Heteronuclear Diatomics and Polarity in Orbital Terms
Different atoms can contribute unequally to a molecular orbital. A two-orbital model connects unequal parent energies with unequal sharing. Hydrogen fluoride and carbon monoxide show why symmetry, overlap and the complete orbital configuration also matter.
What a learner can do afterwards
- Uses an interacting two-orbital model to explain why the lower-energy parent contributes more to the bonding combination
- Explains how energy mismatch affects localisation at fixed interaction, without using it as an absolute ionic-bond cutoff
- Builds and fills a simplified valence-level scheme for carbon monoxide and identifies its usual terminal donor orbital
- Checks relative energy, spatial overlap and symmetry when deciding whether two orbitals can mix strongly
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Keep the filling rules from the homonuclear lesson. Now take two interacting atomic orbitals with unequal energies. In this two-orbital model, the bonding combination has a larger contribution from the lower-energy parent. The antibonding combination has more from the higher-energy parent. A contribution describes the parent's part in the molecular wavefunction; neither atom owns the orbital. Molecules with several interacting orbitals need a fuller scheme.
Strong mixing needs suitable symmetry, nonzero spatial overlap and a small enough energy gap. Use the same molecular axis for both symmetry tests. With the HF bond along z, H 1s and F 2p_z have sigma symmetry and can interact. F 2p_x has pi symmetry. Its positive and negative overlap contributions with H 1s cancel, giving zero interaction for that pair in this model. Equal energies cannot remove this symmetry restriction.
In HF, the interacting F 2p_z level lies below H 1s. Their bonding combination has more fluorine character. Fluorine attracts bonding density more strongly, so F is partially negative and H partially positive. A diatomic has no second bond dipole to cancel this separation. The full molecular dipole depends on all electronic and nuclear charges, not one orbital alone. Transverse F 2p_x and 2p_y remain nonbonding in the simple model.
Hold the nonzero interaction fixed and increase the parent energy gap. Mixing decreases: the bonding combination becomes more localised on the lower-energy parent and the antibonding combination on the higher-energy parent. This can indicate greater ionic character, but the gap alone cannot classify every bond. Electronegativity measures attraction for bonding density. Its difference is a guide, not a fixed cutoff: HF is polar covalent despite its large difference.
CO's simplified valence order is 3sigma, 4sigma, the 1pi pair, 5sigma, the 2pi* pair, then 6sigma*. Core levels are omitted. Leading numbers name orbitals, not electron counts. Each sigma holds 2 electrons; each pi pair holds 4. Fill low levels first, singly across equal-energy orbitals before pairing. The highest occupied orbital is the HOMO. A pair in CO's carbon-centred 5sigma orbital can donate to a metal in the usual terminal mode.
CO's occupied 5sigma orbital contains a pair with strong carbon character. In the usual terminal coordination mode, one CO molecule donates this pair to one metal through carbon. This makes CO a ligand, a species that binds a metal. Other binding modes exist. The carbon-centred donor follows from CO's multiorbital structure; oxygen's lower atomic energies do not make every occupied CO orbital oxygen-centred.
For a molecule with several bonds, bond-dipole contributions must be added with their directions. A vector has both size and direction. CO2 is linear, O=C=O. Its two equivalent C=O bonds give equal contributions directed toward opposite oxygen atoms, so their sum is zero. Equal polar bonds alone do not guarantee cancellation; their directions must also cancel. This geometry test is separate from the symmetry test for orbital mixing.
Check symmetry, overlap and energies. Unequal orbital contributions can explain polar sharing. Use CO's full level scheme to find its donor pair; use bond directions to check dipole cancellation.
Lesson, questions and cards written for this dataset. Chemistry source records were consulted for facts and teaching structure.
Readings and cards written for this dataset. Linked video: Electronegativity and bonding | Structure and bonding | Organic chemistry | Khan Academy, by Khan Academy.
More to read
What the unequal two-orbital model predicts
Take two atomic orbitals with a nonzero interaction and different starting energies. The bonding combination contains more lower-energy-parent character. The antibonding combination contains more higher-energy-parent character. These are statements about contributions to wavefunctions, not ownership of electrons by an atom.
At fixed interaction, a larger parent energy gap makes the mixing smaller. Each combination becomes more localised on one parent. This helps explain unequal sharing, but an energy gap is not an absolute covalent-to-ionic classifier.
A molecule with several interacting orbitals requires its full orbital scheme. Its molecular dipole depends on the complete electronic and nuclear charge distribution. Looking at one occupied orbital cannot determine the whole dipole.
Testing an orbital pair in HF
Choose the HF bond as the z axis. H 1s and F 2p_z have sigma symmetry about that axis and can have nonzero overlap. The fluorine parent is lower in energy, so their bonding combination contains more fluorine character.
F 2p_x and F 2p_y are transverse to this axis and have pi symmetry. Each has positive and negative overlap contributions with H 1s that cancel. They remain nonbonding in the simple HF model. Giving such a pair equal energies would not remove the cancellation.
Strong mixing needs all three checks: suitable symmetry, nonzero spatial overlap and a small enough energy gap. Fluorine attracts HF's bonding density more strongly, giving partial negative charge on F and partial positive charge on H. HF is polar covalent despite its large electronegativity difference.
Checking the whole molecular dipole
Electronegativity describes attraction for bonding electron density. A difference in electronegativity can give a polar covalent bond with partial charges. The difference is a useful guide, but fixed numerical cutoffs have exceptions.
For a molecule with several bonds, a bond-dipole description adds contributions with their sizes and directions. Linear CO2 has two equivalent C=O bonds on opposite sides of carbon. The contributions point toward opposite oxygen atoms, have equal size and cancel. Equal polar bonds would not be enough without the direction check.
HF has only one bond and no second bond contribution to cancel its charge separation. A complete molecular dipole still reflects all electronic and nuclear charges. Bond-dipole arrows are a way to reason about that distribution, not separate objects inside the molecule.
Locating CO's donating pair
CO has ten valence electrons: four from carbon and six from oxygen. With core levels omitted, a common valence scheme orders 3sigma, 4sigma, two 1pi orbitals, 5sigma, two 2pi* orbitals and 6sigma* from lower to higher energy. The leading numbers name orbitals; they do not count electrons.
Fill the listed sets with 2, 2, 4, 2, 0 and 0 electrons. The highest occupied molecular orbital, or HOMO, is 5sigma. Its pair has strong carbon character. In the usual terminal coordination mode, CO donates this pair to one metal through carbon. Other coordination modes also exist.
The donating orbital must be identified from CO's multiorbital structure. Oxygen's lower atomic levels do not imply that every occupied CO orbital is oxygen-centred or that its donating pair must be on oxygen.
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