  In \cite{duck-merle}, T. Duyckaerts and F. Merle studied the variational
structure near the ground state solution $W$ of the energy critical NLS and
classified the solutions with the threshold energy $E(W)$ in dimensions
$d=3,4,5$ under the radial assumption. In this paper, we extend the results to
all dimensions $d\ge 6$. The main issue in high dimensions is the non-Lipschitz
continuity of the nonlinearity which we get around by making full use of the
decay property of $W$.
