  The tensor force, as an important component of strong nuclear force,
generates a variety of intriguing effects ranging from few-body systems to
neutron stars. It is responsible for the nucleon-nucleon correlation beyond
mean-field approximation, and is accordingly proved to play no role in the
standard Skyrme energy density functionals in the present work. Therefore, the
Skyrme's original tensor interaction that is extensively-employed presently is
invalid. As an alternative strategy, we introduced a central interaction, i.e.,
the $\bm{\sigma }_{1}\cdot \bm{\sigma }_{2}$ term, to improve the description
of experimental single-particle structure, and to address its effect, we
established two Skyrme interactions IMP1 and IMP2 complemented by the
calibrated charge-violating interactions. The central $\bm{\sigma }_{1}\cdot
\bm{\sigma }_{2}$ interaction turns out to substantially improve the
description of shell evolution in Sn isotopes and $N=82$ isotones.
