Improved bond length determination technique for C3 and other linear molecules with a large amplitude bending vibration

Abstract

A variety of standard techniques exist for estimating molecular bond lengths from spectroscopic data of the vibrational ground state. In typical order of increasing accuracy these different estimates are known as r0, rs, and rm. However, for the C3 molecule each of these spectroscopically determined values is very different from that obtained in a recent high-quality ab initio calculation. We ascribe this difference to the large-amplitude ν2 bending vibration of C3. By recognizing that vibrational averaging means that the molecule is effectively bent, even in the ground vibrational state, we develop a simple new method for estimating the bond length. This involves approximating the rotational parameter along the axis that becomes the molecular axis at linearity as A0=ν22. This value is then used in the evaluation of rm, rather than assuming the molecule is linear. We test this approximation for A0 and also show that the C–C bond length we obtain is in better agreement, by an order of magnitude, with the ab initio value than any of the standard linear approaches.