THE SYMMETRY BREAKING PHENOMENON IN 1,2,3-TRIOXOLENE AND C2Y3Z2 (Z= O, S, Se, Te, Z= H, F) COMPOUNDS: A PSEUDO JAHN-TELLER ORIGIN STUDY

Ilkhani, Ali Reza

doi:10.21577/0100-4042.20170029

Abstract

1,2,3-Trioxolene (C₂O₃H₂) is an intermediate in the acetylene ozonolysis reaction which is called primary ozonide intermediate. The symmetry breaking phenomenon were studied in C₂O₃H₂ and six its derivatives then oxygen atoms of the molecule are substituted by sulphur, selenium, tellurium (C₂Y₃H₂) and hydrogen ligands are replaced with fluorine atoms (C₂Y₃F₂). Based on calculation results, all seven C₂Y₃Z₂ considered in the series were puckered from unstable planar configuration with C_2v symmetry to a C_s symmetry stable geometry. The vibronic coupling interaction between the ¹A₁ ground state and the first excited state ¹B₁ via the (¹A₁+¹B₁) ⊗b₁ pseudo Jahn-Teller effect problem is the reason of the breaking symmetry phenomenon and un-planarity of the C₂Y₃ ring in the C₂Y₃Z₂ series.

Keywords:
symmetry breaking in five-member rings; PJTE; 1,2,3-trioxolene derivatives; non-planarity in rings; vibronic coupling constant

INTRODUCTION

The reaction with ozone is a well-known reaction in organic chemistry and many unsaturated compounds were participated in ozonolysis reactions.¹1 Komissarov, V. D.; Komissarova, I. N.; Russ. Chem. Bull. 1973, 22, 656.

2 Privett, O. S.; Nickell, E. C.; J. Lipid Res. 1963, 4, 208.

3 Rebrovic, L.; J. Am. Oil Chem. Soc. 1992, 69, 159.

4 Nickell, E. C.; Albi, M.; Privett, O. S.; Chem. Phys. Lipids 1976, 17, 378.^-⁵5 Lee, J. W.; Carrascon, V.; Gallimore, P. J.; Fuller, S. J.; Bjorkeqren, A.; Spring, D. R.; Pope, F.D.; Kalberer, M.; Phys. Chem. Chem. Phys. 2012, 14, 8023. The ozonation mechanism first time were suggested by Criegee⁶6 Criegee, R.; Angew. Chem., Int. Ed. 1975, 87, 745. and based on his mechanism, two intermediates with five-member ring structure were presented in ozonolysis reaction with unsaturated compounds. Those intermediate structures were confirmed through ¹⁷O-NMR spectroscopy method⁷7 Geletneky, C.; Berger, S.; Eur. J. Org. Chem. 1998, 8, 1625. (See Figure 1).

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.⁸8 Sun, Y.; Cao, H.; Han, D.; Li, J.; He; M.; Wang, C.; Chem. Phys. 2012, 402, 6.

9 Kuwata, K. T.; Templeton, K. L.; Hasson, A. S.; J. Phys. Chem. A 2003, 107, 11525.^-¹⁰10 Anglada, J. M.; Crehuet, R.; Bofill, J. M.; Chem. - Eur. J. 1999, 5, 1809. Additionally, activation enthalpy of cycloaddition reaction between ozone and acetylene was investigated through different calculation methods such as CCSD(T), CASPT2, and B3LYP-DFT with 6-311+G(2d,2p) basis set.¹¹11 Cremer, D.; Crehuet, R.; Anglada, J.; J. Am. Chem. Soc. 2001, 123, 6127. Moreover, thiozone adducts on single-walled carbon nanotubes, fullerene (C₆₀) and graphene sheet and geometry optimization of minima and transition structures have been investigated.¹²12 Castillo, A.; Lee, L.; Greer, A.; J. Phys. Org. Chem. 2012, 25, 42.

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.¹³13 Bersuker, I. B.; The Jahn−Teller effect, Cambridge University Press: Cambridge, 2006.^,¹⁴14 Bersuker, I. B.; Chem. Rev. 2013, 113, 1351. Through folding of rings in heterocyclic compounds, symmetry breaking phenomenon has been reported in many studies and the instability of the ground state in planar configuration of those molecules and their coupling with excited states have been explained via PJTE theorem.¹⁵15 Bersuker, I. B.; Chem. Rev. 2001, 101, 1067.

16 Blancafort, L.; Bearpark, M. J.; Robb, M. A.; Mol. Phys. 2006, 104, 2007.

17 Kim, J. H.; Lee, Z.; Appl. Microscopy 2014, 44, 123.

18 Gromov, E. V.; Troﬁmov, A. B.; Vitkovskaya, N. M.; Schirmer, J.; Koppel, H.; J. Chem. Phys. 2003, 119, 737.

19 Soto, J. R.; Molina, B.; Castro, J. J.; Phys. Chem. Chem. Phys. 2015, 17, 7624.

20 Monajjemi, M.; Theor. Chem. Acc. 2015, 134, 1.

21 Liu, Y.; Bersuker, I. B.; Garcia-Fernandez, P.; Boggs, J. E.; J. Phys. Chem. A 2012, 116, 7564.

22 Hermoso, W.; Ilkhani, A. R.; Bersuker, I. B.; Comput. Theo. Chem. 2014, 1049, 109.

23 Liu, Y.; Bersuker, I. B.; Boggs, J. E.; Chem. Phys. 2013, 417, 26.

24 Ilkhani, A. R.; Hermoso, W.; Bersuker, I. B.; Chem. Phys. 2015, 460, 75.

25 Jose; D.; Datta, A.; Phys. Chem. Chem. Phys. 2011, 13, 7304.

26 Monajjemi, M.; Bagheri, S.; Moosavi, M. S.; Moradiyeh, N.; Zakeri, M.; Attarikhasraghi, N.; Saghayimarouf, N.; Niyatzadeh, G.; Shekarkhand, M.; Khalilimofrad, M. S.; Ahmadin, H.; Ahadi, M.; Molecules 2015, 20, 21636.^-²⁷27 Ilkhani, A. R.; Monajjemi, M.; Comput. Theor. Chem. 2015, 1074, 19. Restoring planarity in the systems that are puckered from their planar configurations due to the symmetry breaking phenomenon has been investigated through the PJTE. To do so, their planar configuration restores ether by coordinating two anions, cations, or rings up and down to the nonplanar systems²⁸28 Jose, D.; Datta, A.; J. Phys. Chem. C 2012, 116, 24639.

