  We use a color-magnetic interaction model (CMIM), a traditional constituent
quark model (CQM) and a multiquark color flux-tube model (MCFTM) to
systematically investigate the properties of the states
$[Q_1Q_2][\bar{Q}_3\bar{Q}_4]$ ($Q=c,b$). The dynamical investigation indicates
that the CMIM can not completely absorb QCD dynamical effects through the
effective constituent quark mass and overestimates the color-magnetic
interaction in the states under the assumption of the same spatial
configurations. The Coulomb interaction plays a critical role in the dynamical
model calculations on the heavy hadrons, which induces the fact that none of
bound states $[Q_1Q_2][\bar{Q}_3\bar{Q}_4]$ can be found in the dynamical
models. The color configuration
$\left[[Q_1Q_2]_{\mathbf{6}_c}[\bar{Q}_3\bar{Q}_4]_{\bar{\mathbf{6}}_c}\right]_{\mathbf{1}}$
should be taken seriously in the ground states due to the strong Coulomb
attraction between the $[Q_1Q_2]_{\mathbf{6}_c}$ and
$[\bar{Q}_3\bar{Q}_4]_{\bar{\mathbf{6}}_c}$. The color configuration
$\left[[Q_1Q_2]_{\bar{\mathbf{3}}_c}[\bar{Q}_2\bar{Q}_4]_{\mathbf{3}_c}\right]_{\mathbf{1}}$
is absolutely dominant in the excited states because of the strong Coulomb
attraction within the $[Q_1Q_2]_{\bar{\mathbf{3}}_c}$ and
$[\bar{Q}_2\bar{Q}_4]_{\mathbf{3}_c}$. The $J/\Psi$-pair resonances recently
observed by LHCb are difficult to be accommodated in the CMIM. The broad
structure ranging from 6.2 to 6.8 GeV can be described as the ground tetraquark
state $[cc][\bar{c}\bar{c}]$ in the various dynamical models. The narrow
structure $X(6900)$ can be identified as the excited state
$[cc][\bar{c}\bar{c}]$ with $L=1$ ($L=2$) in the CQM (MCFTM).
