# Overlap Integrals, How do you calc them?

``` My work is based on studying the ligand fields of first row transition metal
complexes. I hope to quantify the "bonding" using the Angular Overlap
Model
which has proven very useful in the past for asessing the strength of Metal
to ligand interactions. The problem however is, in the past most compounds
studied using the AOM were monodentate. I am using tridentate ligands and
these have obvious steric constraints which prevents the bonding being
directed exactly along the M-L bond axis. My compounds are tripodal in nature
with the coordinating part being either pyrazoles or pyridines. For a
monodentate pyrazole the bonding is assumed to be maximum where the lone pair
of the N overlaps with the metal d orbitals. This is seen as being symmetric
about the M-N bond axis. BUT it has come to my attention that this is not
always the case; if you draw the lone pair of my pyridine rings as being
along the long axis of the ring then it may not necessarily point directly
at the Metal, thus causing "bent bonds". (This is easier to draw... so
I'll
attempt a computer drawing below!)
C--C
/    \
M--<--N      C
\    /
C--C
Usual way of looking at bonding.
C--C
/    /    \
/ <--N      C
M      \    /
C--C
(I've rotated the metal in the diagram but pituring the pyridine being
rotated is closer to reality... also this picture is EXAGGERATED, the N
lone pair is only missing by 5-25degrees.)
OK, so what I have been trying to calculate unsuccessfully so far is how much
is the "overlap" changing as the pryidine twists away? I have been
trying to
use a package called Gaussian with no success.
Pure MO calculations just don't work with Transition Metal complexes, hence
why I use the AOM to calculate the energy of my d-orbitals. But, I am hoping
there might be someway to sort of picture the overlap of 2 typical
"dumbbell"
orbitals as one is rotated away... what is the relationship beween the angle
of rotation and overlap? cos alpha, cos squared alpha??
I have started looking at Mathematica recently. I am tempted to use Hydrogen
like wavefunctions using the Spherical Harmonics and Radial functions
and looking at the overlap integral. BUT can someone explain in really simple
language the best way to do this considering that the functions will be
centered at different places, and that the usual way to simplify the
calculations to make phi the same for both atoms which is the assumption I
need to remove!