|Computational Chemistry Comparison and Benchmark DataBase Release 19 (April 2018) Standard Reference Database 101 National Institute of Standards and Technology|
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In a C3v molecule such as CH3F, 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 C2V molecule such as CH2F2
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( (ca2 + cc2 + ce2 - 2*ca*cc*ce - 1) * ((ca2 + cb2 + cd2 - 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)/(ca2 - 1)
cf = (-p + q)/(ca2 - 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).