29 Ilkhani, A.R.; J. Mol. Struc. 2015, 1098, 21.^-³⁰30 Ivanov, A. S.; Bozhenko, K. V.; Boldyrev, A. I.; Inorg. Chem. 2012, 57, 8868. or influences the parameters of the PJTE instability by removing or adding electrons;³¹31 Ilkhani, A.R.; Gorinchoy, N. N.; Bersuker, I. B.; Chem. Phys. 2015, 460, 106. they show that symmetry breaking phenomenon is suppressed in the folded systems. In other applications of the PJTE, the origin of puckering in tricyclic compounds to a pseudo Jahn-Teller (PJT) problem has been traced.³²32 Pratik, S. M.; Chowdhury, C.; Bhattacharjee, R.; Jahiruddin, S.; Datta, A.; Chem. Phys. 2015, 460, 101.^,³³33 Ivanov, A. S.; Miller, E.; Boldyrev, A. I.; Kameoka, Y.; Sato, T.; Tanaka, K.; J. Phys. Chem. C 2015, 119, 12008.

Recently, buckling distortion in the hexa-germabenzene and triazine-based graphitic carbon nitride sheets is rationalized based on the PJT distortion.³⁴34 Ivanov, A. S.; Boldyrev, A. I.; J. Phys. Chem. A 2012, 116, 9591.^,³⁵35 Nijamudheen, A.; Bhattacharjee, R.; Choudhury, S.; Datta, A.; J. Phys. Chem. C 2015, 119, 3802. Structural transition from non-planar of silabenzenes structures to planar benzene-like structures,³⁶36 Pratik, S. M.; Datta, A.; J. Phys. Chem. C, 2015, 119, 15770. Chair like puckering investigation, binding energies, HOMO-LUMO gaps and polarizabilities in the silicene clusters toward found the hydrogen storage materials,³⁷37 Jose, D.; Datta, A.; Phys. Chem. Chem. Phys. 2011, 13, 7304. and origin instability of cylindrical configuration of [6]cycloparaphenylene have analyzed thorough the PJTE,³⁸38 Kameoka, Y.; Sato, T.; Koyama, T.; Tanaka, K.; Kato, T.; Chem. Phys. Lett. 2014, 598, 69. are some more application of the PJT theorem in chemistry.

COMPUTATION DETAILS

An imaginary frequency along b₁ normal coordinate was observed due to optimization and frequency calculations of seven C₂Y₃Z₂ (Y= O, S, Se, Te , Z= H, F) derivatives in planar configuration and it confirms that all C₂Y₃ five-member rings in the C₂Y₃Z₂ series are unstable in their planar configuration. The Molpro 2010 package³⁹39 Werner, H. J.; Knowles, P. J.; Manby, F. R.; Schutz, M.; MOLPRO, version 2010.1, a package of ab initio programs, Availaible from: http://www.molpro.net. Accessed in February 2017.
http://www.molpro.net... 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) wavefunctions⁴⁰40 Werner, H. J.; Meyer, W.; J. Chem. Phys. 1981, 74, 5794.

41 Werner, H. J.; Meyer, W.; J. Chem. Phys. 1980, 73, 2342.^-⁴²42 Werner, H. J.; Knowles, P. J.; J. Chem. Phys. 1985, 82, 5053. have been employed to calculate the APES along the Q_b1 puckering normal coordinates. The B3LYP method level of Density Function Theory⁴³43 Polly, R.; Werner, H. J.; Manby, F. R.; Knowles, P. J.; Mol. Phys. 2004, 102, 2311. with cc-pVTZ basis set⁴⁴44 Wilson, A. K.; Woon, D. E.; Peterson, K. A.; J. Chem. Phys. 1999, 110, 7667.

45 Dunning, T. H.; J. Chem. Phys. 1989, 90, 1007.^-⁴⁶46 Woon, D. E.; Dunning, T. H.; J. Chem. Phys. 1993, 98, 1358. was employed in all steps of optimization, vibrational frequency, and SA-CASSCF calculations (except in C₂Te₃H₂ which cc-pVTZ-pp basis set was used).

SYMMETRY BREAKING PHENOMENON IN THE C₂Y₃Z₂ SERIES

The optimization and follow-up frequency calculations of C₂Y₃Z₂ series illuminated that, the C₂Y₃ ring is folded along b₁ nuclear displacement in all seven C₂Y₃Z₂ under consideration and they are unstable in their C_2v high-symmetry planar configuration. Therefore, symmetry breaking phenomenon occurs in the C₂Y₃Z₂ 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 C₂Y₃Z₂ series illustrates in Figure 2.

Figure 2
The symmetry breaking phenomenon illustrates in two side views of C₂Y₃Z₂ (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.

