Effects of curvilinear motion in large-amplitude bending of C3

Abstract

Large‐amplitude bending of linear, homonuclear, triatomic molecules is analyzed, with curvilinear departure of the atoms from normal coordinate bending included. The curvilinear motion is deduced from the observed variation of rotational constant with bending quantum number. The effect of this motion is to decrease the energy eigenvalues; energy states with lowest angular momentum are decreased most. These effects counteract the effects of a steeper than harmonic bending potential. A harmonic oscillator model of C₃ is fitted to the observed rotational constant within 0.6%, and the bond distance between atoms in the linear configuration of C₃ is found to be 1.287 Å; noticeably larger than the average internuclear distance of the vibrational ground state, 1.277 Å. First order perturbation results, including the effect of a quartic perturbation potential, approximately duplicate the pattern of energy levels observed. Square well bending potential wavefunctions are presumed to represent a limiting approximation for high vibrational levels of C₃ since these provide the divergence of upper levels required to fit the measured vapor pressure of graphite. In this case, the effects of curvilinear motion are similar to those obtained for the harmonic oscillator model, although somewhat larger decreases in energy are obtained. In either case, the average energy decrease is relatively constant—the order of 10%—over a wide range of vibrational quantum number. This means that the usual normal mode analysis can be adjusted to approximate the effects of curvilinear motion and explains why normal mode approximations can often be extended beyond the limits of small‐amplitude bending and yet give reasonably good results.