Molecular Orbital Tour

Introduction and Orientation
        Let us consider formaldehyde.  The pictures of the MO's are shown over the skeleton of the molecule, represented as a set of tubes.  Below I show the molecular skeleton in two common orientations: from above the plane of the molecule and also at a slight angle to it.  Obviously, the hydrogen nuclei are at the ends of the two white (light grey) ends of the tubes, the dark grey represents the carbon atom, and the the oxygen atom nucleus is at the end of the red portion of the tube. Look for these two types of structures underneath or between the lobes of the orbitals to orient yourself with respect to the molecule.
 
 

  The Molecular Orbitals
        Below are the picture of the orbitals, ordered from lowest energy (MO#1, most tightly bound) to highest energy, up to the LUMO (the lowest unoccupied molecular orbital).  You should count the number of electrons in H2C=O to verify that there are 16 total electrons (don't just count the valence electrons!).

1)    How many occupied molecular orbitals are there?

        The transparent blue blob around the oxygen atom below represents the surface within which is found (I believe) 90% of the electron density for the lowest energy orbital (MO #1).  This MO is essentially the 1s atomic orbital of atomic oxygen.  The atomic orbital is much lower in energy than any of the atomic orbitals of the carbon atom or the 1s orbital of the hydrogen atoms.  This large difference in energy means that it does not significantly interact with the other orbitals, and its nature is essentially unchanged from that in the atom, itself.
 
 

2)    By analogy to MO #1, identify the nature of MO #2, below.  This question translates to:
        a)    identify if it is bonding/antibonding/nonbonding;
        b)    if antibonding or bonding, is it s or p, and which atoms are being bonded (or antibonded);
        c)    if nonbonding, is it essentially identical to an atomic orbital or is it something else.

        Different colors represent different signs of the wavefunction, but the use of red rather than blue in the next figures does not make a difference.  However, when a wavefunction has significant amplitude of both signs (shown as the presence of two colors in the picture of a single molecular orbital), that is important in identifying the nature of the MO!

3)    Can you identify the nature of this MO (#3)?  Note that it has no nodes along the C-O internuclear axis, and is a relatively tightly bound (low energy) orbital.

        Now is a good time to take a look at the the pdf file MOcoefficients.  It lists the energies of the MOs, and the coefficients of the atomic-centerd functions used to build them.  These coefficients may be helpful in interpreting the nature of the wavefunction.  You might start by comparing the MO coefficients to the pictures of MO's #1-3.  That may help clarify the nature of the data in the file.  (You may want to print the file so you can refer to it while looking at the pictures).

4)    Which atomic orbitals are involved in MO#3, above?

    By contrast to MO #3,  MO #4 has a node along the C-O internuclear axis. That suggests that it is, in part,  the antibonding form of MO #3.  However, it is largely a C-H bonding MO.   This leads to an....
Important Point:  Molecular orbitals really are spread out over large parts of a molecule, and are not localized the way simple pictures might suggest them to be!  A single MO may simultaneously have the character of more than one type (antibonding or bonding, s or p, etc).

This might look like a standard C-O p bonding MO, but study it more closely.  Where is the electron density with respect to the plane of the molecule?  The usual picture of the p  MO puts electron density above and below the plane. This orbital has p character in that the C-O internuclear axis is a node.  The coefficients in the MOcoefficients file suggest  that this is primarily a CH s-bonding MO, involving the p-orbital of the carbon atom.
5)        What atomic orbitals are involved in the C-H bonding in MO #4?

The picture of MO #6 might suggest it, too, has C-H bonding character.  Look at the coefficients, and you will see this is not true!
6)    What is the nature of  MO#6, below?
7)    How do the atomic orbitals involved in this MO differ from those involved in MO#3?
 
 

8)    What is the nature of MO # 7?

MO #8 is the HOMO (highest occupied molecular orbital).
9)    What is the nature of MO #8?  (Table 17.2 may provide a hint)

MO #9 is the LUMO.
10)     What is the nature of the LUMO?

General Questions
11)    Are the C-O s bonds formed from the 2s orbitals of the C and O higher or lower in energy than those formed from the p-orbitals?
12)    Are the C-H s bonds formed from the 2s orbitals of the C atom higher or lower in energy than those formed from the 2p orbitals of the C atom?
 
 
 

Notes on the Construction of This Page:   This web page presents pictures of the molecular orbitals (MO's) of formaldehyde (H2C=O), and provides a link to quantitative data about them.  The data and pictures are derived from an Hartree-Fock (self-consistent field) calculation employing an STO-3G basis set.  The computational work was done in Spartan, images were saved as color Postscript files, an then converted to pdf files in Acrobat 4.  Depending on your browser settings, you may see part of the Adobe Acrobat window (in Internet Explorer) and/or some extraneous background.  My knowledge of HTML is not up to making everything look neat.