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The Journal of Physical Chemistry A

Exchange-Correlation Interaction and AO-Hybridization of Alkali-Metal Atomic Clusters

Xuan Liu, Haruhiko Ito, E. Torikai

Published Aug 21, 2013• 2 citations
Publisher

Abstract

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.

DOI
10.1021/jp4074575

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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.
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.
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.
Full text: In recent experiments of our group on alkali-metal-doped helium droplets, it could be shown that the hyperfine structure of the dopants is strongly affected by the helium surrounding. A change of the hyperfine splitting of {sup 39}K is observed as a function of the nozzle temperature, indicating a dependence on the helium droplet size. Hence we started a theoretical investigation based on an open shell coupled cluster approach to study this size effect within molecular orbital theory. In our theoretical model we are restricted to very small He{sub N}X clusters (N=1- 5,X=Li,Na,K) due to the high computational demands of the chosen method. However, it is possible to identify two antagonistic effects of the helium surrounding on the electronic wavefunction of the alkali dopant: The first effect is a compression of the wavefunction which leads to higher spin densities |{Phi}{sub 0}|{sup 2} at the core, the second one is a reduction of |{Phi}{sub 0}|{sup 2} due to the Pauli repulsion, i.e. the deformation of the s-orbitals. Despite of the computational limitations we also try to give estimations for larger systems. Here we apply a combination of the quantum chemistry approach with a stochastic geometry optimization. Assuming only two-body-interactions we use the simulated annealing technique to obtain geometry predictions. (author)
The pseudopotential molecular-structure method has been used to calculate the X1{X}^{1}X1\ensuremath{\Sigma} and a3{a}^{3}a3\ensuremath{\Sigma} interaction potentials for the alkali-metal-atom--hydrogen-atom systems. These potentials were then used in a quantum-mechanical calculation to determine the spin-exchange cross sections in the energy range from 2.5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$ eV to 2.5 eV. The cross sections follow the general form Q1/2{Q}^{1/2}Q1/2=a-b lnv. However, abundant structure on the cross sections is present due to orbiting resonances induced by the deeply bound well of the X1{X}^{1}X1\ensuremath{\Sigma} molecular state. The spin-exchange cross sections range from 17\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}16}$ to 25\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}16}$ cm2{\mathrm{cm}}^{2}cm2 at room temperature for H(F=1) transferring to H(F=0) in collision with unpolarized lithium and cesium, respectively.
The electronic, magnetic, and structural properties of small clusters are studied in the framework of the single-band Hubbard Hamiltonian. Results for various ground-state and excited-state many-body properties are presented, which were calculated exactly by means of Lanczos's numerical diagonalization method. A full geometry optimization is performed for N\ensuremath{\le}8 atoms by considering all possible nonequivalent cluster structures with fixed nearest-neighbor bond lengths. The most stable structure and the corresponding total spin S are obtained rigorously as a function of the Coulomb interaction strength U/t and number of electrons \ensuremath{\nu}. The resulting interplay between electron correlations, magnetism, and cluster structure is analyzed and the main trends as a function of N, U/t, and \ensuremath{\nu} are derived. The stability of cluster ferromagnetism is studied from two complementary points of view. First, for N\ensuremath{\le}8 and \ensuremath{\nu}=N+1, we determine exactly the stability of the ferromagnetic ground state with respect to electronic excitations and structural changes. It is shown that in small clusters the structural changes can be as important to the temperature dependence of the magnetization as the purely electronic excitations. Second, we determine the stability of the saturated ferromagnetic state with respect to single spin flips as a function of the band filling \ensuremath{\nu}/N. In this case a few selected larger clusters (7\ensuremath{\le}N\ensuremath{\le}43) in the strongly correlated limit (U/t\ensuremath{\rightarrow}+\ensuremath{\infty}) are considered. It is shown that the \ensuremath{\nu}/N dependence of the spin-flip energy \ensuremath{\Delta}${\mathrm{\ensuremath{\varepsilon}}}_{\mathrm{sf}}$ shows interesting electronic-shell-like oscillations, which reflect the characteristics of the single-particle energy-level structure and its dependence on the symmetry and size of the cluster. Finally, we conclude by discussing some of the limitations of the model together with relevant extensions. \textcopyright{} 1996 The American Physical Society.
A treatment of the spin-rotation coupling between alkali-metal atoms and He atoms is presented. Rotational distortions are accounted for in the wave function using a Coriolis interaction in the rotating frame. The expectation value of the spin-orbit interaction gives values of the spin-rotation coupling that explain previous experimental results. For spin-exchange optical pumping, the results suggest that lighter alkali-metal atoms would be preferred spin-exchange partners, other factors being equal.