Origin of Small Barriers in Jahn–Teller Systems: Quantifying the Role of 3d–4s Hybridization in the Model System NaCl:Ni⁺

Despite its relevance, the microscopic origin of the energy barrier, B, between the compressed and elongated geometries of Jahn–Teller (JT) systems is not well understood yet because of a lack of quantitative data about its various contributions. Seeking to clear up this matter, we have carried out both periodic and cluster ab initio calculations on the model system NaCl:Ni+.

This system is particularly puzzling because, according to experimental data, its barrier is much smaller than that for other d9 and d7 ions in similar lattices. All calculations performed on the model system lead, in fact, to values |B| ≤ 160 cm–1, which are certainly smaller than B = 500 cm–1 derived for NaCl:M2+ (M = Ag, Rh) or B = 1024 cm–1 obtained for KCl:Ag2+.

As a salient feature, analysis of calculations carried out as a function of the Qθ (3z2 – r2) coordinate unveils the microscopic origin of the barrier. It is quantitatively proven that the elongated geometry observed for NaCl:Ni+ is due to the 3d–4s vibronic admixture, which is slightly larger than the anharmonicity in the eg JT mode that favors a compressed geometry.

The existence of these two competing mechanisms explains the low value of B for the model system, contrary to cases where the complex formed by d9 or d7 ions is elastically decoupled from the host lattice. Although the magnitude of B for NaCl:Ni+ is particularly small, the tunneling splitting, 3Γ, is estimated to be below 9 cm–1, thus explaining why the coherence is easily destroyed by random strains and thus a static JT effect is observed experimentally.

As a main conclusion, the barrier in JT systems cannot be understood neglecting the tiny changes of the electronic density involved in small distortions. The present calculations reasonably explain the experimental g tensor of NaCl:Ni+, pointing out that the d–d transitions in NiCl65– are much smaller than those for CuCl64– and the optical electronegativity of Ni+ is only around 1.