Dupre, Jost, Lombardi, Green, Abramson, and Field [``DJLGAF,'' Chem. Phys. 152, 293 (1991)] noted anomalous behavior of the Zeeman anticrossing (ZAC) density of A ¹A_u acetylene as a function of excitation energy; they recorded their spectra with 0-3 quanta in the trans-bending normal mode nu₃ of the A state, covering an energy range of 42200 to 45300 cm^-1 above the rotationless zero-point level of the X ¹Sigma_g⁺ (S₀) ground state, and an unexpected sudden increase in the density of detectable anticrossings over this energy range was observed. DJLGAF found anticrossing densities too large to arise from singlet-triplet intersystem crossings, and they proposed that the anticrossing densities might be related to very highly excited vibrational levels of the S₀ electronic ground state. Direct S₀ ~ S₁ coupling was excluded due to the lack of a reasonable mechanism which would predict a sudden increase in coupling with increasing excitation energy. Furthermore, g/u selection rules forbid such direct couplings. Instead, the authors proposed a three-state model involving intermediating triplet states, i.e. S₁ ~ T ~ S₀, where the sudden increase in the density of detectable anticrossings is attributed to a sudden increase in singlet-triplet coupling strength.

Of the several possible mechanisms for a sudden increase in singlet-triplet couplings, DJLGAF contended that the most likely was the existence of a linear cis-trans isomerization barrier on T_i (i=1,2, or 3) which is approximately isoenergetic with the S₁ nu₃=3 level. The authors explain that such a barrier would lead to a sudden increase in S₁ ~ T coupling strength: near the top of an isomerization barrier on T_i, the overlap between the vibrational wavefunctions of S₁ trans and T_i cis increases rapidly as more quanta are placed in the nu₃ trans-bending mode of S₁ trans state. This is because the classical turning point traps increasingly larger fractions of the vibrational wavefunction as the number of quanta in the bending modes increases.

To shed more light on these intriguing experimental results, we carried out ab initio electronic structure computations on the two lowest-lying linear triplet electronic states of acetylene, ³Sigma_u⁺ and ³Delta_u [G. Vacek, C. D. Sherrill, Y. Yamaguchi, and H. F. Schaefer, J. Chem. Phys. 104, 1774 (1996)]. Double-zeta plus polarization (DZP) complete-active-space self-consistent-field (CASSCF) predictions indicate that the linear geometries of these two states are stationary points with two different degenerate imaginary bending vibrational frequencies. The ³Sigma_u⁺ state is the linear stationary point on the T₁ surface of acetylene, while the ³Delta_u state gives rise to the T₂ and T₃ surfaces via Renner-Teller splitting. More accurate theoretical energies predicted using multi-reference CISD indicate that the T₁ surface is too low in energy to account for the anomalous ZAC spectra. However, the predictions for the ³Delta_u state are in good agreement with the expected energy range of the linear barrier (predicted T₀ = 44940 cm^-1, compared to anomalous ZAC spectra in the 42200 to 45300 cm^-1 energy range). One unusual feature of attributing the observed spectroscopic anomalies to this structure is that it features two doubly-degenerate imaginary frequencies, and is hence a higher-order saddle point. To our knowledge, we are unaware of any compelling experimental evidence for the manifestations of a stationary point with Hessian index four.

Another possible explanation for the observed spetral anomalies is a half-linear transition state for cis-trans isomerization, since such a transition state might still trap a large amount of amplitude in the triplet vibrational wavefunctions near linear geometries. A previous study of isomerization on the T₁ surface found a half-bent transition state [G. Vacek, J. R. Thomas, B. J. DeLeeuw, Y. Yamaguchi, and H. F. Schaefer, J. Chem. Phys. 98, 4766 (1993)]. However, as mentioned before, the T₁ surface lies too low in energy to explain the ZAC anomalies.

We undertook a study of the T₂ surface to look for a similar half-bent transition state for cis-trans isomerization [C. D. Sherrill et al., J. Chem. Phys. 104, 8507 (1996)]. Polarized double and triple-zeta basis sets were used along with the CISD method as well as equation-of-motion (EOM) CCSD to study the excited state potential energy surface. Computations at these same levels of theory were obtained for the A ¹A_u state so that errors in the theoretical values would largely cancel when taking energy differences between the triplet and singlet states.

The ZPVE-corrected energy difference between the T₂ transition state and the A state at the TZ(2df,2pd) CISD+Q level of theory indicates that the transition state is too low in energy to contribute to the anomalous ZAC spectra. This conclusion is reinforced by evaluating the adiabatic excitation energy T₀ of the transition state at the TZ(2df,2pd) CCSD(T) level of theory and comparing to the experimental energy range of the nu₃=3 level of the A state. Hence, if the DJLGAF hypothesis is correct, then the sudden increase in S₁ ~ T_i coupling appears to involve the linear ³Delta_u state or a feature of the T₃ potential energy hypersurface.