  We discuss a variational calculation for nuclear shell-model calculations and
propose a new procedure for the energy-variance extrapolation (EVE) method
using a sequence of the approximated wave functions obtained by the variational
calculation. The wave functions are described as linear combinations of the
parity, angular-momentum projected Slater determinants, the energy of which is
minimized by the conjugate gradient method obeying the variational principle.
The EVE generally works well using the wave functions, but we found some
difficult cases where the EVE gives a poor estimation. We discuss the origin of
the poor estimation concerning shape coexistence. We found that the appropriate
reordering of the Slater determinants allows us to overcome this difficulty and
to reduce the uncertainty of the extrapolation.
