Submitted by Adam Johnson / Harvey Mudd College on Fri, 01/04/2008 - 19:12
My Notes

    After several days of lecturing on the topic of polyatomic molecular orbital diagrams, students break into small groups of 3-4 and form LGO’s that can be used to interact with a central atom to form a Molecular Orbital (MO) diagram.  This assignment is part of a larger 4-5 week unit on MO theory. 

    The first third of my inorganic course is devoted to polyatomic MO theory as it is the basis of modern understanding of bonding, reactivity and spectroscopy.  Generally, even students at the advanced level have not ever formed an MO diagram for a polyatomic compound (MXn;  e.g.  PF5, CCl4,  CoF63-) whether main group or coordination compound.  After lecturing on symmetry and symmetry operations, and a brief review of Lewis theory, Valence Bond theory, and diatomic MO theory, students are shown that interaction of three or more atoms to form a compound is significantly more difficult unless all of the ligand orbitals are taken together as a group.  The LGO’s are derived using an intuitive, symmetry-based approach that does not require linear algebraic techniques (projection operators).  This allows the students to quickly and easily derive LGO’s and thus MO diagrams for complicated molecules and coordination compounds at a “back-of-the-envelope” level of theory suitable for drawing during a seminar or on a cocktail napkin.
    Doing the problems in this way allows me to cover much more complex material that I would not want to ask on a homework assignment.  I circulate through the room answering questions and providing guidance in real time.  The last 15-20 minutes of class are reserved for each group to describe their solution to the problem.

Attachment Size
in class problems for LGO generation 131 KB
Learning Goals

after doing this exercise, a student should be able to:

i)From a predicted molecular geometry, determine the central atom's hybrid orbitals and use them as generator orbitals

ii) Generate the LGOs by taking linear combinations of the ligand bonding orbitals

iii)  assign proper symmetry labels to the LGOs using a character table

iv)  predict the symmetry of lone pairs (if applicable)

Equipment needs


Implementation Notes

I spend a good deal of time explaining the technique in class (one to two lectures) and do simple examples in class.  This in-class practice session really cements it home for them. One of these days I will post a five-slides-about LO in order to more fully explain the technique.  Please email me if you want additional details on implementation.

Time Required
one 50 minute class period


Evaluation Methods

I have weekly in-class problem exercises that emphasize group work and in-class presentation of the answers.  The in-class participation is worth about 10% of the course grade.

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Gerard Rowe / University of South Carolina Aiken

I tried this activity in my class last week after 3 lectures on VB and MO theory where I started from simple diatomics and moved on to the LGO method for methane and HF2-.  I was shocked at just how hard this activity was for my students.  After some thinking, I realized that they have somehow forgotten what the atomic orbitals look like (especially which axes the d-orbitals line up with).

A couple of my groups made it through 2-3 of the molecules, but I had 2 groups that struggled with square planar methane for the entire class period.  I ended up letting the groups finish the activity for homework.  

I'll be trying this again next year, but I think I may need to add in some molecular modeling kits for those students who can't easily picture molecules in 3D to align the LGOs with AOs.  It might also help to have them build models of the orbitals themselves.

Mon, 09/17/2012 - 14:46 Permalink
Adam Johnson / Harvey Mudd College

oh, you definitely need to review the shapes and orientations of the d (and sadly often the p) orbitals. I do that in an early problem set (pretest) review activity. I have used a modified version of some of the ones from this site…


This is NOT an easy assignment. A more detailed version of my LGO creation method is due to appear in J Chem Educ soon. (in press)

Mon, 09/17/2012 - 17:59 Permalink
Sibrina Collins / College of Arts and Sciences at Lawrence Technological University


Thanks for all you do! I think this is an awesome assignment. I lectured on the BH3 molecule, sketching the MO diagram using your pencast. This was not easy for the students to grasp initially, but I had to remind them where the nodal planes are for the p orbitals.  One question I will ask them on the exam is to generate the MO diagram for AlH3, to really see if the understood the MO diagram for BH3. I know "AlH3" is really a polymer, but if they recognize that B and Al are in the same group, they could sketch a similar MO diagram. I then had them generate the LGOs for CH4 and the MO diagram. They had trouble visualizing the molecule in a cube.


Mon, 10/14/2013 - 14:51 Permalink
Vanessa / Albion College

I think this is a great exercise and I have used it several times. I generally just give it out as something for them to work on on their own after covering a few examples in class, but I think that I will make at least parts of it a (group?) homework assignment.

Fri, 07/03/2015 - 12:59 Permalink
Adam Johnson / Harvey Mudd College

I just realized that there is no link from this LO to the J. Chem. Educ. paper that describes this in more detail, though that paper does reference this LO. Here is the reference and link, and I am also adding it as a web resource in the LO itself. 

Johnson, A. R., ”Construction of Ligand Group Orbitals for Polyatomics and Transition-Metal Complexes Using an Intuitive Symmetry-Based Approach,“ Journal of Chemical Education, 2013, 90 (1), 56-62. (

Thu, 02/06/2020 - 16:56 Permalink