Gaussian level broadening

In all chemisorption cluster investigations the Gaussian level broadening parameter a was fixed at 0.3 eV. At least for our nickel clusters this seems a reasonable choice as orbitals near the Fermi levels are of similar spatial character. The results shown in Table II below support this view. 

Table II. Comparison of the icosahedral and octrahedral Niia isomers and study of the Gaussian level broadening...

Fig. 24. Total DOS and atom projected PDOS curves of the M015O56H22 cluster, (a) Total DOS (thick solid) with decomposition into Mo (thin solid) and O (dashed) contributions, (b) PDOSs of the differently coordinated oxygen centers 0(1) (solid), 0(2) (dotted), and 0(3) (dashed). A gaussian level broadening of 0.4 eV is applied and the energetic position of the highest occupied cluster orbital Chomo at -6.1 eV is marked by a thin vertical line.

Fig. 23a. Calculated and measured outer-level excitation spectra. In the uncoupled S(E,) (see fig. 19), the amplitude of the valence and conduction bands is chosen proportional to the hybridization parameters. In the calculation of the f-spectra with coupling, a Gaussian instrumental broadening of 0.4eV FWHM has been included. The experimental spectra have been taken from the following works. XPS Ba (HUfner and Steiner 1985) LaFj (Sato 1976) LajOs, La (Schneider et al, 1985) CeO (Wuilloud et al. 1984b). BIS Ba (Riehle 1978) LaF3 (Motais et al. 1984) LajOs, La (Schneider et al. 1985) CeOj (Wuilloud et al. 1984b). The origin of the total-energy scale is the Fermi energy in metals and the upper valence band edge in insulators. The f contribution corresponds to the hatched areas.

To obtain a qualitative picture of the complex structure of SO3 adsorbed on the Pt (111) surface, the density of states (DOS) was calculated from the DV-Xa molecular orbital method. The level width was broadened by a Gaussian function (1.0 eV FWHM) to mimic the solid state. The results of the studies are summarized in the following paragraphs. In each DOS, Fermi energy is set at 0. In configuration A, the adsorbed O atoms are classified as of two types. One is two O atoms bound to Pt surface atom (0(1)) and the other is one O atom unbound to Pt surface (0(2)). 

Rephasing, baseline correction and Gaussian line narrowing were used as a general procedure to reduce broadening in the H spectra (300 MHz) of a primary /3-alkoxyalcohol and 1,2-cyclohexanediol with Eu(hfc)3 and Yb(hfc)3 at 300 MHz to acceptable levels. ... 

Figure 11 shows the shape-resonant enhanced cross sections for photolonlzatlon of the 5a level in 00 (16). This resonance is analogous to the 30g ka feature in the photolonlzatlon of Nj but the reduced symmetry of the continuum from to a has led to a broadening of the resonance. In Figure 11 we compare these cross sections with those of the STMT (38) and CMSM (24) methods and with the experimental data. The various methods all show the expected resonance feature. There are, however, some differences of consequence between our results and those of the STMT method. The STMT cross sections suggest that the feature at 24 eV Is due to a shape resonance whereas the present results suggest that It may be due to autolonizatlon. A substantial part of the difference between these calculated cross sections arises from the use of Gaussian and Slater SCF bases In the STMT and our studies respectively (39). 

The present treatment of solvent broadening is of course an oversimplification. It does not take into account the dynamic nature of the interaction or the contributions of solvent excitations to the resonant state. On a more elementary level, the representation of A by a Lorentzian is probably unrealistic since solvent-broadened lines often approximate a Gaussian shape. Our choice of a Lorentzian is made to obtain analytical expressions for the cross section a Gaussian lineshape requires numerical procedures, but presents no fundamental difficulties. It turns out (O. Sonnich Mortensen, unpublished) that, for a given halfwidth A, a Gaussian tends to distort REPs and polarization dispersion curves more strongly than a Lorentzian. 

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