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In a textbook1, I found the following clear definition of hydrogen bonds:

The strongest secondary bonding type, the hydrogen bond, is a special case of polar molecule bonding. It occurs between molecules in which hydrogen is covalently bonded to fluorine (as in $\ce{HF}$), oxygen (as in $\ce{H_2O}$), and nitrogen (as in $\ce{NH_3}$). For each $\ce{H-F}$, $\ce{H-O}$, or $\ce{H-N}$ bond, the single hydrogen electron is shared with the other atom. Thus, the hydrogen end of the bond is essentially a positively charged bare proton that is unscreened by any electrons.

This is not an "etc." definition. It is made clear that we only call it a hydrogen bond when we have either of the three bonds: $\ce{H-F}$, $\ce{H-O}$ or $\ce{H-N}$.

My question is why this definition excludes compounds such as $\ce{HCl}$? $\ce{HCl}$ and $\ce{HF}$ are very similar with one covalent bond that pulls the hydrogen electron towards their "shared" region, exposing the hydrogen atom as a positive end of this permanent dipole. Both can create secondary dipole bonds to adjacent molecules of the same type.

Why is $\ce{HF}$ called a hydrogen bond while $\ce{HCl}$ is not?

1 Materials Science and Engineering by W. D. Callister & D. G. Rethwisch, Wiley, 8th edition

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    $\begingroup$ HCl and HF are less similar than you think. $\endgroup$ – Ivan Neretin Aug 29 '18 at 12:38
  • $\begingroup$ @IvanNeretin Please enlighten me. $\endgroup$ – Steeven Aug 29 '18 at 13:04
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    $\begingroup$ As you surely know, HF is more polar. Now consider this: it is really, really much more polar. $\endgroup$ – Ivan Neretin Aug 29 '18 at 13:06
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Very very related.

Short answer:

Chlorine is just too large for a hydrogen bond to form.

One thing you need to realize is that Hydrogen Bonding has a fair bit of covalent character as well which makes it considerably more powerful than van Der Waals forces. The Chlorine molecule has its valence electrons in 3p orbitals. Hydrogen has valence electrons in 1s orbital. For covalent character, the orbitals need to overlap. The overlap between the 1s and 3p is very weak and this is the reason why chlorine lacks that covalent character required for hydrogen bonding.

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Hydrogen bonds to chlorine atoms are known. In the gas phase HCl dimers are hydrogen bonded but the bond has only about half the dissociation energy of $\ce{(HF)2}$ which has a larger electrostatic attraction energy. The adduct $\ce{HCl\cdots OH2}$ is also known and has a similar hydrogen bond energy to that of $\ce{HOH\cdots OH2}$.

Using neutron diffraction hydrogen bonds have been studied in many crystals. From a study of many types of amino acid crystals (and derivatives thereof) the normal $\ce{HOH\cdots O}$ hydrogen bond is found to have a range of lengths, from about 0.175 to 0.2 nm with most lengths at around 0.185 nm. The $\ce{OH\cdots Cl}$ hydrogen bond peaks about 0.2 nm with an range of $\approx \pm$ 0.05 nm. The $\ce{NH^+\cdots Cl}$ bond is longer peaking at 0.21 nm.

Calculations (Singh & Kollman, J. Chem. Phys. v83, p4033, 1985) show that the linear hydrogen bond, X-H-X, has an energy profile that is not that dissimilar to any chemical bond when energy is plotted against X to X separation. There are electrostatic attraction terms and exchange repulsion terms. These form a potential well with repulsion dominating (positive energy) at close separation of the two X atoms, a minimum energy (negative) at about 0.18 nm for water dimers, and a gradual increase in energy as the distance X - X increases reaching zero at large separation. However, there are also polarisation terms and those due to dispersion and charge transfer to take into account. These terms are all attractive and become important only at small separation of the X atoms. However, they are not insignificant and contribute a few tens of percentage to the total energy. The result of these terms is to move the minimum of the potential energy to smaller values that that due to exchange and electrostatic terms alone. Thus one can imagine the H atom residing in the potential energy between the two X atoms and being close to the minimum energy. Having described this ideal case, IR spectroscopy does indicate that in some cases the potential may have two minima rather than just one as described so the nature of these bonds is still a subject of debate.

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