Analysis of pseudo jahn-teller distortion based on natural bond orbital theory: Case study for silicene.

Ground state (GS) instability of nondegenerate molecules in high symmetric structures is understood through Pseudo Jahn-Teller mixing of the electronic states through the vibronic coupling. The general approach involves setting up of a Pseudo Jahn-Teller (PJT) problem wherein one or more symmetry allowed excited states couple to the GS to create vibrational instability along a normal mode. This faces two major complications namely (1) estimating the adiabatic potential energy surfaces for the excited states which are often difficult to describe in case the excited states have charge-transfer or multi-excitonic (ME) character and (2) finding out how many such excited states (all satisfying the symmetry requirements for vibronic coupling) of increasing energies need to be coupled with the GS for a particular PJT problem. An analogous alternative approach presented here for the well-known case of symmetry breaking of planar (D6h ) hexasilabenzene (Si6 H6 ) to the buckled (D3d ) structure involves identifying the second-order donor-acceptor, hyperconjugative interactions (E2 i → j ) that stabilize the distorted structure. Following the recent work of Nori-Shargh and Weinhold, one observes that the orbitals involved in the vibronic coupling between the S0 /Sn states and those for the donor (filled)-acceptor (empty) interactions are identical. In fact, deletion of any particular pair of E2 i → j interaction creates vibrational instability in the buckled structure and as a corollary, deleting it for the planar structure removes its instability. The one-to-one correlation between the natural bond orbital theory and PJT theory assists in an intuitive identification of the relevant (few) excited states from a manifold of computed ones that cause symmetry breaking by vibronic coupling.