How can we qualitatively predict $\sigma-$bond strengths of overlap between:

  • $\ce{s-s}$
  • $\ce{s-p}$
  • $\ce{p-p}$
  • $\ce{sp-s}$
  • $\ce{sp-p}$
  • $\ce{sp-sp}$


My school-book says $\ce{s-s}$ overlap bond strength is greater than $\ce{s-p}$ overlap which is greater than $\ce{p-p}$

Another book Inorganic Chemistry by JD Lee states this:

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Are the facts stated in the above books correct or justified? Is there any order of orbital overlap strengths? If so can we predict it qualitatively?


2 Answers 2


I think the issue might be what orbitals are being referred to. Both books could be correct if they are referring to different $\mathrm{p-p}$ overlap. For example, suppose two atoms are bonding along the z-axis. $\mathrm{p_z}-\mathrm{p_z}$ overlap would be greater than $\mathrm{s-s}$ because the lobes of the p orbitals extend out to meet each other between the two molecules. If however we looked at $\mathrm{p_x}-\mathrm{p_x}$ overlap, the $\mathrm{s-s}$ overlap would be greater because the p lobes don't extend toward each other. Increasing hybridization increases overlap because it combines the directionality of p orbitals (that they extend out away from the atom) and the electronic density of s orbitals (larger space for overlap to occur).

  • $\begingroup$ The schoolbook asked about p orbitals on internuclear axis only! I feel schoolbook may be wrong because as you said p orbitals are more directional and should form stronger bonds.. $\endgroup$
    – jonsno
    Aug 20, 2017 at 2:44
  • 3
    $\begingroup$ @samjoe Well then for now, I would say trust the Inorganic chemistry book and that hybridization increases overlap. I'm not certain what the other textbook is referring to. $\endgroup$
    – Tyberius
    Aug 20, 2017 at 17:03
  • $\begingroup$ @Tyberius According to this reasoning, shouldn't a p-p overlap be stronger than all of the overlap of hybridised orbitals? $\endgroup$ Mar 31, 2018 at 9:47
  • $\begingroup$ @Taufeeque I believe these measures are for the orbitals overlapping head on. The OP mentions the reasoning that the hybrids have larger directed lobes and so should have stronger bonding. $\endgroup$
    – Tyberius
    Mar 31, 2018 at 13:50
  • 1
    $\begingroup$ @YUSUFHASAN so is your confusion why a hybridized orbital overlaps better than a pure p? It's really just a matter of hybridized orbitals having their density focused in one lobe, rather than equal lobes in the bonding and opposite direction. You could think of a chemical reaction changing the hybridization, but we can be more abstract and just think of the hybridization changing. Hybridization is just a mathematical construct and we can always choose an arbitrary mixing of the orbitals; We just happen to know that certain mixings due a better job at describing bonding. $\endgroup$
    – Tyberius
    Oct 4, 2018 at 4:02

Although the general trend $\mathrm{s} < \mathrm{p} < \mathrm{sp}^n$ makes sense, these magic numbers $1.73$, $1.93$, $1.99$, and $2.00$ seem to have just been pulled out of a hat. If these are really "approximate strengths of bonds", a good book would justify these by showing which bonds they use to come up with these numbers.

Just to show one counterexample, it is commonly known that the strength of C–H bonds increase going from alkanes to alkenes to alkynes. That is to say, the bond strengths increase in the order $\ce{C_{sp^3}-H} < \ce{C_{sp^2}-H} < \ce{C_{sp}-H}$. This clearly contradicts the supposed trend given in the book of $\mathrm{sp}$ orbitals forming slightly weaker bonds than $\mathrm{sp^3}$.

From the second table in this Wikipedia section:

Compound Carbon hybridisation C–H bond strength (kcal/mol)
Ethane sp3 101
Ethylene sp2 111
Benzene sp2 113
Acetylene sp 133

As far as I am aware, this trend is mainly rationalised using bond lengths.

Are the facts stated in the above books correct or justified?

Some parts of it (e.g. the general trend of $\mathrm{s} < \mathrm{p} < \mathrm{sp}^n$) might be correct, as already well addressed by Tyberius' answer, but other parts (especially these magic numbers) are highly debatable.

  • $\begingroup$ Also, I think it will depend on principal quantum number $n$ of inter-mixing orbitals. $\endgroup$
    – Apurvium
    Jul 19, 2021 at 12:12

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