Variable covalency

Nitrogen forms $\text{NH}_3$ and stops there — it never makes $\text{NCl}_5$ . Phosphorus, its neighbour one row down, cheerfully forms both $\text{PCl}_3$ and $\text{PCl}_5$ . Same group, same number of valence electrons, wildly different bonding behaviour. The difference is not chemistry's mood swing; it is a hard consequence of which orbitals sit in the valence shell. This article explains variable covalency: the ability of period-3-and-beyond elements like phosphorus, sulphur and chlorine to show more than one covalency (more than one count of shared electron pairs), while period-2 elements like nitrogen, oxygen and fluorine are stuck with one fixed value. The mechanism is electron promotion into empty $d$ orbitals, and the payoff is a clean rule for which covalencies an element can show — and why $\text{PCl}_5$ , $\text{SO}_3$ and $\text{SF}_6$ exist while their period-2 analogues do not.

The core insight

Elements from period 3 onward can promote paired $s$ or $p$ electrons into empty, energetically accessible $d$ orbitals to raise their unpaired-electron count and hence their covalency, so the same element shows different covalencies in different compounds — an option period-2 elements lack because they have no valence-shell $d$ subshell.

The core idea

Covalency starts as an electron-counting rule. In the simplest picture, the covalency of an atom equals the number of unpaired electrons in its ground-state configuration, because each unpaired electron can pair up with one electron from a partner atom to form one shared (covalent) electron pair. Nitrogen (Z = 7) has valence configuration $2s^2\,2p_x^1\,2p_y^1\,2p_z^1$ : three unpaired electrons, so nitrogen always shows covalency 3, as in $\text{NH}_3$ or $\text{NCl}_3$ . That count is fixed — nitrogen's valence shell ( $n = 2$ ) contains only $2s$ and $2p$ subshells, and there is no empty low-energy orbital to promote an electron into. Oxygen and fluorine are similarly locked at covalency 2 and 1.

Period 3 onward, a new subshell opens the door. From phosphorus (Z = 15) onward, the valence shell also contains empty $3d$ orbitals close enough in energy to be reached. If forming extra bonds releases enough energy — typically by bonding to a strongly electronegative partner like chlorine, fluorine or oxygen — a paired electron in the $3s$ or $3p$ subshell can be promoted into an empty $3d$ orbital, breaking a pair into two unpaired electrons and raising the covalency. Because promotion only happens when it is energetically worthwhile, the same atom can show its lower, un-promoted covalency in one compound and its higher, promoted covalency in another — this is variable covalency.

Expanded octets tag along. A species that has been promoted this way ends up with more than eight electrons around the central atom — an expanded octet, one of the standard exceptions to the octet rule — and the extra bond pairs are accommodated by $sp^3d$ or $sp^3d^2$ hybridisation. So whenever you see variable covalency invoked, expect an expanded-octet structure and a $d$ -orbital-involving hybridisation scheme sitting right next to it.

\text{covalency (max)} = \text{unpaired electrons after promotion}, \qquad \text{promotion possible only if an empty valence } d \text{ subshell exists.} \qquad (1)

where: the left side is the highest covalency the atom can display; the right side counts unpaired electrons in the promoted configuration; the condition flags that this route is closed to period-2 elements (N, O, F, C), which is why they never expand their octet this way.

Figure

Two energy level columns comparing phosphorus and nitrogen valence orbitals showing phosphorus promoting an electron into an empty 3d orbital while nitrogen has no d orbital available

Derivation APredicting the maximum covalency of a period-3 p-block element from its group number

The goal is a rule that predicts, from nothing but an element's position in the periodic table, both its minimum (un-promoted) and maximum (fully promoted) covalency, and to show why that maximum caps out at the element's group number in the modern (IUPAC) numbering for period-3 p-block elements — explaining directly why phosphorus tops out at 5, sulphur at 6, and chlorine at 7.

Step 1. Write the ground-state valence configuration for a period-3 p-block element with $g$ valence electrons, split across $3s$ and $3p$ : two fill $3s$ first, and the remaining $g - 2$ fill the three $3p$ orbitals singly before pairing (Hund's rule). For phosphorus, $g = 5$ : $3s^2\,3p^3$ — three singly occupied $3p$ orbitals, three unpaired electrons overall.

Step 2. Count the minimum (un-promoted) covalency as the unpaired-electron count from Step 1. For $g \leq 5$ (P and earlier), the minimum covalency is $g - 2$ : phosphorus gives 3, matching $\text{PCl}_3$ . For $g > 5$ (S, Cl), the $3p$ subshell must start pairing electrons once past three, so the minimum covalency is $8 - g$ : sulphur gives 2, matching the $\text{H}_2\text{S}$ -type covalency.

Step 3. Now promote every available paired electron — first the $3p$ pairs, then the $3s$ pair — into empty $3d$ orbitals, of which there are five, more than enough room. Each promotion converts one pair into two unpaired electrons, raising the unpaired-electron count by exactly one per promotion, until every one of the atom's $g$ valence electrons sits unpaired in its own orbital.

