Three center two electron bond (3c-2e)

 

What is 3c-2e Bond?

How 3c-2e bond can be explained with the help of diboranes?

Three center two electron bond:

3c-2e bond is formed by elements which can form electron deficient compounds. Here two electrons are shared by three nuclei.  

Three atomic orbitals from three molecular orbitals combine to form one bonding, one non- bonding and one anti-bonding molecular orbital. The electrons go into bonding molecular orbital resulting in a net bonding effect and a chemical bond is formed among three atoms.

In these bonds the bonding orbital is shifted toward two of three atoms instead of being spread equally among three. An example of this type of bond is trihydrogen cation H₃⁺. It is also called banana or bent bond.

Bonding in Boranes:

An extended version of the 3c–2e bond model features heavily in cluster compounds described by the polyhedral skeletal electron pair theory, such as boranes and carboranes. These molecules derive their stability from having a completely filled set of bonding molecular orbitals as outlined by Wade’s rule.

Diborane is electron deficient molecule which does not have enough electrons to form separate two electron bond between each pair of bonded atoms.So for eight atoms in B2H6 fourteen electrons are required but it contains only twelve valence electrons. Instead diborane adopts D₂h symmetry containing four terminal and two bridging hydrogen atoms.

 

 

Valence bond treatment of 3c-2e bond:

B₂H₆ can be considered dimeric unit of two BH₃ molecules. Now, as all the three half filled sp³ hybrid orbitals of boron are used to bind hydrogens, dimerization seems impossible.

However VBT still suggests dimerization through sp³ hybridization. Each boron atom can use two of its half filled sp³ orbitals for  two terminal hydrogen atoms and remaining two( one half filled and other empty) for bridging hydrogen atoms.

Valence electron in each bridging hydrogen must get delocalized over all three atoms B-H-B to bond both boron atoms, which is against valence bond theory( likes to bound the electron into region of space that are localized between two participating nuclei).

Additionally molecular geometry of diborane can not be explained usin valence shell electron pair repulsion theory(VSEPR).According to which two bonds around each bridging hydrogen must be linear i.e. B-H-B angle should be 180 with straight line.

Molecular Orbital treatment of 3c-2e bond:

Model determined by molecular orbital theory indicates that bonds between boron and terminal hydrogen atoms are conventional 2c-2e covalent bond. The bonding between boron and bridging hydrogen atoms is different. Each boron uses two electrons for bonding two terminal hydrogen atoms and has only one electron left for additional bonding. The bridging hydrogen atoms provide one electron for each, thus B₂H₂ ring is held by four electrons which form 3c-2e bonds.

The lengths of B-H bridging bond is 1.33A⁰ while the length of B-H terminal bonds is 1.19A⁰ . It is because B-H bridging bond is much weaker than terminal bond. Two hydrogen atoms bridge two boron atoms leaving two H atoms in additional ordinary B-H bonds on each B.

As a result molecule achieves stability since each B participates in total four bonds and all bonding molecular orbitals are filled. Bond order for each bridging B-H bond is 0.5.

MOT diagram of BH3 molecule