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The symmetry breaking phenomenon in 1,2,3-trioxolene and C_{2}Y_{3}Z_{2} (Z= O, S, Se, Te, Z= H, F) compounds: a pseudo Jahn-Teller origin study |

Ali Reza Ilkhani Department of Chemistry, Yazd Branch, Islamic Azad University, 8916871967 Yazd, Iran Recebido em 16/07/2016 Endereço para correspondência
*e-mail: ilkhaniali@iauyazd.ac.ir RESUMO
1,2,3-Trioxolene (C _{2}Y_{3} ring in the C_{2}Y_{3}Z_{2} series.Palavras-chave: symmetry breaking in five-member rings; PJTE; 1,2,3-trioxolene derivatives; non-planarity in rings; vibronic coupling constant.
The reaction with ozone is a well-known reaction in organic chemistry and many unsaturated compounds were participated in ozonolysis reactions.
Figure 1. Two intermediates five-member ring structure in ozonolysis reaction of unsaturated compounds (atomic representations: O = red, C = gray, H = white)
Several computational studies of unsaturated compounds ozonolysis reaction have been done to rationalize the ozonolysis reaction mechanism. By quantum-chemical simulations, we are able to reveal the electronic states of heterocyclic systems such as ground and excited states and their coupling. In all of the above experimental and theoretical studies, some important features of the structure and properties of acetylene ozonolysis reaction and their intermediates have been analyzed, but less attention has been paid to the origin of their common features which should be explained through pseudo Jahn-Teller effect (PJTE). The PJTE includes excited states in the vibronic coupling interactions and is the only possible source of the instability of planarity of cyclic systems in nondegenerate states. It is also a powerful tool to rationalize symmetry breaking phenomenon in the compounds with a symmetrical structure. Recently, buckling distortion in the hexa-germabenzene and triazine-based graphitic carbon nitride sheets is rationalized based on the PJT distortion.
An imaginary frequency along _{2}Y_{3}Z_{2} (Y= O, S, Se, Te , Z= H, F) derivatives in planar configuration and it confirms that all C_{2}Y_{3} five-member rings in the C_{2}Y_{3}Z_{2} series are unstable in their planar configuration. The Molpro 2010 package^{39} were carried out in these geometrical optimization and vibrational frequency calculations of the series and the state-average complete active space self-consistent field (SA-CASSCF) wavefunctions^{40-42} have been employed to calculate the APES along the Q_{b1} puckering normal coordinates. The B3LYP method level of Density Function Theory^{43} with cc-pVTZ basis set^{44-46} was employed in all steps of optimization, vibrational frequency, and SA-CASSCF calculations (except in C_{2}Te_{3}H_{2} which cc-pVTZ-pp basis set was used).
The optimization and follow-up frequency calculations of C _{2}Y_{3}Z_{2} under consideration and they are unstable in their C_{2v} high-symmetry planar configuration. Therefore, symmetry breaking phenomenon occurs in the C_{2}Y_{3}Z_{2} series and all systems are puckered to lower C_{s} symmetry with less symmetry elements. Two different side views of unstable planar configuration with C_{2v} symmetry and C_{s} symmetry equilibrium geometry in the C_{2}Y_{3}Z_{2} series illustrates in Figure 2.
Figure 2. The symmetry breaking phenomenon illustrates in two side views of C_{2}Y_{3}Z_{2} (Y= O, S, Se, Te, Z= H, F) series in unstable high-symmetry planar C_{2v} and stable puckered C_{s} equilibrium geometry
Geometrical parameters provided in the form of bonds length, angles, and dihedral angles for similar displacements of atoms in planar and equilibrium configurations, imaginary frequency and normal modes displacements of non-planarity in Cartesian X coordinates together and they are presented in Table 1.
From Table 1 illuminate that although the bond lengths and angles in planar and equilibrium configurations for the C The Y-Y-Y-C and Y-Y-C=C dihedral angles were the most important parameters to show the folding in the C Replacing H ligands in the C
Several active spaces have been checked in SA-CASSCF calculations and the result of calculations were compared together. The results revealed that ten electrons and eight active orbitals which was composed the CAS(10,8) active space is appropriate in under considered C _{2}Y_{3} rings in the series.
If Γ was supposed as the ground state and first non-degenerate excited state (Γ') was separated with Δ energy gap, |Γ〉 and |Γ'〉 will be denoted as the wave-functions of those mixing states. Based on the PJTE theorem where From these definitions for 2×2 case of two interacting states, it is revealed that the PJTE substantially involves excited states, specifically the energy gap to them and the strength of their influence of the ground state via the vibronic coupling constant The vibronic coupling between the two states reduces and adds the force constant of the ground and excited states by an amount of ( This leads to the condition of instability in Equation (1) at which the curvature Since an B In above Equations, Δ is the energy gap between the ground and excited states and for simplicity, the With respect to the ab initio calculation, it was founded that the lowest excited state with _{2}Y_{3}H_{2} (Y = O, S, Se, Te, Z -= H, F) series were compared with theirs ab initio calculated energy profiles and the first and second A' states in puckered stable geometry with C_{s} symmetry were denoted by A_{I}' and A_{II}', respectively.
Figure 3. The APES profiles of C_{2}Y_{3}H_{2} (Y= O, S, Se, Te) series (lines) and the numerical fitting of the energies obtained from the PJTE equations (points) along the b_{1} puckering direction in eV
Figure 4. The APES profiles of C_{2}Y_{3}F_{2} (Y= O, S, Se) series (lines) and the numerical fitting of the energies obtained from the PJTE equations (points) along the b_{1} puckering direction in eV
As from Figures 3 and 4 were illuminated, instability in planar configuration occurs in all C K, K' and Fparameters were estimated by the numerical fitting of Equation (7) with the APES energy profiles along the twisting direction (Qb_{1}) which is revealed in Table 4. Since small values of higher order of Q^{4} parameters in comparison with Q^{2} and Q^{4}, the numerical fitting of the equation was done up to the second term of the series in Equation (7).
By the estimated parameters and the energy gaps (Δ) in Table 4 and with respect to the PJTE the ground state instability in Equation (1), the PJTE origin and value of instability in the C
An imaginary frequency coordinate in out-of-plane of the molecules was observed through the ab initio DFT optimization and following frequency calculations in planar configuration of C ^{1}A_{1}+^{1}B_{1}) ⊗b problem is the reason of instability of the C_{1}_{2}Y_{3}Z_{2} series in their planar configuration. Estimation of the vibronic coupling constant values, F, in the C_{2}Y_{3}H_{2} series illuminate that the most unstable planar configuration in the series is corresponded to C_{2}Te_{3}H_{2} five-member ring compound. It is also clear that planar stability in the systems rises by decreasing the Y atoms size in the series, except in C_{2}Se_{3}H_{2}. Additionally, the molecules puckering in both C_{2}S_{3}F_{2} and C_{2}Se_{3}F_{2} compounds were decreased by replacing the H atoms with F ligands in the C_{2}Y_{3}H_{2} series, although C_{2}O_{3}F_{2} compound shows opposite behavior in the C_{2}Y_{3}F_{2} under consideration series.
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