next up previous
Next: High B's Up: What Does This Mean? Previous: Separate XYZ and B

Heavy Atoms

When refining with the Conjugate Gradient method the assumption is made that all the diagonal elements are equal. For the positional parameters these elements usually are similar enough that the real differences can be accommodated with the usual number of cycles. However one factor which contributes to the magnitude of the diagonal elements is the number of electrons surrounding the atom. Heavy atoms such as iron, calcium, and chlorine have much larger diagonal elements and will be shifted much larger distances. In fact, with Conjugate Gradient they will be shifted too far.

This is why heavy atoms tend to oscillate in refinement. The amount of shift is determined based on the average atom, which is about the size of carbon, so the heavy atoms will be over shifted. The next cycle of refinement will attempt to correct their position but again will over shift. The atoms will slip back and forth from cycle to cycle. This problem occurs for all parameters of the heavy atom, both positional and thermal.

The problem can easily be overlooked if only the overall statistics are monitored. The mean and rms shift may be very small even though one or two atoms continue to move a great deal in each cycle. One must monitor the atoms with the largest shifts and try to understand why they continue to shift.

A minimization method which uses at least the diagonal elements will correct the problem.



Dale Edwin Tronrud
January 4, 1994