Vibronic coupling in the icosahedralC602+Jahn-Teller cation: Repercussions of the nonsimple reducibility of theH⊗H

Abstract

Coulomb coupling between the two holes in the fullerene cation C 60 2+ results in high-and low-spin terms.Vibronic coupling of the high-spin terms to a single mode of vibration of h g symmetry can distort the lowest adiabatic potential-energy surface into wells of D 3d , D 5d , D 2h , or C 2h symmetry depending upon the precise nature of the coupling produced by different admixtures of the two sets of coupling coefficients arising from the two H-type irreducible representations appearing in the symmetric part of the H H Kronecker product. The symmetry of dynamic distortions of C 60 2+ ions when coupling to all eight of the possible h g modes is takeninto account depends very closely on both the vibronic coupling parameters and the splittings between different Coulomb terms. Using estimates for these parameters from the literature leads us to conclude that the distortional symmetry is most likely to be D 2h , but there is also the possibility that it could be D 3d .

Quadratic Jahn-Teller effect of fullerene anions

“…The expression of the symmetrized h g displacements has been presented in Refs. [39,61,73]. The following symmetrized displacements contain those by g g modes as well as the h g displacements.…”

Interplay between Coulomb and Jahn-Teller effects in icosahedral systems with triplet electronic states coupled toh-type vibrations

“…This is the usual approach for combining interelectron and JT interactions, 1,2 which has been used in a number of previous works. 1,2,[15][16][17][18][19][20]24 Starting from this basis, Hamiltonians can be constructed that incorporate the interelectron interactions by placing different terms at different energies. Additional contributions to the Hamiltonian are then added to incorporate JT interactions within the terms and between coupled terms.…”

“…Furthermore, applying operations of the icosahedral group to the Q γ (γ ∈ {θ, , 4,5,6}) shows that at least one minimum of each of D 5d , D 3d , D 2h , and C 2h can be found that involves just Q θ , Q , and Q 6 , so we can set Q 4 = Q 5 = 0. 18 Further conditions to generate minima of a given symmetry are given in Table I. 18 Using these conditions greatly simplifies the problem of finding JT minima, as instead of minimizing the energy with respect to the five Q γ , it is only necessary to carry out a minimization in one dimension (for D 5d / D 3d symmetry), two dimensions (for D 2h symmetry), or three dimensions (for C 2h ).…”

“…18 Further conditions to generate minima of a given symmetry are given in Table I. 18 Using these conditions greatly simplifies the problem of finding JT minima, as instead of minimizing the energy with respect to the five Q γ , it is only necessary to carry out a minimization in one dimension (for D 5d / D 3d symmetry), two dimensions (for D 2h symmetry), or three dimensions (for C 2h ).…”

Jahn–Teller Effects in Molecules on Surfaces with Specific Application to C60

“…Although this complication can be dealt with (see e.g. [48]), it is often easier to work in terms of a single, effective mode as this is far simpler and reproduces most of the important aspects of the problem. In fact, in the current context, even the details of some effective mode of vibration are effectively irrelevant as we are ignoring the distortion of the C 60 cage.…”