The cis-trans isomerization reaction on the T2 surface of acetylene and the lowest excited singlet state of acetylene, A 1Au, are investigated by ab initio electronic structure theory. We report optimized geometries, dipole moments, and harmonic vibrational frequencies of stationary points and adiabatic energy differences between them using basis sets as large as triple-zeta plus double polarization with higher angular momentum functions, TZ(2df,2pd), and theoretical methods up to coupled-cluster singles and doubles with perturbative triples correction [CCSD(T)] and the equation-of-motion coupled-cluster method (EOM-CCSD). Our theoretical predictions should aid the interpretation of observations from a series of recent spectroscopic studies involving excited electronic states of acetylene. In particular, the present theoretical results rule out several possible explanations for the anomalous sudden increase in detectable Zeeman anticrossings reported by Dupre et al. [Chem. Phys. 152, 293 (1991)].