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Metallic bond strength in $\mathrm{d}$-block elements increases up to the middle and then decreases. Why does pairing decrease the strength of metallic bond? What does pairing have to do with metallic bonding?

Some books [1, p. 1129] say there is covalent bonding, which is related to unpaired electrons, and that is why their inter-atomic interaction strength increases up to the middle:

Hardness of these metals indicates the presence of covalent bonds. The unpaired $d$-electrons may overlap to form covalent bonds. The number of such covalent bonds would be regarded as a measure of overall bond strength and hardness of the metal. In a transition series tire number of unpaired $d$-electrons increases on moving from group IIIB $[(n-1)d^1,ns^2]$ to VIB $[(n-1)d^5,ns^1]$ after which pairing begins.
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The high melting and boiling points of transition elements show that they arc held by strong forces. This is due to the presence of (a) strong metallic bonding because of the overlapping of $(d-1)d$ orbitals, and (b) covalent bonding by the unpaired $d$-orbital electrons. As Zn, Cd and Hg are having completely filled $(d—1)d$-orbitals, their atoms arc not expected to form covalent bonding amongst themselves; hence they arc having relatively low m.p. than the other $d$-block elements.

Are unpaired electrons taking part in covalent bonding or metallic bonding? Why can't paired electrons take part in metallic bonding?

  1. Gurdeep, R. Advanced Inorganic Chemistry, 3rd ed.; Krishna Prakashan Media, 2008; Vol. 1. ISBN 978-81-87224-03-7.
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Unpaired electrons are not the only thing that are used for bonding in d-block elements. The outermost ns electrons are also present for bonding. and when you ask what type of bonding is present in d-block elements, it means you mean to ask the type of bonding present only amongst these metals, and not with some other element(like p-block elements, say F, Cl). If that is the case, then only metallic bonds are present in d-block elements. For example, copper atoms are held by metallic bonds in the metal crystal.

The factors affecting the strength of a metallic bond are-

  1. No. Of valence electrons (more number means higher attractive forces, and hence stronger bond)
  2. Distance of ionic core from the valence electrons (lesser distance means a smaller size of the metal ion, and hence higher value of the force)
  3. Presence of vacant d-orbitals (the free valence electrons in metal travel through the metal crystal using these vacant d-orbitals. So, if there are more number of vacant d-orbitals, the free electrons are more easily "accessible" for attraction by the ionic cores)
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