Hypervalent Molecules: SF₆, PCl₅ and the Expanded Octet Debate

Sulfur hexafluoride, SF₆, is one of the most chemically inert gases known. It is used as an insulating gas in high-voltage electrical equipment because it doesn’t break down easily. It is also a molecule that, according to the simple Lewis rules most students learn first, shouldn’t exist. Six fluorines bonded to one sulfur means six bonding pairs, twelve electrons, around an atom whose “full shell” is supposed to be eight.

Molecules like SF₆, PCl₅, XeF₂ and the triiodide ion, I₃⁻, are called hypervalent: the central atom appears to be surrounded by more than eight valence electrons. How they manage it has been argued about for decades, and the textbook answer many of today’s teachers learned (d orbitals) is not the answer most chemists give now. This article walks through both.

The facts that need explaining

Whatever model we pick has to account for some clear observations.

• Shapes follow VSEPR. SF₆ is octahedral, PCl₅ in the gas phase is trigonal bipyramidal, SF₄ is see-saw shaped, ClF₃ is T-shaped and XeF₂ is linear. VSEPR predicts all of these correctly if you count five or six electron domains around the centre.
• Only period 3 and heavier atoms do it. Phosphorus forms PCl₅ and PF₅; nitrogen, right above it, forms NCl₃ and NF₃ but no NF₅. Sulfur forms SF₆; oxygen forms nothing like OF₆.
• The outer atoms are almost always very electronegative. Hypervalent compounds typically have F, O or Cl around the centre. SH₆ and PH₅ are not known as stable molecules.
• Bonds are not all equal in PCl₅. The two axial P–Cl bonds are longer than the three equatorial ones.

Keep these four points in mind. A good model should explain all of them, not just the electron count.

Model 1: the expanded octet with d orbitals

The traditional explanation runs like this. Period 3 atoms have an empty 3d subshell in the same shell as their valence 3s and 3p orbitals. To make five or six bonds, the atom promotes electrons into 3d orbitals and forms hybrids:

• sp³d (five hybrids) for PCl₅: trigonal bipyramidal
• sp³d² (six hybrids) for SF₆: octahedral

Each hybrid holds one electron and pairs with an electron from an outer atom, giving five or six normal 2c-2e bonds. Nitrogen and oxygen, the argument continues, have no 2d subshell, so they can’t expand.

This model is tidy, matches VSEPR shapes neatly and explains the period 2 versus period 3 split. It’s still found in many school and introductory courses, and the hybridisation explained article covers how the sp³d and sp³d² labels are used there.

Why it fell out of favour

From the 1980s onwards, quantum-chemical calculations on molecules like SF₆ and PF₅ gave a consistent message: the 3d orbitals of sulfur and phosphorus are too high in energy and too spread out to take a large part in bonding. When they are included in calculations, they do improve the results, but they do so as small polarisation functions, slightly reshaping the s and p orbitals. They are not acting as real valence orbitals holding bonding pairs. The electron population in them is small.

Promoting electrons into 3d orbitals would cost a lot of energy that the extra bonds would struggle to repay. So “sp³d²” is best treated today as a label for an octahedral geometry, not a description of which orbitals are doing the bonding.

Model 2: three-centre four-electron bonding

The leading alternative, developed in the early 1950s by George Pimentel and Robert Rundle, needs only the s and p orbitals of the central atom.

Take XeF₂, the simplest case. It is linear: F–Xe–F. Look at the xenon 5p orbital pointing along the F–Xe–F axis and one p orbital on each fluorine pointing at the xenon. Three atomic orbitals combine into three molecular orbitals:

1. Bonding MO: all in phase, spread over F, Xe and F.
2. Nonbonding MO: the two fluorine orbitals with opposite signs, with a node at xenon. Its electron density sits on the fluorines.
3. Antibonding MO: empty and high in energy.

The system holds four electrons: two in the bonding MO and two in the nonbonding MO. This is a three-centre four-electron bond (3c-4e). One pair holds all three atoms together, and the second pair adds negative charge to the two ends.

Consequences:

• Each Xe–F link has a bond order of about ½, so the bonds are weaker and longer than a typical single bond.
• The nonbonding pair puts extra electron density on the fluorines, making them partly negative and the central atom partly positive.
• The central atom never holds more than eight electrons of its own. The “extra” electrons live mainly on the outer atoms.

This model also explains why the outer atoms must be electronegative. The nonbonding pair sits on the ends of the three-centre unit, so the ends must be atoms that are comfortable holding negative charge. Fluorine is ideal; hydrogen is not. That is one reason XeF₂ exists and “XeH₂” doesn’t.

Compare this with the three-centre two-electron bridges in boranes (see electron-deficient molecules). The orbital recipe is the same. The only difference is whether the nonbonding orbital is filled: empty in electron-deficient molecules, full in hypervalent ones.

Applying it to SF₆ and PCl₅

In SF₆, a simple picture uses three 3c-4e bonds at right angles, one along each axis (F–S–F), built from sulfur’s three 3p orbitals. The sulfur 3s orbital adds some further bonding shared across all six fluorines. Twelve electrons are involved in S–F bonding, but a large share of that density sits on the fluorines.

