Question

When applying MO theory to heteronuclear diatomic molecules, the atomic orbitals used may be of different energies. If two atomic orbitals of different energies make two molecular orbitals, how are the energies of the molecular orbitals related to the energies of the atomic orbitals? How is the shape of the resultant molecular orbitals related to the shape of the atomic orbitals?

Short answer

In heteronuclear diatomic molecules, the energies of the bonding molecular orbital is lower than the original atomic orbitals, while the energy of the antibonding molecular orbital is higher. The shapes of these molecular orbitals are derived from the constructive and destructive overlap of the atomic orbitals, respectively.

Step-by-step solution

Understanding the MO Theory for Heteronuclear Diatomic Molecules

Molecular Orbital (MO) Theory posits that when atoms combine to form molecules, their atomic orbitals overlap to create molecular orbitals, which belong to the entire molecule. In heteronuclear diatomic molecules, the atomic orbitals involved can have different energies due to the different atoms.

Energy Relationship of the Molecular Orbitals

When two atomic orbitals of different energies combine, they form two molecular orbitals: a bonding molecular orbital and an antibonding molecular orbital. The bonding orbital is lower in energy than the original atomic orbitals because it is more stable, while the antibonding orbital is higher in energy due to its decreased stability.

Shapes of the Resultant Molecular Orbitals

The shape of the resultant molecular orbitals is influenced by the shapes of the original atomic orbitals. The bonding molecular orbital has a shape that allows for constructive overlap of the atomic orbitals, leading to electron density between the nuclei. Conversely, the antibonding molecular orbital has a node between the nuclei, where electron density is decreased, and is formed from destructive overlap.

Key concepts

Heteronuclear Diatomic Molecules

Understanding heteronuclear diatomic molecules is fundamental to grasping the concepts of Molecular Orbital Theory. These are molecules composed of two different atoms, resulting in orbitals, energy levels, and other properties that differ from those found in homonuclear diatomic molecules. The distinct properties of each atom, including electronegativity and atomic radius, contribute to the behavior and energy of the molecular orbitals formed upon bonding.

For instance, when oxygen and hydrogen atoms come together to form water, the differences in their atomic makeup give rise to bonding characteristics specific to water. In learning about these molecules, consider how the unique combination of disparate elements leads to the diverse chemistry of the compounds they form.

Bonding and Antibonding Orbitals

Within Molecular Orbital Theory, the concept of bonding and antibonding orbitals is pivotal. When two atomic orbitals combine during molecule formation, they create two new orbitals: a lower-energy bonding molecular orbital and a higher-energy antibonding molecular orbital. The bonding orbital is associated with stability and lower energy, as it facilitates an increased electron density between the atomic nuclei. This density is what essentially represents the 'bond' in a molecule.

In contrast, the antibonding orbital, marked by the presence of a node where electron density is significantly reduced, corresponds to instability and higher energy. Electrons in antibonding orbitals can destabilize the molecule if they outnumber those in bonding orbitals. Thus, the distribution of electrons between these orbitals can predict the bond order and stability of the molecule.

Orbital Energy Relationship

The orbital energy relationship is a cornerstone in predicting the properties of molecules formed from heteronuclear diatomic combinations. When addressing the relationship between the energies of atomic and molecular orbitals, it's important to note that the energy of the bonding molecular orbital is always lower than that of the parent atomic orbitals because this configuration enables electrons to be more stabilized through increased electron sharing between the two nuclei.

On the other hand, the energy of the antibonding molecular orbital will be higher, making it less stable compared to the original atomic orbitals. This is because the antibonding orbitals reduce the likelihood of electron density between the atomic nuclei, which is not favorable in terms of energy stability. Consequently, electrons will preferentially occupy the lower energy bonding orbitals when available.

Orbital Shape Overlap

The overlap of orbital shapes is essential when considering the formation of bonding and antibonding molecular orbitals. When atomic orbitals combine to form molecular orbitals, the resulting shape of the molecular orbital is determined by the constructive or destructive interference patterns created by the overlapping atomic orbital shapes.

A bonding molecular orbital is formed through constructive overlap, where the wave functions of the atomic orbitals add together to increase electron density in the region between the nuclei. This type of overlap produces an electron cloud that encourages the bonding of the two atoms. In contrast, an antibonding molecular orbital results from destructive overlap, where the wave functions of the atomic orbitals subtract from each other, creating a node and decreasing electron density between the nuclei. The shape of these overlapped orbitals directly impacts the strength and type of the bond formed in the molecule.