Problem 17 - Chemistry An Atoms First Approach

Question

Compare and contrast bonding molecular orbitals with antibonding molecular orbitals.

Step-by-Step Solution

Answer

Bonding molecular orbitals (BMOs) form due to in-phase overlapping of atomic orbitals, resulting in lower energy levels and electron density between atomic nuclei. This stabilizes the molecule. Antibonding molecular orbitals (ABMOs) form due to out-of-phase overlapping of atomic orbitals, resulting in higher energy levels and decreased electron density between atomic nuclei. This destabilizes the molecule. Electrons fill bonding orbitals before antibonding orbitals, according to the Aufbau principle. The bond order is determined by \(\dfrac{(n_{BMO} - n_{ABMO})}{2}\) and indicates a stable molecule when positive.

Step 1: 1. Formation of Molecular Orbitals

Bonding and antibonding molecular orbitals are formed due to the overlapping of atomic orbitals in a molecule. When two atomic orbitals overlap in-phase (constructive interference), a bonding molecular orbital is formed. When two atomic orbitals overlap out-of-phase (destructive interference), an antibonding molecular orbital is formed.

Step 2: 2. Energy Levels

Bonding molecular orbitals (BMOs) are formed due to constructive interference and are lower in energy than the individual atomic orbitals (AOs) contributing to the BMO. Antibonding molecular orbitals (ABMOs) are formed due to destructive interference and are higher in energy than the individual atomic orbitals contributing to the ABMO.

Step 3: 3. Electron Occupancy

Electrons in a molecule occupy molecular orbitals according to the Aufbau principle, which states that electrons fill orbitals in order of increasing energy. Since bonding molecular orbitals have lower energy than antibonding molecular orbitals, they are filled with electrons before the antibonding orbitals are filled.

Step 4: 4. Effects on Bond Order

The bond order of a molecule is determined by the difference between the number of electrons in bonding orbitals and the number of electrons in antibonding orbitals, divided by 2: \(Bond\: order = \dfrac{(n_{BMO} - n_{ABMO})}{2}\). A positive bond order indicates a stable molecule, whereas a negative or zero bond order indicates an unstable or non-existent molecule. Bonding molecular orbitals stabilize the molecule by increasing the electron density between the atomic nuclei, which causes an attractive force between the positively charged nuclei of both atoms. Antibonding molecular orbitals destabilize the molecule by decreasing the electron density between the atomic nuclei, causing a repulsive force between the positively charged nuclei of both atoms.