Dynamical Jahn-Teller effect of fullerene anions

Abstract

The dynamical Jahn-Teller effect of C n− 60 anions (n = 1-5) is studied using the numerical diagonalization of the linear p n ⊗ 8d Jahn-Teller Hamiltonian with the currently established coupling parameters. It is found that in all anions the Jahn-Teller effect stabilizes the low-spin states, resulting in the violation of Hund's rule. The energy gain due to the Jahn-Teller dynamics is found to be comparable to the static Jahn-Teller stabilization. The Jahn-Teller dynamics influences the thermodynamic properties via strong variation of the density of vibronic states with energy. Thus, the large vibronic entropy in the low-spin states enhances the effective spin gap of C 3− 60 quenching the spin crossover. From the calculations of the effective spin gap in function of the Hund's rule coupling, we found that the latter should amount 40 ± 5 meV in order to cope with the violation of Hund's rule and to reproduce the large spin gap. With the obtained numerical solutions the matrix elements of electronic operators for the low-lying vibronic levels and the vibronic reduction factors are calculated for all anions. arXiv:1711.00340v3 [cond-mat.mtrl-sci]

Dynamical Jahn‐Teller effect in the first excited

“…From this table, ground vibronic levels with vibronic angular momentum J = 1 for the T 1 u () and T 1 g () electronic states are −96.5 (−111.8) and −113.8 (−136.1) meV for B3LYP (CAM‐B3LYP) calculations, respectively. A previous study shows that for ground electronic states, contributions from the static and dynamic JT effect to ground vibronic energy are almost the same, and the ratios of dynamical contribution to static contribution are smaller in the case than that in the case by both B3LYP and CAM‐B3LYP, which is consistent with the fact that the orbital vibronic couplings for t 1 g NLUMOs are stronger than that in t 1 u LUMOs.…”

“…Besides, these coupling parameters derived from B3LYP functional were shown in good agreement with those from the gradients of GW quasiparticle levels . Furthermore, with these parameters, the spin gap of was well reproduced . Although vibronic coupling parameters of have been derived using local density approximation, generalized gradient approximation, and also post Hartree‐Fock calculations, but the former two methods underestimate and the latter one overestimates vibronic coupling parameters.…”

“…Dynamical JT effect in T 1 g electronic states has been discussed in, for example, References and . Indeed, as found in Section 2.5, the stabilization energies by dynamical JT effect calculated by both B3LYP and CAM‐B3LYP are stronger than that in ground electronic states (Table , with the data with B3LYP for LUMOs), suggesting the importance of vibronic dynamics in the excited electronic states. And most importantly, CAM‐B3LYP may work better than B3LYP in the study of fullerene‐related material as it gives much closer vibronic coupling constants to experimental data.…”

“…Here, n h = ( n hθ , n hɛ , n hξ , n hη , n hζ ) is the set of vibrational quantum numbers of the harmonic oscillation part of Equation , and are elements of Clebsch‐Gordan coefficient matrices. Such an expansion using the direct products of electronic states and eigenstates of harmonic oscillator has been proposed long time ago and has been routinely used as a reliable approach to quantitatively study dynamical JT systems including fullerene anions …”

“…Since the molecular nature strongly remains in these materials, thorough understanding of the JT effect of C 60 anions is crucial. Although JT effect, including dynamic one, of C 60 anions has been intensively investigated, it is only past few years that the actual situation of the ground electronic states of molecule (n = 1‐5) has been established with accurate vibronic coupling parameters …”