Thumbnail

Table 1
Calculated structural parameters of C₂Y₃Z₂ (Y= O, S, Se, Te, Z= H, F) series in planar and equilibrium configurations, normal modes of planar instability in Cartesian coordinates displacements X and imaginary frequency values

From Table 1 illuminate that although the bond lengths and angles in planar and equilibrium configurations for the C₂Y₃Z₂ (Z = H, F) were almost similar (except parameter in Y atom contributing) but the variety of dihedral values in their planar and equilibrium configurations were different.

The Y-Y-Y-C and Y-Y-C=C dihedral angles were the most important parameters to show the folding in the C₂Y₃ rings. While the absolute values of Y-Y-Y-C dihedral angle (which is 0.0 in planar configuration) were decreased in the equilibrium configuration from 24.5 degrees in C₂O₃H₂ to 13.8 (C₂S₃H₂), 8.8 (C₂Se₃H₂), 6.8 (C₂Te₃H₂) degrees in the C₂Y₃H₂ series.

Replacing H ligands in the C₂Y₃H₂ series by F ligands were also decreased Y-Y-Y-C, Y-Y-C=C, Y-Y-C-Z and Y-C-C-Z dihedral angle varieties of C₂Y₃F₂ in comparison with their values in equilibrium configuration.

ACTIVE SPACE IN SA-CASSCF CALCULATION

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 C₂Y₃Z₂ series. Additionally, the CAS(10,8) results comparison to the smaller CAS(4,3), CAS(6,6), and CAS(8,8) and lager CAS(12,12) active spaces that previously have been applied in similar PJTE origin studies;²²22 Hermoso, W.; Ilkhani, A. R.; Bersuker, I. B.; Comput. Theo. Chem. 2014, 1049, 109.^,²⁴24 Ilkhani, A. R.; Hermoso, W.; Bersuker, I. B.; Chem. Phys. 2015, 460, 75.^,²⁷27 Ilkhani, A. R.; Monajjemi, M.; Comput. Theor. Chem. 2015, 1074, 19.^,³¹31 Ilkhani, A.R.; Gorinchoy, N. N.; Bersuker, I. B.; Chem. Phys. 2015, 460, 106. was proved that CAS(10,8) active space sufficiently is good in present study. From Table 2 is also appeared that the eight orbitals included 2a₁, 2b₁, 2b₂, and 2a₂ were being contributed to the electron excitations of the C₂Y₃Z₂ series. The main electronic configuration calculation for all C₂Y₃Z₂ considered compounds (see Table 3) was showed that b₁'→a₁', electron excitation occurred and it proved that (¹A₁+¹B₁) ⊗b₁ PJTE problems are the reason of the breaking symmetry phenomenon and non-planarity of C₂Y₃ rings in the series.

Thumbnail

Table 2
Arrangement of HOMO and LUMO energies level and their symmetries, and electron excitation in the C₂Y₃Z₂ series contributing in the (¹A₁+¹B₁) ⊗b₁ PJTE through SA CASSCF calculation with (10,8) active space

Thumbnail

Table 3
Main electronic configuration and their weight coefficients in wave-functions of ground state (¹A₁) and ¹B₁ excited state of C₂Y₃Z₂ series in planar configuration

THE PJTE DUE TO PUCKERING

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 theorem¹³13 Bersuker, I. B.; The Jahn−Teller effect, Cambridge University Press: Cambridge, 2006., the ground state in the nuclear displacements direction (Q) is instable if

(1)

Δ < \frac{{(F_{Γ Γ'})}^{2}}{K_{0}}

where K₀ and F_(ΓΓ') are the primary force constant of the ground state and the vibronic coupling constant. With respect to Hamiltonian, H, and the electron-nucleon interaction operator, V, the K₀, K₀' (the primary force constant of excited state) and F_(ΓΓ') constants indicate by Equations (2) and (3):

(2)

K_{0} = ⟨Γ |\frac{\partial H}{\partial Q}| Γ⟩, K'_{0} = ⟨Γ' |\frac{\partial H}{\partial Q}| Γ'⟩

(3)

F_{Γ Γ'} = ⟨Γ |\frac{\partial V}{\partial Q}| Γ'⟩

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 F_(ΓΓ').

The vibronic coupling between the two states reduces and adds the force constant of the ground and excited states by an amount of (F_(ΓΓ'))²/Δ and making the total constant of the ground and excited states as followed equalities.¹⁴14 Bersuker, I. B.; Chem. Rev. 2013, 113, 1351.

(4)

K = K_{0} - \frac{{(F_{Γ Γ'})}^{2}}{Δ}, K' = K_{0}^{'} + \frac{{(F_{Γ Γ'})}^{2}}{Δ}

This leads to the condition of instability in Equation (1) at which the curvature K of the adiabatic potential energy surface (APES) for the ¹A₁ ground state in Q_b1 direction becomes negative but for the effective PJT interaction, the curvature K’ of the APES for the ¹B₁ excited (which is the first one in all of C₂Y₃Z₂ compounds in the series) must be positive.

Since an B₁ excited state contribute to the A₁ ground state instability in the C₂Y₃Z₂ series planar configuration, the PJTE emerges directly from the secular equation for the vibronically coupled the ground and excited state that is formulated by two-level PJTE problem as a 2×2 secular Equation (5) and quadratic Equation (6).

