The combination of time-dependent density functional theory and quantum optimal control formalism is used to optimize the shape of ultra-short laser pulses in order to achieve the photodissociation of the hydrogen molecule. The very short pulse durations used in this work (a few femtoseconds) do not allow for significant nuclear movement during irradiation, and thus the dissociation mechanism is sequential. During pulse irradiation, a large sudden momentum is communicated which can be understood in terms of population of excited, bound or unbound, dissociative electronic states. The target is defined in terms of the average opposing force during the action of the pulse, or equivalently, in terms of the final dissociative velocity.
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