  The spin-dependent trial wave functions with rotational symmetry are
introduced to describe rotating Wigner molecular states with spin degree of
freedom in four- and five-electron quantum dots under magnetic fields. The
functions are constructed with unrestricted Hartree-Fock orbits and projection
technique in long-range interaction limit. They highly overlap with the
exact-diagonalized ones and give the accurate energies in strong fields. The
zero points, i.e. vortices of the functions have straightforward relations to
the angular momenta of the states. The functions with different total spins
automatically satisfy the angular momentum transition rules with the increase
of magnetic fields and explicitly show magnetic couplings and characteristic
oscillations with respect to the angular momenta. Based on the functions, it is
demonstrated that the entanglement entropies of electrons depend on the
z-component of total spin and rise with the increase of angular momenta.
