Molecular Shapes and Hybrid Orbitals
Because the s orbitals are spherical and the p orbitals extend out at 90°, we might expect that all molecules would bond at right angles, because the sharing of electrons necessary for covalent bonds must occurs between s or p subshells. However, this is not the case: water, for example, has a bond angle of 104°;other substances have angles of 120°, in addition to the expected 180° and 90° bond angles. To explain these findings, scientists had to modify the theory of electron orbitals and covalent bonding.
The basic premise of molecular geometry is the valence shell electron-pair repulsion theory (or VSEPR theory for short), which assumes that the electron-electron repulsion between atoms bonding to another central atom will want to keep them as far away from each other as possible, just as inflatable balloons tied together will naturally seek the greatest angles of separation. The shapes described below do not apply with if the central atom is a transition metal, due to the interference of the d subshell.
The shape of the molecule depends on the number of atoms bonding to the central atom and the central atom's number of non-bonding pairs. Non-bonding pairs occupy one "position" of the normal geometry, and because non-bonding pairs are held closer to the central atom (the other shared pairs are attracted by the bonding atom's protons and stretched out a little), the other bond angles will be slightly distorted away from the non-bonding pair.
If there are two atoms bonding to the central atom, as in CO2, the two atoms will be on opposite sides of the central atom, making a linear molecule. The angle between the two bonding atoms is 180°. One non-bonding pair on the central atom will produce a two-atom molecule that cannot be anything but linear.
Three atoms bonding to the central atom will be best spread out when each atom is at a 120° angle to its neighbors. This molecule is flat, and the geometry is called trigonal-planar. One non-bonding pair will produce an angular, three-membered molecule with a bond angle of a little less than 120°. Two non-bonding pairs will generate a two-membered linear molecule.
Four atoms will spread out through all three dimensions, forming a tetrahedral molecule with 109.5° bond angles between atoms. Losing one bond to a non-bonding electron pair will generate a trigonal-pyramidal molecule, with bond angles slightly smaller than expected (about 107° versus 109.5°). Two non-bonding pairs will generate another angular molecule, this time with a smaller bonding angle of around 105°. This is the model that explains the water molecule: oxygen's two nonbonding pairs, along with the bonds to the hydrogen atoms, creates the bent molecule with an angle of about 104.5°.
Five atoms bonding to a central atom form a trigonal bipyrimidal structure, with three "equatorial" atoms at 120° bonding angles and two "polar" atoms at 90° angles to the other three. One non-bonding pair will always occupy an equatorial position, forming a seesaw molecule. Two non-bonding pairs will both take equatorial positions, creating a T-shaped molecule, with three bonding atoms at 90° angles. Three non-bonding pairs will take all the equatorial spots, resulting in a linear, 180° bond-angle molecule.
Finally, six atoms hooked to a center atom produce an octahedral molecule with 90° bond angles between all atoms. One non-bonding electron pairs will cause a square-pyramidal molecule to form, still with 90° bond angles. Two non-bonding pairs will take up positions opposite each other, creating a flat square-planar molecule. Further non-bonding pairs will result in T-shaped and linear molecules, although this many non-bonding pairs is very rare.
Muliple-order bonds are shorter than single-bonds, but otherwise do not greatly affect molecular shape, so when predicting geometry, treat double and triple bonds as single bonds. Non-bonding pairs also affect multiple-order bonds, but not as strongly as single bonds.
The chart below gives the shapes of all these molecules; by simply knowing the Lewis structure for any covalent molecule, you can predict its geometry to within a few degrees!
Despite its extremely accurate predictions of molecular geometry, the VSEPR theory still cannot explain why the shared electron pairs should have the same bond angles, because some come from the spherical s orbital, some from the barbell p orbitals, and others from the double-barbell d orbitals, in cases of expanded octets. For example, the methane molecule (CH4) is tetrahedral, but the carbon atom's shared electrons come from the p orbitals, which have angles of 90°, not 109.5°. Further, the electron configuration of carbon is 2s [+-] 2p [+ ][+ ][- ] --it only has two atoms to share! How, then, does carbon so commonly form four bonds?
Chemists and physicists have created the hybrid orbital theory to explain these discrepancies. In the case of carbon, the single 2s and three 2p orbitals hybridize, creating four sp3 orbitals, each with one electron:
Old orbitals: 2s [+-] 2p [+ ][+ ][- ]
New hybrid orbitals: 2sp3 [+ ][+ ][+ ][+ ]
All sp3 orbitals have the same energies, and carbon can now form four bonds by sharing its four unpaired sp3 electrons. The geometry of the hybrid orbital is also different: the spherical s orbital and barbell p orbitals (which were separated by 90°) combine to create four hybrid orbitals that point to the corners of a tetrahedron, explaining the tetrahedral structure of methane and many other carbon-based molecules.
The oxygen atoms in water also form sp3 hybrids: 2s [+-] 2p [+-][+ ][+ ] becomes 2sp3 [+-][+-][+ ][+ ], with the two non-bonding pairs creating the angular water molecule. The two unpaired electrons are shared with the two hydrogen atoms.
In fact, all of the molecular geometries above can be explained using orbital hybridization: linear results when one s and one p orbital hybridize, creating two sp orbitals that point in 180° angles, as expected. Unhybridized p orbitals are left over; they may be empty or can be used in double-bonding (explained on the next page). The s orbital and two p orbitals can form three sp2 orbitals that point in 120° angles, creating the trigonal-planar geometry. We've already discussed how the all the s and p orbitals form the four sp3 orbitals, each pointing 109.5° away from the others. However, we're out of orbitals--how can we explain the other two geometries?
Luckily, even more orbitals can be brought in to hybridize: the d orbitals can participate as well. This can only occur once the d orbitals are accessible, of course, which is why the octet rule cannot be broken until phosphorus: no d orbitals are available to hybridize. To form the trigonal-bipyrimidal structure, all the s and p orbitals, along with one d orbital, combine to form five sp3d orbitals. Four d orbitals are left over. Finally, two d orbitals will hybridize with the s and p orbitals into the six-orbital sp3d2 subshell. This arrangement produces the octahedral molecular geometry.
Let's consider the two main allotropes of carbon, diamond and graphite, using what we've just learned about hybrid orbitals. Diamond is an extremely hard three-dimensional network solid, in which each carbon bonds with four others. The bond angles are 109.5°, meaning that sp3 hybridization occurs. All of carbon's available orbitals are used in bonding (remember, the d orbitals are not available yet), so the crystal structure is exceptionally strong. Graphite forms flat sheets (there's a clue!), in which each carbon is bonded to only three others. Therefore, the carbons must form the trigonal-planar geometry with sp2 hybridization. The carbon atoms therefore form planes of graphite, with very weak interactions between the left-over p orbitals. The result is that the planes can slide over one another, making graphite a weak, slippery solid. This example is an excellent illustration of how important just one extra hybrid orbital is!
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