Hydbridizations, bond (valence) angles and bond lengths are the three principal factors defining the 3D structure of organic compounds, as they control the size and overall shape of building blocks from which matter is made up. These factors are considered to be fundamental of all chemistry, and must have been given during the PrePharm chemistry courses. The chapter below is provided as an auxiliary material to be reviewed by the students outside of the normal lecture hours. The more in debths coverage can be found in any undergraduate texbook of organic chemistry.

1. Carbon Atom:

   The outer shell electronic structure of the atomic carbon is:
   

   The C atom should, therefore, be capable of forming two bonds only using its half-filled 2p orbitals, and the resulting valence angle (the planar angle between the bonds formed) should be 90^o.

   In contrast, valency of carbon in most compounds is four, and the valence angle is 109^o28'. To account for this behavior it is considered (and also proven by theoretical calculations) that in carbon bearing molecules there is a promotion of one 2s electron into 2p orbital with subsequent mixing of all four orbitals 2s, 2p_x, 2p_y and 2p_z to give four half-filled identical orbitals termed sp³ hybrid orbitals. Each of these orbitals is then be able to make a single bond to another atom.

   

   Since all four sp³ orbitals are identical(other than orientation), they are evenly distributed in space to give 109^o 28' valence angle. Thus, for example the structure of methane(Figure on right) is a regular tetrahedron, with each hydrogen position equidistant from the central carbon atom and all hydrogen atoms equivalent.

   

   

   The sp³ orbitals have their electronic density extending much further from the central C atom giving rise to strong bonding interactions at the beginning of the process of bond formation, and stronger bonds in general, since most electron density is now localized between the two atoms (e.g. C and H) engaged in bonding. The new orbitals exist only in molecularly bonded atoms (i.e. not in atomic carbon). The bonds between atoms using either two sp³ orbitals, or two s orbitals, or s-sp³ combination are termed (sigma) bonds, and are the strongest covalent bonds known. Saturated hydrocarbons in general feature only bonds.

2. sp² Hybridization:

   sp³ Hybridization is not the only manner in which the carbon atom can realize the bond formation. Mixing of the two 2p orbitals with one 2s orbital gives three identical sp² orbitals each having a similar shape of electron density as that of single sp³ orbitals.

   However, in contrast to sp³ hybridized carbon atom, uniform spatial distribution of three sp² orbitals gives planar geometry; i.e. all orbitals are positioned within a single plane and form 120^o valence angle with each other.

   

   Furthermore, the unused electron occupies the 2p orbital oriented along the axis perpendicular to the hybridization plane. This pattern is termed sp² hybridization and gives rise to different bond length, strength and geometry than those of the sp³ hybridized molecules.

   • First, all atoms bonded to the central carbon atom with hybrid sp² orbitals will be coplanar with this carbon atom.
   • Second, the unused orthogonal 2p orbital is available for further bonding with other orbitals, (e.g. 2p orbital on another carbon molecule), giving rise to a different type of bonding, where the orbital overlap is edge-to-edge instead of tail-to-tail. The bond formed in such way is called a -bond (pi).

   Due to a less efficient overlap than in the case of a bond, the -bonds are somewhat weaker (lower bond energy). A common example of this type of bonding is an olefinic (alkene) double bond. Note, that the carbon geometry is planar, and that due to the edge-to edge overlap in the -bond no rotation about the double bond is allowed, as it would disrupt 2p-2p orbital overlap. This factor has a profound restricting effect on the ability of unsaturated molecules to rotate about the double bond.

   

3. sp Hybridization:

   Mixing of one 2s orbital with one 2p orbital gives two identical sp hybrid orbitals. Since they are identical, their uniform distribution in space is achieved by localization along a single axis with central C atom (180^o valence angle). The two remaining orbitals are capable of forming two orbitals with the analogous orbitals of adjacent atoms (e.g. sp hybridized carbon). This will give rise to a triple bond consisting of a single bond and two mutually orthogonal -bonds. This situation is represented by acetylenes. The geometrical consequence of the sp hybridization is the linearity of the structure.

Nitrogen in its atomic ground state has the following electronic structure:

Analogously to carbon atom the nitrogen atom should be able to form bonds with the valence angle of 90^o (three such bonds). Orbital hybridization gives instead four orbitals, one of which is filled (two electrons) and does not participate in bonding (two 2p nonbonding electrons frequently called a lone electon pair). The remaining three hybrid orbitals form the normal bonds, analogously to a carbon atom. The geometry of ammonia is therefore similar to that of methane, except it features a free electron pair. This electron pair determines property of nitrogen in sp³ hybridized compounds as an electron donation (Lewis base) to electron deficient atomic centers (Lewis acids), and as an acceptor of hydrogen bonding.

Inversion of Ammonia

To see an inversion of Ammonia, please click on the image above.

Other hybridizations of nitrogen such as sp² and sp are also possible (see examples of compounds below).

The electronic structure of atomic oxygen is:1s² 2s² 2p_x² 2p_y 2p_z. Mixing of the two 2p orbitals and 2s orbital gives four sp³ hybridized orbitals, of which two are half-filled and available for bonding. Each of the two remaining orbitals feature two electrons not available for bonding (nonbonding). The valency of oxygen is therefore 2, and the valence angle is close to that of tetrahedral.

Similarly to the carbon- and nitrogen-containing molecules the sp² hybridization is also possible. In this case only one of the sp² orbitals is half-filled and can form a bond. The remaining orbitals are: two sp² orbitals fully filled and oriented in-plane with the -bond (nonbonding), and one 2p orbital available for -bonding. This situation is realized in the carbonyl group. The sp hybridization is normally not encountered in oxygen compounds.