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Since the overlap increases with directional properties of orbital,

$$\ce{p - p > s - s > s - p}$$

However it is also observed that the bond strength of

$$\ce{H-F > H-H > F-F}$$ $$\ce{\{s - p > s - s > p - p\}}$$

Why does this happen? I've done some research and found this which says that it may depend on the p orbital's alignment with inter-nuclear axis.

The reference doesn't seem to apply here, since all the above orbitals are aligned along the inter-nuclear axis.

What am I missing here?

Bond dissociation enthalpies:

$$\begin{array}\\ \ce{H-F} &&& \pu{568 kJ/mol} \\ \ce{H-H} &&& \pu{436 kJ/mol} \\ \ce{F-F} &&& \pu{157 kJ/mol} \\ \end{array} $$ Source

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  • $\begingroup$ It may have to do with the fact that HF bonds are partly covalent and ionic, increasing the bond strength by introducing more ionic character then the latter two bonds $\endgroup$
    – dval98
    Oct 17 '20 at 2:53
  • $\begingroup$ @dval98 Quite possibly. But this was specifically mentioned as an application of VBT in my textbook. $\endgroup$
    – newbie105
    Oct 17 '20 at 3:15
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    $\begingroup$ @Alchimista so what you are saying is $\ce{ p - p > s - s > s - p }$ is not universal and the bond strength depends on other factors as well. So is it safe to say that VBT even fails to achieve what it was devised for? $\endgroup$
    – newbie105
    Oct 17 '20 at 12:38
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    $\begingroup$ @newbie105 I would say that I do not need valence bond theory to justify why a Cation and an Anion stick to each other. Newtownian mechanics works well when not out of scope. I do not see the reason for both generalisations you made. In other words you certainly need a covalent bond in H2 and F2. For HF that's not straight forward $\endgroup$
    – Alchimista
    Oct 17 '20 at 17:36
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    $\begingroup$ The images often used for the 'phenomenological interpretation' of VBT are crap, and even if these orbitals existed and had such a shape they would be wrong. Also, with more overlap doesn't only come more 'attraction', but also more 'repulsion'. VBT as often applied in OC may provide a good starting point for descriptions, but it'll never be enough to shed actual light on the bonding patterns and is most likely not yielding the right description. Additionally $\ce{F2}$ is a molecule where there is still quite some debate about the bonding, some going as far as introducing new concepts. $\endgroup$
    – Martin - マーチン ♦
    Oct 21 '20 at 14:13

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