We present a detailed investigation of static dipole polarizability of lithium clusters containing up to 22 atoms. We first build a database of lithium clusters by optimizing several candidate structures for the ground state geometry for each size. The full polarizability tensor is determined for about 5-6 isomers of each cluster size using the finite-field method. All calculations are performed using large Gaussian basis sets, and within the generalized gradient approximation to the density functional theory, as implemented in the NRLMOL suite of codes. The average polarizability per atom varies from 11 to 9 Angstrom^3, within the 8-22 size range and show smoother decrease with increase in cluster size than the experimental values. While the average polarizability exhibits a relatively weak dependence on cluster conformation, significant changes in the degree of anisotropy of the polarizability tensor are observed. Interestingly, in addition to the expected even odd (0 and 1 $\mu_B$) magnetic states, our results show several cases where clusters with an odd number of Li atoms exhibit elevated spin states (e.g. 3 $\mu_B$).
Materials composed purely of alkali atoms are expected to closely mimic the free-electron gas or jellium models as they have only one very delocalized electron outside of a noble-gas shell. Because of the relative simplicity of pure alkali systems they are often viewed as good systems for benchmarking quantum-mechanical methods and for investigating the transition from localized to intinerent electronic behavior [1,2]. This is especially true for density-functional-based calculations since the original approximations to density-functional theory [3] were based upon analytical expressions derived from exchange-only treatments of the the free-electron gas. For example Slater derived an expression for a local potential which reproduced the Hartree-Fock trace of the free electron gas [4]. Later, Kohn and Sham derived an expression that reproduced the Fermi energy of the free electron gas [5]. The latter expression also reproduces the total exchange-energy of a free-electron gas (See for example Ref. [6]). The factor of 3/2 difference in the Kohn-Sham and Slater approximations also lead to the use of the X α approximations [4,7] and approximations along the lines of this method continue to be investigated as an attractive means for developing approximate element dependent functionals that permit fully analytic implementation of density functional theory [8,9]. Such analytic implementation is computationally very efficient and has been used for structure optimization of icosahedral fullerenes containing more than two thousand atoms using triple-zeta quality basis set [10,11].
The ability to accurately reproduce polarizabilities of large systems is of significant importance to many forefront research areas in computational chemistry, materials science and quantum physics. The ability to accurately determine polarizabilities is required to account for hydrogen bonding, van der Waal’s interactions, [12,13] solvation effects, [14] and a materials dielectric response. As discussed in Ref. [12], the same interactions or matrix elements required for an accurate determination of phenomena that are directly mediated by polarizabilities also determine a variety of transition rates which include spontaneous emission, stimulated absorption and emission, and Foerster-energy transfer rates. Such rates are of direct importance to the problem of many photovoltaic applications. The radiative transition rates must also be quantified for applications to quantum-control of matter or any type of light-mediated manipulation of molecular-and clustermaterials. Derivatives of the polarizability tensor with respect to normal-mode displacement also determine the intensity of the Raman shifts of a given molecule or cluster [15,16].
Because of the central role that polarizabilities play in materials science and chemistry there have been significant efforts aimed at experimentally validating theoretically predicted polarizabilities. However, such experiments are themselves very difficult to interpret for a variety of reasons. From the standpoint of comparison to experiments on bulk systems, the polarizability of an array of nonoverlapping polarizable molecules may be approximated from the Clausius-Mossotti relation. Such comparisons have been performed with some success on very idealized systems such as fullerene molecules [17,18,19,20]. However, for pure-metal clusters the polarizability may not be determined from such a means because the individual clusters would coalesce into the the bulk material if placed upon a lattice. As such the preferred experimental approach for measurement of metal-cluster polarizabilities rely upon the electrostatic equivalent of a Stern-Gerlach experiment in which a beam of metal clusters traverse a nonuniform electric field and are deflected due to the the induced polarization of the cluster [21,22,23,24,25]. Again, for simple systems such a fullerene molecules quantitative agreement between theory and experiment has been achieved. However, for metallic clusters deviations exist between different experiments and also between experiment and theory. Generally, it appears that the theoretically predicted polarizabilties display a more monotonic and smooth behavior than the experimental measurements. Moreover, earlier comparisons suggested that the experimental polarizabilities tended to be larger than theory. Such discrepancies are now largely understood to be due to temperature dependent corrections that depend upon the permanent dipole of the clusters. However, some discrepancies still exist and it is not understood why. One possibility that we attempt to investigate here is that different low-lying geometries of a cluster may have significantly different polarizabilites or anisotropies in their polarizabilities.
Experimental measurements of polarizability of Li clusters containing up to 22 atoms have been reported [25]. Here, we present and compare our density functional predictions of polarizabilities of Li
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