Nuclear Wavepacket Dynamics at Surfaces

This chapter will first describe the principles of experimental techniques which enable us to study the nuclear wavepacket dynamics at surfaces. We focus... 

In this chapter we have surveyed recent experimental progress on the investigation of ultrafast nuclear wavepacket dynamics at surfaces. Nuclear (or vibrational) wavepackets of adsorbates are excited with ultrashort laser pulses, and subsequently their evolutions are probed with surface nonlinear spectroscopy such as 2PPE and SHG. These studies provide rich information on the initial stages of photoinduced... 

Nevertheless, detailed information on nudear wavepacket dynamics of surface adsorbates is important both from fundamental and from practical points of view. As is evidenced from the huge success of catalysis, solid surfaces sustain various kinds of reactions [8]. In order to understand the elementary steps of these reactions, the electronic and vibrational dynamics of surface adsorbates should be investigated in depth. Photochemistry at surfaces involves the photoinduced nuclear dynamics of adsorbates, which needs to be elucidated by ultrafast spectroscopy. Furthermore, combining with recently developed pulse shaping technologies [9], elucidation of the wavepacket dynamics will open up a novel laser control scheme of surface photochemical reactions. 

Quantum chemical methods, exemplified by CASSCF and other MCSCF methods, have now evolved to an extent where it is possible to routinely treat accurately the excited electronic states of molecules containing a number of atoms. Mixed nuclear dynamics, such as swarm of trajectory based surface hopping or Ehrenfest dynamics, or the Gaussian wavepacket based multiple spawning method, use an approximate representation of the nuclear wavepacket based on classical trajectories. They are thus able to use the infoiination from quantum chemistry calculations required for the propagation of the nuclei in the form of forces. These methods seem able to reproduce, at least qualitatively, the dynamics of non-adiabatic systems. Test calculations have now been run using duect dynamics, and these show that even a small number of trajectories is able to produce useful mechanistic infomiation about the photochemistry of a system. In some cases it is even possible to extract some quantitative information. 

The electronic energy thus computed at each molecular shape serves as a potential function working on nuclei, called (adiabatic) potential energy surface (PES), which drives nuclear wavepackets on it, and only in this stage time-variable is retrieved, to the time scale of nuclear dynamics mostly of the order of femtosecond. This is the standard theoretical framework for the study of the dynamics of molecules [59]. Very well structured and fast computer codes for quantum chemistry are now available, which can serve even as an alternative for experimental apparatus. 

Both the BO dynamics and Gaussian wavepacket methods described above in Section n separate the nuclear and electronic motion at the outset, and use the concept of potential energy surfaces. In what is generally known as the Ehrenfest dynamics method, the picture is still of semiclassical nuclei and quantum mechanical electrons, but in a fundamentally different approach the electronic wave function is propagated at the same time as the pseudoparticles. These are driven by standard classical equations of motion, with the force provided by an instantaneous potential energy function... 

Considering the dynamics of nuclei at the top of the barrier, it is impossible at these velocities to obtain such time scales if a wavepacket is moving translationally on a flat, one-dimensional surface. For example, over a distance of 0.5 A, which is significantly large on a bond scale, the time in the transition-state region will be -40 fs. The reported (sub)picosecond times therefore reflect the involvement of other nuclear degrees of freedom. 

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