(5)

|\begin{matrix} \frac{1}{2} {KQ}^{2} - ε & FQ \\ FQ & \frac{1}{2} K' Q^{2} + Δ - ε \end{matrix}| = 0

(6)

ε^{2} - [\frac{1}{2} (K + K') Q^{2} + Δ] ε + \frac{1}{4} KK' Q^{4} + \frac{Δ}{2} {KQ}^{2} - F^{2} Q^{2} = 0

In above Equations, Δ is the energy gap between the ground and excited states and for simplicity, the Q_b1 and 〖F〗_(ΓΓ') are abbreviated to Q and F. The solution of Equation (6) around Q = 0 of the APES for the ground and excited states around the planar configuration bring us the fallowing solutions in Equation (7):

(7)

\begin{matrix} ε_{1} = \frac{1}{2} (K - \frac{2 F^{2}}{Δ}) Q^{2} - \frac{F^{2}}{2 Δ^{2}} ((K - K') - \frac{2 F^{2}}{Δ}) Q^{4} + ... \\ ε_{2} = \frac{1}{2} (K' + \frac{2 F^{2}}{Δ}) Q^{2} + Δ + \frac{F^{2}}{2 Δ^{2}} ((K - K') - \frac{2 F^{2}}{Δ}) Q^{4} + ... \end{matrix}

With respect to the ab initio calculation, it was founded that the lowest excited state with ¹B₁ symmetry is interacting with the ground state (in ¹A₁ symmetry). For all under study C₂Y₃Z₂ compounds, the condition of the PJTE ground state instability in Eq. (1 (are observable from the APES profiles of C₂Y₃H₂ and C₂Y₃F₂ (see Figures 3 and 4) and it appears that the ground state in all C₂Y₃Z₂ under consideration compounds are unstable in Q = 0 of the APES (planar configuration) along the b₁ puckering direction. Additionally, In Figures 3 and 4, the numerical fitting of the energies obtained from Equation (7) for C₂Y₃H₂ (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 C₂Y₃H₂ (Y= O, S, Se, Te) series (lines) and the numerical fitting of the energies obtained from the PJTE equations (points) along the b₁ puckering direction in eV

Figure 4
The APES profiles of C₂Y₃F₂ (Y= O, S, Se) series (lines) and the numerical fitting of the energies obtained from the PJTE equations (points) along the b₁ puckering direction in eV

As from Figures 3 and 4 were illuminated, instability in planar configuration occurs in all C₂Y₃Z₂ (Y= O, S, Se, Te, Z= H, F) compounds and the origin of the PJTE in the series are may explained via solution of the PJTE (¹A₁+¹B₁) ⊗b₁ problem. For explanation of origin of the PJTE in the series, K, K' and Fparameters were estimated by the numerical fitting of Equation (7) with the APES energy profiles along the twisting direction (Qb₁) which is revealed in Table 4. Since small values of higher order of Q⁴ parameters in comparison with Q² and Q⁴, the numerical fitting of the equation was done up to the second term of the series in Equation (7).

Thumbnail

Table 4
Total constant constants in ground and excited state, K and K', PJTE coupling constants, F, and energy gaps, Δ, of the C₂Y₃Z₂ (Y= O, S, Se, Te, Z = H, F ) series for (¹A₁+¹B₁) ⊗b₁ problem

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 C₂Y₃Z₂ series were evaluated. The highest and lowest PJTE coupling constants for the C₂Y₃H₂ series are belonged to C₂Te₃H₂ and C₂O₃H₂ compounds and the F values for the C₂Y₃F₂ series were increased from 2.28 ev / Å, in C₂O₃F₂ to 2.43 ev / Å, in C₂Se₃F₂ compound, respectively.

CONCLUSIONS

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 C₂Y₃Z₂ (Y = O, S, Se, Te, Z = H, F) series. It provides very important information about the symmetry breaking phenomenon in all under consideration compounds in the series. In other hand all those compounds in the C₂Y₃Z₂ series do not hold their planarity due to the PJTE and they distort from their unstable planar configuration with C_2v symmetry to the stable C_s symmetry geometry. The APES cross sections of the series were revealed that the ground state (¹A₁) and the excited ¹B₁ state along b₁ nuclear displacements could interact vibronically and the (¹A₁+¹B₁) ⊗b₁ problem is the reason of instability of the C₂Y₃Z₂ series in their planar configuration. Estimation of the vibronic coupling constant values, F, in the C₂Y₃H₂ series illuminate that the most unstable planar configuration in the series is corresponded to C₂Te₃H₂ 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 C₂Se₃H₂. Additionally, the molecules puckering in both C₂S₃F₂ and C₂Se₃F₂ compounds were decreased by replacing the H atoms with F ligands in the C₂Y₃H₂ series, although C₂O₃F₂ compound shows opposite behavior in the C₂Y₃F₂ under consideration series.

