  The performance of time-independent, orbital optimized calculations of
excited states is assessed with respect to charge transfer excitations in
organic molecules in comparison to the linear-response time-dependent density
functional theory (TD-DFT) approach. A direct optimization method to converge
on saddle points of the electronic energy surface is used to carry out
calculations with the local density approximation (LDA) and the generalized
gradient approximation (GGA) functionals PBE and BLYP for a set of 27
excitations in 15 molecules. The time-independent approach is fully variational
and provides a relaxed excited state electron density from which the extent of
charge transfer is quantified. The TD-DFT calculations are generally found to
provide larger charge transfer distances compared to the orbital optimized
calculations, even when including orbital relaxation effects with the Z-vector
method. While the error on the excitation energy relative to theoretical best
estimates is found to increase with the extent of charge transfer up to ca.
$-2$ eV for TD-DFT, no correlation is observed for the orbital optimized
approach. The orbital optimized calculations with the LDA and the GGA
functionals provide a mean absolute error of $\sim$0.7 eV, outperforming TD-DFT
with both local and global hybrid functionals for excitations with long-range
charge transfer character. Orbital optimized calculations with the global
hybrid functional B3LYP and the range-separated hybrid functional CAM-B3LYP on
a selection of states with short- and long-range charge transfer indicate that
inclusion of exact exchange has a small effect on the charge transfer distance,
while it significantly improves the excitation energy, with the best performing
functional CAM-B3LYP providing an absolute error typically around 0.15 eV.
