Why are bridge bonds weaker than terminal bonds and, H-B-H terminal bond angles larger than H-B-H bridging bond angles in diborane? [duplicate]

Question

In Concise Inorganic Chemistry by J.D.Lee (Adapted by Sudarsan Guha, Fourth Edition), on page 83, under the topic "Bridge Bonding" it is given for diborane $(\ce{B2H6}):$

The $d_\ce{B-H}(\text{terminal bonds}) < d_\ce{B-H}(\text{bridge bonds})$

The energy required to replace hydrogen atoms from the bridged position is more than that needed for the terminal position. This is supported by the fact that on reaction with methyl chloride, terminal hydrogen atoms are replaced by methyl group in preference to the bridged hydrogen atoms.

The reason for this could be the fact that to break the bridge bond, the overlapping zone should be broken from both sides and the overall energy required is more as compared to do so for terminal bonds.

Structure of Diborane:

Image Credit: Wikipedia

Based on the second paragraph it can be concluded that terminal bonds are weaker than bridge bonds. But some sources on the internet including Wikipedia state the bridge bonds are weaker than the terminal bonds without any satisfactory reason. I wish to know the reason for this.

Further, kindly explain why the terminal H-B-H bond angle is larger than bridging H-B-H bond angle as evident from the molecular structure as given above. I have searched my book as well as google to my best, but I didn't get any reason for this.

Kindly note, I read the unaccepted answer to this question. But still my doubt persists and makes me type this question by adding relevant details from my book and internet.

Kindly clarify this doubt.

Answer 1

It depends on what you define as a bond. A three-center two electron bond is in general stronger than an ordinary two-center bond because delocalizing the bond over three atoms instead of two makes the bonding MO more stable. But, the bridge bond is also shared between two linkages so each individual linkage has less bonding than a single two-center bond linkage.

The question of bond angles is a bit more complex because it hides a couple other issues. Superficially, the bond angles in the bridge region are forcibly reduced by forming a four-membered ring. But that begs the following questions:

• Why is the dimer formed instead of a trimer or tetramer, which would enable a larger ring and more natural bond anges?

• Why is the bond angle through boron actually greater than the bond angle through hydrogen? Since hydrogen forms smaller atoms steric factors would favor the reverse.

An answer to both questions may lie in the tendency of 3c-2e bonds to form closed structures. The bonding orbital described above gets an extra bonding linkage by bringing the end atoms of a chain together. Such a tendency is seen in the formation of a triangular trihydrogen cation in interstellar space, and in the intermediate stage of a carbocation rearrangement.

In the case of diborane this tendency shows up as boron-boron bonding. The dimer has a favorable geometry for forming such a boron-boron bond, whereas an oligomer with larger bond angles in the center would tend to hold the boron atoms too far apart.

The nature of this boron-boron bonding is revealed in molecular-orbital calculations reported by Prof. Bruce Tattershall at Newcastle Universitywinnoplus=2&outputype=HTML5.0_JSmol&basis=MO&orbital=B(p_x)_H_bridge*&plane=xz&orbno=10). The diagram taken from this source is shown below to reveal six occupied valence MOs and defines the $x$ and $z$ axes in the molecule for later reference.

Below are the quantitative data behind this diagram for the occupied molecular orbitals. Entries marked with a blue dot indicate boron-boron bonding, while those with a gold dot are boron-boron antibonding.

The boron $s$ and $p_x$ interactions along the sigma-bonding axes show a mixture of bonding and antibonding overlaps; but the $p_z$ interaction, using orbitals that overlap the hydrogen atoms, shows a single bonding interaction with large boron components. This indicates that the closure of the 3c-2e bonds in the dimer occurs through the $p_z$ lobes rather than along the actual boron-boron axis, forming a "$\pi$ bond over a gap" analogous to what an organic chemist might find in a homoaromatic molecule.

Note also that the 3c-2e bond closure occurs around a hydrogen atom. A larger group in the bridging position could leave the boron atoms too far apart to overlap well and thus inhibit formation of the b9ron-boron bond in a dimer. This would explain the greater tendency of trialkylboranes to exist as monomers compared with the parent (di)borane.