Effective electron number

In line with the above discussion, the term effective electron number , neff, defined as... 

The nonelectrostatic terms include van der Waals, polarization, repulsive, and zero-point energies. The van der Waals energy has been calculated in several ways with results ranging from 5 to 15 kcal./mole. Examples of these results are indicated in Table I. In the first two entries polarizabilities were taken from Bottcher (3), and the nitrate group was treated as a single entity with an ionization potential of 99 kcal./mole for the London equation (23) and an effective electron number of 24 for the Slater-Kirkwood equation (23). A simple CsCl type of lattice was assumed. 

Fig. 19 Effective electron number at 1.5eV (solid circles) as a function of x. The dashed straight line indicates = x. The open diamond with an error bar represents a free-carrier contribution estimated from a Drude fit to the optical conductivity [3]...

We note that the factors containing the effective electron numbers in the expression for a and P are set equal to unity for the molecules A By, as in the case of the molecules AB , if one or both atoms have radii smaller than the radius of the H atom. In the case of the molecules A ByC and ApB CjD, the same applies, if the radii of the atoms are smaller than or equal to the radius of the H atom. 

New calculation was suggested to include the possibility of subshell contributions and effective electron numbers are derived for all the ions including rare earths whose polarizabilities are experimentally published [31]. They suggest that, in the case for rare earth ions, probably more than one contributing electron subshell appears. From Table 3, it becomes clear that as the number of 4f electrons increases from zero (La to 14(Lu ), both the polarizability and the effective number of electrons decrease monotoneously (See Table 5-3 and Fig. 5-7)). 

To quantity the changes in the optical conductivity induced by doping it is instructive to explore the behavior of the effective electron number iVeirCcu) ... 

Theoretical investigation [69] of the most familiar mechanism types (EQat, ECirrE or DISP) has shown a weak discrimination force in the RDE technique (cf. Fig. 10). The only possibility seems to be the determination of effective electron numbers in the rather broad region of > -RDE>0-l- For Arde<0-1 fhe application of chronoamperometry (polarography) operating with X — ktp and X == ki, respectively, is more feasible. 

Figure 1.7 shows the calculated ries versus E plots for A1 obtained by introducing the experimental 2(E) values listed in this book into Equation (1.21). rises to a value near three, the free electron value. The absorptions of the conduction and core electrons are well separated at the L edge ( 73 eV). The effective electron numbers, eight and two, observed at E > 100 eV correspond to the L and K shell electrons respectively. The K edge is observed to occur at -1200 eV. 

For many species the effective atomic number (FAN) or 18- electron rule is helpful. Low spin transition-metal complexes having the FAN of the next noble gas (Table 5), which have 18 valence electrons, are usually inert, and normally react by dissociation. Fach normal donor is considered to contribute two electrons the remainder are metal valence electrons. Sixteen-electron complexes are often inert, if these are low spin and square-planar, but can undergo associative substitution and oxidative-addition reactions. 

Earlandite structure, 6,849 Edge-coalesced icosahedra eleven-coordinate compounds, 1, 99 repulsion energy coefficients, 1,33,34 Edta — see Acetic acid, ethylenediaminetetra-Effective atomic number concept, 1,16 Effective bond length ratios non-bonding electron pairs, 1,37 Effective d-orbital set, 1,222 Egta — see Acetic acid,... 

As well as being attracted to the nucleus, each electron in a many-electron atom is repelled by the other electrons present. As a result, it is less tightly bound to the nucleus than it would be if those other electrons were absent. We say that each electron is shielded from the full attraction of the nucleus by the other electrons in the atom. The shielding effectively reduces the pull of the nucleus on an electron. The effective nuclear charge, Z lle, experienced by the electron is always less than the actual nuclear charge, Ze, because the electron-electron repulsions work against the pull of the nucleus. A very approximate form of the energy of an electron in a many-electron atom is a version of Eq. 14b in which the true atomic number is replaced by the effective atomic number ... 

The symbols in the second column represent the electronic state in particular the first number is the total quantum number of the excited electron. We shall see later that in one case at least the symbol is probably incorrect. The third column gives the wave-number of the lowest oscillational-rotational level, the fourth the effective quantum number, the fifth and sixth the oscillational wave-number and the average intemuclear distance for the lowest oscillational-rotational level. The data for H2+ were obtained by extrapolation, except rQ, which is Burrau s theoretical value (Section Via). 

When the effective atomic number becomes a little greater than the value for iron, however, the stable atomic orbitals are occupied by one electron per orbital, and further electrons can enter this set of orbitals only by becoming paired accordingly, the magnetic moment begins to fall, as is indicated by the experimental data. The magnetic moment drops to the value 1.7 for cobalt and 0.6 for nickel, and to zero at a point 60 percent of the way between nickel and copper. 

Here the indices a and b stand for the valence orbitals on the two atoms as before, n is a number operator, c+ and c are creation and annihilation operators, and cr is the spin index. The third and fourth terms in the parentheses effect electron exchange and are responsible for the bonding between the two atoms, while the last two terms stand for the Coulomb repulsion between electrons of opposite spin on the same orbital. As is common in tight binding theory, we assume that the two orbitals a and b are orthogonal we shall correct for this neglect of overlap later. The coupling Vab can be taken as real we set Vab = P < 0. 

The rapid and reversible formation of complexes between some metal ions and organic compounds that can function as electron donors can be used to adjust retention and selectivity in gas and liquid chromatography. Such coordinative interactions are very sensitive to subtle differences in the composition or stereochemistry of the donor ligand, owing to the sensitivity of the chemical bond towards electronic, steric and strain effects. A number of difficult to separate mixtures of stereoisomers and isotopomers have been separated by complexation chromatography. 

Many other TT-organometallic compounds have been prepared. In the most stable of these, the total number of electrons contributed by the ligands (e.g., four for allyl anions and six for cyclopentadiene anion) plus the valence electrons on the metal atom or ion is usually 18, to satisfy the effective atomic number rule.31 ... 

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. 

The effective atomic number rule (the 18-electron rule) was described briefly in Chapter 16, but we will consider it again here because it is so useful when discussing carbonyl and olefin complexes. The composition of stable binary metal carbonyls is largely predictable by the effective atomic number (EAN) rule, or the "18-electron rule" as it is also known. Stated in the simplest terms, the EAN rule predicts that a metal in the zero or other low oxidation state will gain electrons from a sufficient number of ligands so that the metal will achieve the electron configuration of the next noble gas. For the first-row transition metals, this means the krypton configuration with a total of 36 electrons. 

On the basis of the available mechanistic information, a challenging question is to what extent can the substitution mechanism of metal complexes be adjusted by structural modifications of the systems. These usually involve the tuning of steric and electronic effects. A number of such examples are treated in the following sections. 

Intraactions between elections in three-membered rings and unsaturated groups in the same molecule have been detected via 13C chemical-shift variations in a number of instances. Thus, introduction of the carbonyl function in tricy-clo[3.2.1,02,7]decane (e.g., 274) leads to significant downfield shifts of the signals of C(l) (+8.0), C(2) (+15.5), and C(7) (+7.7) (385), whereas corresponding effects in bicyclo[3.1.0]hexan-2-one (275) are smaller (385,386). A corresponding dependence was reported for 276 and 277 and related to more effective electron withdrawal in 276 (387). An even more pronounced deshielding effect was observed by Murata and co-workers (388,389) in the ketone 278 when they compared it with 279. 

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