Polyelectronic systems excited states

Quantum mechanics has made important contributions to the development of theoretical chemistry, e.g. the concept of quantum mechanical resonance in the interpretation of the perturbation in the excited states of polyelectronic systems, the concept of exchange in the formation of a covalent bond, the concept of non-localized bonds (though, in my view, unsatisfactory and only arising from a neglect of electronic repulsions), the concept of dispersion forces etc., but it is noteworthy that all these ideas owe their success and justification to their ability to account qualitatively for previously unexplained experimental facts rather than to their quantitative mathematical aspect. 

In a series of papers since 1993-1994, we have demonstrated that it is possible to solve quantitatively a variety of TDMEPs in atoms and small molecules, by expanding the nonstationary in terms of the state-specific wavefunc-tions for the discrete and the continuous energy spectrum of the unperturbed system. This SSEA to the solution of the TDSE bypasses the serious, and at present insurmountable, difficulties that the extensively used "grid" methods have, when it comes to solving problems with arbitrary polyelectronic, ground or excited states. Furthermore, it allows, in a transparent and systematic way, the monitoring and control of the dependence of the final resulfs on the type and number of fhe sfafionary states that enter into the expansion that defines fhe wavepackef 4>(f). 

With the above introduction to excited state electronic structure and having established the notation conventions to be used from now on, we can begin to deal with state manifolds of polyelectronic systems. Before we proceed to do so, we note parenthetically the lucid discussion and ingenius utilization of the "two electron-... 

A much harder calculation of coherenf fime-dependent excitation and decay in a polyelectronic, open-shell system was published in 2007 [118]. Specifically, as a prototypical application of the SSEA to a complex system, we chose the problem of the time-resolved coherent excitation and decay of the 2s-hole ls 2s2p 3s 3p P° Auger states of Aluminum, where the dominant channels representing one- as well as two-electron continua are taken into account. In the following paragraphs, we explain how these computations were done. 

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