Laser-driven Intramolecular Hydrogen Transfer

The conceptionally simplest approach for IR-driven HT, the pump-dump scheme [45], can be illustrated using a one-dimensional double minimum potential as shown in Fig. 4.1. First we notice that the potential is asymmetric which allows one to distinguish between the initial state S and the final state S f of the HT reaction. Initially a pump-pulse excites the system from the localized ground state S to a delocalized intermediate state which usually is energetically above the reaction barrier. From there a second pulse dumps the system into the product 

Here Ef is the amplitude, t the duration, and co the frequency of the ith pulse. This scheme has been applied in Ref [46] to a generic two-dimensional HT model which incorporated a H-atom reaction coordinate as well as a low-frequency H-bond mode. In a subsequent work [47] the approach has been specified to a simple model of HT in thioacetylacetone. The Hamiltonian was tailored to the form of Eq. (4.1) based on the information available for the stationary points, that is, the energetics as well as the normal modes of vibration. From these data an effective two-dimensional potential was constructed including the H-atom coordinate as well as a coupled harmonic oscillator, which describes the 0-S H-bond motion. Although perhaps oversimplified, this model allowed the study of some principle aspects of laser-driven H-bond motion in an asymmetric low-barrier system. 

A field like Eq. (4.3) with separate and overlapping pulses is capable of giving an almost 100% population transfer. This above-the-barrier mechanism is also obtained when using the more sophisticated optimal control theory. Here the laser pulse form is obtained from maximizing the functional (see, e.g.. Ref [48]) 

The pulse forms in the simplest case where only the two lowest states are involved in the through-the-barrier tunneling dynamics are of plateau type see Fig. 4.2. They serve to compensate for the potential asymmetry (initial rise), facilitate tunneling (plateau phase), and restore the asymmetry to stabilize the products (switch-off phase). It turns out that more realistic few-cycle pulses may realize the same net effect although not in the step-wise fashion as a plateau pulse [47, 51, 52]. In Fig. 4.3 we show such a few-cycle pulse together with the population dynamics of the two lowest states of a double minimum potential adapted to the situation in thioacetylacetone. 

The influence of the interaction with an environment on the control yield and pathways can be modeled using different strategies. In principle it is possible to determine optimized pulses in the presence of energy and phase relaxation [12, 

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