Energy Variation Under Transition from Bulk to Clusters

2 Energy Variation Under Transition from Bulk to Clusters 

Let us begin with energetic properties of polyatomic homoatomic molecules (clusters) of metals (Mn) and nonmetals (An). Because clusters lie somewhere between molecules and bulk solids, approaches and models to study them have come from both sides in most cases, condensed matter theorists have applied solid-state models while quantum chemists have moved from calculations on complex molecules to 

When atoms combine into molecules or clusters, the atomic orbitals are transformed into molecular orbitals and finally merge into continuous bands (see Fig. 2.5). The density of states (DOS) within a band is roughly equal to the number of atoms in the ensemble per eV. In works [27,28] at first were established the general dependences for clusters, the ionization potentials (4) decrease and the electron affinities (Ac) increase as the size of the cluster (i.e. the number n of atoms in it) increases. The linear extrapolations of both dependences ultimately converge to the work function ( I ) of the corresponding bulk material, viz. 

As mentioned above (see Sect. 2.3.4, Table 2.16), the experimental values of the band gaps ( g) in most substances increase as the grain sizes decrease. Diamond is an exception, its g decreasing together with the grain sizes. Here, an important role is played by the curvature of the surface layer, which results in the negative electron affinity of nano-diamond particles [30, 31]. 

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