  We derive the crossing conditions at conical intersections between electronic
states in coupled cluster theory, and show that if the coupled cluster Jacobian
matrix is nondefective, two (three) independent conditions are correctly placed
on the nuclear degrees of freedom for an inherently real (complex) Hamiltonian.
Calculations using coupled cluster theory on an $2 {^{1}}A' / 3 {^{1}}A'$
conical intersection in hypofluorous acid illustrate the nonphysical artifacts
associated with defects at accidental same-symmetry intersections. In
particular, the observed intersection seam is folded about a space of the
correct dimensionality, indicating that minor modifications to the theory are
required for it to provide a correct description of conical intersections in
general. We find that an accidental symmetry allowed $1 {^{1}}A" / 2 {^{1}}A"$
intersection in hydrogen sulfide is properly described, showing no artifacts as
well as linearity of the energy gap to first order in the branching plane.
