# Derivative of SVD V and U matrices

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I find a rotation matrix which best describes how to get from one set of atomic coordinates (molecular geometry) to another by just a pure rotation.

The rotation matrix R is defined

$$R=V \left( \begin{array}{ccc} 1 & & \\ & 1 & \\ & & \left|VU^T\right| \end{array} \right)U^T$$

where V and U are from the SVD of matrix K:

[tex]K=V\Lambda U^T[\tex]

K is formed by summing over i the outer products of the coordinate vectors of atom i in the first and second geometry. (i follow the method described at http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/MARBLE/high/pose/least.htm" [Broken])

I.e K depends on atomic coordinates, and so do U and V.

I require the derivative of each element of R with respect to atomic coordinate. (The rotation matrix is used in an energy approximation and I need analytic forces)

Any answers or hints much appreciated.

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