Chemistry · Ch 4 — Chemical Bonding and Molecular Structure
Conditions for the Combination of Atomic Orbitals
Conditions for the Combination of Atomic Orbitals
Why Atomic Orbitals Combine Selectively
Not every pair of atomic orbitals can combine to form molecular orbitals. The process is governed by three strict conditions. If any one of them is violated, the linear combination of atomic orbitals (LCAO) simply does not produce a stable molecular orbital. These conditions arise from the wave nature of electrons and the requirement that the resulting molecular wavefunction be physically meaningful.
Condition 1: Comparable Energies
The combining atomic orbitals must have the same or nearly the same energy.
This is the most intuitive condition. When two atomic orbitals of very different energies combine, the resulting molecular orbitals are not shared equally. The lower-energy orbital contributes almost entirely to the bonding MO, while the higher-energy orbital contributes almost entirely to the antibonding MO. The net stabilisation is negligible, and no effective bond forms.
Example: A 1s orbital (energy ≈ –13.6 eV for hydrogen) can combine with another 1s orbital, but not with a 2s orbital (energy ≈ –3.4 eV for hydrogen). The energy gap of about 10 eV is far too large for effective mixing.
This condition has an important exception. If the two atoms are very different (e.g., one is much more electronegative than the other), the energy match is judged relative to the valence orbitals of each atom. For example, in HF, the hydrogen 1s orbital (≈ –13.6 eV) and the fluorine 2p orbital (≈ –18.6 eV) have a significant energy difference, yet they still combine because the fluorine 2p is the valence orbital closest in energy to the hydrogen 1s. The condition is "same or nearly the same" — it is not absolute equality.
Condition 2: Same Symmetry About the Molecular Axis
The combining atomic orbitals must have the same symmetry about the molecular axis.
By convention, the internuclear axis is taken as the z-axis. Symmetry here means that the orbital's shape and sign pattern (its phase) must match when rotated around this axis.
Why this matters: The overlap integral between two orbitals depends on their relative orientation. If the orbitals have different symmetries, the positive and negative contributions to the overlap integral cancel exactly, giving zero net overlap. No bond forms.
Example: The orbital of one atom can combine with the orbital of another atom because both are symmetric about the z-axis (they have a single lobe along the axis). But a orbital cannot combine with a or orbital. The orbital has a node along the z-axis and its lobes lie perpendicular to it — its symmetry is completely different.
Quick reference:
| Orbital pair | Symmetry match? | Can combine? |
|---|---|---|
| + | Both spherical (full symmetry) | Yes |
| + | Both symmetric about z-axis | Yes |
| + | Different symmetry | No |
| + | Both symmetric about x-axis, but not about z-axis | Yes (forms MOs) |
Condition 3: Maximum Overlap
The combining atomic orbitals must overlap to the maximum possible extent.
Greater overlap means a larger value of the overlap integral . A larger overlap integral leads to:
- A larger energy lowering for the bonding MO
- A larger energy raising for the antibonding MO
- A greater electron density between the nuclei, which strengthens the bond …