Asymmetric adiabatic correction to the rotation–vibration levels of H2D+ and D2H+

Abstract

Calculations on H₂D⁺ and D₂H⁺ have shown that the energy levels of these asymmetric isotopomers of H₃⁺ cannot be reproduced using effective potential energy surfaces with D_3h symmetry. It is shown that for these ions the adiabatic correction to the Born–Oppenheimer approximation has an asymmetric component which can be expressed as a mass‐independent surface multiplied by a mass factor. An expression for this function is obtained from ab initio calculations. Use of this adiabatic correction is found to resolve the discrepancy with the levels of H₂D⁺ and D₂H⁺. The ab initio calculations reported reproduce the observed H₂D⁺ transitions with an average error (obs−calc) of −8 MHz for the rotational transitions, −0.06 cm⁻¹ for the ν₁ band, −0.13 cm⁻¹ for ν₂, and −0.19 cm⁻¹ for ν₃. These errors are nearly constant for all transitions within a vibrational band. This gives a very accurate ab initio framework for predicting unobserved transition frequencies.