Anharmonic potential constants and the large amplitude bending vibration in nitrogen dioxide

Abstract

The anharmonic potential function of the ground electronic state of nitrogen dioxide has been determined within the framework of three different vibrational Hamiltonians. The first of these, which involves a perturbation expansion of the vibrational wave functions in terms of normal coordinate harmonic oscillator wave functions, is the most widely used and generally applicable of the three. It suffers, however, from demonstrably large systematic errors. The other two are vibration–rotation Hamiltonians which allow explicitly for a large amplitude vibration in the bending vibration of a triatomic molecule; they set up the Hamiltonian operator as an explicit function of the bond angle and solve the Schrödinger equation numerically. The more sophisticated of these, the so-called nonrigid bender Hamiltonian, reproduces the spin-free virtual term values to the (0, ν2, 0) manifold of 14NO2 to a standard deviation of 0.026 cm−1 for states with N ≤ 10 and ν2 ≤ 3. It is, moreover, observed to be a more useful tool for extrapolation than is the ordinary parametrized Hamiltonian.The potential function for the bending coordinate is defined by αe = 133.888 ± 0.002°, fαα = 1.61022 ± 0.00005 mdyn Å/rad2, fααα = −2.1172 ± 0.0003 mdyn Å/rad3, and fαααα = 6.0228 ± 0.0020 mdyn Å/rad4. The equilibrium bond length, re, is found to be 1.19464 ± 0.00015 Å.