2.4.9. Root Mean Square Deviation (RMSD)

The Root Mean Square Deviation (RMSD) is a measure of the average distance between atoms in a superimposed structure. You will see this analysis used to judge convergence of an MD simulation in just about every MD paper. The equation is

\[ \mathrm{RMSD} = \sqrt{\frac{1}{N} \sum_{i = 1}^{N} \|v_i - w_i\|^2} \]

Where, \(N\) is the number of points for the structures \(v_i\) and \(w_i\). With xyz-coordinates, we have

\[ \mathrm{RMSD}(\mathbf{v}, \mathbf{w}) = \sqrt{\frac{1}{n} \sum_{i=1}^n ((v_{ix} - w_{ix})^2 + (v_{iy} - w_{iy})^2 + (v_{iz} - w_{iz})^2}) \]