A Quantum Model for Bending Vibrations and Thermodynamic Properties of C3

Abstract

A quadratically perturbed square well potential is used to derive quantized bending mode vibrational energy levels for the C3 molecule. Coupling with rotational modes and l doubling is neglected for simplicity. The model is constrained to a best fit with observed lower vibrational levels in the lowest rotational state, and subject to this constraint the upper vibrational levels have maximum possible divergence. Thus a lower limit for the partition function and the entropy of C3 is established; the neglected rotational coupling has little influence on these quantities because the splitting of levels is almost symmetrical. The limits obtained support the classical model of Strauss and Thiele for the thermodynamic properties of C3 rather than the estimates listed in current JANAF Thermochemical Tables, and imply that recent graphite vapor pressure measurements made by Zavitsanos and by Wachi and Gilmartin are more correct than earlier measurements.