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Alkali metals have spherical outer s orbitals unlike elements like carbon which have protruding p orbitals that can "attach" onto other orbitals to form covalent compounds. Even in cases like methane elements like carbon can form hybrid orbitals that still have a protruding p like character.

So how can covalent alkali metals form covalent bonds given that their orbitals are spherical and not protruding?

Does the s orbital distort to be more p like in covalent compounds?

Can the s orbital hybridize and steal a more protruding like character from internal orbitals or from the orbitals of another atom?

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    $\begingroup$ hydrogen atom also only has s orbital. They can form covalent bond in H2. $\endgroup$ – Rodriguez Jul 6 '16 at 21:27
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    $\begingroup$ You should really read about bonding and antibonding orbitals. $\endgroup$ – Mithoron Jul 6 '16 at 21:30
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For the most part, they don't. However, lithium sometimes can. This is due to their valence shells being relatively close to the nucleus, so they have some electronegativity and can form somewhat covalent bonds.

For more info see this.

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A covalent bond can be described as a bond between two atoms, where the bonding electrons are "shared" more-or-less equally between both atoms.

Therefore, for an alkali metal to form a covalent bond, it will need to be bonding to an element of similar electronegativity.
If this were to happen, then the s-orbital of the alkali metal will hybridize with an orbital from the bonded atom to form 2 molecular orbitals: one that is bonding (has significant electron density between both atoms) and one that is anti-bonding.

As mentioned above, the molecular orbitals of $\ce{H2}$ are a good example of how s-orbitals can form bonding molecular orbitals.

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