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!
 Thank you for your time.
 Tim Astley,
 Inorganic Chemistry, Univeristy of Tasmania
 Australia