Nonadiabatic treatment of the intensity distribution in the V–N bands of ethylene

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Abstract
The V–N band system of ethylene between 6.0 and 8.5 eV has been investigated through ab initio nonadiabatic vibronic calculations. The N1(π2), V1(π,π*), and Ry1(π,3py) electronic states and energies involved in this transition have been calculated as functions of the torsional angle around the CC bond, at an extended CI level and the adiabatic torsional states have been expanded in a free‐rotor basis. The nonadiabatic states corresponding to the V and Ry species have then been expanded in the adiabatic electronic–torsional basis with the help of explicit calculations of the vibronic coupling functions. The V and Ry electronic states undergo a sharply avoided crossing and configurational mixing during the torsion and have a significant contribution from (π,ndπ) species, the lower state changing from Ry at D2h to V at the D2d conformation and the upper showing the opposite variation. The V–Ry vibronic couplings are thus quite large in the region of the avoided crossing and the nonadiabatic states above 7.5 eV are strongly mixed; by contrast the lowest‐lying species derive mainly from the π→π*V excitation. The computed 0–0 torsional origin at 6.00 eV and the following two levels are in very good agreement with the locations of the first three observed bands, whereas the deviations increase for higher levels in a regular way owing to a small overestimation of the computed ω4′ value; the discrete portion of the V–N system is well reproduced by the present calculations provided a renumbering of the observed bands is undertaken. The nonadiabatic coupling of the V and Ry states is very important near the intensity maximum of the V–N system, yielding a very diffuse intensity distribution in good agreement with the observed broad continuum. A theoretical progression shows two intensity maxima at 7.78 and 8.06 eV, somewhat above that deduced experimentally at 7.66 eV, which has been estimated by subtracting off the intensity of the sharp R 1(π, 3s)–N bands superimposed on the apparent continuum. Numerical tests show that the maximum at 8.06 eV is shifted to about 7.9 eV by taking into account some limitations of the present investigation. Finally, calculated vertical transition energies to various excited states of ethylene, obtained with a large AO basis set indicate that other Rydberg states should have nonadiabatic couplings in the 7.0–8.5 eV region with the electronic species here considered when antisymmetric vibrations are excited, thus leading to a further broadening of the V–N band system; accordingly a vibronically mixed Rx1(π,3px)–V1(π,π*) species is indicated as being the upper state in Wilkinson’s R′–N transition of T0 = 8.26 eV, as has earlier been suggested by various authors.