Reexamination of the origin of the pseudo Jahn–Teller puckering instability in silicene

Abstract

Silicene, the graphene-like crystal formed by the Si hexagonal lattice, presents a periodic buckled structure whose origin is due to the pseudo Jahn-Teller instability on each of its planar six membered rings. This has been attributed to the coupling of the planar D6h ground state with the first b2g excited state through a b2g vibrational mode. Here we show, by explicitly calculating the vibronic coupling constants through a complete study of the PJT effect, that the vibronic coupling of the ground state with only one excited state to explain the planar instability is inconsistent with the linear multilevel PJT effect theory. It is also shown that in order to have consistency, the PJT model should include the next excited state, which is symmetry compatible coupled to the puckering mode. This is done by the analysis, based on DFT and TDDFT calculations, of the vibronic instability of the ground state of hexasilabenzene, the basic silicon hydrogenated hexagonal ring unit defining silicene.

Pseudo Jahn–Teller effect in the decasilanaphthalene molecule: Towards the origin of the buckling in silicene

“…The average bond lengths obtained with the methods B3LYP/TZ2P and TPSSH/TZ2P have very similar values with a maximum difference of 0.007 Å for D 2h and 0.019 Å for the distorted C 2h . It should be notice that the calculated bond lengths for the planar structure differ at most 0.043 Å compared to Si 6 H 6 (2.208 Å) [25], whose value is within the range of decasilanaphthalene. The Si 10 H 8 average puckering angle was of 36.6 for TPSSH/TZ2P and 40.5 for B3LYP/TZ2P; while a puckering angle of 30.9 and 40.0 were obtained for Si 6 H 6 with the same methods, respectively.…”

“…Jose and Datta [28] reported an average puckering angle of 33.7 and 34.3 for Si 6 H 6 and Si 10 H 8 , respectively, obtained with the methods M05-2X/TZVP and B3PW91/TZVP, which are closer to our TPSSH/TZ2P results. The HOMO-LUMO gaps obtained for planar Si 10 H 8 are 2.0 and 2.35 eV for TPSSH/TZ2P and B3LYP/TZ2P, respectively, against 3.31 and 2.94 eV for Si 6 H 6 with the same methods [25].…”

“…The exchange and correlation terms were approximated through the GGA B3LYP and meta-GGA TPSSH hybrids functionals, and all electrons TZ2P basis sets were used for the valence orbitals. The power of prediction of these methods have been previously tested for the hexasilabenzene molecule [25]. We followed the method developed by Molina et al [29] to estimate the JahnTeller energy gain (EJT).…”

“…Planar hexasilabenzene structure instability with D 6h symmetry to a puckered D 3d structure was originally attributed to the pseudo Jahn-Teller (PJT) effect through the coupling of the planar D 6h ground state with just one excited state through a b 2g vibrational mode, with the argument that the coupling to other excited states can be neglected due to their larger energy gap [11][12][13][14][15]24]. However, it was recently shown that in order to have consistency with the linear multilevel PJT effect theory, the coupling should be at least with two excited states [25]. It is worth stressing that the relative size of the energy gaps is not an a priori argument to discard the possible couplings; and the instability condition is given by the interplay of the energy gap, the vibronic coupling constant and the primary force constant of the ground state [26,27].…”

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

“…13,14 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. [15][16][17][18][19][20][21][22][23][24][25][26][27] 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 systems [28][29][30] or influences the parameters of the PJTE instability by removing or adding electrons; 31 they show that symmetry breaking phenomenon is suppressed in the folded systems.…”