DFT investigation of the influence of Jahn–Teller distortion on the aromaticity in square-planar arsenic and antimony clusters

Calculation of the Jahn-Teller parameters with DFT

“…37,64 A pragmatic way for a detailed calculation of the JT effect was developed by Daul et al, 37,64,65 and it has been successfully applied for the analysis of many JT active molecules. [64][65][66][67][68][69][70][71][72][73][74][75] 2. METHODOLOGY Within vibronic coupling theory, Hamiltonian, ℋ, is expanded as a Taylor series around the HS molecular structure, along the normal modes, Q i :…”

“…The parameters used to construct the surface were obtained by DFT. 70 Another example is the VCl 4 tetrahedral molecule (T d point group) with an E ground electronic state coupled with double degenerate vibrations also belonging to E irrep. Distortion lowers the symmetry to D 2d , and the degenerate state splits into 2 A 1 and 2 B 1 .…”

“…1, the relations are E JT = F 2 /2K and R JT = F/K, where F is the linear vibronic coup-ling constant, and K is the force constant of the normal mode. 70 In the case of VCl 4 , Fig. 2, second-order vibronic coupling is operational, and the relations are: E JT = F 2 /2(K-|G|), R JT (min) = |F|/(K-2|G|), R JT (TS)=|F|/(K+2|G|), Δ=4E JT /(K+2|G|), where F, K and G are the linear vibronic coupling constant, the force constant and the quadratic vibronic coupling constants, respectively.…”

“…Our analysis based on the IDP model indicated that totally symmetric modes do not contribute to the distortion in these molecules. 37,70 Thus, the JT effect in VCl 4 is in essence an example of ideal, single mode JT distortion, and Sb 4…”

“…is completely an analog to Sb 4 -. 70 Vibronic coupling constants for all three molecules were calculated by IDP, by their relation to the DFT obtained JT parameters, and by fit to the potential energy curves along the JT active normal modes. The results of the different approaches are consistent.…”