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The Pseudo Jahn–Teller effect and NBO analysis for untangling the symmetry breaking in the planar configurations of M2X4+ (M = Si, Ge and X = Cl, Br, I): effect on electronic structure and chemical properties

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Abstract

Context

The Pseudo Jahn- Teller effect is a significant tool for evaluating molecular distortion and symmetry breaking. The PJT effect associated with NBO analysis can be a powerful method for studying the structural properties variations arising from D2h → C2h distortions. The theoretical studies on Si2X4+ and Ge2X4+ radical cations have been rare. The calculations have shown that C2h non-planar structures are more stable than planar structures with D2h symmetry. The \(({B}_{3u}+{B}_{1u})\otimes {b}_{2g}\) PJTE problem of M2X4+ compounds is a result of the coupling between the ground B3u state and the exited B1u state in the Qb2g direction causes. Also, the difference in M and X atoms can affect the PJT instability of compounds. The findings of this work show that the energy gap between the ground and excited states that have D2h symmetry decreases from M2Cl4+ to M2I4+ and increases from Si2X4+ to Ge2X4+. In fact, there is a significant relationship between instability of high-symmetry configurations, geometric parameters, electron delocalization, chemical hardness, electronegativity, electrophilicity index, and PJT stabilization energies. These results may serve to evaluate the distortion of similar systems.

Methods

The structures of Si2X4+ and Ge2X4+ are optimized by LC˗BLYP, M06˗2X, and B3LYP methods with def2˗TZVPP basis set in GAMESS software. The details of the excited states of compounds are studied by the TD-DFT method. NBO analysis for planar and non˗planar structures is carried out at B3LYP/def2˗TZVPP level by the NBO 5. G program that demonstrates HOMO, LUMO, ED, bonding and antibonding orbital occupancies, bond order, and E2.

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Abbreviations

Pseudo Jahn–Teller:

(PJT)

Natural Bond Orbital:

(NBO)

Electron delocalization:

(ED)

M2X4 + :

(M = Si, Ge, X = Cl, Br, I)

Density functional theory:

(DFT)

Adiabatic potential energy surface:

(APES)

Time-dependent density functional theory:

(TD-DFT)

The PJT stabilization energies:

(ΔEPJT)

The highest occupied molecular orbital:

(HOMO)

The lowest unoccupied molecular orbital:

(LUMO)

Localized molecular orbitals:

(LMO)

Canonical molecular orbitals:

(CMO)

The stabilization energy:

(E2)

Wiberg bond index matrix:

(WBI)

The natural atomic charges:

(NAC)

The natural atomic orbitals:

(NAO)

Hardness:

(η)

Electronegativity:

(χ)

Chemical potential:

(μ)

Electrophilicity index:

(ω)

Electron donating power:

(ω−)

Electron accepting power:

(ω+)

Net electrophilicity:

(∆ω±)

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Acknowledgements

The authors thank Professor Dr Davood Nori-Shargh for very useful and instructive guidance.

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  1. Department of Chemistry, Khorramabad Branch, Islamic Azad University, Khorramabad, Iran

    Ghazaleh Kouchakzadeh

  2. The Ministry of Education Tehran, Tehran, Iran

    Golrokh Mahmoudzadeh

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Ghazaleh Kouchakzadeh and Golrokh Mahmoudzadeh carried out computational calculations and analyzed them together, and finalized the results of the manuscript. Ghazaleh Kouchakzadeh wrote the manuscript. The authors were contributed in this research work.

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Kouchakzadeh, G., Mahmoudzadeh, G. The Pseudo Jahn–Teller effect and NBO analysis for untangling the symmetry breaking in the planar configurations of M2X4+ (M = Si, Ge and X = Cl, Br, I): effect on electronic structure and chemical properties. J Mol Model 30, 1 (2024). https://doi.org/10.1007/s00894-023-05792-1

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