The torsion energy is the sum of N_torsion terms where each term has the form:

ktors { 1 + f cos( p * tijkl ) }

where k_tors is a force constant, t_ijkl is the current torsion angle spanned by four atoms numbered atom_i, atom_j, atom_k and atom_l, f is a phase constant and p is the period. Normally f is either 1 or -1 but any number may be specified. p must be an integer from 1 to 6.

The graph on the left ( p = 3, k_tors = 2, f = ±1/2) shows that p determines the number of periods in the range 0 to 180 degrees, k_tors determines the height of the centerline of the cosine curve and the magnitude of f controls the displacement of the centerline from zero and the sign of f determines whether a maximum or minimum energy is attained at zero angle (among other things).

The torsion record in the descriptor file has the form:

tors	Ntorsion
	atomi	atomj	atomk	atoml	p	ktors	f
	...	...	...	...	...	...	...

The torsion record starts with the keyword tors followed by the number of torsions N_torsion, then N_torsion lines of seven fields each: the four atoms that define the torsion atom_i, atom_j, atom_k and atom_l, the period p, the force constant k_tors and the phase f. The order of the four atom numbers is significant (1,3,2,4 does not constitute the same torsion angle as 1,2,3,4) although the sign of the torsion angle is not (1,2,3,4 has the same magnitude as but is opposite in sign to 4,3,2,1). Example:

tors   5

 1    2    3   4   2   50.16   1.0
 6    2    5   7   2   710.6   1.0
 8    5    9  10   1   204.8   -1.0
11   12   13  14   5   8.361   0.5
13   15   16   9   3   41.80   -1.0

Five torsions showing a range of periodicities (1, 2, 3 and 5), and phases (±1 and 1/2).