That seems an interesting approach. I'll check it for sure. In the mean time I was digging into what I did a while ago. It is possible to find appropriate functions for each coordination type if the right conditions are taken into account. In Rappe's paper they mentioned that Cn coefficients are chosen so that boundary conditions are correctly described. One can see that for the mentioned cases eq. 10 does not reproduced this. However by making use of the following facts one can find better expressions. Linear 1 minimum (theta = 180; E_theta(180) = 0) 1 maximum (theta=0) Trigonal 1 minimum (E_theta = 120; E_theta(120) = 0) 2 maxima (theta=0,180) Square planar / octahedral 2 minima (theta = 90,180; E_theta (90) = 0) 2 maxima (theta = 0, 135) In all cases it is imposed that d^2E_theta/dtheta^2 = ka at minimum (most favorable, meaning 90 for square planar and octahedral). To satisfy those conditions of course up to three terms in the fourier expansion should be included. If not, the boundary conditions cannot be effectively imposed. Those expressions can all be rewritten in terms of cos(theta), sin(theta) and their squares. I attached a picture to show you how they look like.
angle-uff.pdf
Description: Adobe PDF document
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