Characterizing the excess electron of Li(NH3)4

Small lithium ammonia clusters are model systems for the dissociation of metals into solvated cations and electrons in ammonia. Metal–ammonia solutions display a complex behavior with increasing metal concentration including a phase change from a paramagnetic to a metallic dia- magnetic phase, and small clusters should be useful models in the low concentration regime, where one one may expect the ammoniated electron to show a behavior similar to that of the hydrated electron. Yet, even in the low concentration regime the nature of the ammoniated electron is still controversial with cavity models supported by optical and density measurements whereas localized radical models have been invoked to explain magnetic measurements. Small clusters can shed light on these open questions, and in particular the Li–NH3 tetramer represents the smallest cluster with a complete solvation shell for the Li+ cation. In view of the controversies about the character of the excess electron, the first question investigated is whether different theoretical characteri- zations of the ‘excess electron’ lead to different conclusions about it. Only small differences are found between orbital-based and spin density-based and between self-consistent-field and coupled- cluster-based methods. Natural orbitals from equation-of-motion coupled-cluster calculations are then used to analyze the excess electron’s distribution of Li(NH3)4 with particular emphasis on the portion of the excess electron’s density that is closely associated with the N atoms. Three different comparisons show that only about 6% of the excess electron’s density are closely associated with the atoms, with about 1% being closely associated with any N atom, and that the electron is best characterized as a Rydberg-like electron of the whole cluster. Finally, it is shown that in spite of the small amount of density close to the N atoms, the spin-density at the N nuclei is substantial, and that the magnetic observations can plausibly be explained within the cavity model.

Although solvated electrons and their finite analogues, electron-molecule clusters, have been the focus of a large body of research, the molecular level understanding of these species remains the topic of lively debate. One of the most fundamental questions pertains to the very nature of a solvated electron. In aqueous solutions, the cavity model is now widely accepted, even though the cavity itself is thought of as much more flexible and dynamic than the rigid, spherical cavity originally envisioned. In ammonia, however, the situation is less clear cut, and alternative models that view the electron as closely associated with one or several molecular or atomic species, that is, as a possibly distributed, but still localized radical anion, are very much alive .

In the first place, the ammoniated electron is a much richer phenomenon than the aqueous electron, because it exists over far larger concentration ranges and far longer time scales. Its properties depend drastically on the concentration, and owing to its longer lifetime there is a larger variety of experimental data including NMR and ESR measurements. Yet, even in the low concentration regime, where one might expect the ammoniated electron and the aqueous electron to behave similarly, the debate between cavity models, which place the solvated electron in a cavity of the solvent, and radical models, which view the electron as closely associated with one or several molecular or atomic species, that is, as a localized or delocalized, but essentially atom-centered radical anion is still ongoing. It is important to emphasize that both models apply to the ammoniated electron in the sense of ‘the long-lived intermediate that is responsible for the intensive absorption in the visible’. Solvated electrons are very reactive and will at some point form radicals in all but the most inert solvents .

Here we can only briefly summarize the gist of the debate; a recent review discusses open questions in all concentration regimes, and regarding the present context, the two models have been most clearly juxtaposed. With a grain of salt, the intensive optical absorption, which is largely metal independent, and the substantial molar excess volume of metal ammonia solutions are most easily explained within a cavity model, whereas magnetic measurements, in particular the Knight shifts of the N nuclei, can be used to argue for a substantial N-centered radical character. The particular number often cited in this context goes back to Symons who concluded on the basis of magnetic measurements that “the electron spends some 20% of its time in the N 2s orbital.” Calculations for finite systems yield vastly different results. For ammonia cluster anions a recent analysis of the spin density from density functional calculations (BLYP functional) suggests that “most of the excess electron density is on the nitrogen atoms” [5], whereas equation-of-motion coupled-cluster calculations predict that only a small percentage of the excess electron is associated with the N atoms (less than 1% per N atom). For the Li–ammonia tetramer Rydberg-like orbitals of the whole cluster were found in both, self- consistent-field, and density functional (revPBE functional) calculations, but the detailed analysis of the Hartree-Fock and Kohn-Sham orbitals involved radial averaging so that the amount of density closely associated with the N atoms is not obvious. On the other hand, the authors also emphasize N 2s contributions to the orbital of the excess electron (in terms of NH3 valence orbitals) as well as large values of the excess electron orbital around the H and N atoms.

Here we start with the question whether different conclusions about the excess electron are due to the different choices of how to characterize it and compare five different ab initio methods. Then coupled-cluster methods are used to study the dissociation of a Li atom into a solvated Li+ ion and a ‘solvated’ electron with particular emphasis on the excess electron density closely associated with the N atoms. On the one hand, the sequence Li(NH3)n with n = 0 − 4 is examined, on the other hand the dissociation is investigated by changing the Li-N distance in the tetramer, Li(NH3)4, from infinity to the equilibrium value. Moreover, the radial analysis of is complemented, again, so as to reveal the amount of density closely associated with the N atoms. Last, the apparent conflict between a high spin density on the N atoms, but only a small percentage of the spin density being closely associated with the N atoms is resolved.

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