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Bulletin of the Chemical Society of Japan

A Density Functional Analysis on Formation of Rubidium and Cesium Atomic Clusters in the Highest Spin State

Xuan Liu, Haruhiko Ito, E. Torikai

Published Aug 9, 2013• 3 citations
Publisher

Abstract

Abstract We select a couple of density functional formalisms suitable for the computation of the highest spin clusters composed of a small number of heavy alkali-metal atoms such as Rb and Cs. Using B3P86 and PW91PW91 density functional methods with Lanl2dz basis set, we analyze the geometry, the binding energy, and the bond length of Rbn and Csn with n = 2–14 in the highest spin state. The exchange energy of the highest spin clusters increases the binding energy with the number of the constituent atoms.

DOI
10.1246/bcsj.20130165

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Abstract We select a couple of density functional formalisms suitable for the computation of the highest spin clusters composed of a small number of heavy alkali-metal atoms such as Rb and Cs. Using B3P86 and PW91PW91 density functional methods with Lanl2dz basis set, we analyze the geometry, the binding energy, and the bond length of Rbn and Csn with n = 2–14 in the highest spin state. The exchange energy of the highest spin clusters increases the binding energy with the number of the constituent atoms.
The structure of alkali-metal atomic clusters is optimized with B3P86 hybrid functional for the highest spin state as well as with B3LYP hybrid functional for the lowest spin state. A dramatic change from plane to solid occurs in the highest spin state when the number of constituent atoms is four. The binding, exchange, and correlation energies are evaluated for both the highest and lowest spin states. Next, we explore the dependence of the exchange and correlation energies on the binding energy. The exchange energy contributes to the formation of the highest spin clusters, whereas the correlation energy contributes to the formation of the lowest spin clusters. The highest spin clusters are most stable when the exchange energy is a minimum. Then, to see why the ferromagnetic bond among spin-aligned identical atoms arises against Pauli exclusion principle, we estimate the mixing ratio of p orbitals in molecular orbitals. The s-p hybridization increases the binding energy in absolute value due to the extensive overlap of molecular orbitals and leads to generation of the highest spin clusters.
The study of small clusters is intended to fill the knowledge gap between single atoms and bulk material. He nanodroplets are an ideal matrix for preparing and investigating clusters in a superfluid environment. Alkali-metal atoms are only bound very weakly to their surface by van der Waals forces. Due to the formation process, high-spin states of alkali-metal clusters on He nanodroplets are favorably observed, which is in contrast to the abundance in other preparation processes. Until now, the prevailing opinion was that stable clusters of the heavy alkali-metal atoms, rubidium (Rb) and cesium (Cs) on He nanodroplets, are limited to 5 and 3 atoms, respectively (Schulz et al., Phys. Rev. Lett. 2004, 92, 13401). Here, we present stable complexes of Rb(n)⁺ and Cs(n)⁺ consisting of up to n = 30 atoms, with the detection of large alkali-metal clusters being strongly enhanced by one-photon ionization. Our results also suggest that we monitored both high-spin and low-spin state clusters created on nanodroplets. The van der Waals bound high-spin alkali-metal clusters should show strong magnetic behavior, while low-spin states are predicted to exhibit metallic characteristics. Alkali-metal clusters prepared in these two configurations appear to be ideal candidates for investigating nanosized particles with ferromagnetic or metallic properties.
Helium nanodroplet isolation has been applied to agglomerate alkali clusters at temperatures of 380 mK. The very weak binding to the surface of the droplets allows a selection of only weakly bound, high-spin states. Here we show that larger clusters of alkali atoms in high-spin states can be formed. The lack of strong bonds from pairing electrons makes these systems nonmetallic, van der Waals-like complexes of metal atoms. We find that sodium and potassium readily form such clusters containing up to 25 atoms. In contrast, this process is suppressed for rubidium and cesium. Apparently, for these heavy alkalis, larger high-spin aggregates are not stable and depolarize spontaneously upon cluster formation.
A simple approximate version of the Fock-space relativistic coupled-cluster method is developed and applied for modeling the spin-orbit-coupling effect in the ${A}^{1}{\mathrm{\ensuremath{\Sigma}}}_{(u)}^{+}$ and ${b}^{3}{\mathrm{\ensuremath{\Pi}}}_{(u)}$ states of the heavy alkali diatomics RbCs and Cs2{\mathrm{Cs}}_{2}Cs2​. Numerical stability in a wide range of molecular geometries is achieved at the cost of a very moderate loss of accuracy for low-lying states and negligibly small deviations of the computational scheme from strict size consistency. The adiabatic potential energy curves computed for the (2,3)0+(2,3){0}^{+}(2,3)0+ (RbCs) and (1,2)0u+(1,2){0}_{u}^{+}(1,2)0u+​ (Cs2{\mathrm{Cs}}_{2}Cs2​) states are converted into ``quasidiabatic'' potentials and effective spin-orbit-coupling functions via projection of the scalar relativistic states onto the subsets of fully relativistic states. A detailed comparison of the present ab initio results with their experimental and preceding theoretical counterparts is performed.