A Computational Theoretical Study of the Stability of Distorted Structures in Multi-Mode Problem

The purpose of this research is to provide a deeper understanding of the planar highsymmetryconfiguration instability. To this end, compounds of neutral and anion radicaltetrafluoroethylene (C2F4) with a planar geometry (D2h symmetry) were considered. Geometryoptimization and calculation of vibration frequencies were performed using the Gaussian-09suites of the program[1]. The frequencies analysis of C2F4 neutral molecule optimized byHF/Def2-TZVPP showed that are all positive eigenvalue and real and this result confirmsequilibrium structure with the minimum energy in its electronic ground state (1Ag). In contrastwith adding an electron to C2F4 neutral molecule and formation of an anion radical C2F4,appeared three negative eigenvalues that with respect to the symmetry of the displacements wereQb2g, Qb3u and Q au. The advent of imaginary frequencies means that the structure of the planarconfiguration anion radical C2F4 is instable and leading to symmetry breaking which causesstructural distortion and affects the alternating the length of the bond (ALB) and these imaginaryfrequencies called unstable modes. As each imaginary frequency (unstable modes) is responsiblefor creation particular configurations, so that the instability of the high-symmetry D2h is distortedcorresponding symmetric distortion modes b2g, b3u and au qas trans-bent (D2h→C2h), cis-bent(D2h→C2v) and twisted (D2h→D2,) configurations, respectively. It is worth noting that thesymmetry breaking removes the degeneracy of electronic and generation non-degenerate states.According to relative energies of bending configurations, the favorable structure is the trans-bentwith C2h symmetry and this stability is based on energy considerations. Essentially lowest-energygeometry for a C2F4 radical anion (isomer with the lowest energy) as the initial structureintroduced and this is based on energy considerations that a symmetric system can lose itssymmetry and lower energy, because the Hamiltonian system changes, and the new Hamiltonianwill not have previous symmetry, that is, the so-called symmetry breaking .

Keywords:

Multi-Mode Problem , Symmetry Breaking , Imaginary Frequencies , Natural bond orbital and Trans-bent configuration