On resonance-type effective vibrational Hamiltonians for CO2 II. Results Original Research Article

This is the second one of a series of two papers aimed at investigating the relation of resonance-type effective Hamiltonians to molecular potential energy surfaces (PES) for linear ABA triatomic molecules, and more precisely for CO2. Whereas the first paper dealt with the theoretical background, this paper contains explicit numerical results for CO2. A six-parameter PES is first fitted to 57 observed transition frequencies of 12CO2 and 13CO2 up to 8000 cm−1 above the ground state, using the fifth-order polynomial expansion of energy in terms of dimensionless coordinates. The average absolute error is 1.8 cm−1. The six parameters of the PES need only be varied by 3.1 times the uncertainty to minimize the errors for the single-resonance Hamiltonian (again 1.8 cm−1), which takes into account only the ϕ1 − 2ϕ2 Fermi term (the 1:2 stretch/bend resonance). In contrast, the variations are much larger if the energy is expanded up to only fourth order in dimensionless coordinates. Plots of quantum wavefunctions and Poincaré surfaces of section further indicate that the coordinates for the single-resonance Hamiltonian are rather far from those of the polynomial expansion. The second most important term is then shown to be the angle ϕ1. Again, the 6 parameters need only be varied by 4.1 times the uncertainty to minimize the error for the two-resonance Hamiltonian (2.1 cm−1), whereas the spectroscopic anharmonic parameters xij are shown to vary widely between the single- and the two-resonance Hamiltonians, sometimes by more than 25 cm−1. Moreover, quantum wavefunctions and classical SOS show that the coordinates of the two-resonance Hamiltonian are now close to those of the polynomial Hamiltonian. At least, a third angle ϕ1 + 2ϕ2 is taken into account, in order for the sets of coordinates of the effective and polynomial Hamiltonians to be in still better agreement, as demonstrated by Poincaré surfaces of section. Variations are only 2.1 times the uncertainties and the average error 2.1 cm−1. None of the anharmonic parameters varies by more than 2 cm−1 compared to the two-resonance approximation. Quite interestingly, the number of quanta in the antisymmetric stretching motion then remains a nearly good quantum number in the investigated energy range.