P. Dupre, R. Jost, M. Lombardi, P. G. Green, E. Abramson,
and R. W. Field have observed anomalous behavior of the
anticrossing density in the Zeeman anticrossing (ZAC)
spectra of gas phase A ^{1}A_{u} acetylene
in the 42200 to 45300 cm^{-1} energy range. To best
explain this result, they hypothesize a large
singlet-triplet coupling due to the existence of a linear
isomerization barrier connecting a triplet-excited cis- and
trans-acetylene in the vicinity of the studied energy range
(~45500 cm^{-1}). Theoretically such a linear
stataionary point, however, must have two different
degenerate bending vibrational frequencies which are either
imaginary or exactly zero. Neither case has yet been
experimentally detected. Here we have studied the two
lowest-lying linear triplet-excited-state stationary points
of acetylene, ^{3}Sigma_{u}^{+} and
^{3}Delta_{u}, to see if they fit Dupre et
al.'s hypothesis. We have completed geometry optimization
and harmonic vibrational frequency analysis using
complete-active-space self-consistent-field (CASSCF)
wavefunctions as well as determined energy points at those
geometries using the second-order configuration interaction
(SOCI) method. Harmonic vibrational analyses of both
stationary points reveal two different doubly-degenerate
vibrational modes with imaginary vibrational frequencies
(or negative force constants) indicating that they are
indeed saddle points with a Hessian index of four. At the
DZP SOCI//CASSCF level of theory with zero-point
vibrational energy (ZPVE) correction, the ^{
3}Sigma_{u}^{+} stationary point lies
35840 cm^{-1} above the ground state of acetylene.
This is much too low in energy to contribute to the ZAC
spectral anomaly. At the same level of theory with ZPVE
correction, the ^{3}Delta_{u} stationary
point lies 44940 cm^{-1} above the ground state
consistent with Dupre et al.'s hypothesis. Several
solutions to the anomalous ZAC spectra are discussed. We
propose that the anomaly may also be due to the coupling
with a nearly linear structure on the T_{3} surface
of acetylene.