N-nearest neighbors

The relationship between IR and chemical similarity searching is discussed in detail by Edgar et al. (11) who summarize the various effectiveness measures in terms of the 2 x 2 contingency table shown in Table 1. In this table, it is assumed that a search has been carried out resulting in the retrieval of the n nearest neighbors at the top of the ranked output. Assume that these n nearest neighbors include a of the A active molecules in the complete database, which contains a total of N molecules. Then the recall, R, is defined to be the fraction of the active molecules that are retrieved, i.e.,... 

Finally, dopant inhomogeneities due to statistical dopant density fluctuations are also problematic, but this problem is shared with the analogous bulk materials and is not unique to the nanocrystals. Equation 3 describes the probability of finding N nearest neighbors around a central dopant ion in an infinite crystalline lattice for a given dopant concentration, x, where M is the number of cationic sites in the first shell around the central cation (12 in II-VI and III—V semiconductors) (39)... 

If the excitation is to jump, the acceptor node is chosen fi om a uniform distribution of the n nearest neighbors. This condition means that k does not depend on the acceptor state but is the same for the acceptors with and without excitation. This assumption is justified by the fact that the B850 ring contains 18 BChl molecules and even if the excitation is delocalized over 2-4 BChl molecules the accepting BChls remain most of the time unaffected. 

One may consider a molecule in the surface region as being in a state intermediate between that in the vapor phase and that in the liquid. Skapski [11] has made the following simplified analysis. Considering only nearest-neighbor interactions, if n, and denote the number of nearest neighbors in the interior of the liquid and the surface region, respectively, then, per molecule... 

The simplest model is the lattice-gas or Ising model. The whole space is divided into a lattice of N sites, and on each site two different states are possible a crystalline state denoted by the variable 5, = 1 and a gaseous state by Sj = -. The variable s denotes the degree of crystalline order. The cohesion of nearest-neighboring solid atoms leads to the following interaction energy... 

These functions are truncated and shifted to zero at a cutoff-distance between the third and fourth nearest neighbor shell. N ai is the number of valence electrons and U4s is a parameter. Following Daw and Baskes further on we use cubic spline functions to represent the functions and Z(r). The splii s have been fitted to... 

In the pure solvent let each particle have z nearest neighbors in contact with it. Let us ask how, removing two adjacent solvent particles from the interior, we may insert a solvent molecule. When a particular site is to be occupied by the B-half of the molecule BC, there are clearly z choices for the position of its C-half. This is true for each of the nB solute particles, provided that the solution is so dilute that they do not compete for the available sites to an appreciable extent. From the independent oiientations of nB solute particles, the quantity Wc/ receives the factor z if the molecules are heteronuclear and receives the factor (z/2)n if the molecules are homonuclear. 

In this discussion of the transition elements we have considered only the orbitals (n— )d ns np. It seems probable that in some metals use is made also of the nd orbitals in bond formation. In gray tin, with the diamond structure, the four orbitals 5s5p3 are used with four outer electrons in the formation of tetrahedral bonds, the 4d shell being filled with ten electrons. The structure of white tin, in which each atom has six nearest neighbors (four at 3.016A and two at 3.17.5A), becomes reasonable if it is assumed that one of the 4d electrons is promoted to the 5d shell, and that six bonds are formed with use of the orbitals 4dSs5p35d. 

Table 2. Surface density (0 ), direct band gap energy (Egd), and number of next nearest neighbors (N ) on WO -ZrOi calcined at 1073 K.

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