Which of the following MO has lowest energy for \(\mathrm{B}_{2}\) molecule? (1) \(\sigma 2 p_{x}\) (2) \(\sigma^{*} 2 p_{x}\) (3) \(\pi 2 p_{y}\) (4) \(\pi^{*} 2 p_{y}\)

Molecular Orbital Theory (MOT) is a fundamental concept in chemistry that helps explain how atoms combine to form molecules. According to MOT, atomic orbitals from each atom mix to form new orbitals called Molecular Orbitals (MOs). These MOs belong to the entire molecule, not just individual atoms.

Each MO can hold two electrons with opposite spins, similar to atomic orbitals. However, the energy levels and shapes of these MOs differ from those of the original atomic orbitals. In a molecule, electrons fill the MOs starting from the lowest energy level upward, following the same principles as for atoms: Aufbau principle, Pauli exclusion principle, and Hund's rule.

• The combination of atomic orbitals can result in either constructive interference or destructive interference.
• Constructive interference leads to lower-energy bonding orbitals.
• Destructive interference creates higher-energy antibonding orbitals.

Understanding how MOs are formed and their energy ordering is crucial for predicting and explaining the chemical behavior of molecules.

The energy levels of Molecular Orbitals (MOs) determine the stability and reactivity of a molecule. For \(\text{B}_2\), like many other diatomic molecules, the MOs are formed by the overlap of the atomic orbitals from both boron atoms. The relative energies of these orbitals can be mapped out in a Molecular Orbital Diagram, which helps us see which electrons are in which orbitals.

In general, the order of energy levels from lowest to highest for \(\text{B}_2\) is: \textbf{\boldmath\text{σ 2s}} < \textbf{\boldmath\text{σ^{*} 2s}} < \textbf{\boldmath\text{π 2p_y}} = \textbf{\boldmath\text{π 2p_x}} < \textbf{\boldmath\text{σ 2p_z}} < \textbf{\boldmath\text{π^{*} 2p_y}} = \textbf{\boldmath\text{π^{*} 2p_x}} < \textbf{\boldmath\text{σ^{*} 2p_z}}.

MOs with the lowest energy levels are the most stable and are filled first by electrons. As we move to higher energy levels, the orbitals become less stable. This ordering affects the chemical properties of the molecule. For example, bonding orbitals (\textbf{\boldmath\text{σ}} and \textbf{\boldmath\text{π}}) are lower in energy and more stable than their corresponding antibonding (\textbf{\boldmath\text{σ^{*}}} and \textbf{\boldmath\text{π^{*}}}) counterparts.

Bonding and antibonding orbitals play a critical role in Molecular Orbital Theory.

• **Bonding Orbitals**: These result from the constructive interference of atomic orbitals. Electrons in these orbitals are in a lower energy state and help to stabilize the molecule. For example, in \(\text{B}_2\), the lower-energy MOs such as \textbf{\boldmath\text{σ 2s}} and \textbf{\boldmath\text{π 2p_y}} are bonding orbitals.


• **Antibonding Orbitals**: These are created by destructive interference of atomic orbitals. Electrons in these orbitals are in a higher energy state and potentially destabilize the molecule. They are denoted by an asterisk (\text{*}) next to the orbital symbol. Examples include \textbf{\boldmath\text{σ^{*} 2s}} and \textbf{\boldmath\text{π^{*} 2p_y}}.

Understanding the difference between bonding and antibonding orbitals is essential for predicting the stability and reactivity of molecules. In general, molecules are most stable when they have more electrons in bonding orbitals than in antibonding orbitals.