Vibrational wavepacket evolution in parallel with superfast electron transfer reaction

An animation of the wavepacket dynamics along high- and low-frequency vibrational coordinates accompanying the transition from the reactant to the product state.

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This video provides a schematic visualization of the vibrational wavepacket evolution during the electron transfer (ET) reaction reported in our recent publication in Nature Chemistry. In this animation, we simplify the wavepacket as a classical particle traversing the two-dimensional energy landscape of the reactant and product states. The reactant (red) and product (yellow) potential energy surfaces (PESs) are plotted as a function of a high- and a low-frequency vibrational coordinates.

The initial state of the system, prepared by the laser pulse, is on the reactant state PES with the wavepacket nonstationary along the high-frequency coordinate and stationary along the low-frequency coordinate. This condition is represented by the classical particle located at a displaced position from its equilibrium position along the high-frequency coordinate. This initial non-equilibrium configuration serves as a driving force for the particle to roll along the high-frequency coordinate toward the curve crossing between the reactant and the product PESs. At the curve crossing intersection, the particle hops to the product potential well.

As soon as the particle hops, it is brought out of equilibrium along both high- and low-frequency coordinates on the product potential well. Therefore, the particle subsequently relaxes to its new equilibrium positions.  Due to the fast response of the high-frequency vibration, owing to its faster timescale, the particle relaxes much more quickly along this coordinate. The equilibration along the high-frequency coordinate is followed by relatively slower equilibration along the low-frequency coordinate due to its slower response. Note that, the equilibration terminology used here refers to the adjustment of the normal modes to new equilibrium positions associated with the product state. The response timescales of the particle along the two coordinates are assumed separated in the same spirit as the Born-Oppenheimer approximation. 

The visualization of the wavepacket dynamics could be better understood by watching the wavepacket evolution on the one-dimensional projected PESs along the high-and low-frequency coordinates separately. What becomes evident is that the high-frequency vibration actively drives the wavepacket toward the crossing for the hopping from the reactant to the product potential well, while, instead, the hopping along the low-frequency coordinate proceeds passively. By “passively”, we mean that it is the motion along the high-frequency coordinate that brings the particle to the crossing by modulating the gap of the projected PESs, while the position of the particle along the low-frequency coordinate is kept unchanged prior to the hopping. Once the system crosses passively to the product state along the low-frequency coordinate, the system starts equilibrating to the equilibrium position of the product potential well.

In summary, the high-frequency vibration brings the particle to the crossing point and thus drives the reaction. On the other hand, the low-frequency vibration is responsible for the observed vibrational wavepacket on the product potential well. The dissipation of the vibrational energy prevents the coherent recurrence of the reactant state. 

Read more at: Rafiq, S., Fu, B., Kudisch, B. & Scholes, G. D. Interplay of vibrational wavepackets during an ultrafast electron transfer reaction. Nat. Chem. (2020).

Shahnawaz Rafiq

Research Associate, Princeton University

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