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%"e present a comparative study of several empirical and nonempirical models for the absorption potential, which is the imaginary part of an optical-model potential, for electron scattering by rare gases. %C show that the elastic differential cross section is most sensitive to the absorption potential fo1 high"1IIlpact cncrgy Rnd 18I'gc scattcllng angles. %c compare dlffcIcnt181 CI'oss scctlons calculRted by several models for the absorption potential and by several arbitrary modifications of these model potentials. %C are able to associate the effect of the absorption potential on the elastic differential cross section with its form at small electron-atom distances r, and we are able to deduce various qualitative features that the absorption potential must possess at small and large r in order to predict both accurate differential cross sections and accurate absorption cross sections. Based on these observations, the Pauli blocking conditions of the quasifree scattering model for the absorption potcnt181 alc modif lcd empirically, thUs producing 8 morc 8ccuratc ITlodcl that Inay be Rppl1cd to other systems; e.g. , electron-molecule scattering, with no adjustable parameters.

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We calculated the atomization energy of aluminum clusters (Al 2 -Al 7 ) with several multilevel methods, including MCG3/3 and G3X, that have been previously shown to provide high accuracy for atomization energies. We used the results to test a number of hybrid density functional theory (HDFT) methods and found that the PBE0 method is in best agreement with the accurate methods. We then used the PBE0/MG3 method to develop a more extensive data set for the energies of small aluminum clusters (Al 2 -Al 13 ), and this was used to test a number of semiempirical methods, in particular Austin model 1 (AM1), modified neglect of differential overlap (MNDO), modified symmetric-orthogonalized intermediate neglect of differential overlap (MSINDO) with and without d-functions, parametrized model 3 (PM3), and the tight-binding total energy (TBTE) method, for geometries, energies, and multiplicities of Al clusters. The AM1 model and MSINDO model are the most accurate of the semiempirical methods for energetics, and PM3 is the most accurate method for geometries.