Atomic Orbitals and Valence

One of the most powerful tools available to the chemist is the electronic theory of valence. Still it is not yet being used generally to full advantage. The two principal factors responsible for the delay seem to be reluctance to abandon the rule of eight and failure to make use of the concept of atomic orbitals. 

Ever since the proposal of the theory of the covalent bond by G. N. Lewis in 1916, it has been obvious that there are numerous compounds which do not obey the rule of eight, which was strongly emphasized by Kossel and Langmuir. However, elementary textbooks have stressed it so thoroughly that the rule of eight is still generally accepted by those unfamiliar with the recent literature in the field. 

There is little doubt that boron trichloride is a covalent compound and, therefore, that the boron atom in the compound has only six electrons in its valence shell (crosses represent original boron electrons)  

Beryllium chloride also seems to be covalent, as shown by its high solubility in benzene. If the compound is covalent the beryllium atom has four outer electrons in beryllium chloride (the two crosses represent the two electrons from the beryllium atom)  

When the third period is considered, three out of seven atoms show exceptions to the rule of eight aluminum, phosphorus, and sulfur. Aluminum chloride, phosphorus pentafluoride, and sulfur hexafluoride are typical covalent compounds. They must, therefore, contain six, ten, and twelve bonding electrons, respectively. 

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Table II Atomic orbitals and valence orbital ionization potentials in the form VOIP = a + Pq + 7 q2 (Ref. 46).

Comparison of Linear Combination of Atomic Orbitals and Valence Bond Methods... 

The electron propagator can be used to calculate the charge distribution and other electronic indices that are relevant for a discussion of ground state properties of molecules. We will examine in detail the Mulliken population analysis, which attempts to relate charge distributions to a partial occupation of atomic orbitals and valence shells. 

In our qualitative descriptions of chemical bonding we have used LCAOMOs made from two atomic orbitals and valence-bond factors containing two atomic orbitals. In this section we discuss molecules for which this description is unsatisfactory. 

The valence theory (4) includes both types of three-center bonds shown as well as normal two-center, B—B and B—H, bonds. For example, one resonance stmcture of pentaborane(9) is given in projection in Figure 6. An octet of electrons about each boron atom is attained only if three-center bonds are used in addition to two-center bonds. In many cases involving boron hydrides the valence stmcture can be deduced. First, the total number of orbitals and valence electrons available for bonding are determined. Next, the B—H and B—H—B bonds are accounted for. Finally, the remaining orbitals and valence electrons are used in framework bonding. Alternative placements of hydrogen atoms require different valence stmctures. 

What valence orbital and valence electron conditions must exist if a chemical bond is to form between two approaching atoms ... 

C08-0044. Determine the atomic number and valence orbital that is filling for the element that would appear below lead in the periodic table. 

The Lewis structure shows that methyl methaciylate has the formula C5 Hg O2, with 40 valence electrons. You should be able to verily that the two CH3 groups have. s -hybridized carbons, the inner oxygen atom is s hybridized, the outer oxygen atom uses 2 p atomic orbitals, and the three double-bonded carbons are s p hybridized. These assignments lead to the following inventory of a bonds and inner-atom lone pairs ... 

The spherically averaged atomic core and valence densities are obtained as the sum over products of the radial orbital functions, or, including normalization,... 

Figure 6-21 Atomic-orbital model, valence-bond structures, and resonance-hybrid formula for the 2-propenyl radical...

Six of the seven valence electrons in a fluorine atom are already paired in three filled atomic orbitals and thus are not shared in bonding. The seventh fluorine valence electron, however, is unpaired and can be used in forming a covalent bond to another fluorine. Each atom in the resultant F2 molecule thereby achieves a filled valence-shell octet. The three pairs of nonbonding electrons on each fluorine atom are called lone pairs, or nonbonded pairs, and the shared electrons are called a bonding pair. 

Here It and I) are the valence-state ionization potentials of the atomic orbitals and xpj, calculated for the appropriate barycenters. I ab is the intemuclear distance between the atoms of which y>i and y>) are atomic orbitals. Sy is calculated using Slater orbitals. The quantity [2 1b + (qi + pf)]-1/2 is essentially equal to 7y (Eq. 62). 

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