In PCl₅, the three equatorial bonds are fairly ordinary 2c-2e bonds using phosphorus sp² hybrids, while the two axial bonds form a 3c-4e unit through a phosphorus p orbital. This neatly explains the experimental observation that the axial bonds are longer than the equatorial ones. The Lewis-style “five equal bonds” picture can’t explain that difference without extra assumptions.

An analogy

A 3c-4e bond is like two people sharing one umbrella in a downpour. They are connected and sheltered, but neither is as dry as they would be under a personal umbrella. Each bond is only a “half” bond, and the outer atoms carry most of the load.

The ionic contribution

The third ingredient is simple electronegativity. Fluorine is far more electronegative than sulfur (see bond polarity), so S–F bonds are strongly polar. Modern calculations assign a large positive charge to the sulfur in SF₆ and a matching negative charge spread over the fluorines. In a resonance description, much of the bonding can be written as structures like [SF₅]⁺ F⁻, in which sulfur has an ordinary octet and one fluorine is an ion.

Solid PCl₅ gives a striking real-world hint. In the crystal it is not made of PCl₅ molecules at all but of [PCl₄]⁺ and [PCl₆]⁻ ions. The tetrahedral PCl₄⁺ cation has phosphorus with a normal octet.

So why only period 3 and below?

The modern answer is mainly about size, not d orbitals.

• A small central atom like nitrogen can’t fit five chlorines or fluorines around it without the outer atoms crowding each other.
• Larger central atoms have less electronegative, more polarisable valence shells. They can carry a significant positive charge in a highly polar bonding arrangement more easily than nitrogen or oxygen can.

Some chemists prefer the word hypercoordinate for molecules like SF₆, since the central atom has more neighbours than usual without necessarily having more than eight electrons of its own. You will meet both terms; “hypervalent” (coined by Jeremy Musher in 1969) is the more common.

Drawing Lewis structures: the practical choice

For exam purposes, you will usually be asked to draw SF₆ with six single S–F bonds and PCl₅ with five single P–Cl bonds. That is fine. The Lewis structure is a bookkeeping tool that predicts shape correctly through VSEPR, and it is the expected answer in most courses (see exceptions to the octet rule).

A related debate concerns ions like sulfate. One drawing gives sulfur two S=O double bonds and zero formal charge; another gives four S–O single bonds, +2 on sulfur and −1 on each oxygen. The modern bonding analysis favours the second picture (highly polar single bonds strengthened by ionic attraction) over genuine sulfur d-orbital double bonds. Check which convention your syllabus uses.

For the sulfur and phosphorus data used here, see the sulfur and phosphorus element pages.

Model comparison

Question	d-orbital (sp³d²) model	3c-4e + ionic model
Electrons “owned” by the central atom in SF₆	12	About 8 or fewer
Orbitals used by the centre	s, p and d	s and p (d only as minor polarisation)
Why F, O, Cl as outer atoms?	Not explained well	Ends of 3c-4e units must hold negative charge
Why are PCl₅ axial bonds longer?	Needs extra assumptions	Axial 3c-4e bonds have lower bond order
Why no NF₅?	No 2d orbitals	Nitrogen too small and too electronegative
Predicts VSEPR shapes?	Yes	Yes

Common mistakes

• Stating that d orbitals are “the” reason for expanded octets. It’s a historical model, still used as a label, but modern calculations show d-orbital participation is minor.
• Thinking hypervalency breaks physics. No rule of quantum mechanics limits an atom to eight electrons; the octet rule is an empirical guide for period 2 elements.
• Forgetting the outer atoms. Hypervalent compounds depend on electronegative partners. PH₅ is not a stable molecule, whereas PF₅ and PCl₅ are.
• Assuming all bonds in PCl₅ are identical. Axial and equatorial bonds differ in length. (In PF₅ the fluorines swap positions rapidly, which is why they can look equivalent in some experiments.)
• Mixing up 3c-4e and 3c-2e bonding. Hypervalent molecules have four electrons in the three-centre unit (bonding + nonbonding filled). Boranes have two.
• Believing SF₆ is inert because its bonds are “super strong”. Its inertness is largely kinetic: the sulfur is crowded by six fluorines and has no easy pathway for attack.

Key takeaways

• Hypervalent molecules (SF₆, PCl₅, XeF₂, I₃⁻) appear to have more than eight electrons on the central atom.
• The old sp³d / sp³d² model uses d orbitals, but calculations show d orbitals play only a minor, polarising role.
• The modern view combines three-centre four-electron bonds (bond order about ½ per link, extra charge on the outer atoms) with a large ionic contribution.
• This explains why outer atoms are electronegative (F, O, Cl), why PCl₅ has longer axial bonds, and why period 2 atoms like nitrogen don’t form NF₅.
• VSEPR shapes and “expanded octet” Lewis structures remain valid tools for predicting geometry and answering most exam questions.