The inversion of tetrahedral p-block element compounds: general trends and the relation to the second-order Jahn-Teller effect

Abstract

The tetrahedron is the primary structural motif among the p-block elements and determines the architecture of our bio- and geosphere. However, a broad understanding of the configurational inversion of tetrahedral compounds is missing. Here, we report over 250 energies (DLPNO-CCSD(T)) for square planar inversion of third- and fourth-period element species of groups 13, 14, and 15. Surprisingly low inversion barriers are identified for compounds of industrial relevance (e.g., ≈100 kJ mol^-1 for Al(OH)₄ ^-). More fundamentally, the second-order Jahn-Teller theorem is disclosed as suitable to rationalize substituent and central element effects. Bond analysis tools give further insights into the preference of eight valence electron systems with four substituents to be tetrahedral. Hence, this study develops a model to understand, memorize, and predict the angular flexibility of tetrahedral species. Perceiving the tetrahedron not as forcingly rigid but as a dynamic structural entity might leverage new approaches and visions for adaptive matter.

Fig. 1. (A) Examples of eight valence electron p-block element species with a tetrahedral ground state. (B) The C_s symmetric inversion transition state for CH₄ and its higher energy square planar state of D_4h symmetry. (C) Edge inversion process for group 15 element fluorides. (D) Trigonal inversion of ammonia and other group 15 element compounds. (E) The inversion process of p-block tetrahedrons analyzed within this work.

Fig. 2. (A) Schematic Walsh diagram for the distortion from the tetrahedral to the square planar state of CH₄ and SiH₄. (B) Deformation vibrations that transform the tetrahedral ground state into the square planar inversion transition state and vice versa. (C) Second-order contributions for the deformation coordinate q to the energy of a given system. (D) Direct product of the b_1g and a_2uirrep within the D_4h point group. It transforms under b_2u, which is also the symmetry of the inversion vibration.

Fig. 3. Relative inversion barriers of EH₃Rⁿ with respect to EH₄ⁿ (grey panels), for E = Al (A), Ga (B), = Si (C), Ge (D), P (E), As (F). The label on each bar states the respective absolute inversion barrier of EH₃Rⁿ. No inversion transition state was found for AsH₃(CH₃)⁺.* The transition structure optimization converged to a dissociative structure (GaH₃ and R⁻). ** The inversion barriers were obtained with NEVPT2/cc-pVQZ//CASSCF(8,8)/cc-pVTZ.

Fig. 4. Additive substituent effects for the inversion barrier of (A) SiH_4−yR_y, (B) GeH_4−yR_y, with R = F, Cl, Br, I, of (C) AlH_4−y(OH)_y⁻ and GaH_4−y(OH)_y⁻, and of (D) EH_4−yR_y, with E = Si, Ge and R = CN, CCH.

Fig. 5. Kohn–Sham frontier molecular orbital energies along the inversion reaction coordinate and the corresponding molecular orbital isodensity plots (contour value 0.03 a.u.) of the D_4h symmetric inversion transition state of (A) SiH₄, (B) SiF₄, and (C) Si(CN)₄.

Fig. 6. Correlation plots of the inversion barrier height versus the Kohn–Sham HOMO–LUMO gap in the inversion transition state for (A) EH₄ⁿ, (B) E(CN)₄ⁿ and E(CCH)₄ⁿ, and (C) EF₄ⁿ, for which the correlation vanishes. (D) Correlation plot of the inversion barrier height versus the difference in electronegativity between the central element and substituents for ER₄ⁿ, R = H, CH₃, CN, CCH. Pauling (group) electronegativities are given in parenthesis in the legend.

Fig. 7. Simplified presentation of the factors that determine the height of the planar inversion barrier of tetrahedral p-block element-based species, for which the substituents are more electronegative than the central elements.