  Three more $X$ particles are established in the 2014 Particle Data compared
with the 2012 ones. There are now five established $X$ particles named as
$X(3872)$, $X(3900)$, $X(4260)$, $X(4360)$, and $X(4660)$. Since the first $X$
particle $X(3872)$ was discovered during the search for the remaining P
charmonium states, it is valuable to check whether the established $X$
particles can be explained by quarkonium model. In this paper, we try to
calculate the mass spectra of charmonium system by considering spin-dependent
forces deduced from one gluon exchange diagrams. The confining potential form
is taken to be linear and the free parameters are determined by least squares
method comparing the theoretical and the observed masses of charmonium states.
