Distribution electron density

One way that provides further insight into the energy changes that occur when Xi and X2 are allowed to interact is to use equation 1.13 along with the form of the to calculate the new orbital energies 

Plot of the electronegativity versus row for the main group atoms in the periodic table. 

terms greater than second order in t and S12 have been omitted. It is easy to show that equations 2.38 and 2.18 are identical. An analogous equation holds for 62  

The origin of the various terms in these two equations is well known by looking at the electron density distribution associated with and 2- This is given in general by In a way analogous to the derivation of equations 2.38 and 2.39, this can seen to be 

Upon integration over space and recalling that the atomic orbitals are normalized, 

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The electron density distributions are approximated by a series of poin t charges. There are four possible types of coninbniion s, i.e. 

The Total Electron Density Distribution and Molecular Orbitals... 

I he electron density distribution of individual molecular orbitals may also be determined and plotted. The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are often of particular interest as these are the orbitals most cimimonly involved in chemical reactions. As an illustration, the HOMO and LUMO for Jonnamide are displayed in Figures 2.12 and 2.13 (colour plate section) as surface pictures. 

A different scheme must be used for determining polarization functions and very diffuse functions (Rydberg functions). It is reasonable to use functions from another basis set for the same element. Another option is to use functions that will depict the electron density distribution at the desired distance from the nucleus as described above. 

The most common way of including relativistic effects in a calculation is by using relativisticly parameterized effective core potentials (RECP). These core potentials are included in the calculation as an additional term in the Hamiltonian. Core potentials must be used with the valence basis set that was created for use with that particular core potential. Core potentials are created by htting a potential function to the electron density distribution from an accurate relativistic calculation for the atom. A calculation using core potentials does not have any relativistic terms, but the effect of relativity on the core electrons is included. 

The alkali metals tend to ionize thus, their modeling is dominated by electrostatic interactions. They can be described well by ah initio calculations, provided that diffuse, polarized basis sets are used. This allows the calculation to describe the very polarizable electron density distribution. Core potentials are used for ah initio calculations on the heavier elements. 

Electrophilic Aromatic Substitution. The Tt-excessive character of the pyrrole ring makes the indole ring susceptible to electrophilic attack. The reactivity is greater at the 3-position than at the 2-position. This reactivity pattern is suggested both by electron density distributions calculated by molecular orbital methods and by the relative energies of the intermediates for electrophilic substitution, as represented by the protonated stmctures (7a) and (7b). Stmcture (7b) is more favorable than (7a) because it retains the ben2enoid character of the carbocycHc ring (12). 

In PMD radicals, the bond orders are the same as those in the polymethines with the closed electron shell, insofar as the single occupied MO with its modes near atoms does not contribute to the bond orders. Also, an unpaired electron leads the electron density distribution to equalize. PMD radicals are characterized by a considerable alternation of spin density, which is confirmed by epr spectroscopy data (3,19,20). 

In principle, it is possible to calculate the detailed three-dimensional electron density distribution in a unit cell from the three-dimensional x-ray diffraction pattern. 

Figure 5 Electron density distributions along the bilayer normal from an MD simulation of a fully hydrated liquid crystalline phase DPPC bilayer. (a) Total, lipid, and water contributions (b) contributions of lipid components in the interfacial region.

One possible explanation for the abnormal results noted above comes from considering the 7t-electron density distribution when + M substituents are present. This is indicated on the structure (XII) such that a solid constituent p orbital is a region of higher... 

Charge Distribution, Electron Density Distribution and Walsh Diagrams 69,1166,1405,1697... 

Electron density distributions in inorganic compounds. K. Toriumi and Y. Saito, Adv. Inorg. Chem. Radiochem., 1983, 27,27-81 (94). 

It must be emphasized once again that neither by the resonance nor by the field effect are any electrons actually being donated or withdrawn, though these terms are convenient (and we shall use them). As a result of both effects, the electron-density distribution is not the same as it would be without the effect (see pp. 17, 42). One thing that complicates the study of these effects on the reactivity of compounds is that a given group may have an effect in the transition state which is considerably more or less than it has in the molecule that does not react. 

Fig. 9.10 CASTER densities of states for LigZn2Ge3. Nonbonding electron density distribution over selected bunches of crystal orbitals in the valence-band dispersion (a) six orbitals between -2.4 and -0.7 eV, (b) four orbitals ranging from -3.3 to -1.9 eV.

Electronegativities, which have no units, are estimated by using combinations of atomic and molecular properties. The American chemist Linus Pauling developed one commonly used set of electronegativities. The periodic table shown in Eigure 9 7 presents these values. Modem X-ray techniques can measure the electron density distributions of chemical bonds. The distributions obtained in this way agree with those predicted from estimated electronegativities. 

In the bond framework in Figure 10-18. all the bonds form from end-on overlap of orbitals directed toward each other. As illustrated by the three examples in Figure 10-20. this type of overlap gives high electron density distributed symmetrically along the intemuclear axis. A bond of this type is called a sigma (cr) bond, and a bonding orbital that describes a cr bond is a (7 orbital. 

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. 

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