IDEAL - A Program to compare one set of atomic cordinates with one or more other similar sets

R.O. Gould, N. Moulden and P. Taylor, University of Edinburgh
Version of September, 1988. 

General Principle of operation:
An initial set of atomic coordinates is read in from the previously prepared file IDEAL.INS, and stored in orthogonal Angstrom form. As each subsequent set is read in, atom names common to it and the first set are identified, and providing that at least three such atoms are found, an attempt is made to superimpose the two sets. The initial fit is made by:

1. Translating the origin of both sets to the centres of gravity of the common atoms.
2. Defining the positive z-axis to lie in the direction of the atom furthest from the origin in the first set.
3. Defining the x-axis to lie such that the atom lying furthest from the z-axis lies in the xz-plane with a positive x- coordinate.
4. Rotating the atoms in the second set using both the rotations calculated for it and the inverse of the rotations calculated for the first set.

The initial fit is then refined by iterative least squares, rotating the second set about the x-, y- and z-axes to minimise the sum of the squares of the deviations of equivalent atoms from one another until convergence (a change in the r.m.s. deviation of less than 0.1% of its previous value) occurs.