Electron precise atom

An electron-precise -atom cluster will have 5n (15n) electrons, of which 3n are used to bond the cluster (to form 3 /2 skeleton electron pairs). Notice that the total number of electrons in a cluster is given by the sum of the electrons on cluster vertex atoms plus the electrons, on vertex atoms, from covalent bonds with exocyclic groups. 

Its charge density distribution is like that of the cation (with sign reversal) because the added electron goes into the nonbonded orbital with a node at the central carbon atom. The probability of finding that electron precisely at the central carbon atom is zero. 

In our design, divalent Ca was chosen to partially substitute the trivalent atoms, and La and Ce were selected for a trivalent element because their ionic size (rLas+ = l.SOA rce3+=l-48A) was close to that of Ca (rca2+ = T48A) [21]. Like La, the Ce element also generally shows a formal -i-3 oxidation state in in-termetallics. Erom the reactions of the elements, we have identified as major phases the electron-precise/deficient alloys, Ln5.xCaxGe4 (Ln=La, Ce x=3.37,... 

For more electropositive elements, which have an inferior number of valence electrons in the first place, and which in addition have to supply electrons to a more electronegative partner, the number of available electrons is rather small. They can gain electrons in two ways first, as far as possible, by complexation, i.e. by the acquisition of ligands and second, by combining their own atoms with each other. This can result in the formation of clusters. A cluster is an accumulation of three or more atoms of the same element or of similar elements that are directly linked with each other. If the accumulation of atoms yields a sufficient number of electrons to allow for one electron pair for every connecting line between two adjacent atoms, then each of these lines can be taken to be a 2c2e bond just as in a common valence bond (Lewis) formula. Clusters of this kind have been called electron precise. 

This mode of calculation has been called the EAN rule (effective atomic number rule). It is valid for arbitrary metal clusters (closo and others) if the number of electrons is sufficient to assign one electron pair for every M-M connecting line between adjacent atoms, and if the octet rule or the 18-electron rule is fulfilled for main group elements or for transition group elements, respectively. The number of bonds b calculated in this way is a limiting value the number of polyhedron edges in the cluster can be greater than or equal to b, but never smaller. If it is equal, the cluster is electron precise. 

Mo6 octahedron) the cluster is electron-precise, the valence band is fully occupied and the compounds are semiconductors, as, for example, (Mo4Ru2)Se8 (it has two Mo atoms substituted by Ru atoms in the cluster). In PbMo6Sg there are only 22 electrons per cluster the electron holes facilitate a better electrical conductivity below 14 K it becomes a superconductor. By incorporating other elements in the cluster and by the choice of the electron-donating element A, the number of electrons in the cluster can be varied within certain limits (19 to 24 electrons for the octahedral skeleton). With the lower electron numbers the weakened cluster bonds show up in trigonally elongated octahedra. 

KT1 does not have the NaTl structure because the K+ ions are too large to fit into the interstices of the diamond-like Tl- framework. It is a cluster compound K6T16 with distorted octahedral Tig- ions. A Tig- ion could be formulated as an electron precise octahedral cluster, with 24 skeleton electrons and four 2c2e bonds per octahedron vertex. The thallium atoms then would have no lone electron pairs, the outside of the octahedron would have nearly no valence electron density, and there would be no reason for the distortion of the octahedron. Taken as a closo cluster with one lone electron pair per T1 atom, it should have two more electrons. If we assume bonding as in the B6Hg- ion (Fig. 13.11), but occupy the t2g orbitals with only four instead of six electrons, we can understand the observed compression of the octahedra as a Jahn-Teller distortion. Clusters of this kind, that have less electrons than expected according to the Wade rules, are known with gallium, indium and thallium. They are called hypoelectronic clusters their skeleton electron numbers often are 2n or 2n — 4. 

The electron precise bonding, as sketched in Figure 38a, was based on the structural analogy between the Te72+ structure and those of the Te72 and Te65 anions that contain similar square planar coordinated Te atoms. However, it is unlikely to invoke the presence of a dianionic Te site within the... 

Multicenter bonding is the key to understanding carboranes. Classical multicenter n bonding gives rise to electron-precise structures characteristic of Hiickel aromatics, which are planar and have 4n + 2 n electrons. Clusters are defined here as ensembles of atoms connected by non-classical multicenter bonding , i.e., all... 

Heteroboranes are those in which one or more non-boron atoms replace a BH vertex, together with groups that may be attached to these heteroatoms. Boranes that contain CH vertices constitute the vast family of carbaboranes. The possibility for carbon to participate in electron-deficient frameworks contradicted the former prejudice of the always electron-precise carbon as the well-behaved brother of naughty boron. So far, most elements have been introduced as heteroatoms into borane frameworks, with the exception of the halogens and the noble gases. 

A simple, previously mentioned example may be represented by the tetrahedral molecule P4. In this structure there are 4 vertex atoms (n = 4) and there are no exocyclic groups. On the other hand, P has 5 valence electrons, so the number of cluster electrons is 4 X 5 = 20 electrons. This number (20) is therefore related to the number of vertices by the condition 20 = 5n. The cluster is electron-precise. 

An even broader range of ring sizes is found for the cyclo-phosphazenes (R2PN)x (x=3-1T) but these inorganic heterocycles are ir-electron precise (l.e. the number of ir-electrons is equal to the number of atomic centers in the ring system). Although both bicyclic and condensed structures have been identified, simple anions or cations of cyclophosphazenes are unknown ( ). ... 

For molecules with more than one electron, precise solutions become even more difficult and time consuming, and additional approximations are sought. The simplest molecule is that of hydrogen, where there are two nuclei A and B, and two electrons 1 and 2. The potential energy of the system is the sum of six electrostatic terms the four attractive terms between A-1, A-2, B-1, and B-2, and the two repulsive terms between A-B and 1-2. We seek solutions to the Schrodinger equation of this hydrogen molecule, and the solution is assumed to be a linear combination of the products of the atomic orbitals, of nucleus A associated with electron 1 multiplied by nucleus B associated with electron 2, plus nucleus A associated with electron 2 multiplied by... 

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