The angn angle energy power series function is used to approximate unusual functional forms in angle. There are N_angle terms of the form:

kn uijkn, if ul <= uijk < uh
   0, elsewhere

where u_ijk is the current angle spanned by the atoms atom_i, atom_j and atom_k, k_n is a constant and n is zero or a positive integer power and the term is evaluated only when the angle is greater than u_l and less than or equal to u_h. The angn record has the form:

angn	Nangle
	atomi	atomj	atomk	kn	n	ul	uh
	...	...	...	...	...	...	...

The angle power series record starts with the keyword angn followed by the number of such terms N_angle. There are N_angle lines each consisting of seven fields: the three atoms that make up the bond atom_i, atom_j and atom_k, the force constant k_n, the power n, the lower end of the range u_l and the upper end of the range u_h. You can define more than one term over the same triplet of atoms to form a power series in the angle. For example:

  
angn 6

1      2      3      9491.56    0    0.0000    1.7453
1      2      3    -10876.71    1    0.0000    1.7453
1      2      3      3116.00    2    0.0000    1.7453
 
2      3      4      9491.56    0    0.0000    1.7453
2      3      4    -10876.71    1    0.0000    1.7453
2      3      4      3116.00    2    0.0000    1.7453

In this example, six terms are defined. The first three are defined for the atoms 1, 2 and 3 and the last three are defined for the atoms 2, 3 and 4. In each, three constants are defined for the zeroth, first and second power in angle u. This creates the power series: 9491.56 - 10876.71u + 3116u², for 0 <= u < 1.7453 radians (100 degrees). Which is a function that starts at a value of 9491.56 CEU (22.7 kcal/mol) when the angle u is 0 degrees and which falls gradually until the energy is 0 kcal/mol at an angle of 100 degrees. The gradient at that point is also zero. For angles beyond 100 degrees the energy is not evaluated and is assumed to have the value 0 kcal/mol.

Although the individual terms of the power series can be scattered through the entire angn record, keeping them together can result in faster calculations.