Step 4. Read off the maximum covalency: it equals $g$ , the total number of valence electrons, because full promotion makes every valence electron unpaired and available for bonding. Phosphorus ( $g = 5$ ) tops out at covalency 5, matching $\text{PCl}_5$ ; sulphur ( $g = 6$ ) tops out at covalency 6, matching $\text{SF}_6$ and $\text{SO}_3$ ; chlorine ( $g = 7$ ) tops out at covalency 7, matching $\text{ClF}_7$ . The rule collapses for period 2, which has no $2d$ subshell to promote into, so N, O and F stay frozen at their Step 2 minimum. Result: minimum covalency $= g - 2$ (or $8 - g$ once $g > 5$ ); maximum covalency $= g$ , achieved only where an accessible valence-shell $d$ subshell exists.

Worked example

Predict, without looking anything up beyond the group numbers, the two covalencies each of phosphorus and sulphur can show, and confirm them against $\text{PCl}_3$ / $\text{PCl}_5$ and $\text{SO}_2$ / $\text{SO}_3$ .

Step 1. Phosphorus has $g = 5$ valence electrons ( $3s^2\,3p^3$ ). By Step 2 of the derivation, its un-promoted covalency is $g - 2 = 3$ : three unpaired $3p$ electrons, matching the three P–Cl bonds in $\text{PCl}_3$ .

Step 2. By Step 4, phosphorus's maximum covalency equals $g = 5$ : promoting the paired $3s$ electron into an empty $3d$ orbital ( $3s^1\,3p^3\,3d^1$ ) gives five unpaired electrons, matching the five P–Cl bonds in $\text{PCl}_5$ with $sp^3d$ hybridisation.

Step 3. Sulphur has $g = 6$ valence electrons ( $3s^2\,3p^4$ ), one $3p$ orbital already paired. Its un-promoted covalency is $8 - g = 2$ , but sulphur virtually always bonds through at least one promoted state rather than this bare minimum.

Step 4. Promoting one $3p$ pair gives $3s^2\,3p^3\,3d^1$ , four unpaired electrons — the two $\sigma$ plus two $\pi$ bonds of $\text{SO}_2$ (covalency 4). Promoting the $3s$ pair as well gives $3s^1\,3p^3\,3d^2$ , six unpaired electrons — the three S=O double bonds of $\text{SO}_3$ (covalency 6), matching $g = 6$ exactly as predicted by Step 4 of the derivation. Both predictions match the standard examples: P shows 3 and 5; S shows (2,) 4 and 6, with the maximum in each case equal to the element's own valence-electron count.

Competitive stretch

Chlorine ( $g = 7$ , $3s^2\,3p^5$ ) has only one unpaired electron un-promoted, giving covalency 1 in $\text{HCl}$ . Successive promotions of the $3p$ and then $3s$ pairs give covalencies 3, 5 and 7 — realised in $\text{ClF}_3$ , $\text{ClF}_5$ and the rare $\text{ClF}_7$ , again capping exactly at $g = 7$ .

Common traps

Assuming every element can show variable covalency: it is essentially restricted to period 3 and heavier $p$ -block elements with an accessible valence-shell $d$ subshell; period 2 elements (N, O, F, C) can never expand their octet this way.
Thinking electron promotion happens automatically: it occurs only when the energy released by forming additional strong bonds outweighs the promotion energy, which is why not every compound of P or S uses the highest possible covalency.
Confusing covalency (the number of shared electron pairs/bonds formed) with oxidation state: the two are related but not identical, and only covalency connects directly to unpaired-electron counts and hybridisation.
Forgetting that variable covalency and expanded octets go hand in hand with $sp^3d$ / $sp^3d^2$ hybridisation, so a predicted higher covalency should come with a matching hybridisation and molecular shape.

Ask the tutor: Want to work through the orbital-promotion picture for chlorine in $\text{ClF}_3$ or $\text{ClF}_5$ step by step?

Why does the promotion only happen with electronegative partners like Cl, F or O?

Promoting an electron into a $3d$ orbital costs energy — you are breaking a stable pair and moving one electron to a higher-energy orbital. That cost is only worth paying if the extra bonds formed release enough energy to more than compensate. Highly electronegative atoms like chlorine, fluorine and oxygen form unusually strong, energy-releasing bonds with phosphorus or sulphur, so the trade pays off. With a weakly electronegative or bulky partner, the promotion energy is not recovered and the atom simply stays at its lower, un-promoted covalency instead.

Does variable covalency mean the atom's electron count or charge is changing between compounds?

No. The total number of valence electrons on the atom stays exactly the same in every compound — promotion only redistributes those electrons among the $3s$ , $3p$ and $3d$ orbitals, converting paired electrons into unpaired ones. Covalency counts unpaired electrons available for bond formation, not the atom's overall charge or electron total, which is why it is a distinct idea from oxidation state even though the two often move together in these examples.

Is there a hard upper limit, or could an element theoretically show covalency higher than its group number?

Within this promotion picture the ceiling is the element's total valence-electron count, because full promotion makes every valence electron unpaired and there are no more electrons left to unpair. That is exactly why chlorine's theoretical maximum is 7 (realised, rarely, in $\text{ClF}_7$ ) and sulphur's is 6, not higher. In practice most compounds stop well short of the maximum, since each extra promotion needs an increasingly favourable partner to pay for the rising promotion cost, so the highest covalencies are seen only with the most electronegative partners such as fluorine.

Variable covalency

The core idea

Worked example

Competitive stretch

Common traps

Before this

Where this leads