Orbitals and Bonding


  Atomic orbitals and electronic configuration.


s p d

  Electrons contribute to atomic and molecular structure through orbitals. Each orbital is a probabilistic description of the location of an electron assigned to that orbital. Through a property called spin no more than two electrons can be assigned to the same orbital (Pauli Principle).

Orbitals are in many ways similar to waves. They have an amplitude, a phase, and an energy. Their energies depend upon their distribution around the nucleus, and can be ranked in the following manner, for the H atom. Electrons are assigned to orbitals starting from the lowest energy and working up (Aufbau Principle).


  The electronic configuration of hydrogen through boron can be assigned unambiguously using these two principles. At carbon, two possibilities arise, either to assign both electrons to the same p orbital or to different p orbitals of similar energies. The latter assignment keeps the electrons as far away from one another as possible and thus reduces the coulombic electron-electron repulsion and lowers the potential energy (Hund's Rule).


  Configurations where the maximum number of electrons are assigned to a given shell are called closed shell configurations. Neutral atoms with with closed shell configurations are less reactive than open shell atoms. Neutral atoms with open shell configurations tend to form form ions with closed shell configurations (eg. F-, O2-, Na+, Mg2+). For atoms of groups Ia-VIIIa, the outermost shell comprises one s orbital and three p orbitals, and holds eight electrons when in a closed shell configuration (Octet).

This outermost shell is called the valance shell, and most of the chemistry of these atoms is dictated by the interactions of orbitals from this shell. The lower shells are called the electronic core of the atom.

In a covalent bond, electrons are shared among the atoms. The simplest case occurs when two atoms are bonded together using two electrons. This is a two-center two-electron bond. Certain constraints apply to the formation of a covalent bond: 1) there must be orbitals; 2) they must be proximal enough to overlap; 3) they must be oriented properly to overlap; 4) they must have the correct phase to form a bond.

The orbitals we must consider are those of the valence shell, which are the s and p orbitals for our interests. Bonding distance is about 1.5 Å for atoms of the first row and 2.0 Å for atoms of the second row. The combinatorics of phase and orientation are shown below.



  Combination of 1s and 1s to form [[sigma]] and [[sigma]]* orbitals



  Combination of 2s and 2s to form [[sigma]] and [[sigma]]* orbitals



  Combination of 2p and 2p to form [[sigma]] and [[sigma]]* orbitals, and [[pi]] and [[pi]]* orbitals from different orientations.

  Molecular orbitals with cylindrical symmetry are called [[sigma]] orbitals; those with a different phase on the top than on the bottom are called [[pi]] orbitals. Antibonding orbitals are marked with a superscript *.

  Hybridization of orbitals occurs when different orbitals on the same atom are combined and then repartitioned to give orbitals that have characteristics of each of the contributing orbitals. For our interests it is the s and the p orbitals that will hybridize. Three classes of spn hybrids exist, sp, sp2, sp3. They correspond to the mixing of one s with one, two, or three p orbitals, respectively.




Compared to an s orbital an spn hybrid has greater directionality and more rigid orientational constraints. The added directionality allows it to form bonds with greater overlap than those formed from s orbitals. The directionality dictates the geometry around the hybridized atom.



  Relationship between Hybridization and Geometry



Combination of s and sp3 to form [[sigma]] and [[sigma]]* orbitals



  Combination of sp3 and sp3 to form [[sigma]] and [[sigma]]* orbitals