A persistent problem with macromolecular refinement is that the R-factors of the final models are higher than those obtained in small molecule structures. Over the last ten years, even though the same basic type of model is used to represent the molecule, average R-factors have decreased from about 20 percent to 16 percent. The difference is the sophistication of the refinement methods used. It seems likely that further improvement could be achieved if more powerful techniques were available.
In pursuit of this goal a modification of the conjugate gradient method of function minimization (Fletcher, 1964) has been developed which uses more information about the function being minimized than any method currently used. In particular, it uses explicit knowledge of the diagonal elements of the normal matrix together with implicit knowledge of the off-diagonal terms learned from the history of the refinement to determine better directions in parameter space to search. This method can determine a set of parameters which agree better with the observations in a shorter amount of computer time than the methods described previously.