  Cluster dynamics and single-particle correlation are simultaneously treated
for the description of the ground state of ${}^{12} \mathrm{C} $. The recent
development of the antisymmetrized quasi cluster model (AQCM) makes it possible
to generate $jj$-coupling shell-model wave functions from $\alpha$ clusters
models. The cluster dynamics and the competition with the $jj$-coupling
shell-model structure can be estimated rather easily. In the present study, we
further include the effect of single-particle excitation; the mixing of the
two-particle-two-hole excited states is considered. The single-particle
excitation is not always taken into account in the standard cluster model
analyses, and the two-particle-two-hole states are found to strongly contribute
to the lowering of the ground state owing to the pairing-like correlations. By
extending AQCM, all of the basis states are prepared on the same footing, and
they are superposed based on the framework of the generator coordinate method
(GCM).
