  We formulate a hyperspherical approach within standard configuration
interaction calculations aiming at a description of large-scale dynamics of
$N$-particle system. The channel wave function and the adiabatic channel energy
are determined by solving a hyperradius-constrained eigenvalue problem of the
adiabatic Hamiltonian. The needed matrix elements are analytically evaluated
using correlated Gaussians with good orbital angular momentum and parity. The
feasibility of the approach is tested in three-$\alpha$ system. A spectrum of
the adiabatic channel energies is determined depending on the degree of
localization of the basis functions.
