Influence of fourth-order vibrational corrections on semi-experimental (reSE) structures of linear molecules

Abstract

Semi-experimental structures (reSE) 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 Å. Larger corrections, nearly 0.0002 Å, 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 Å). Certain molecules with shallow bending potentials, e.g., HOC+, are not amenable to a VPT2 description and are not improved by VPT4.

The Semiexperimental Approach at Work: Equilibrium Structure of Radical Species

“…For NH, our r e (SE) value of 1.03631(4) Å is in good agreement with that reported in the literature by Melosso et al 100 (1.03606721(13) Å), while both values are ∼1 mÅ shorter than that derived using the VPT4 contribution, this being 1.037286 Å. 156 The discrepancy reduces to about 0.5 mÅ if r e (SE) full is considered. For the OH radical, our best estimate is 0.96988(9) Å and the value obtained using VPT4 is 0.969789 Å; thus, the difference is only ∼0.1 mÅ.…”

“…For NH, CH and OH, the r e (SE) value can be compared with the results from ref , where the effects of fourth-order vibrational perturbation theory (VPT4) on the SE equilibrium structure were considered. According to that work, the CH bond distance is 1.119913 Å, which is thus in very good agreement with our r e (SE) value of 1.119791(4) Å and deviates by about 2 mÅ from the other literature value of 1.11810 Å reported in Table , which is a pure, extremely accurate, computed result. , Such a difference vanishes once we move from r e (SE) to r e (SE) full .…”