REFERENCES

¹
Komissarov, V. D.; Komissarova, I. N.; Russ. Chem. Bull. 1973, 22, 656.
²
Privett, O. S.; Nickell, E. C.; J. Lipid Res. 1963, 4, 208.
³
Rebrovic, L.; J. Am. Oil Chem. Soc. 1992, 69, 159.
⁴
Nickell, E. C.; Albi, M.; Privett, O. S.; Chem. Phys. Lipids 1976, 17, 378.
⁵
Lee, J. W.; Carrascon, V.; Gallimore, P. J.; Fuller, S. J.; Bjorkeqren, A.; Spring, D. R.; Pope, F.D.; Kalberer, M.; Phys. Chem. Chem. Phys. 2012, 14, 8023.
⁶
Criegee, R.; Angew. Chem., Int. Ed. 1975, 87, 745.
⁷
Geletneky, C.; Berger, S.; Eur. J. Org. Chem. 1998, 8, 1625.
⁸
Sun, Y.; Cao, H.; Han, D.; Li, J.; He; M.; Wang, C.; Chem. Phys. 2012, 402, 6.
⁹
Kuwata, K. T.; Templeton, K. L.; Hasson, A. S.; J. Phys. Chem. A 2003, 107, 11525.
¹⁰
Anglada, J. M.; Crehuet, R.; Bofill, J. M.; Chem. - Eur. J. 1999, 5, 1809.
¹¹
Cremer, D.; Crehuet, R.; Anglada, J.; J. Am. Chem. Soc. 2001, 123, 6127.
¹²
Castillo, A.; Lee, L.; Greer, A.; J. Phys. Org. Chem. 2012, 25, 42.
¹³
Bersuker, I. B.; The Jahn−Teller effect, Cambridge University Press: Cambridge, 2006.
¹⁴
Bersuker, I. B.; Chem. Rev. 2013, 113, 1351.
¹⁵
Bersuker, I. B.; Chem. Rev. 2001, 101, 1067.
¹⁶
Blancafort, L.; Bearpark, M. J.; Robb, M. A.; Mol. Phys. 2006, 104, 2007.
¹⁷
Kim, J. H.; Lee, Z.; Appl. Microscopy 2014, 44, 123.
¹⁸
Gromov, E. V.; Troﬁmov, A. B.; Vitkovskaya, N. M.; Schirmer, J.; Koppel, H.; J. Chem. Phys. 2003, 119, 737.
¹⁹
Soto, J. R.; Molina, B.; Castro, J. J.; Phys. Chem. Chem. Phys. 2015, 17, 7624.
²⁰
Monajjemi, M.; Theor. Chem. Acc. 2015, 134, 1.
²¹
Liu, Y.; Bersuker, I. B.; Garcia-Fernandez, P.; Boggs, J. E.; J. Phys. Chem. A 2012, 116, 7564.
²²
Hermoso, W.; Ilkhani, A. R.; Bersuker, I. B.; Comput. Theo. Chem. 2014, 1049, 109.
²³
Liu, Y.; Bersuker, I. B.; Boggs, J. E.; Chem. Phys. 2013, 417, 26.
²⁴
Ilkhani, A. R.; Hermoso, W.; Bersuker, I. B.; Chem. Phys. 2015, 460, 75.
²⁵
Jose; D.; Datta, A.; Phys. Chem. Chem. Phys. 2011, 13, 7304.
²⁶
Monajjemi, M.; Bagheri, S.; Moosavi, M. S.; Moradiyeh, N.; Zakeri, M.; Attarikhasraghi, N.; Saghayimarouf, N.; Niyatzadeh, G.; Shekarkhand, M.; Khalilimofrad, M. S.; Ahmadin, H.; Ahadi, M.; Molecules 2015, 20, 21636.
²⁷
Ilkhani, A. R.; Monajjemi, M.; Comput. Theor. Chem. 2015, 1074, 19.
²⁸
Jose, D.; Datta, A.; J. Phys. Chem. C 2012, 116, 24639.
²⁹
Ilkhani, A.R.; J. Mol. Struc. 2015, 1098, 21.
³⁰
Ivanov, A. S.; Bozhenko, K. V.; Boldyrev, A. I.; Inorg. Chem. 2012, 57, 8868.
³¹
Ilkhani, A.R.; Gorinchoy, N. N.; Bersuker, I. B.; Chem. Phys. 2015, 460, 106.
³²
Pratik, S. M.; Chowdhury, C.; Bhattacharjee, R.; Jahiruddin, S.; Datta, A.; Chem. Phys. 2015, 460, 101.
³³
Ivanov, A. S.; Miller, E.; Boldyrev, A. I.; Kameoka, Y.; Sato, T.; Tanaka, K.; J. Phys. Chem. C 2015, 119, 12008.
³⁴
Ivanov, A. S.; Boldyrev, A. I.; J. Phys. Chem. A 2012, 116, 9591.
³⁵
Nijamudheen, A.; Bhattacharjee, R.; Choudhury, S.; Datta, A.; J. Phys. Chem. C 2015, 119, 3802.
³⁶
Pratik, S. M.; Datta, A.; J. Phys. Chem. C, 2015, 119, 15770.
³⁷
Jose, D.; Datta, A.; Phys. Chem. Chem. Phys. 2011, 13, 7304.
³⁸
Kameoka, Y.; Sato, T.; Koyama, T.; Tanaka, K.; Kato, T.; Chem. Phys. Lett. 2014, 598, 69.
³⁹
Werner, H. J.; Knowles, P. J.; Manby, F. R.; Schutz, M.; MOLPRO, version 2010.1, a package of ab initio programs, Availaible from: http://www.molpro.net Accessed in February 2017.
» http://www.molpro.net
⁴⁰
Werner, H. J.; Meyer, W.; J. Chem. Phys. 1981, 74, 5794.
⁴¹
Werner, H. J.; Meyer, W.; J. Chem. Phys. 1980, 73, 2342.
⁴²
Werner, H. J.; Knowles, P. J.; J. Chem. Phys. 1985, 82, 5053.
⁴³
Polly, R.; Werner, H. J.; Manby, F. R.; Knowles, P. J.; Mol. Phys. 2004, 102, 2311.
⁴⁴
Wilson, A. K.; Woon, D. E.; Peterson, K. A.; J. Chem. Phys. 1999, 110, 7667.
⁴⁵
Dunning, T. H.; J. Chem. Phys. 1989, 90, 1007.
⁴⁶
Woon, D. E.; Dunning, T. H.; J. Chem. Phys. 1993, 98, 1358.

Publication Dates

Publication in this collection
June 2017

History

Received
16 July 2016
Accepted
23 Jan 2017

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License which permits unrestricted non-commercial use, distribution, and reproduction in any medium provided the original work is properly cited.

[1] ¹
Komissarov, V. D.; Komissarova, I. N.; Russ. Chem. Bull. 1973, 22, 656.

[2] ²
Privett, O. S.; Nickell, E. C.; J. Lipid Res. 1963, 4, 208.

[3] ³
Rebrovic, L.; J. Am. Oil Chem. Soc. 1992, 69, 159.

