Trends in inversion barriers. I: Group-15 hydrides

Inversion barriers for the group-15 hydrides NH3, PH3, AsH3, SbH3 and BiH3 have been studied using ab initio self-consistent-field methods including electron correlation and relativistic effects. A modified symmetric inversion potential is introduced to describe the inversion from the minimum C3v arrangement through the D3h transition state. Tunneling rates and frequencies are calculated at the Hartree–Fock and Mo/ller–Plesset (MP2) level within the Wentzel–Kramers–Brillouin approximation. At the MP2 level the calculated 0+/0− ν2 frequency splitting of the vibronic ground state of NH3/ND3 (0.729 cm−1/0.041 cm−1) is in excellent agreement with the experimental values (0.794 cm−1/0.053 cm−1). The tunneling rate for PH3 suggests that previously published values are wrong by orders of magnitude. Correlation effects do not change the barriers significantly in accordance with Freed’s theorem. This has been studied in more detail for BiH3 at the quadratic configuration-interaction (QCI) level. Relativistic effects increase the barrier height of BiH3 by 81.6 kJ/mol at the QCI level. Nonrelativistic and relativistic extended Hückel calculations suggest that the a1 highest occupied molecular orbital, which is antibonding to the Bi 6s, relieves part of its antibonding character near equilibrium geometry due to the relativistic radial contraction of the 6s orbital and hence increases the barrier height. In the planar transition state this orbital is a nonbonding a″2. The increasing trend in barrier heights from NH3 to BiH3 can be explained by a second-order Jahn–Teller distortion of the trigonal planar geometry. Vibrational frequencies are predicted for BiH3.