What is a molecular orbital diagram and how does it show bonding?

A molecular orbital diagram displays the relative energies of atomic orbitals from each atom on the sides and the resulting molecular orbitals in the center. Each horizontal line represents an orbital holding up to two electrons with opposite spins. Dashed lines connect atomic orbitals that combine to form bonding and antibonding molecular orbitals, illustrating how atomic orbitals overlap to create molecular bonding.

How is bond order calculated and what does it tell us?

Bond order is calculated by subtracting antibonding electrons from bonding electrons and dividing by two. A bond order greater than zero indicates stable covalent bonds exist, while zero means no bond forms. For example, hydrogen has a bond order of one, representing a single bond, whereas hypothetical dihelium would have zero bond order and no stable bond.

Why do molecular orbital diagrams typically show only valence orbitals?

Valence orbitals are emphasized because valence electrons contribute significantly to chemical bonding, while core electrons have minimal impact. For instance, in dilithium, the 1s-1s overlap of core electrons contributes nothing to bond order, whereas the valence electrons in the σ2s bonding molecular orbital create the molecule's bond order of one.

What is s-p mixing and how does it affect molecular orbital ordering?

s-p mixing occurs when 2s and 2p orbitals have similar energies, causing their wavefunctions to mathematically combine. This phenomenon raises the σ2p orbital above the π2p set in period 2 diatomic molecules like boron, carbon, and nitrogen. In contrast, oxygen, fluorine, and neon show negligible s-p mixing because their 2s and 2p energy difference is greater.

How do bonding and antibonding orbitals differ in energy and stability?

When two atomic orbitals combine, they form one lower-energy bonding orbital and one higher-energy antibonding orbital. Bonding orbitals stabilize molecules by concentrating electron density between nuclei, while antibonding orbitals destabilize them by creating nodes between nuclei. Electrons in bonding and antibonding orbitals have opposite effects on overall bond strength.

Why does dihelium not form a stable molecule?

Dihelium would have four electrons: two in the σ1s bonding orbital and two in the σ*1s antibonding orbital. The stabilizing effect of bonding electrons is offset by the destabilizing effect of antibonding electrons, resulting in a bond order of zero. Since no net bonding occurs, dihelium does not exist as a stable molecule.

How does molecular orbital theory explain bonding in polyatomic molecules like benzene?

Molecular orbital theory assigns delocalized electrons in benzene to three π bonding molecular orbitals that extend across the entire carbon ring. Unlike the Lewis model, which cannot accurately represent this delocalization, molecular orbital theory shows how atomic orbitals combine to create bonding orbitals spanning multiple atoms.

10.9

Molecular Orbital Theory II

22.6K views03:51 min

A molecular orbital diagram represents the relative energies of the constituent atomic orbitals, shown on the left and right, and the resultant molecular orbitals, shown in the middle.

As with atomic orbitals, each molecular orbital can accommodate a maximum of two electrons with opposite spins.The electrons from the overlapping atomic orbitals are placed in the molecular orbitals from lowest to highest energy, following Hund’s rule as needed.

For example, the two electrons of molecular hydrogen are both in the lower-energy σ_1s bonding molecular orbital.

Molecular orbital theory predicts the stability of covalent bonds from the bond order of the molecule, which is the number of electrons in bonding orbitals minus the number of electrons in antibonding orbitals divided by two.

A bond order of greater than zero indicates that one or more covalent bonds can exist, whereas a bond order of zero means that bonds should not exist. Molecular hydrogen has a bond order of one and a single bond between the hydrogens. However, covalently bound dihelium does not exist as it would have a bond order of zero.

Molecular orbital diagrams typically only include valence orbitals because the contributions of valence electrons to chemical bonding are more significant than that of core electrons.

For example, the 1s–1s overlap in dilithium has no net contribution to the bond order of the molecule. The valence electrons in the σ_2s bonding molecular orbital are responsible for its bond order of 1.

Diatomic molecules of period 2 must consider both 2s and 2p orbitals. The 2p atomic orbitals are higher in energy than the 2s orbitals, so the corresponding molecular orbitals follow the same trend.

The amount of overlap between the atomic orbitals determines how much more or less stable the molecular orbitals are. Thus, the π orbitals formed from 2p–2p sideways overlap typically fall between the σ orbitals formed from 2p–2p end-to-end overlap along the internuclear axis.

However, effects like orbital mixing between 2s and 2p orbitals, which occurs in diatomic boron, carbon, and nitrogen, leads to a different order, with the σ_2p orbital higher in energy than the π_2p.

In heteronuclear diatomic molecules, such as lithium hydride, the more electronegative atom will have lower-energy atomic orbitals. The resulting bonding molecular orbital energies will be closer to the more electronegative atomic orbital whereas the antibonding molecular orbital energies will be closer to the less electronegative atomic orbital.

Molecular orbital theory is also useful for polyatomic molecules like benzene. The Lewis model of benzene cannot accurately represent its delocalized electrons, whereas molecular orbital theory assigns those electrons to three π bonding molecular orbitals covering the entire carbon ring.