[4] ⁴
Nickell, E. C.; Albi, M.; Privett, O. S.; Chem. Phys. Lipids 1976, 17, 378.

[5] ⁵
Lee, J. W.; Carrascon, V.; Gallimore, P. J.; Fuller, S. J.; Bjorkeqren, A.; Spring, D. R.; Pope, F.D.; Kalberer, M.; Phys. Chem. Chem. Phys. 2012, 14, 8023.

[6] ⁶
Criegee, R.; Angew. Chem., Int. Ed. 1975, 87, 745.

[7] ⁷
Geletneky, C.; Berger, S.; Eur. J. Org. Chem. 1998, 8, 1625.

[8] ⁸
Sun, Y.; Cao, H.; Han, D.; Li, J.; He; M.; Wang, C.; Chem. Phys. 2012, 402, 6.

[9] ⁹
Kuwata, K. T.; Templeton, K. L.; Hasson, A. S.; J. Phys. Chem. A 2003, 107, 11525.

[10] ¹⁰
Anglada, J. M.; Crehuet, R.; Bofill, J. M.; Chem. - Eur. J. 1999, 5, 1809.

[11] ¹¹
Cremer, D.; Crehuet, R.; Anglada, J.; J. Am. Chem. Soc. 2001, 123, 6127.

[12] ¹²
Castillo, A.; Lee, L.; Greer, A.; J. Phys. Org. Chem. 2012, 25, 42.

[13] ¹³
Bersuker, I. B.; The Jahn−Teller effect, Cambridge University Press: Cambridge, 2006.

[14] ¹⁴
Bersuker, I. B.; Chem. Rev. 2013, 113, 1351.

[15] ¹⁵
Bersuker, I. B.; Chem. Rev. 2001, 101, 1067.

[16] ¹⁶
Blancafort, L.; Bearpark, M. J.; Robb, M. A.; Mol. Phys. 2006, 104, 2007.

[17] ¹⁷
Kim, J. H.; Lee, Z.; Appl. Microscopy 2014, 44, 123.

[18] ¹⁸
Gromov, E. V.; Troﬁmov, A. B.; Vitkovskaya, N. M.; Schirmer, J.; Koppel, H.; J. Chem. Phys. 2003, 119, 737.

[19] ¹⁹
Soto, J. R.; Molina, B.; Castro, J. J.; Phys. Chem. Chem. Phys. 2015, 17, 7624.

[20] ²⁰
Monajjemi, M.; Theor. Chem. Acc. 2015, 134, 1.

[21] ²¹
Liu, Y.; Bersuker, I. B.; Garcia-Fernandez, P.; Boggs, J. E.; J. Phys. Chem. A 2012, 116, 7564.

[22] ²²
Hermoso, W.; Ilkhani, A. R.; Bersuker, I. B.; Comput. Theo. Chem. 2014, 1049, 109.

[23] ²³
Liu, Y.; Bersuker, I. B.; Boggs, J. E.; Chem. Phys. 2013, 417, 26.

[24] ²⁴
Ilkhani, A. R.; Hermoso, W.; Bersuker, I. B.; Chem. Phys. 2015, 460, 75.

[25] ²⁵
Jose; D.; Datta, A.; Phys. Chem. Chem. Phys. 2011, 13, 7304.

[26] ²⁶
Monajjemi, M.; Bagheri, S.; Moosavi, M. S.; Moradiyeh, N.; Zakeri, M.; Attarikhasraghi, N.; Saghayimarouf, N.; Niyatzadeh, G.; Shekarkhand, M.; Khalilimofrad, M. S.; Ahmadin, H.; Ahadi, M.; Molecules 2015, 20, 21636.

[27] ²⁷
Ilkhani, A. R.; Monajjemi, M.; Comput. Theor. Chem. 2015, 1074, 19.

[28] ²⁸
Jose, D.; Datta, A.; J. Phys. Chem. C 2012, 116, 24639.

[29] ²⁹
Ilkhani, A.R.; J. Mol. Struc. 2015, 1098, 21.

[30] ³⁰
Ivanov, A. S.; Bozhenko, K. V.; Boldyrev, A. I.; Inorg. Chem. 2012, 57, 8868.

[31] ³¹
Ilkhani, A.R.; Gorinchoy, N. N.; Bersuker, I. B.; Chem. Phys. 2015, 460, 106.

[32] ³²
Pratik, S. M.; Chowdhury, C.; Bhattacharjee, R.; Jahiruddin, S.; Datta, A.; Chem. Phys. 2015, 460, 101.

[33] ³³
Ivanov, A. S.; Miller, E.; Boldyrev, A. I.; Kameoka, Y.; Sato, T.; Tanaka, K.; J. Phys. Chem. C 2015, 119, 12008.

[34] ³⁴
Ivanov, A. S.; Boldyrev, A. I.; J. Phys. Chem. A 2012, 116, 9591.

[35] ³⁵
Nijamudheen, A.; Bhattacharjee, R.; Choudhury, S.; Datta, A.; J. Phys. Chem. C 2015, 119, 3802.

[36] ³⁶
Pratik, S. M.; Datta, A.; J. Phys. Chem. C, 2015, 119, 15770.

[37] ³⁷
Jose, D.; Datta, A.; Phys. Chem. Chem. Phys. 2011, 13, 7304.

[38] ³⁸
Kameoka, Y.; Sato, T.; Koyama, T.; Tanaka, K.; Kato, T.; Chem. Phys. Lett. 2014, 598, 69.

