How do pi bonds work?

Answer 1

ORBITAL PERSPECTIVE

Pi (#pi#) bonds are made by overlapping two atomic orbitals sidelong, as shown below. In contrast, sigma (#sigma#) bonds are made by overlapping two atomic orbitals head-on.

Either way, this overlap can either be in-phase or out-of-phase.

  • The in-phase one (same colors overlapping) is lower in energy and is called the bonding #pi# overlap. It generates a #pi# molecular orbital.
  • The out-of-phase one (opposite colors overlapping) is higher in energy and is called the antibonding #pi# overlap. It generates a #pi^"*"# molecular orbital.

    A double bond has one #sigma# and one #pi# bond, while a triple bond has one #sigma# and two #pi# bonds.

    MOLECULAR ORBITAL DIAGRAM PERSPECTIVE

    The MO diagram depiction is:

    where:

    • #pi_(npx)# is the bonding molecular orbital formed by the in-phase overlap of an #np_x# with an #np_x# atomic orbital.
    • #pi_(npy)# is the bonding molecular orbital formed by the in-phase overlap of an #np_y# with an #np_y# atomic orbital.
    • #pi_(npx)^"*"# is the antibonding molecular orbital formed by the out-of-phase overlap of an #np_x# with an #np_x# atomic orbital.
    • #pi_(npy)^"*"# is the antibonding molecular orbital formed by the out-of-phase overlap of an #np_y# with an #np_y# atomic orbital.

      We have three common ways that we can occupy the #pi# and #pi^"*"# molecular orbitals.

      • When the #pi# molecular orbitals are filled but the #pi^"*"# ones are not, we have a #pi# bond.
      • When both kinds of molecular orbitals are filled, those electrons are nonbonding and are lone pairs.
      • When neither kind of molecular orbital is filled, there is no lone pair or bond.

        The #sigma# overlaps are the ones that are head-on, and are not our focus (though you should know those as well).

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Answer 2

Pi bonds form when two p-orbitals overlap side by side, allowing for the sharing of electrons above and below the plane of the bonded atoms. This overlapping region creates a cloud of electron density, resulting in a strong electrostatic attraction between the nuclei and the shared electrons. Pi bonds are typically found in double and triple bonds and contribute to the stability of molecules by increasing electron density between bonded atoms.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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