Neighboring atoms

Neighboring atoms stand next to each other. 

Figure 2-43. The EC value or the atom classification of each atom, respectively, is calculated by summing the EC values of the directly connected neighboring atoms of the former sphere (relaxation process).

In the fir.st iteration proces.s, the class values of the atoms of the structure. show information already known (the degree of the nodes). Hence Morgan takes the neighboring atoms into account. He considers the environment of an atom by summing class values of all directly adjacent atoms. This process results in a new class value called the extended connectivity (EC) value of the atom. The new EC value expresses indirectly the neighborhood of the adjacent atoms in a second sphere (Figure 2-43). 

In this simplified example of phenylalanine, in the first iteration the methyl groups arc given a value of I in the first classification step because they contain a primaiy C-atom, The methylene group obtains a value of 2, and the methine carbon atom a value of 3. In the second step, the carbon atom of the methyl group on the left-hand side obtains an extended connectivity (EC) value of 2 because its neighboring atom had a value of 2 in the first classification step. 

The c arlrnn atoms of the other two methyl groups (on the right-hand side) obtain an EC value of 3 because they arc adjacent to the racthinc carbon atom. The carbon atom of the methylene group obtains an EC value of 4 in the second rcla.xation process, as the sum (1 + 3) of the eonncctivity values of its neighboring atoms in the first iteration. 

The extended connectivity (EC) value of an atom of the first sphere (i) results from the number (n) of neighboring atoms (NA) according to Eq, (7) ... 

Figure 2-44, The EC values of the atoins of phenylalanine (without hydrogens) are calculated by considering the class values of the neighboring atoms, After each relaKatlon process, c, the number of equivalent classes (different EC values), is determined.

In the next step, the neighbor atoms of the second atom (or the current atom plus 1), which are not yet labeled, are assigned in an equivalent manner. This is done for all the atoms arbitrai y decisions are made when numbering the equivalent atoms (Figure 2-45). 

In contrast to the van der Waals surface, the Connolly surface [183, 184] has a smoother surface structure. The spiky and hard transition between the spheres of neighboring atoms is avoided. The Connolly surface can be obtained by rolling... 

The HOSE code can be determined to various degrees of resolution, depending on how many spheres of neighbor atoms are considered. Figure 10.2-1 shows the first, second, and third spheres of neighbors for the carbon atom being considered, for C NMR spectra a HOSE code for each carbon atom in a molecule has to be determined. 

The off-diagonal elements in the E matr ix F are defined for neighboring atoms, which are not necessarily adjacent. There are no rr interactions for neighbor atoms. 

Valence Atomic Orbitals on Neighboring Atoms Combine to Form Bonding, Non-Bonding and Antibonding Molecular Orbitals... 

If aos on one atom overlap aos on more than one neighboring atom, mos that involve amplitudes on three or more atomic centers can be formed. Such mos are termed delocalized or multicenter mos. 

It is sometimes convenient to combine aos to form hybrid orbitals that have well defined directional character and to then form mos by combining these hybrid orbitals. This recombination of aos to form hybrids is never necessary and never provides any information that could be achieved in its absence. However, forming hybrids often allows one to focus on those interactions among directed orbitals on neighboring atoms that are most important. 

It is well known that bonding and antibonding orbitals are formed when a pair of atomie orbitals from neighboring atoms interaet. The energy splitting between the bonding... 

Xv reside on neighboring atoms that are ehemieally bonded. If X i and Xv reside on atoms that are not bonded neighbors, then the off-diagonal matrix element is set equal to zero. 

Utilize periodic boundary conditions, which permit reduction of the number of nonbonded interactions at greater distances by involving only the "nearest neighbor" atoms from copies of the system which are in different but adjacent cells. 

The arc and spark spectra of the individual lanthanides are exceedingly complex. Thousands of emission lines are observed. For the trivalent rare-earth ions in soUds, the absorption spectra are much better understood. However, the crystal fields of the neighboring atoms remove the degeneracy of some states and several levels exist where only one did before. Many of these crystal field levels exist very close to a base level. As the soUd is heated, a number of the lower levels become occupied. Some physical properties of rare-earth metals are thus very sensitive to temperature (7). 

Neutron-rich lanthanide isotopes occur in the fission of uranium or plutonium and ate separated during the reprocessing of nuclear fuel wastes (see Nuclearreactors). Lanthanide isotopes can be produced by neutron bombardment, by radioactive decay of neighboring atoms, and by nuclear reactions in accelerators where the rate earths ate bombarded with charged particles. The rare-earth content of solid samples can be determined by neutron... 

V n der W ls Interactions. Van der Waals iateractions result from the asymmetric distribution of electronic charge surrounding an atom, which induces a complementary dipole in a neighboring atom, resulting in an attractive force. In general, the attractive force of van der Waals interactions is very weak (<4.2 kJ/mol (1 kcal/mol)) but may become significant if steric complementarity creates an opportunity to form a large number of van der Waals attractions. 

This initial assignment is, of course, not at equilibrium. In particular, the expected velocity correlation between neighboring atoms is not guaranteed, and most likely it is nonexistent (i.e., in general, neighboring atoms, such as bonded pairs, are expected to... 

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