Initial state-selected time-dependent

Abstract. Over the last deeade, advances in quantum dynamics, notably the development of the initial state selected time-dependent wave packet method, coupled with advances in constructing ab initio potential energy surfaces, have made it possible for some four-atom reactions to be addressed from first principles, in their full six internal degrees of freedom. Attempts have been made to extend the time-dependent wave packet method to reactions with more internal degrees of freedom. Here, we review the full-dimensional theory for the A + BCD four-atom reaction and use it to guide the reduced-dimensionality treatment of the X + YCZ3 reaction. Comparison of rigorous calculations with recent experiments are presented for (a) the benchmark H + H2O abstraction reaction, and (b) the H + CH4 H2 + CH3 reaction. 

The initial state-selected total dissociation probability of the diatom is obtained by projecting out the energy-dependent reactive flux. If i /,) denotes the time-independent (TI) full scattering wavefunction, where the labels i and E denote the initial state and energy, the total dissociation probability from an initial state i can be obtained by the flux formula (95). We choose the diatomic distance r to be the 5 coordinate in Eq. (96). The full TI scattering wave function is normalized as (if/,) NV/. ) = 2/nhh(E - E ). The total dissociation probability, according to Eq. (98), is given by... 

In principle, time dependent formulations exist for computing the cumulative reaction probability [16, 17] and the thermal reaction rate constant [16]. However, an efficient implementation which gives results at many energies or temperatures, respectively, is difficult because of the mixed state nature of these dynamical quantities. On the other hand, efficient time dependent wavepacket ABC formulations exist for computing the state-to-state reaction amplitude [10] and the initial state selected reaction probabihty [15]. Thus, if one is interested in state resolved reaction probabilities for systems which form long lived collision complexes, the time dependent wavepacket ABC formulation is advocated. 

It can be seen from this figure that the steady state production of nitrosobenzene is preceded by an induction period, in which aniline is the main product. Further, small amounts of azobenzene and azoxybenzene are formed throughout the reaction. The existence of an autoredox reaction implies that a selectivity of 100% from nitrobenzene to nitrosobenzene is impossible. After the induction period the selectivity of nitrobenzene to nitrosobenzene becomes above 90% of the reduction products. The extent of conversion of nitrobenzene is also time dependent. In the steady state situation about 20% of the nitrobenzene is converted, after an initial conversion of 65%. 

Note added in proof It has come to our attention after this review was completed that the work by Holme and Hutchinson, (Ref. 28), accidentally neglected the time-dependent phase of the initial state prepared by the laser. This has been confirmed through private communication with the authors. As far as we know there is no physical justification for this neglect, which played a crucial role in the selectivity which they observed. 

These complementary experimental results can be explained to a great extent by quantum dynamical simulations of the real-time experiments. In Sect. 3.2.2, first the results obtained by means of two-dimensional (2d) ab initio potential-energy surfaces are briefly summarized. Even more sophisticated calculations are performed on three-dimensional (3d) ab initio potential-energy and transition dipole surfaces (Sect. 3.2.3). There, all three vibrational degrees of freedom of the Nas molecule are included in the theoretical treatment. The time-dependent wave packet dynamics elucidate the effect of ultrafast state preparation on the molecular dynamics. Extensive theoretical calculations indicate the possibility of initiating the molecular dynamics predominantly in selected modes during a certain time span by variation of the pump pulse duration (Sect. 3.2.4). 

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