@TechReport{ it:2009-022,
author = {Katharina Kormann and Sverker Holmgren and Hans O.
Karlsson},
title = {A {F}ourier-Coefficient Based Solution of an Optimal
Control Problem in Quantum Chemistry},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2009},
number = {2009-022},
month = sep,
abstract = {We consider an optimal control problem for the
time-dependent Schr{\"o}dinger equation modeling molecular
dynamics. Given a molecule in its ground state, the
interaction with a tuned laser pulse can result in an
excitation to a state of interest. By these means, one can
optimize the yield of chemical reactions. The problem of
designing an optimal laser pulse can be posed as an optimal
control problem. We reformulate the optimization problem by
Fourier-transforming the electric field of the laser and
narrow the frequency band. In this way, we reduce the
dimensionality of the control variable. This allows for
storing an approximate Hessian and, thereby, we can solve
the optimization problem with a quasi-Newton method. Such
an implementation provides superlinear convergence. We show
computational results for a Raman-transition example and
give numerical evidence that our algorithm can outperform
the standard Krotov-like method which does not employ
approximative second derivatives. \end{abstract} }
}