[39] ³⁹
Werner, H. J.; Knowles, P. J.; Manby, F. R.; Schutz, M.; MOLPRO, version 2010.1, a package of ab initio programs, Availaible from: http://www.molpro.net Accessed in February 2017.
» http://www.molpro.net

[40] ⁴⁰
Werner, H. J.; Meyer, W.; J. Chem. Phys. 1981, 74, 5794.

[41] ⁴¹
Werner, H. J.; Meyer, W.; J. Chem. Phys. 1980, 73, 2342.

[42] ⁴²
Werner, H. J.; Knowles, P. J.; J. Chem. Phys. 1985, 82, 5053.

[43] ⁴³
Polly, R.; Werner, H. J.; Manby, F. R.; Knowles, P. J.; Mol. Phys. 2004, 102, 2311.

[44] ⁴⁴
Wilson, A. K.; Woon, D. E.; Peterson, K. A.; J. Chem. Phys. 1999, 110, 7667.

[45] ⁴⁵
Dunning, T. H.; J. Chem. Phys. 1989, 90, 1007.

[46] ⁴⁶
Woon, D. E.; Dunning, T. H.; J. Chem. Phys. 1993, 98, 1358.

Geometry parameters		Molecules
		C₂O₃Z₂				C₂S₃Z₂				C₂Se₃Z₂				C₂Te₃Z₂
		Planar (C_2v)		Equilibrium (C_s)		Planar (C_2v)		Equilibrium (C_s)		Planar (C_2v)		Equilibrium (C_s)		Planar (C_2v)	Equilibrium (C_s)
		Z=H	Z=F	Z=H	Z=F	Z=H	Z=F	Z=H	Z=F	Z=H	Z=F	Z=H	Z=F	Z=H	Z=H
Bond length (Å)	Y-Y	1.43	1.43	1.44	1.44	1.72	1.68	2.06	2.15	1.80	1.80	2.30	2.40	2.02	2.70
	Y-C	1.39	1.40	1.38	1.37	1.52	1.52	1.71	1.78	1.74	1.75	1.84	1.90	1.78	2.03
	C=C	1.34	1.35	1.36	1.32	1.35	1.36	1.39	1.33	1.36	1.37	1.40	1.39	1.37	1.40
	C-Z	1.08	1.25	1.07	1.29	1.07	1.25	1.08	1.32	1.08	1.24	1.08	1.33	1.08	1.09
Angle (Degree)	Y-Y-Y	109.9	111.8	107.0	107.8	101.4	103.2	98.9	99.6	106.9	107.3	95.4	96.9	103.0	91.0
	Y-Y-C	103.7	102.8	103.1	101.1	107.0	104.4	99.5	94.6	106.9	103.7	100.2	94.6	106.1	98.4
	Y-C=C	111.2	111.3	111.6	112.2	112.3	114.0	119.6	123.8	109.7	112.6	121.6	126.7	112.4	125.8
	Z-C=C	129.5	128.3	131.7	132.3	126.8	127.3	127.1	122.1	126.5	127.9	122.4	120.9	125.9	119.5
Dihedral angle (Degree)	Y-Y-Y-C	0.0	0.0	±24.5	±24.0	0.0	0.0	±13.8	±11.2	0.0	0.0	±8.8	±6.4	0.0	±6.8
	Y-Y-C=C	0.0	0.0	±16.0	±15.5	0.0	0.0	±9.7	±8.7	0.0	0.0	±6.7	±5.3	0.0	±5.6
	Y-Y-C-Z	180	180	±168	±170	180	180	±177	±176	180	180	±176	±177	180	±175
	Y-C=C-Y	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
	Z-C=C-Z	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
	Y-C-C-Z	180	180	±175	±173	180	180	±172	±174	180	180	±177	±177	180	±179
Imaginary freq. b₁(cm^-1)		135.3	201.2	——		304.7	150.1	——		179.3	74.8	——		148.4	——
Normal modes in Cartesian X	X_Y-C	+0.1551	+0.1704	——		+0.0942	+0.1096	——		+0.0483	+0.0645	——		+ 0.0300	——
	X_C	-0.1269	-0.1259			-0.0861	-0.0907			-0.0463	-0.0544			-0.0308
	X_Z	+0.0571	+0.0244			+0.0966	+0.0426			+0.1304	+0.0449			+0.1480
	X_Y	+0.1032	+0.0188			+0.0885	+0.0337			+0.1834	+0.0638			+0.2399

	C₂O₃H₂		C₂S₃H₂		C₂Se₃H₂		C₂Te₃H₂		C₂O₃F₂		C₂S₃F₂		C₂Se₃F₂
Arrangement of MO’s energy level	a ₁	HOMO-3	a ₁	HOMO-4	a ₁	HOMO-3	a ₁	HOMO-3	a ₁	HOMO-4	a ₁	HOMO-4	a ₁	HOMO-3
	a₁ '	LUMO+2	a₁ '	LUMO+1	a₁ '	LUMO+2	a₁ '	LUMO+1	a₁ '	LUMO+2	a₁ '	LUMO+2	a₁ '	LUMO+2
	a₂	HOMO	a₂	HOMO-1	a₂	HOMO-4	a₂	HOMO-4	a₂	HOMO	a₂	HOMO-1	a₂	HOMO-4
	a₂ '	LUMO	a₂ '	LUMO+2	a₂ '	LUMO	a₂ '	LUMO+2	a₂ '	LUMO+1	a₂ '	LUMO	a₂ '	LUMO
	b₁	HOMO-1	b₁	HOMO	b₁	HOMO	b₁	HOMO-1	b₁	HOMO-1	b₁	HOMO	b₁	HOMO
	b₁ '	HOMO-4	b₁ '	HOMO-3	b₁ '	HOMO-2	b₁ '	HOMO-2	b₁ '	HOMO-3	b₁ '	HOMO-3	b₁ '	HOMO-2
	b₂	HOMO-2	b₂	OMO-2	b₂	HOMO-1	b₂	HOMO	b₂	HOMO-2	b₂	HOMO-2	b₂	HOMO-1
	b₂ '	LUMO+1	b₂ '	LUMO	b₂ '	LUMO+1	b₂ '	LUMO	b₂ '	LUMO	b₂ '	LUMO+1	b₂ '	LUMO+1
Electron excitation	b₁'® a₁'		b₁'® a₁'		b₁'® a₁'		b₁'® a₁'		b₁'® a₁'		b₁'® a₁'		b₁'® a₁'
Electron excitation	HOMO-4 to LUMO+2		HOMO-3 to LUMO+1		HOMO-2 to LUMO+2		HOMO-2 to LUMO+1		HOMO-3 to LUMO+2		HOMO-3 to LUMO+2		HOMO-2 to LUMO+2

