Gaussian smearing

The remaining terms in Eq. (4-24) are the nth-order corrections to approximate the real system, in which the expectation value ( c is called cumulant, which can be written in terms of the standard expectation value ( by cumulant expansion in terms of Gaussian smearing convolution integrals ... 

All calculations in this chapter used the PBE GGA functional. For calculations related to Cu surfaces, a cutoff energy of 380 eV and the Methfessel-Paxton scheme was used with a smearing width of 0.1 eV. For calculations related to Si surfaces, the cutoff energy was 380 eV and Gaussian smearing with a width of 0.1 eV was used. The k points were placed in reciprocal space using the Monkhorst-Pack scheme. For all surface calculations, the supercell dimensions in the plane of the surface were defined using the DFT-optimized bulk lattice parameter. 

Figure 5 Calculated absorption spectra for four different Si clusters (a) Sii4H2o, (b) Sii4H2o>C>2, (c) Sii4Hi8=0, (d)Sii3Hi6>0=0 (an artificial Gaussian smearing of 0.05 eV has been applied).

Figure 8.5 (a) The DOS for MgO and the smearing function (f( )) used for calculating the state occupancy. (This has a maximum value of 1.) (b) The DOS ofTi02 (rutile). Both calculations used the VASP code with PAW pseudopotentials and the PW91 functional a Gaussian smearing of 0.2eV has been used... 

A. Gaussian smearing of 0.001 eV, planewave cut-ojf energy of 400 eV and real space projection... 

Fig. 9 Form factor contribution P(Q) of the plate with brushes on both sides for different contrasts. C is core contrast (Apb = 0)> B brush contrast (Apc = O), and Z approximate zero average contrast, ([b( )Apb + Cc(2)Apc] dz = 0). The lower part of this figure displays the projected average volume fractions of brush c z) and the core Cq z), The dotted lines indicate the results for a larger Gaussian smearing of the brush. The form factor in core contrast stays nearly constant below Q = 0.1 whereas the brush contrast factor has a sharp minimum around Q = 0.025, which is directly related to the brush...

Fig. 10 a Schematic sketch of an aggregate stack, b Resulting structure factors Sn(Q) for a finite and S(Q) for an infinite staple calculated for an average interlamellar distance of D = 400 A and a Gaussian smearing of cr = 200 A... 

In the case of Gaussian and uniform distributions of the adsorption energy, the smearing of the phase transition region in the the first as well as higher layers was observed. Thus, insead of vertical jumps, the adsorption isotherms exhibited only finite slope even at quite low temperatures. This result is consistent with the predictions of Dash and Puff [32]. 

Fast methods for evaluating these integrals for the case of gaussian basis functions are known [12], Also, Hall has described how to get the symmetry operators (B) 1SjB, r, for any crystal space group [13]. The parameters account for thermal smearing of the charge density. In this work I use the form recommended by Stewart [14],... 

Figure 3.58. (a) Normalized X-ray reflectivity (R/Rj,) as a function of the scattering vector transfer for arachidic acid monolayers on pure water (T = 20°C). For better visibility the curves marked (, yand 5 are displaced upward by 0.25, 0.5 and 1.0, respectively. Here a, /3, yand 6 correspond to the surface pressures indicated in the tc[a ] isotherm of the insert, (b) Two-box density profile used to fit the data in (a). The boxes describing the tall region (T) and the polar head region (H), respectively, are smeared by a Gaussian, as indicated by the solid line. (Redrawn from J. Als-Nielsen and K. Kjaer, loc. cit.)... 

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