Electron density concentration

The quantum number / — 1 corresponds to a p orbital. A p electron can have any of three values for Jitt/, so for each value of tt there are three different p orbitals. The p orbitals, which are not spherical, can be shown in various ways. The most convenient representation shows the three orbitals with identical shapes but pointing in three different directions. Figure 7-22 shows electron contour drawings of the 2p orbitals. Each p orbital has high electron density in one particular direction, perpendicular to the other two orbitals, with the nucleus at the center of the system. The three different orbitals can be represented so that each has its electron density concentrated on both sides of the nucleus along a preferred axis. We can write subscripts on the orbitals to distinguish the three distinct orientations Px, Py, and Pz Each p orbital also has a nodal plane that passes through the nucleus. The nodal plane for the p orbital is the J z plane, for the Py orbital the nodal plane is the X Z plane, and for the Pz orbital it is the Jt plane. 

All a bonds have high electron density concentrated along the intemuclear axis and axial symmetry, so their end-on profiles are circles. ... 

A a bond has high electron density distributed symmetrically along the bond axis. A 71 bond has high electron density concentrated above and below the bond axis. 

Bond and size surfaces offer some significant advantages over conventional skeletal and space-filling models. Most important, bond surfaces may be applied to elucidate bonding and not only to portray known bonding. For example, the bond surface for diborane clearly shows a molecule with very little electron density concentrated between the two borons. 

Because of the high energy of a of the quaternary nitrogen, it is hypothesized that the electron density concentrates on the metal moiety. However, these materials do not behave as simple salts. The formula shown is the simplest empirical one derived from the ratio of the components. The real structure may involve several units or may even be a solid macrostructure on the cathode surface. 

Figure 1 (a) Portion of a molecular orbital that distributes electron density between two /raw -carbonyl groups, (b) electron density concentrated in M-CO bond trans to poor jr-acceptor... 

Third, the asterisk denotes an antibonding orbital. As discussed later, antibonding orbitals have much less electron density concentrated between the nuclei, and the density goes to zero at a node between the nuclei. In addition, the energy of an electron in an antibonding orbital of Hj is greater than that of the corresponding H and species, so it is unstable with respect to dissociation. 

The 2p and 2py orbitals from the two atoms do not approach head-on in this confignration, but rather side by side. Therefore, the positive lobes of the 2p orbitals can overlap laterally, as can the negative lobes. Together, they form a TT bond, which has a node through the plane containing the bond axis with electron density concentrated above and below the plane. The wave function for the bond pair is... 

Sigma bond. A covalent bond formed by orbitals overlapping end-to-end it has its electron density concentrated between the nuclei of the bonding atoms. (10.5)... 

Ann (a) carbanion such as CH - has its electron density concentrated on one carbon atom where it could be more readily available for some type of localized interaction with the metal and thus may lead to the unusual optical and magnetic effects. 

Density functional theory (DFT) calculations [33] on the model complex Cp2Ti 72-HB(OH)2 2 accurately reproduced the short B- -B distance. A Laplacian electron density analysis (Fig. 2) based on the DFT calculations showed that significant electron density concentrations were found along the B- -B bonding path, indicating bonding interactions between the two borons. The four concentrations around the Ti center shown in the Laplacian electron density plot have been associated with the electron density contributed from... 

Another characteristic feature of x-ray diffraction is that each diffracted wave automatically sums the vector amplitude from all unit cells of each coherent crystal unit. Hence, random occupancy of 1 site by A1 and Si atoms results in just 1 electron density concentration. Thermal vibration and random positional displacements of atoms from 1 unit cell to another yield a similar blurring-out of the electron density furthermore, it is difficult experimentally to distinguish between reduction of height of an electron density peak resulting from the above 2 factors and that from a lower occupancy factor. 

One way to consider covalent bond formation is to look at what happens to the individual atomic orbitals (AOs) on adjacent atoms as they overlap at short distances to form molecular orbitals (MOs). The simplest case is that of two Is orbitals. At relatively large separations (>lnm) the electron orbital on one atom is not influenced significantly by the presence of the other atom. As the two atoms approach each other the orbitals overlap and the electron density between the nuclei increases. At ro, the individual AOs become a single MO—called a bonding MO—with the electron density concentrated between the nuclei. 

Transition Metals. - In order to fiuther elucidate the non-classical feature of dinuclear transition metal bis(//- 7 -silane) complexes Choi and Lin analysed V p on the plane defined by the [Pd(//- / -HSi)]2unit. The Laplacian shows higher electron density concentrations along the Si... H BP when compared to other non-classical mononuclear -silane complexes previously studied. 

In general, a more polarized bond will have less electron density concentrated between the nuclei. If the electron density is distorted more toward one atom than the other, a cross-section of the bond will show that there is less electron density between the nuclei. This does not necessarily mean that it will be a weaker bond because other factors contribute to bond strength, but it does contribute to bond strength. In Table 3.5, it is clear that more energy is associated with a C-F bond than with a C-N bond, even though the C-F bond is more polarized. In a chemical reaction that involves transfer of electrons from one atom to another, it is usually easier to break a polarized bond than a nonpolarized bond, if one atom of the bond can readily accept electrons. This statement is illustrated by Figure 3.15, where the polarized C-Cl bond breaks and the two electrons in that bond are transferred to Cl, forming the chloride ion. 

A molecular orbital with a nodal plane that cuts through both atomic nuclei, with electron density concentrated above and below the nodal plane. 

Figure 1 Schematic representation of electron density in the antibiotic cefaclor. The density of dots schematically conveys the notion that electron density concentrates near the nuclei and diminishes near die periphery of the molecule.

The hybrid orbital has electron density concentrated on one side of the nucleus, i.e. it has one lobe relatively larger than the other. Hence, the hybrid orbitals can form stronger bonds compared to unhybridized atomic orbitals because they can undergo more effective overlap. The hybrid orbitals repel each other and adopt a configuration that minimizes the electron repulsion. Hybridization is simply a mathematical model that is convenient for describing localized bonds. It is not a phenomenon that can be studied or measured. 

All of these orbitals are sigma (a) orbitals and formed by the direct head-on or end-to-end overlap of atomic orbitals resulting in electron density concentrated between the nuclei of the atoms. 

FIGURE 12.16 Representations of molecular orbitals from linear combinations of hydrogen atomic orbitals. The MO in the middle plot is the sum of the two AOs at the top, with electron density concentrated between the nuclei. The lower MO is the difference of the two AOs, with electron density concentrated more outside the two nuclei. 

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