Influence of fourth-order vibrational corrections on semi-experimental (r_e^SE) structures of linear molecules

Semi-experimental structures (r(e)(SE)) are derived from experimental ground state rotational constants combined with theoretical vibrational corrections. They permit a meaningful comparison with equilibrium structures based on high-level ab initio calculations. Typically, the vibrational corrections are evaluated with second-order vibrational perturbation theory (VPT2). The amount of error introduced by this approximation is generally thought to be small; however, it has not been thoroughly quantified. Herein, we assess the accuracy of theoretical vibrational corrections by extending the treatment to fourth order (VPT4) for a series of small linear molecules. Typical corrections to bond distances are on the order of 10(-5) & Aring;. Larger corrections, nearly 0.0002 & Aring;, are obtained to the bond lengths of NCCN and CNCN. A borderline case is CCCO, which will likely require variational computations for a satisfactory answer. Treatment of vibrational effects beyond VPT2 will thus be important when one wishes to know bond distances confidently to four decimal places (10(-4) & Aring;). Certain molecules with shallow bending potentials, e.g., HOC+, are not amenable to a VPT2 description and are not improved by VPT4.