Symmetry breaking in the planar configurations of disilicon tetrahalides: Pseudo-Jahn–Teller effect parameters, hardness and electronegativity

Abstract

CCSD(T), MP2, LC-BLYP, LC-ωPBE and B3LYP methods with the Def2-TZVPP basis set and natural bond orbital (NBO) interpretations were performed to investigate the correlations between the Pseudo-Jahn–Teller Effect (PJTE) parameters [i.e. vibronic coupling constant values (F), energy gaps between reference states (Δ) and the primary force constant (K₀)], structural and configurational properties, global hardness, global electronegativity, natural bond orders, stabilization energies associated with electron delocalizations and natural atomic charges of disilicon tetrafluoride (1), disilicon tetrachloride (2), disilicon tetrabromide (3) and disilicon tetraiodide (4). All levels of theory showed the trans-bent (C_2h) configurations as the energy minimum structures of compounds 1–4, and the flap angles between the X₂Si planes and the SiSi bonds in the distorted (C_2h) configurations decrease from compound 1 to compound 4. The negative curvatures of the ground state electronic configurations and the positive curvatures of the excited states of the adiabatic potential energy surfaces (APESs) which resulted from the mixing of the ground A_g and excited B_2g states are due to the PJTE (i.e. PJT(A_g + B_2g) ⊗ b_2g problem). Contrary to the usual expectation, with the decrease of the energy gaps between reference states (Δ), the PJTE stabilization energy, E_PJT, decreases from compound 1 to compound 4. The canonical molecular orbital (CMO) analysis revealed that the contributions of the ψ_HOMO(b_3u) and ψ_LUMO(b_1u) molecular orbitals in the vibronic coupling constant (F) decrease from compound 1 to compound 4. This fact clearly justifies the decrease of the vibronic coupling constant (F) and the primary force constant (the force constant without the PJTE) values on going from compound 1 to compound 4, leading to the decrease of the negative curvatures of the ground state electronic configuration curves of their corresponding APESs. The results obtained showed that the stabilization energies associated with the mixing of the distorted donor π_Si–Si(b_u) bonding and acceptor σ_Si–Si*(b_u) antibonding orbitals along the b_2g bending distortions decrease from compound 1 to compound 4. This fact reasonably explains the increase of the Si–Si natural bond orders (nbo) on going from compound 1 to compound 4. With the increase of the Si–Si natural bond orders, the corresponding E_PJT decreases from compound 1 to compound 4. Importantly, the variations of the global hardness (η) differences (Δ[η(C_2h) − η(D_2h)]) do not correlate with the trend observed for their corresponding total energy differences, justifying that the configurational properties of compounds 1–4 do not obey the maximum hardness principle. Interestingly, the trans-bent (C_2h) configurations of compounds 1–4 are more electronegative than their corresponding planar (D_2h) forms and the variations of their global electronegativity (χ) differences (Δ[χ(C_2h) − χ(D_2h)]) succeed in accounting for the decrease of the E_PJT stabilization energies for the D_2h → C_2h conversion processes on going from compound 1 to compound 4.