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In chemistry, isovalent or second order hybridization is an extension of orbital hybridization, the mixing of atomic orbitals into hybrid orbitals which can form chemical bonds, to include fractional numbers of atomic orbitals of each type (s, p, d). It allows for a quantitative depiction of bond formation when the molecular geometry deviates ...
The hybrid can certainly be normalized, as it is the sum of two normalized wavefunctions. Orthogonality must be established so that the two hybrid orbitals can be involved in separate covalent bonds. The inner product of orthogonal orbitals must be zero and computing the inner product of the constructed hybrids gives the following calculation.
Two atomic orbitals in phase create a larger electron density, which leads to the σ orbital. If the two 1s orbitals are not in phase, a node between them causes a jump in energy, the σ* orbital. From the diagram you can deduce the bond order, how many bonds are formed between the two atoms. For this molecule it is equal to one.
The angle between any two bonds is the tetrahedral bond angle of 109°28' [3] (around 109.5°). Pauling supposed that in the presence of four hydrogen atoms, the s and p orbitals form four equivalent combinations which he called hybrid orbitals. Each hybrid is denoted sp 3 to indicate its composition, and is directed along one of the four C–H ...
Molecular orbitals are said to be degenerate if they have the same energy. For example, in the homonuclear diatomic molecules of the first ten elements, the molecular orbitals derived from the p x and the p y atomic orbitals result in two degenerate bonding orbitals (of low energy) and two degenerate antibonding orbitals (of high energy). [13]
Double and triple bonds are usually represented by two or three curved rods, respectively, or alternately by correctly positioned sticks for the sigma and pi bonds. In a good model, the angles between the rods should be the same as the angles between the bonds , and the distances between the centers of the spheres should be proportional to the ...
Walsh diagrams in conjunction with molecular orbital theory can also be used as a tool to predict reactivity. By generating a Walsh Diagram and then determining the HOMO/LUMO of that molecule, it can be determined how the molecule is likely to react. In the following example, the Lewis acidity of AH 3 molecules such as BH 3 and CH 3 + is predicted.
This exercise generates the diagram at right (Figure 1). Three molecular orbitals result from the combination of the three relevant atomic orbitals, with the four electrons occupying the two MOs lowest in energy – a bonding MO delocalized across all three centers, and a non-bonding MO localized on the peripheral centers.