  Background: Applications of nuclear time-dependent density functional theory
(TDDFT) are often capable of providing quantitative description of heavy ion
reactions. However, the structure of pre-compound states produced in heavy ion
reactions are difficult to assess theoretically in TDDFT as the s.p. density
alone is a weak indicator of shell structure and cluster states. Purpose: We
employ the time-dependent nucleon localization function (NLF) to reveal
structure of pre-compound states in nuclear reactions involving light and
medium-mass ions. We primarily focus on spin saturated systems with N = Z.
Furthermore, we study reactions with oxygen and carbon ions, for which
experimental evidence for {\alpha} clustering in pre-compound states exists.
Method: We utilize the symmetry-free TDDFT approach and compute the NLFs to
describe $^{16}$O + $^{16}$O, $^{40}$Ca + $^{16}$O, $^{40}$Ca + $^{40}$Ca, and
$^{16,18}$O + $^{12}$C collisions at energies above the Coulomb barrier.
Results: We show that NLFs reveal a variety of time-dependent modes involving
cluster structures. For instance, the $^{16}$O + $^{16}$O collision results in
a vibrational mode of a quasi-molecular \alpha-$^{12}$C-$^{12}$C-\alpha{}
state. For heavier ions, a variety of cluster configurations are predicted. For
the collision of $^{16,18}$O + $^{12}$C, we showed that the pre-compound system
has a tendency to form {\alpha} clusters. This result supports the experimental
findings that the presence of cluster structures in the projectile and target
nuclei gives rise to strong entrance channel effects and enhanced {\alpha}
emission. Conclusion: The time-dependent NLF is a good indicator of clusters
structures in complex pre-compound states formed in heavy-ion fusion reactions.
The localization reveals the presence of collective vibrations involving
cluster structures, which dominate the initial dynamics of the fusing system.
