the construction of diabatic states and the coupling of the states. Employing the new method, the actual computation of nonadiabatic coupling terms at just a few geometries before and after the guessed conical intersection is enough, and the remaining steps are straightforward and almost automatic. The new method was tested for the one-dimensional LiF system and the two-dimensional space of the collinear case of NH3Cl, and promising results were achieved.

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