  By variational Monte-Carlo method developed Ceperley et al. for the
simulation of fermi systems in macroscopic confining potential well we simulate
various spin ground states of the coulomb clusters with 2,3 and 4 particles in
a broad two-dimensional (2D) parabolic well. In this method quantum state
numbers determining the variational wave function are not the numbers of well
quantum states but numbers of the equilibrium spatial positions of particles
that give a minimum of the system potential energy. The ground states with
parallel, antiparallel spins and as well, as bose state are simulated. For the
cluster with three particles it is also simulated the state when two particles
have one direction of spin and third opposite. The simulation shows that
clusters with parallel spins have lower ground state energy than clusters with
other spin configurations and bose state. That reminds a Hund's rule in atomic
physics when in not full filled atomic shells electrons prefer to have a state
with parallel spins.
