Geometry, Electronic Structure, and Pseudo Jahn-Teller Effect in Tetrasilacyclobutadiene Analogues

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

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 [Formula: see text] 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.

The Jahn–Teller and Pseudo-Jahn–Teller Effects: A Unique and Only Source of Spontaneous Symmetry Breaking in Atomic Matter

In a mostly review paper, we show that the important problem of symmetry, broken symmetry, and spontaneous broken symmetry of polyatomic systems is directly related to the Jahn–Teller (JT) and pseudo-Jahn–Teller (PJT) effects, including the hidden-JT and hidden-PJT effects, and these JT effects (JTEs) are the only source of spontaneous symmetry breaking in matter. They are directly related to the violation of the adiabatic approximation by the vibronic and other nonadiabatic couplings (jointly termed nonadiabaticity) in the interaction between the electrons and nuclei, which becomes significant in the presence of two or more degenerate or pseudodegenerate electronic states. In a generalization of this understanding of symmetry, we suggest an improved (quantum) definition of stereo-chemical polyatomic space configuration, in which, starting with their high-symmetry configuration, we separate all atomic systems into three distinguishable groups: (1) weak nonadiabaticity, stable high-symmetry configurations; (2) moderate-to-strong nonadiabaticity, unstable high-symmetry configurations, JTEs, spontaneous symmetry breaking (SSB); (3) very strong nonadiabaticity, stable distorted configurations. The JTEs, inherent to the second group of systems, produce a rich variety of novel properties, based on their multiminimum adiabatic potential energy surface (APES), leading to a short lifetime in the distorted configuration. We show the role of the Curie principle in the possibilities to observe the SSB in atomic matter, and mention briefly the revealed recently gamma of novel properties of matter in its interaction with external perturbation that occur due to the SSB, including ferroelectricity and orientational polarization, leading to enhanced permittivity and flexoelectricity.

Sub-lattice of Jahn-Teller centers in hexaferrite crystal

A novel type of sub-lattice of the Jahn-Teller (JT) centers was arranged in Ti-doped barium hexaferrite BaFe₁₂O₁₉. In the un-doped crystal all iron ions, sitting in five different crystallographic positions, are Fe³⁺ in the high-spin configuration (S = 5/2) and have a non-degenerate ground state. We show that the electron-donor Ti substitution converts the ions to Fe²⁺ predominantly in tetrahedral coordination, resulting in doubly-degenerate states subject to the [Formula: see text] problem of the JT effect. The arranged JT complexes, Fe²⁺O₄, their adiabatic potential energy, non-linear and quantum dynamics, have been studied by means of ultrasound and terahertz-infrared spectroscopies. The JT complexes are sensitive to external stress and applied magnetic field. For that reason, the properties of the doped crystal can be controlled by the amount and state of the JT complexes.

The symmetry principle of antiaromaticity

Current definitions of aromaticity are purely phenomenological and relate symmetry, reactive stability and the occurrence of molecular diamagnetic response currents. The antithetical concept of antiaromaticity provides a connection between the contrary properties: structural instability or distortion out of higher symmetry, a small HOMO-LUMO gap, and paramagnetic response currents. We reveal the symmetry principle that is underlying antiaromaticity by showing an intimate and strict symmetry induced relation between these properties. The principle is mathematically rigorous and can be formulated like: First order (and related) Jahn-Teller distorted molecules out of non-cubic and non-icosahedral point groups are prone to induced paramagnetism in magnetic fields parallel to the main axis of symmetry. We show by the exemplary cases of cyclobutadiene, cyclcooctatetraene, pentalene and manganese trifluoride how this principle works and discuss this new perspective on antiaromaticity.

Natural Bond Orbital Theory of Pseudo-Jahn-Teller Effects

We describe a unified picture of symmetry-breaking electronic interactions that are usually described as "pseudo-Jahn-Teller (PJT) effects" and attributed to vibronic coupling but can also be associated with hyperconjugative donor-acceptor interactions in the framework of natural bond orbital (NBO) and natural resonance theory (NRT) analysis. We show how NBO/NRT descriptors offer a simplified alternative to the vibronic coupling picture of PJT effects that yields both improved cause-effect specificity and chemically enriched understanding of symmetry-breaking phenomena but with no necessary input from ground-state vibrational or excited-state electronic properties. Comparative NBO/NRT vs vibronic coupling analyses of PJT effects are illustrated for two well-known cases: trans-bending in Si₂H₄ and higher Group-14 homologues of ethylene and chain-kinking in cyclopentadienylideneketene (C₅H₄CCO) and related cumulene ketones. The conceptual and practical advantages of the NBO-based hyperconjugative approach may be expected to extend to numerous PJT-type symmetry-breaking phenomena throughout the chemical sciences.

General formalism for vibronic Hamiltonians in tetragonal symmetry and beyond

We derive general expansion formulas in vibrational coordinates for all bimodal Jahn–Teller and pseudo-Jahn–Teller Hamiltonians in tetragonal symmetry.

Toward the Mechanism of Perchlorinated Cyclopentasilane (Si5Cl10) Ring Flattening in the [Si5Cl10·2Cl]2- Dianion

We report the detailed computational study of flattening of the puckered Si₅ ring by suppression of the pseudo-Jahn-Teller (PJT) effect through coordination of two Cl^- anions to the molecule forming an inverse sandwich dianion [Si₅Cl₁₀·2Cl]^2- complex. The PJT effect that causes nonplanarity of the Si₅Cl₁₀ structure (C_s) results from vibronic coupling of pairs of occupied molecular orbitals (OMOs) and unoccupied molecular orbitals (UMOs). It was shown that filling the intervenient molecular orbitals of puckered Si₅Cl₁₀ with valent electron pairs of Cl^- donors suppresses the PJT effect, with the Si₅ ring becoming planar (D_5h) upon complex formation. In this paper, the stabilization energy E(2) associated with donor-acceptor charge transfer (delocalization) was estimated using NBO analysis for all studied inverse sandwich compounds [Si₅Cl₁₀·2X]^2- (where X = F, Cl, Br). It was found that the polarizability of the donor ion might significantly affect the stabilization energy value and should be taken into account when choosing the ligands suitable for forming Si-based one-dimensional compounds and other nanoscale materials.

Numerical Estimation of the Pseudo-Jahn-Teller Effect Using Nonadiabatic Coupling Integrals in Monocyclic and Bicyclic Conjugated Molecules

The pseudo-Jahn-Teller (pJT) effect in monocyclic and bicyclic conjugated molecules was investigated by using the state-averaged multiconfiguration self-consistent field (MCSCF) method, together with the 6-31G(d,p) basis sets. Following the perturbation theory, the force constant along a normal mode Q is given by the sum of the classical force constant and the vibronic contribution (VC) resulting from the interaction of the ground state with excited states. The latter is given as the sum of individual contributions arising from vibronic interactions between the ground state and excited states. In the present work, each VC was calculated on the basis of nonadiabatic coupling (NAC) integrals. Furthermore, the classical force constant was estimated by taking advantage of the VC and the force constant obtained by vibrational analyses. For pentalene and heptalene, the present method seems to overestimate the VC in absolute value because of the small energy gap between the ground state and the lowest excited state. However, we are confident that the VC and the classical force constant for the other molecules are reasonable in magnitude in comparison with available literature information. Thus, it is proved that the present method is applicable and useful for numerical estimation of pJT effect.

Steric and electric field driven distortions in aromatic molecules: spontaneous and non-spontaneous symmetry breaking

The present calculations provide a unified picture of molecular distortions, both spontaneous and external field driven.