Cluster density of states

A cluster density of states of Niia, literally (not just formally) broadened by 0.2 eV, is presented in Figure 2a for the icosahedral geometry near the equilibrium structure. The general features are roughly similar to that derived from a spin-polarized band structure calculation of bulk nickel. Near the Fermi level a very high density of states of the minority spin is found, the d band of the... 

Figure 2. Cluster density of states (in arbitrary units) generated by Gaussian broadening of the one-electron energies and cluster Fermi energy Cf a) icosahedral Niia (spin-polarized calculation, majority spin above the axis a = 0.2 eV). b) NiirNa (solid line a = 0.3 eV). Also shown are the sum of the contnbutions from the s and p populations of the nickel atoms (dashed line) and the population of the sodium atom (dotted line).

Pisani [169] has used the density of states from periodic FIP (see B3.2.2.4) slab calculations to describe the host in which the cluster is embedded, where the applications have been primarily to ionic crystals such as LiE. The original calculation to derive the external Coulomb and exchange fields is usually done on a finite cluster and at a low level of ab initio theory (typically minimum basis set FIP, one electron only per atom treated explicitly). 

Figure 2.14. The molecular orbitals of gas phase carbon monoxide, (a) Energy diagram indicating how the molecular orbitals arise from the combination of atomic orbitals of carbon (C) and oxygen (O). Conventional arrows are used to indicate the spin orientations of electrons in the occupied orbitals. Asterisks denote antibonding molecular orbitals, (b) Spatial distributions of key orbitals involved in the chemisorption of carbon monoxide. Barring indicates empty orbitals.5 (c) Electronic configurations of CO and NO in vacuum as compared to the density of states of a Pt(lll) cluster.11 Reprinted from ref. 11 with permission from Elsevier Science.

Could a change in shape of the small Pt clusters produce sufficiently large changes In the density of states to cause the effect One of us (Horsley) has made preliminary multiple... 

Figure 1. Density of states for various Ag clusters computed for 4d-, 5 s-, and 5p-orbitals within the extended Hiickel method. (Reprinted from Ref [32], 1981, with permission from Elsevier.)...

The valence DOS has been computed for Ni and Ag clusters within the CNDO formalism. Blyholder [54] examined the Nis and M13 clusters. In both cases of s- and p-orbitals are occupied and lie well below the d-orbitals. Most of the intensity is near the middle of the d-orbitals with a fall-off in intensity as the HOMO is approached. Density of states for Agv, Agio, Agi3, and Agig clusters shows a strong d-component cc. 3.5 eV wide. The... 

Figure 11, Density of states of a water sample, referring to two-, three-, tetra- and penta-coordinated 3D clusters and to the total of the sample, as resulting from MD simulation, T=305 K. Dotted lines indicate vibrational frequencies for a single water molecule in gas phase.

Fig. 1 Schematic drawing to show the concept of system dimensionality (a) bulk semiconductors, 3D (b) thin film, layer structure, quantum well, 2D (c) linear chain structure, quantum wire, ID (d) cluster, colloid, nanocrystal, quantum dot, OD. In the bottom, it is shown the corresponding density of states [A( )] versus energy (E) diagram (for ideal cases).

Figure 5 Density of states of Ni V clusters with N — 5, 6, and 7, calculated by the tight binding method sp (dashed lines) and d (continuous lines). Positive and negative values correspond to up and down J, spins, respectively. The Fermi level is at the energy zero. Adapted with permission from Ref. 45.

Our XPS results on AU55 can also be examined to decide whether metallic shielding is present. The presence of a finite density of states at the Fermi level in AU55 was clearly detected in our XPS valence band spectrum, as indicated by the arrow in Fig. 10. This presence can be considered as an indication of metallic character in a cluster, even though this view has been questioned [74, 152,157]. In addition, the near full bulk value of the valence band splitting of AU55 is also... 

The shape and splitting of the XPS Au5d band in the 55 atom cluster material, with its insulating jacket of ligands, reproduces nicely the basic shape of the 5d band of bulk gold, including a clearly visible density of states at the Fermi level. 

The lattice cluster theory (LCT) for glass formation in polymers focuses on the evaluation of the system s configurational entropy Sc T). Following Gibbs-DiMarzio theory [47, 60], Sc is defined in terms of the logarithm of the microcanonical ensemble (fixed N, V, and U) density of states 0( 7),... 

The problem is that photoemission spectroscopy may meet some difficulty in unraveling the f-p mixing in cases when the broad valence band emission and the 5 f emission overlap. The former, in fact, is described well by the ground state one electron density of states the latter reflects, in general, not the initial state but rather the final state after the excitation. Band as well as cluster calculations yield at present, on the other hand, only ground state properties with sufficient precision. 

In the cellular multiple scattering model , finite clusters of atoms are subjected to condensed matter boundary conditions in such a manner that a continuous spectrum is allowed. They are therefore not molecular calculations. An X type of exchange was used to create a local potential and different potentials for up and down spin-states could be constructed. For uranium pnictides and chalcogenides compounds the clusters were of 8 atoms (4 metal, 4 non-metal). The local density of states was calculated directly from the imaginary part of the Green function. The major features of the results are ... 

Figure 4- Left Density of states (DOS) of cage-like and amorphous structures of Au clusters with 18 and 20 atoms, calculated at the LDA and GGA levels of theory. Right Total energy difference between cage-like and compact equilibrium structures of cationic, neutral, and anionic clusters with 18 (starts), 20 (crosses), and 32 (circles) atoms.

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