TerpyridylFormFactor
Now for a true research problem. Supramolecules are self-assembled structures with
near-molecular stability (there must be a better definition, as some people take this stuff
very seriously, but that one is good enough for me). A supramolecule being studied by
Newkome’s group at the University of Akron is shown below in several perspectives.
These pictures come from molecular modeling, but how would one know if such
structures actually exist in solution? Answer: small angle X-ray scattering, because the
molecules are too small for detailed analysis by static light scattering. One could obtain
limited info from DLS, but SAXS or SANS (small angle neutron scattering) is the way to
go. One strategy would be to compute the particle shape factor, P(q), using the
coordinates supplied by molecular modeling. Then one could compare to experimental
SAXS or SANS data. The necessary equation is almost the one we know from light
scattering, which was (assuming rotational averaging):
P(q) =
1
N2
N
N
sin qRij
i 1
j 1
qRij

In this expression, N is the number of scattering centers and Rij the distance between
pairs. It was assumed that all the scatterers were identical, but we can do better because
we have atomic coordinates. For the purpose of a SAXS calculation, we can take each
and every atom as one scatterer. The scattering power is proportional to the number of
electrons in the atom, f. The result is:
N
N
i 1
j 1

P(q) =
N
f i f j sin qRij
qRij
N
 f
i 1 j 1
i
fj
Once the molecular modeling program supplies (x,y,z) coordinates for every atom, it is a
straightforward matter to write a program to do that calculation, just a series of do loops
over the indices i and j, plus a calculation of the Rij values that Pythagoras would
recognize. While you are at it, you can get the radius of gyration, Rg.
Download the (x,y,z) data as shown on the Assignments page
(http://macro.lsu.edu/corecourses/MSWeb4/IntegratedTraining/SupramoleculeSAXS/mol
ecule.csv).
 Use a general purpose programming language or any other tool (MathCad, Excel,
etc) to compute P(q) in the range 0 – 1Ǻ-1 using a step size of 0.01 Ǻ-1 (that is, get
P(q) at 0, 0.01, 0.02, 0.03 Ǻ-1, etc.).
 How long did your program take to accomplish the calculation?
 Account for the unusual shape details of your P(q) plot.
 Report the Rg value.
 Determine Rg from a Guinier plot of the theoretical data and compare it.
Congratulations! That’s real, live research. In just a few weeks, most of you will be able
to devote full time attention to such fun stuff. Meanwhile, do not hesitate to ask for help
with the program or anything else.