Molecular dynamics control theory applications

The methodology used in calculations of the field required to maximize a particular product yield is optimal control theory. The first application of a full version of optimal control theory to the quantum dynamics of molecular... 

The approach has been tested by controlling nuclear wavepacket motion in a two-dimensional model system [23], The relative simplicity of the system makes it possible to compare the semiclassical results with exact quantum ones. Numerical applications to the control of HCN-CNH isomerization [24] demonstrates that the new semiclassical formulation of optimal control theory provides an effective and powerful tool for controlling molecular dynamics with many degrees of freedom. 

As will be shown throughout this book, quantum control of molecular dynamics has been applied to a wide variety of processes. Within the framework of chemical applications, control over reactive scattering has dominated. In particular, the two primary chemical processes focused upon are photodissociation, in which a molecule is irradiated and dissociates into various products, and bimolecular reactions, in which two molecules collide to produce new products. In this chapter we formulate fie quantum theory of photodissociation, that is, the light-induced breaking of a chemical bond. In doing so we provide an introduction to concepts essential for the 1 remainder of this book. The quantum theory of bimolecular collisions is also briefly ydiscussed. 

Bandemer considered the role of fuzzy set theory in analytical chemistry. The applications they described focused on pattern recognition problems, the calibration of analytical methods,quality control, and component identification and mixture evaluation. Gordon and Somorjai applied a fuzzy clustering technique to the detection of similarities among protein substructures. A molecular dynamics trajectory of a protein fragment was analyzed. In the following subsections, some applications based on the hierarchical fuzzy clustering techniques presented in this chapter are reviewed. 

Analysis and control of ultrafast processes in atomic clusters in the size regime in which each atom counts are of particular importance from a conceptual point of view and for opening new perspectives for many applications in the future. Simultaneously, this research area calls for the challenging development of theoretical and computational methods from different directions, including quantum chemistry, molecular dynamics, and optimal control theory, removing borders between them. Moreover, it provides stimulation for new experiments. 

A different theory of local control has been derived from the viewpoint of global optimization, applied to finite time intervals [58-60]. This approach can also be applied within a classical context, and local control fields from classical dynamics have been used in quantum problems [61]. In parallel, Rabitz and coworkers developed a method termed tracking control, in which Ehrenfest s equations [26] for an observable is used to derive an explicit expression for the electric field that forces the system dynamics to reproduce a predefined temporal evolution of the control observable [62, 63]. In its original form, however, this method can lead to singularities in the fields, a problem circumvented by several extensions to this basic idea [64-68]. Within the context of ground-state vibration, a procedure similar to tracking control has been proposed in Ref. 69. In addition to the examples already mentioned, the different local control schemes have found many applications in molecular physics, like population control [55], wavepacket control [53, 54, 56], control within a dissipative environment [59, 70], and selective vibrational excitation or dissociation [64, 71]. Further examples include isomerization control [58, 60, 72], control of predissociation [73], or enantiomer control [74, 75]. 

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