State symmetry	Main electronic configuration	Weight Coefficients
State symmetry	Main electronic configuration	C₂O₃H₂	C₂S₃H₂	C₂Se₃H₂	C₂Te₃H₂	C₂O₃F₂	C₂S₃F₂	C₂Se₃F₂
A₁	*a₁² a₂² b₁² b₁' ² b₂²*	0.9946	0.9930	0.9917	0.9922	0.9935	0.9944	0.9919
	*a₁¹ a₁' ^-1 a₂² b₁² b₂² b₂' ²*	-0.0836	-0.0901	0.0899	-0.0850	0.0798	0.0935	0.0832
	*a₁^-1 a₁' ¹ a₂² b₁² b₂² b₂' ²*	0.0836	0.0901	-0.0899	0.0850	-0.0798	-0.0935	-0.0832
	*a₁² a₂² b₁² b₁' ²b₂¹ b₂' ^-1*	0.0792	0.0801	-0.0820	0.0802	-0.0813	-0.0788	-0.0795
	*a₁² a₂² b₁² b₁' ²b₂^-1 b₂' ¹*	-0.0792	-0.0801	0.0820	-0.0802	0.0813	0.0788	0.0795
	*a₁² a₂² a₂' ² b₁² b₂²*	-0.1035	-0.1041	-0.1080	-0.1106	-0.1091	-0.1033	-0.1076
B₁	**a₁² a₁' ¹ a₂² b₁² b₁' ^-1 b₂²**	-0.7013	-0.6988	-0.7019	-0.7023	-0.7012	-0.7009	-0.7007
	**a₁² a₁'^{- 1} a₂² b₁² b₁' ¹ b₂²**	0.7013	0.6988	0.7019	0.7023	0.7012	0.7009	0.7007
	a₁² a₁' ¹ a₂² b₁² b₁' ^-1 b₂^-1 b₂' ¹	0.0628	0.0631	0.0645	0.0622	0.0625	0.0634	0.0601
	**a₁² a₁' ^-1 a₂² b₁² b₁' ¹ b₂¹ b₂'^{- 1}**	0.0628	0.0631	0.0645	0.0622	0.0625	0.0634	0.0601
	**a₁² a₁' ¹ a₂¹ a₂' ^-1 b₁² b₁' ^-1 b₂²**	-0.0611	-0.0613	-0.0603	-0.0614	-0.0596	-0.0602	-0.0606
	**a₁² a₁' ¹ a₂^-1 a₂' ¹ b₁² b₁' ^-1 b₂²**	-0.06211	-0.0613	-0.0603	-0.0614	-0.0596	-0.0602	-0.0606

Molecules	K in eV/Å²	K' in eV/Å²	F in eV/Å	D in eV
C₂O₃H₂	0.82	1.47	1.03	4.35
C₂S₃H₂	3.20	1.45	2.70	2.84
C₂Se₃H₂	1.92	1.34	2.22	2.28
C₂Te₃H₂	3.33	1.75	2.83	1.85
C₂O₃F₂	1.93	1.43	2.28	3.50
C₂S₃F₂	2.02	1.50	2.34	2.30
C₂Se₃F₂	1.89	1.38	2.43	2.15

Brasil

Brasil

THE SYMMETRY BREAKING PHENOMENON IN 1,2,3-TRIOXOLENE AND C₂Y₃Z₂ (Z= O, S, Se, Te, Z= H, F) COMPOUNDS: A PSEUDO JAHN-TELLER ORIGIN STUDY

Abstract

INTRODUCTION

COMPUTATION DETAILS

SYMMETRY BREAKING PHENOMENON IN THE C₂Y₃Z₂ SERIES

ACTIVE SPACE IN SA-CASSCF CALCULATION

THE PJTE DUE TO PUCKERING

CONCLUSIONS

REFERENCES

Publication Dates

History

Brasil

Brasil

THE SYMMETRY BREAKING PHENOMENON IN 1,2,3-TRIOXOLENE AND C2Y3Z2 (Z= O, S, Se, Te, Z= H, F) COMPOUNDS: A PSEUDO JAHN-TELLER ORIGIN STUDY

Abstract

INTRODUCTION

COMPUTATION DETAILS

SYMMETRY BREAKING PHENOMENON IN THE C2Y3Z2 SERIES

ACTIVE SPACE IN SA-CASSCF CALCULATION

THE PJTE DUE TO PUCKERING

CONCLUSIONS

REFERENCES

Publication Dates

History

THE SYMMETRY BREAKING PHENOMENON IN 1,2,3-TRIOXOLENE AND C₂Y₃Z₂ (Z= O, S, Se, Te, Z= H, F) COMPOUNDS: A PSEUDO JAHN-TELLER ORIGIN STUDY

SYMMETRY BREAKING PHENOMENON IN THE C₂Y₃Z₂ SERIES