Question

Borazine, \(\mathrm{B}_{3} \mathrm{N}_{3} \mathrm{H}_{6}\) is often referred to as inorganic benzene because of its similar structure. Like benzene, borazine has a delocalized \(\pi\) system. Describe the molecular orbitals of the \(\pi\) system. Identify the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). How many nodes does the LUMO possess?

Short answer

The HOMO for Borazine is a non-bonding molecular orbital and LUMO is an antibonding molecular orbital. The LUMO possesses one node.

Step-by-step solution

Analysing π system

Start by understanding that a π system is formed by the overlap of p orbitals above and below the plane of the molecule. In Borazine(\(\mathrm{B}_{3} \mathrm{N}_{3} \mathrm{H}_{6}\)), boron and nitrogen atoms contribute to the π system. Each boron atom donates one electron and each nitrogen atom donates two electrons to the π system, making a total of 6 π electrons.

Describing the Molecular Orbitals

With six electrons in the π system, we can build molecular orbitals similar to benzene. The six molecular orbitals of the π system can be arranged in increasing energy levels, and filled with the 6 electrons. The two lowest energy molecular orbitals are bonding, followed by two non-bonding, and two anti-bonding molecular orbitals.

Identifying HOMO and LUMO

The HOMO (Highest Occupied Molecular Orbital) is the molecular orbital that has the highest energy and is filled with electrons. In borazine, the HOMO is one of the nonbonding molecular orbitals. The LUMO (Lowest Unoccupied Molecular Orbital) is the molecular orbital with the lowest energy that does not contain electrons. In borazine, the LUMO is one of the antibonding molecular orbitals.

Finding the Number of Nodes in LUMO

A node in a molecular orbital is a region where there is zero probability of finding an electron. As we go up in energy level, the number of nodes increases. Since our LUMO is the first antibonding molecular orbital, it has one node.

Key concepts

Borazine

Borazine, also known as inorganic benzene, is a fascinating compound due to its structural similarity to benzene. Chemically represented as \(\mathrm{B}_{3} \mathrm{N}_{3} \mathrm{H}_{6}\), borazine consists of alternating boron and nitrogen atoms, forming a six-membered ring. This structure creates an overall neutral compound, with each boron donating one electron and each nitrogen contributing two electrons to the π system.

The term "inorganic benzene" is due to borazine's planar, hexagonal shape, resembling that of benzene, and because it has an aromatic character similar to benzene's. However, unlike benzene, borazine includes boron and nitrogen instead of only carbon atoms. These atoms are bound to each other through covalent bonds, and each is also bound to a hydrogen atom, complementing the symmetrical ring formation.

The π system in borazine arises from overlapping p orbitals, as in benzene, leading to a delocalized network that allows the molecule to maintain stability and exhibit unique electronic properties.

HOMO and LUMO

In molecular orbital (MO) theory, understanding the concept of HOMO and LUMO is crucial for predicting molecular reactivity. Each acronym stands for vital energy levels within a molecule:

• HOMO: Highest Occupied Molecular Orbital, the highest energy molecular orbital occupied by electrons.
• LUMO: Lowest Unoccupied Molecular Orbital, the lowest energy orbital that remains unfilled.

These orbitals play a key role in chemical reactions, where electrons are excited from the HOMO to interact with the LUMO. This excitation can involve movement within the same molecule or between different molecules, contributing to reactivity and bonding.

In the case of borazine, the π system's HOMO is among the non-bonding molecular orbitals, reflecting moderate energy and the fact that it houses some of the π electrons. The LUMO, meanwhile, is an antibonding molecular orbital, positioned higher in energy than the HOMO, and it is typically the first to interact in chemical processes needing electronic transitions.

Delocalized π System

A delocalized π system is central to understanding the characteristics of borazine. This term refers to electrons that are shared over several atoms, providing stability and lower energy compared to localized electrons.

In borazine, the delocalization occurs because electrons can move across overlapping p orbitals above and below the plane of the ring, composed of boron and nitrogen atoms. This system is achieved through conjugation, the alignment of orbitals that allows for such interaction and sharing, akin to the electron delocalization seen in aromatic compounds like benzene.

Delocalization in borazine allows the molecule to maintain an aromatic character, stabilizing the ring. With six π electrons, it forms three bonding molecular orbitals, which are the result of constructive interference of wave functions, and distribute these electrons, creating nodes where the probability of finding electrons is zero, especially seen in antibonding orbitals like the LUMO, which typically exhibits one node. This distribution is essential in understanding the non-reactive nature of borazine and its aromatic-like stability.