# Bond angle variations in XH<inf>3</inf> [X = N, P, As, Sb, Bi]: The critical role of Rydberg orbitals exposed using a diabatic state model

- Authors
- Publication Date
- Jul 02, 2015
- Source
- UTS Institutional Repository
- Keywords
- License
- Unknown
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## Abstract

© 2015 the Owner Societies. Ammonia adopts sp<sup>3</sup> hybridization (HNH bond angle 108°) whereas the other members of the XH<inf>3</inf> series PH<inf>3</inf>, AsH<inf>3</inf>, SbH<inf>3</inf>, and BiH<inf>3</inf> 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 NH<inf>3</inf> 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 XH<inf>3</inf><sup>+</sup> 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 XH<inf>3</inf> renormalize this to acos[3sin<sup>2</sup>(2<sup>1/2</sup>atan(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 NH<inf>3</inf> 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.