Lecture #21 March 7, 1997
Introduction to the valence bond theory picturing bond formation in H2 in which the two valence electrons now mostly occupy the region of space where the atomic orbitals overlap. The electron density here effectively attracts both nuclei together.
If the atoms are too close together, nucleus-nucleus repulsion (both positive charges) becomes more effective than the slight attraction due to some electron density still between the nuclei.
The compromise position of the two atoms giving rise to the most binding corresponds to a distance that equals the bondlength
In constructing a valence bond picture for methane, the valence electron configuration on carbon, 2s22p2 will not return the correct directional properties for the bonds produced by overlap with hydrogen's 1s atomic orbitals.
The 2s, 2px, 2py atomic orbital geometries are not tetrahedrally directed. We need orbitals that have the correct directional properties and we can synthesize these from our known atomic orbitals by mixing, a process known here as hybridization.
Constructing hybrid orbitals from the 2s, 2px, and 2py atomic orbitals by taking appropriate mixtures. These are being shown for illustrative purposes. The math is not part of the required material.
Hybridizing from the 2s and 2px atomic orbitals giving a hybrid orbital pointing in the x-direction.
Hybridizing from the 2s, 2px and 2py atomic orbitals giving a hybrid in the x-y plane, pointing at 120o to the previous hybrid.
Hybridizing from the 2s, 2px and 2py atomic orbitals with a different combination than before, giving a third hybrid in the x-y plane, pointing at 120o to the previous two hybrids.
Hybridization of s and p valence orbitals in a tetrahedral environment. That is, the carbon in this case is surrounded by a tetrahedral arrangment of (four) objects (hydrogens) which influence the behavior of carbons valence electrons. The net result of all the forces (carbon at the center and a tetrahedral arrangement of perturbations) gives four orbitals that are identical in shape to each other and that are directed to the vertices of a tetrahedron. These orbitals can be simulated by hybridizing the four previous pure orbitals through mixing mathematically and are each symbolized as sp3 hybrid orbitals.
Hybridization of s and p valence orbitals in a linear environment (two perturbing sites). Two of the orbitals, the s and one of the p orbitals are mixed forming two sp hybrid orbitals, leaving the remaining two p orbitals as pure atomic orbitals.
Hybridization of s and p valence orbitals in a trigonal planar environment (three perturbing sites around the central atom). Three valence orbitals, the s and two of the p's, are hybridized to give three sp2 hybrid orbitals, leaving one pure atomic p orbital unchanged.
Summary of the effect of various perturbing geometries on the s/p valence shells in a central atom. By "vacuum" is meant the atom in isolation from any external influence.
For expanded octets, the d orbitals come into consideration. There are five d orbitals (since d implies the angular momentum quantum number l = 2 and hence ml = -2, -1, 0, +1, +2. The trigonal bipyramid and octahedral geometries involve five and six hybrids as indicated.
An illustration of a central atom's two sp hybrid orbitals present for a linear geometry about the central atom. Bear in mind that it is implied that there are also two pure pure p orbitals (not shown) perpendicular to the indicated axis.
Three sp2 hybrid atomic orbitals, constructed in some detail on an earlier slide, showing their trigonal planar directionality. It is implied that there is one remaining pure p atomic orbital perpendicular to the plane shown.
Four sp3 hybrid atomic orbitals that will be present in a tetrahedral environment about a central atom.
Six sp3d2 hybrid atomic orbitals that will be present in an octahedral environment about a central atom. It should be understood that there are three pure d orbitals to be considered as well, although they are not illustrated.
Five sp3d hybrid atomic orbitals that will be present in a trigonal bipyramidal environment about a central atom. There will be four pure d atomic orbitals present as well, but are not shown.