Controlling quantum wavepacket motion in reduced-dimensional spaces: reaction path analysis in optimal control of HCN isomerization

112

The general approach to classical unimolecular reaction rates due to Thiele is revisited in light of recent advances in the phase space formulation of transition state theory for multidimensional systems. Key concepts, such as the phase space dividing surface separating reactants from products, the average gap time, and the volume of phase space associated with reactive trajectories, are both rigorously defined and readily computed within the phase space approach. We analyze in detail the gap time distribution and associated reactant lifetime distribution for the isomerization reaction HCN CNH, previously studied using the methods of phase space transition state theory. Both algebraic ͑power law͒ and exponential decay regimes have been identified. Statistical estimates of the isomerization rate are compared with the numerically determined decay rate. Correcting the RRKM estimate to account for the measure of the reactant phase space region occupied by trapped trajectories results in a drastic overestimate of the isomerization rate. Compensating but as yet not fully understood trapping mechanisms in the reactant region serve to slow the escape rate sufficiently that the uncorrected RRKM estimate turns out to be reasonably accurate, at least at the particular energy studied. Examination of the decay properties of subensembles of trajectories that exit the HCN well through either of two available symmetry related product channels shows that the complete trajectory ensemble effectively attains the full symmetry of the system phase space on a short time scale t Շ 0.5 ps, after which the product branching ratio is 1:1, the "statistical" value. At intermediate times, this statistical product ratio is accompanied by nonexponential ͑nonstatistical͒ decay. We point out close parallels between the dynamical behavior inferred from the gap time distribution for HCN and nonstatistical behavior recently identified in reactions of some organic molecules.

Section: Introductionmentioning

confidence: 99%

Microcanonical rates, gap times, and phase space dividing surfaces

Ezra

Waalkens

Wiggins

2009

112

“…Furthermore, the analysis of the population dynamics showed that the mechanism can be understood as an essentially one-dimensional ͑1D͒ process along the reaction coordinate, which predominantly involves bend motion. 2, 3 These findings set the stage for the present paper. We replace the internal pump-dump mechanism by a pumpdump setup 7,8 using pairs of single-lobe half-cycle pulses 9 with variable time-delay.…”

Section: Introductionmentioning

confidence: 93%

Molecular isomerization induced by ultrashort infrared pulses. II. Pump–dump isomerization using pairs of time-delayed half-cycle pulses

Uiberacker

Jakubetz

2004

We investigate population transfer across the barrier in a double-well potential, induced by a pair of time-delayed single-lobe half-cycle pulses. We apply this setup both to a one-dimensional (1D) quartic model potential and to a three-dimensional potential representing HCN-->HNC isomerization. Overall the results for the two systems are similar, although in the 3D system some additional features appear not seen in the 1D case. The generic mechanism of population transfer is the preparation by the pump pulse of a wave packet involving delocalized states above the barrier, followed by the essentially 1D motion of the delocalized part of wave packet across the barrier, and the eventual de-excitation by the dump pulse to localized states in the other well. The correct timing is given by the well-to-well passage time of the wave packet and its recurrence properties, and by the signs of the field lobes which determine the direction and acceleration or deceleration of the wave packet motion. In the 3D system an additional pump-pump-dump mechanism linked to wave packet motion in the reagent well can mediate isomerization. Since the transfer time and the pulse durations are of the same order of magnitude, there is also a marked dependence of the dynamics and the transfer yield on the pulse duration. Our analysis also sheds light on the pronounced carrier envelope phase dependence previously observed for isomerization and molecular dissociation with one-cycle and sub-one-cycle pulses.

“…As our specific model system, we have chosen the HCN→HNC isomerization, which has become a prototype system for the simulation of laser-controled isomerization reactions. [6][7][8][9][10] However, due to the formal similarity of the respective Hamiltonians our analysis should also apply to other reactions involving vibrationally excited states, and more generally to other problems involving barrier crossing in double well potentials. Indeed the spirit of our investigation is that of a model treatment: we put our emphasis on the principles of the action of few-cycle pulses in double-well systems and on the response of the dynamical behavior to variations of the laser-and system-parameters.…”

Section: Introductionmentioning

confidence: 98%

Molecular isomerization induced by ultrashort infrared pulses. I. Few-cycle to sub-one-cycle Gaussian pulses and the role of the carrier-envelope phase

Uiberacker

Jakubetz

2004

Using 550 previously calculated vibrational energy levels and dipole moments we performed simulations of the HCN-->HNC isomerization dynamics induced by sub-one-cycle and few-cycle IR pulses, which we represent as Gaussian pulses with 0.25-2 optical cycles in the pulse width. Starting from vibrationally pre-excited states, isomerization probabilities of up to 50% are obtained for optimized pulses. With decreasing number of optical cycles a strong dependence on the carrier-envelope phase (CEP) emerges. Although the optimized pulse parameters change significantly with the number of optical cycles, the distortion by the Gaussian envelope produces nearly equal fields, with a positive lobe followed by a negative one. The positions and areas of the lobes are also almost unchanged, irrespective of the number of cycles in the half-width. Isomerization proceeds via a pump-dumplike mechanism induced by the sequential lobes. The first lobe prepares a wave packet incorporating many delocalized states above the barrier. It is the motion of this wave packet across the barrier, which determines the timing of the pump and dump lobes. The role of the pulse parameters, and in particular of the CEP, is to produce the correct lobe sequence, size and timing within a continuous pulse.