Two topics will be covered in this lecture: (i) The visualization and
analysis of electronic motion by means of the so-called electron
localization function (ELF), and (ii) optimal control theory of
electronic dynamics. The ELF provides a way to visualize chemical bonds.
It is derived from the conditional probability of finding an electron in
the vicinity of a point r if one knows with certainty that there is
another electron with the same spin at r. The shape of the ELF (as
function of r) allows a topological classification of the different
types of chemical bonds [1]. Here we generalize the ELF to the
time-dependent case [2]. Two movies of the time-dependent ELF will be
presented, one that shows the formation and breaking of chemical bonds
in a proton-ethylene scattering process and another one that visualizes
a laser-induced π-π* transition in acetylene in a time-resolved
fashion.
In the context of optimal control we first present two generalizations
of the standard formulation [3] of optimal-control theory: The first
generalization [4] allows the calculation of optimized pulses with
frequency constraints. The second generalization [5] achieves the
optimization of time-dependent control targets. The
latter allows one to drag the density of the system along a
given trajectory, as shown in the figure above.
Finally, some aspects of marrying optimal control theory with
time-dependent density functional theory will be discussed.
[1] A. Savin et al, Angew. Chem. 36, 1808 (1997).
[2] T. Burnus, M.A.L. Marques, E.K.U. Gross, Phys. Rev. A (Rapid Comm.)
71, 010501 (2005).
[3] W. Zhu, J. Botina, H. Rabitz, J. Chem. Phys.
108, 1953 (1998).
[4] J. Werschnik, E.K.U.Gross, J. Opt. B 7, S300
(2005).
[5] I Serban, J. Werschnik, E.K.U.Gross Phys. Rev. A
71, 053810 (2005).
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