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Separate XYZ and B

Whenever no part of the normal matrix is directly calculated, as in Steepest Descent and Conjugate Gradient, the method tends to minimize the function by shifting only those parameters which have large diagonal elements. Because the diagonal elements are larger for positional parameters (like x, y, and z) than the thermal factors, the B values will not be shifted to their correct values. This is why routinely these classes of parameters are refined in separate cycles. One first refines the positional parameters holding the B values fixed and then refines the thermal factors holding the positions of the atoms constant.

However because these parameters are correlated to one another it is difficult for both types of parameters to reach their optimal values. One must repeat the cycle many times for the parameters to settle down, more cycles than are usually done.

All parameters may be varied simultaneously when the diagonal elements of the normal matrix are explicitly included in the calculation of the shifts. This is one reason why Conjugate Direction refinement requires fewer cycles.



Dale Edwin Tronrud
January 4, 1994