How to calculate dihedral (not torsion) angles?

Andrew Martin amartin at
Sun Mar 21 19:10:37 EST 1999

Antonio (osrisfol at wrote:

: I agree with you that calculations of improper dihedrals  is made in the
: same way as the proper ones. My problem is *the sequence* of the 4 atoms
: involved in the improper dihedral. After you find
: the correct sequence, you can directly apply any code for the
: dihedral angle calculation. Finding this sequence is not a trivial problem,
: in particular when you have to calculate a complicated function of
: several improper dihedral angles, so that they should be *all*
: treated in the same way. For example, in a six-ring, the angle
: between 135 and 561 planes can be obtained as the 3-5-1-6
: dihedral, and/or as the 3-1-5-6 one (the 1356 is obviously wrong,
: as it would give the angle between 135 and 356 planes).
: These two possible choices give opposite dihedral angles, which
: may not be important for general considerations, but it's very
: important when you have to sum/multiply such angles.

OK, now I understand your point :-) I'm not sure of the solution - I
need to think this through properly, but does it not work out as
you want if you apply a simple rule like the second atom in your
sequence is always clockwise to the first?

Does the sign matter in any case? For your purposes can you not
take the modulo (or the square). Why not calculate an RMSD? That's
how one normally gets around the sign problem in cartesian or
torsional problems... Without knowing more about exactly what
you want to achieve it's difficult to say :-)

Best wishes,


Dr. Andrew C.R. Martin
Technical Director, Inpharmatica
& Lecturer, UCL

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