Fits to the Potential
The ab initio points for the A1Πu and X1Σg+ states were individually fitted to the simple polynomial form:
The ± sign refers to the upper and lower surfaces of the A1Πu state. The fits are still being finalised, but we have already achieved excellent results.
For the ground state, we have 443 ab initio points sampling the potential up to 10 000 cm-1 and 28 potential parameters can fit the surface with an average error of 24 cm-1. This surface can reproduce the 85 observed J = 0 and 1 vibrational levels up to 7500 cm-1 above the zero point level (at 1715 cm-1) with an average error of 24 cm-1. Fitting with 7 of the more significant parameters reduces the average error to 5 cm-1.
For the excited state we fitted 205 points up to 4650 cm-1 (to avoid the first crossing) for the lower (antisymmetric surface) with an average error of 36 cm-1 with 19 potential parameters. The upper (symmetric) surface could then be reproduced over the same energy range by allowing just three of the potential energy terms to vary. The resulting parameters could fit the 39 of observed vibrational levels with < 2170 cm-1 of vibrational energy with an average error of 26 cm-1 (the zero point energy is 965 cm-1). Allowing 6 of the more important to float reduces the average error to 4.5 cm-1.