Size-dependent potential energy function

II. Development of a Size-Dependent Potential Energy Function... 

II. DEVELOPMENT OF A SIZE-DEPENDENT POTENTIAL ENERGY FUNCTION... 

One may consider a wide variety of adsorbed molecules and nanotube sizes. The morphology of the adsorbed film depends on the relationship between the particle diameter (o ) and the diameter, 2R, of the mbe. This dependence stems from the potential energy function an example is shown in Fig. 9.3 for the case of a Cgo molecule in nanotubes of different sizes [23]. 

The density dependence of the entropy can also be studied by introducing fluctuations in volume rather than particle number. Typically the particle number approach is favored the computational demands of volume scaling moves scale faster with system size than do addition and deletion moves. Nevertheless, the Wang-Landau approach provides a means for studying volume fluctuations as well. In this case, the excess entropy is determined as a function of volume and potential energy for fixed particle number one, therefore, calculates (V, U). Here the microstate probabilities follow ... 

In diamond, Sahoo et al. (1983) investigated the hyperfine interaction using an unrestricted Hartree-Fock cluster method. The spin density of the muon was calculated as a function of its position in a potential well around the T site. Their value was within 10% of the experimental number. However, the energy profiles and spin densities calculated in this study were later shown to be cluster-size dependent (Estreicher et al., 1985). Estreicher et al., in their Hartree-Fock approach to the study of normal muonium in diamond (1986) and in Si (1987), found an enhancement of the spin density at the impurity over its vacuum value, in contradiction with experiment this overestimation was attributed to the neglect of correlation in the HF method. 

Figure 3 shows the Eg values of 1-D silicon clusters ls a function of size. The calculated Eg value decreases with increase of the number of silicon atoms, that is, the cluster size. Figure 3 also indicates the Eg values evaluated by Matsumoto s quantum-well (QW) modell l in which the wavefunctions are confined in the potential well and asolute Eg values were determined by interpolating the experimental Eg values of disilane (6.5eV) and polysilane (4eV) by the size dependance of the energy levels of the wavefunctions. 

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