Bond angle variations in XH3 [X = N, P, As, Sb, Bi]: the critical role of Rydberg orbitals exposed using a diabatic state model

Jeffrey R. Reimers; Laura K. McKemmish; Ross H. McKenzie; Noel S. Hush

doi:10.1039/C5CP02237A

Bond angle variations in XH₃ [X = N, P, As, Sb, Bi]: the critical role of Rydberg orbitals exposed using a diabatic state model

Jeffrey R. Reimers,*^ab Laura K. McKemmish,^cd Ross H. McKenzie^e and Noel S. Hush^df

* Corresponding authors

^a International Centre for Quantum and Molecular Structure, College of Sciences, Shanghai University, Shanghai 200444, China
Tel: +86-15618155341

^b School of Mathematical and Physical Sciences, University of Technology Sydney, NSW 2007, Australia
E-mail: Jeffrey.Reimers@uts.edu.au

^c Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK

^d School of Chemistry, The University of Sydney, Sydney, NSW 2006, Australia

^e School of Mathematics and Physics, The University of Queensland, QLD 4072, Australia

^f School of Molecular Biosciences, The University of Sydney, NSW 2006, Australia

Abstract

Ammonia adopts sp³ hybridization (HNH bond angle 108°) whereas the other members of the XH₃ series PH₃, AsH₃, SbH₃, and BiH₃ instead prefer octahedral bond angles of 90–93°. We use a recently developed general diabatic description for closed-shell chemical reactions, expanded to include Rydberg states, to understand the geometry, spectroscopy and inversion reaction profile of these molecules, fitting its parameters to results from Equation of Motion Coupled-Cluster Singles and Doubles (EOM-CCSD) calculations using large basis sets. Bands observed in the one-photon absorption spectrum of NH₃ at 18.3 eV, 30 eV, and 33 eV are reassigned from Rydberg (formally forbidden) double excitations to valence single-excitation resonances. Critical to the analysis is the inclusion of all three electronic states in which two electrons are placed in the lone-pair orbital n and/or the symmetric valence σ* antibonding orbital. An illustrative effective two-state diabatic model is also developed containing just three parameters: the resonance energy driving the high-symmetry planar structure, the reorganization energy opposing it, and HXH bond angle in the absence of resonance. The diabatic orbitals are identified as sp hybrids on X; for the radical cations XH₃⁺ for which only 2 electronic states and one conical intersection are involved, the principle of orbital following dictates that the bond angle in the absence of resonance is acos(−1/5) = 101.5°. The multiple states and associated multiple conical intersection seams controlling the ground-state structure of XH₃ renormalize this to acos[3 sin²(2^1/2atan(1/2))/2 − 1/2] = 86.7°. Depending on the ratio of the resonance energy to the reorganization energy, equilibrium angles can vary from these limiting values up to 120°, and the anomalously large bond angle in NH₃ arises because the resonance energy is unexpectedly large. This occurs as the ordering of the lowest Rydberg orbital and the σ* orbital swap, allowing Rydbergization to compresses σ* to significantly increase the resonance energy. Failure of both the traditional and revised versions of the valence-shell electron-pair repulsion (VSEPR) theory to explain the ground-state structures in simple terms is attributed to exclusion of this key physical interaction.

Physical Chemistry Chemical Physics

Bond angle variations in XH₃ [X = N, P, As, Sb, Bi]: the critical role of Rydberg orbitals exposed using a diabatic state model

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Bond angle variations in XH₃ [X = N, P, As, Sb, Bi]: the critical role of Rydberg orbitals exposed using a diabatic state model

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