VII.C.8. (XII.E.1.) |
In a C_{3v} molecule such as CH_{3}F, the angles FCH and HCH are
related by symmetry.
The angles a (FCH) and b (HCH)
are related using the following formulas:
Please note that the latter solution is not unique, and that solving for angle a may return 180° - a |
In a C_{2V} molecule such as CH_{2}F_{2}
the angle HCF can be related to the two angles HCH and FCF by symmetry.
The angle e (HCF)
is related to the angles c (HCH)
and d (FCF) by:
Please note that the latter solution is not unique, and that solving for angle e may return 180° - e |
We use fluorochloromethane as an example. We know:
angle c (H-C-H) (there is only one) angle d (F-C-Cl) (there is only one) angle e (H-C-Cl) (there are two equivilant) We want angle f (F-C-H) (there are two equivilant) |
In a arbitrary tetravalent center their are six angles.
We define these angles as:
a is angle H-C-Cl b is angle F-C-Br c is angle H-C-Br d is angle F-C-Cl e is angle Cl-C-Br f is angle H-C-F Assume we want angle f as a function of the other five angles. We can work with the cosines of the angles: ca = cos(a), cb = cos(b),etc. Define p and q: p = sqrt( (ca^{2} + cc^{2} + ce^{2} - 2*ca*cc*ce - 1) * ((ca^{2} + cb^{2} + cd^{2} - 2*ca*cb*cd - 1) ) q = ca*(cb*ce + cc*cd) - cb*cc - cd*ce The two solutions for cos(f) are: cf = ( p + q)/(ca^{2} - 1) cf = (-p + q)/(ca^{2} - 1) |
Given the three angles:
a is angle F-C-Cl b is angle H-C-Cl c is angle H-C-F We want the dihedral angle d (the angle between the two planes defined by F-C-Cl and H-C-Cl). |