  The existence of permanent electric dipole moments (EDMs) and magnetic
quadrupole moments (MQMs) violate both time reversal invariance ($T$) and
parity ($P$). Following the $CPT$ theorem they also violate combined $CP$
symmetry. Nuclear EDM are completely screened in atoms and molecules while
interaction between electrons and MQM creates atomic and molecular EDM which
can be measured and used to test CP-violation theories. Nuclear MQM are
produced by the nucleon-nucleon $T,P$-odd interaction and by nucleon EDM. In
this work we study the effect of enhancement of the nuclear MQM due to the
nuclear deformation. Using the Nilsson model we calculate the nuclear MQMs for
deformed nuclei of experimental interest and the resultant MQM energy shift in
diatomic molecules of experimental interest $^{173}$YbF , $^{177,179}$HfF$^+$,
$^{181}$TaN, $^{181}$TaO$^+$, $^{229}$ThO and $^{229}$ThF$^+$.
