Determining if a Protein Model Contains a Backbone Clash

I have an ensemble of homology models of a protein, and I now wish to remove those models which have backbone clashes. I could obviously check by eye but this is subjective and probably will not be accepted for publication.

What is the best (reproducible) method to determine if a particular protein model contains a backbone clash?

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The way to check for steric clashing between any two atoms, backbone or otherwise, is to compute their Euclidean distance. If a and b represent two atoms (with a_x being the X coordinate of atom a and so forth), you can calculate their Euclidean distance as follows.
d(a, b) = sqrt( (a_x - b_x)^2 + (a_y - b_y)^2 + (a_z - b_z)^2) )
Yes, a and b are 3-dimensional vectors each containing the X, Y, and Z coordinates of the two atoms. However, the value inside the sqrt() will always be non-negative since each of the three differences is squared, so getting an undefined value shouldn't be a problem. I have updated the answer. – Daniel Standage Aug 22 '12 at 13:56