Net electron population

Thus, the net electron population on H is reduced (by 0.002e), even though AH becomes... 

Of rows in the next group for electric properties, the fourth shows the total electric dipolar moment. The next five rows present an analysis of net electronic populations associated with each atomic centre, according to an atomic polar tensor [13] each value listed represents the net alteration of electronic population associated with a particular atomic centre through its participation as a constituent of the particular molecule in a specific isomeric form. To distinguish the two hydrogenic atomic centres if they lie in chemically inequivalent positions, is nearer a carbon atom than H likewise if the two nitrogens have inequivalent positions N, is nearer a carbon atom than Ni,. The next six rows present elements of a symmetric... 

For a polyatomic molecule with molecular orbitals described in general by equation 2.44, this analysis may be extended to give the net electron population of an atomic orbital and (lie overlap population (P u) between two atomic orbitals... 

For a molecular orbital describing an electron, factors and represent the net electron population on atoms A and B. The overlap population is given by the labS/ Q term (5ab s the overlap integral). Distributing the overlap population equally over the atoms, and assigning each part to the atoms, the global atomic populations are obtained (Mulliken populations [4]). Since atoms A and B have different abilities to attract electrons, the charge distribution between nuclei is asymetrical. 

The quantity PJS can then be regarded as the electronic population of the atomic overlap distribution < > < >. Diagonal terms such as P S give the net electronic charge re-... 

Crystal data (by X-ray diffraction analysis) and calculation of net 7r-electron population for 7V,7V-dialkyl-p-nitroaniline and for 3,5- and 2,6-dimethyl-4-nitroaniline indicate that... 

Results expressed relative to 1, 5, and 6 electrons, respectively, for the tt, a, and total net charges. A negative sign indicates an increase in electron population. 

In this equation, q = q C ) + ( 2)] is one-half the sum of the charges of the electron-richest bonded C atoms in each alkane molecule, expressed by means of the appropriate formulas given in Table 7.1. The net atomic charges qc and qc are both positive because n < 0. A decreasing ratio qc/q°c thus means that a carbon atom gains electronic charge with respect to that of ethane. Figure 7.1 indicates that the IPs of the alkanes are lowered as the joint electron population of the electron-richest pair of atoms increases. 

Comparison of adiabatic ionization potentials (IP) of normal and branched alkanes with carbon net charges, which indicates a lowering of the IPs with increasing electron population of the electron-richest bonded pair of carbon atoms in the molecule [170]. A monotonic correlation (which turns out to be linear and remarkably accurate) is possible only with atomic charges adjusted for n = 4.4083 and the corresponding p given by Eq. (5.14). 

Up to here, it was convenient to carry out the calculations using the valence-electron populations N, Ni, and so on as variables. For the final step, however, it is more practical to express the results using net (i.e., nuclear minus electronic) charges, so that... 

Two approaches have been applied to estimate the net charges of atoms from the observed electron-density distribution in crystals. The first method is a direct integration of observed density in an appropriate region around an atom (hereafter abbreviated as DI method) (64). The second is the so-called extended L-shell method (ELS method) (19, 81) in which a valence electron population of an atom is calculated by a least-squares method on the observed and calculated structure amplitudes. 

In metal oxides and silicates, the net charges of transition metal atoms are quite different. Table III shows the net charges of metal atoms in these crystals, which are slightly neutralized but almost equal to their oxidation numbers. The ionic characters of these crystals may be demonstrated by the electron population analysis of the CoA1204 crystal. The net charges of Co(II), Al(III), and O(II) atoms were estimated by the ELS method to be +1.5(1), +2.8(1), and -1.8 e, respectively (84). 

Equation 6.55 represents the Mulliken population analysis, where the first sum in the parentheses containing only quadratic terms is called net atomic population, the second sum is the overlap population, and nA is the total sum of all electrons associated with atom A, the gross atomic population (Mulliken, 1955, 1962). Note the difference between Equation 6.54 and Equation 6.55 in the former the summation includes all AOs of the molecule, while in the latter the sum is confined to those AOs that belong to atom A. Obviously ... 

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