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Molecular Orbital Theory

Molecular Orbital Theory
    Molecular orbital theory describes bonding in terms of orbitals which encompass the entire molecule.  These orbitals are viewed as resulting from the constructive or destructive interaction of atomic orbitals of the atoms in the molecule.  In a simple diatomic molecule, molecular orbitals can be viewed as overlap between the atomic orbitals on each atom.  For overlap to occur, the atomic orbitals must be of similar energy, and must have the proper symmetry.  If the overlap is constructive, electron density will increase in the region between the two nuclei, and a bonding orbital results.  That is, the system is stabilized relative to two separate atoms.  If the interaction of the two atomic orbitals is destructive, nodal planes result between the nuclei, resulting in a destabilizing, or antibonding orbital.
    Atomic orbitals can overlap in a variety of ways.  End-on-end overlap, which results in electron density along the internuclear axis (usually specified as the z axis) results in a s (sigma) bond.  This type of overlap is possible between two neighboring s orbitals, between an s orbital and a pz orbital, or between two neighboring pz orbitals.  The shapes of the bonding orbitals are illustrated below.

    Adjacent atomic orbitals can also overlap side-by-side.  This type of constructive overlap results in electron density above and below the internuclear axis, and is called a p bond.  Neighboring px or neighboring py orbitals can overlap in this way.  A nodal plane which passes through the internuclear axis results.

    Atomic orbitals on neighboring atoms can also overlap face-to-face.  This occurs between d orbitals, and is seen in transition metal compounds.  The bond, which is called a d bond, results in two nodal planes which intersect along the internuclear axis.

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    Energy level diagrams can be created for molecular orbitals, and they are similar to atomic energy level diagrams.  Bonding orbitals (constructive overlap) are always lower in energy than their antibonding (destructive overlap) counterparts.  Each level is designated by its number, type (s,p,d), and its symmetry with relation to inversion through the center of the molecule.  If a molecular orbital is symmetrical with respect to inversion, it has a subscript g (gerade, for even).  If it is asymmetrical with respect to inversion, it is given a subscript u (ungerade, for uneven).  The molecular orbitals for the combination of s orbitals on neighboring atoms are drawn below.  The bonding orbital is given the designation sg, and will be lower in energy.  The antibonding orbital, which will be higher in energy, is given the designation su, because the sign of the orbital changes upon inversion through the center.

    The possible combinations between neighboring p orbitals are shown below.  The orbitals can combine end-to-end to form bonding and antibonding s orbitals, or side-by-side to produce bonding and antibonding p orbitals.  It is important to note that the notations of gerade and ungerade are unrelated to the bonding or antibonding nature of the resulting molecular orbital.  Each type of orbital and its symmetry must be considered separately.

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  The above molecular orbitals differ in energy, and an energy level diagrams can be constructed for simple diatomic molecules.  The simplest diagram, which assumes no interaction between s orbitals on one atom and p orbitals on the other has the following form:  (Please note that the numerical prefixes for the orbitals are not correct.  The lowest orbital should be 1sg, and the p orbitals in the upper section should both have the prefix 1p - see figure 3.14 of the text.)

    The lower orbitals represent the sigma bonding and antibonding orbitals.  The upper section shows the sigma (end-to-end) bonding orbital between two pz orbitals (lowest in energy), then the two degenerate p bonding orbitals.  Next in energy are the two degenerate antibonding p orbitals, and highest in energy, the s antibonding orbital.  This type of diagram, which assumes that the 2p orbitals are high enough in energy so that they do not interact with the 2s orbitals, is appropriate for the diatomic molecules O2 and F2.  For the diatomic molecules Li2 through N2, there is evidence for significant interaction between the 2p and the 2s orbitals.  The energy diagram will be altered as follows: (Please note that the numbering is again incorrect.  Your text contains the correct numbering for the orbitals - see figure 3.18)


 
 

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    Molecular orbital diagrams can also be developed for heteronuclear diatomic molecules.  For these molecules, the overlap is often less, since the energy levels of the orbitals on each atom usually differ.  The simplest case is for a molecule such as HF, where only the 1s orbital of hydrogen need be considered.  It can overlap with both the 2s and 2pz orbitals on fluorine to produce the following MO diagram.

    Note that the notation gerade and ungerade are no longer used, as the molecule no longer has a center of inversion.  Since the orbitals on fluorine are lower in energy than those of hydrogen, the bonding orbitals reside mostly on fluorine.  This is consistent with the high electronegativity of fluorine.  The p molecular orbitals are non-bonding, and represent the lone pairs of electrons in the px and py orbitals of fluorine.  The molecule can be viewed as having bonds resulting from the overlap of the hydrogen 1s orbital with both the 2s and 2p orbitals of fluorine, or with sp hybrid orbitals on fluorine.  The 3s molecular orbital, which is antibonding, resides predominantly on hydrogen, because it is closer in energy to the orbitals on the hydrogen atom.
    A similar treatment for the bonding in carbon monoxide is significant, as CO serves a ligand in many transition metal complexes.  Here, the energies of the orbitals in carbon and oxygen are a bit closer, so more interaction is possible.

    In considering bonding of CO to transiton metals, the highest occupied molecular orbital (2s) and the lowest unoccupied molecular orbital (3s) are key.  The HOMO is essentially the lone pair of electrons on carbon, and the LUMO are the 2p antibonding orbitals which are also skewed more towards the carbon atom.  Depictions of the electron density of each orbital follows. Note that the lower energy orbitals will tend to reside more on the oxygen atom, and the higher energy orbitals will reside more on the carbon atom.

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Copyright ©1998 Beverly J. Volicer and Steven F. Tello, UMass Lowell.  You may freely edit these pages  for use in a non-profit, educational setting.  Please include this copyright notice on all pages.