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3.4.2: Molecular Orbitals from s Orbitals

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    Sigma Bonding with s-orbitals (ex: Dihydrogen)

    In the case of the hydrogen molecule, two atomic orbitals are combined to form two molecular orbitals. These new molecular orbitals have different wavelengths than the two atomic orbitals: one has a longer wavelength and is a little lower in energy, while the other has a shorter wavelength and is a little higher in energy. If we take into account the energy of the two original atomic wavefunctions, and compare them to the total energy of the two new molecular wavefunctions, there is no change overall.

    We started with two atomic orbitals, and by combining them we produced two molecular orbitals. The average energy of the orbitals has remained almost constant, and the number of wavefunctions has remained constant.

    A molecular orbital diagram of dihydrogen. Two atomic 1s orbitals combine to give two molecular orbitals with sigma symmetry. The lower energy sigma binding orbital has both nuclei surrounded by electron density, while the higher energy orbital possesses two lobes that are separated by a node. Figure \(\PageIndex{1}\): Molecular Orbital Diagram for H2 [LibreText]

    Of course, from the point of view of the two real electrons, some remarkable changes have occurred. Both of these electrons have adopted a longer wavelength and a lower energy and that has made all the difference. There is an occupied molecular orbital and an unoccupied molecular orbital; only the occupied orbital makes a real energetic contribution to the overall stability of the molecule. The unoccupied orbital is completely imaginary. The electrons have a lower kinetic energy in the bond than they had before bonding; lectronic energy has decreased. A stable bond has formed.

    A bonding picture of He2 would look exactly the same because it would also involve the overlap of 1s electrons on one atom with 1s electrons on the other atom. However, there would be a difference in the electronic energy because each He has two valence electrons: both the bonding and antibonding orbitals would be occupied. Having both orbitals fully occupied results in no net gain in stability, which makes the helium-helium bond unlikely to form.

    Problems

    Exercise \(\PageIndex{1}\)

    Construct molecular orbital diagrams for the following diatomic species and discuss the likelihood of bond formation in each case.

    1. He2.
    2. Li2.
    3. Be2.
    Answer

    MO3pt1soln.png

    3.4.2: Molecular Orbitals from s Orbitals is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Chris Schaller, Kathryn Haas, Kathryn A. Newton, Northern Michigan University, & Kathryn A. Newton, Northern Michigan University.