4.7.3. Types of Molecular Orbitals

Molecular orbitals of diatomic molecules are designated as σ (sigma), π (pi), δ (delta), etc.

Molecular orbitals are specific regions in a molecule where electrons can be found, and they are characterized by their shape and symmetry. The term 'sigma' (σ) refers to molecular orbitals that are symmetrical around the bond axis, while 'pi' (π) orbitals lack this symmetry. For example, the combination of two atomic 1s orbitals results in bonding and antibonding molecular orbitals, represented as σ1s and σ*1s, respectively.

Think of molecular orbitals like highways for electron traffic in a city. Sigma highways are straight and direct, allowing cars (electrons) to move smoothly between two banks (nuclei), while pi highways are more like winding roads, which can be less direct and may not facilitate direct travel between the banks.

If the internuclear axis is taken to be in the z-direction, it can be seen that a linear combination of 2pz orbitals of two atoms also produces two sigma molecular orbitals designated as 2pz and *2pz.

Molecular orbitals can also be formed from the linear combination of specific atomic orbitals such as 2pz. When the z-axis is defined along the internuclear axis, the 2pz orbitals from each participating atom combine to form new molecular orbitals. This means you have one bonding molecular orbital (2pz) and one antibonding molecular orbital (*2pz). The bonding orbital holds electrons that contribute to the stability of the bond, while the antibonding molecular orbital can destabilize the bond if occupied.

Imagine two people trying to hold hands directly in front of each other. Their hands represent the bonding orbital that keeps them close together. If one tries to take their hand away or pushes away, forming space between them, that's like an antibonding orbital that weakens the connection.

Molecular orbitals obtained from 2px and 2py orbitals are not symmetrical around the bond axis because of the presence of positive lobes above and negative lobes below the molecular plane.

The pi molecular orbitals, formed from the lateral overlap of 2px and 2py orbitals, do not have the same symmetry as sigma orbitals. Instead of being symmetrically located around the axis between atoms, pi orbitals have electron density that exists above and below this axis, creating regions of higher probability for finding electrons in these lobes rather than directly between the nuclei. This asymmetry influences the bond's strength and the molecular properties, such as reactivity.

Think of pi orbitals like two floating balloons tied to a string—representing bond between two atoms. The balloons (electron density) drift above and below the line connecting the atoms (bond axis), demonstrating how the bond can present different properties compared to a direct line of a sigma bond.

The energy levels of these molecular orbitals have been determined experimentally from spectroscopic data for homonuclear diatomic molecules.

Energy level diagrams for molecular orbitals map out the relative energies of the different molecular orbitals in a homonuclear diatomic molecule. For example, in oxygen molecules (O2), the order of increasing energy levels is: σ1s < σ1s < σ2s < σ2s < (π2px = π2py) < σ2pz < (π2px = π2py) < σ*2pz. These energy levels are influenced by the atomic orbitals that formed them and play a crucial role in determining the molecule's stability and bonding characteristics.

You can think of energy levels like steps on a staircase. The lower steps represent stable bonding situations (bonding orbitals), while the higher steps represent unstable configurations (antibonding orbitals). The location of an electron along this staircase determines whether the molecule is stable (lower energy) or unstable (higher energy).

If Nb is the number of electrons occupying bonding orbitals and Na the number occupying the antibonding orbitals, then the stability of a molecule can be determined.

The stability of molecules can be evaluated using the bond order, which can be derived from the differences in the number of electrons in bonding and antibonding orbitals. A higher proportion of electrons in bonding orbitals (Nb) compared to antibonding orbitals (Na) indicates that the molecule is stable, while the opposite suggests instability.

Consider a seesaw balanced in the playground. If more kids (electrons) are sitting on one end (bonding orbitals) than the other (antibonding orbitals), the seesaw is stable and levels out. If it's tilted the other way, it can flip over, representing an unstable molecule.

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