International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2010 
International Tables for Crystallography (2010). Vol. B, ch. 1.3, p. 99

The impossibility of carrying out a fullmatrix leastsquares refinement of a macromolecular crystal structure, caused by excessive computational cost and by the paucity of observations, led Diamond (1971) to propose a realspace refinement method in which stereochemical knowledge was used to keep the number of free parameters to a minimum. Refinement took place by a leastsquares fit between the `observed' electrondensity map and a model density consisting of Gaussian atoms. This procedure, coupled to iterative recalculation of the phases, led to the first highly refined protein structures obtained without using fullmatrix least squares (Huber et al., 1974; Bode & Schwager, 1975; Deisenhofer & Steigemann, 1975; Takano, 1977a,b).
Realspace refinement takes advantage of the localization of atoms (each parameter interacts only with the density near the atom to which it belongs) and gives the most immediate description of stereochemical constraints. A disadvantage is that fitting the `observed' electron density amounts to treating the phases of the structure factors as observed quantities, and to ignoring the experimental error estimates on their moduli. The method is also much more vulnerable to seriestermination errors and accidentally missing data than the leastsquares method. These objections led to the progressive disuse of Diamond's method, and to a switch towards reciprocalspace least squares following Agarwal's work.
The connection established above between the Cruickshank–Agarwal modified Fourier method and the simple use of the chain rule affords a partial refutation to both the premises of Diamond's method and to the objections made against it:
References
Bode, W. & Schwager, P. (1975). The refined crystal structure of bovine βtrypsin at 1.8Å resolution. II. Crystallographic refinement, calciumbinding site, benzamidine binding site and active site at pH 7.0. J. Mol. Biol. 98, 693–717.Deisenhofer, J. & Steigemann, W. (1975). Crystallographic refinement of the structure of bovine pancreatic trypsin inhibitor at 1.5 Å resolution. Acta Cryst. B31, 238–250.
Diamond, R. (1971). A realspace refinement procedure for proteins. Acta Cryst. A27, 436–452.
Huber, R., Kulka, D., Bode, W., Schwager, P., Bartels, K., Deisenhofer, J. & Steigemann, W. (1974). Structure of the complex formed by bovine trypsin and bovine pancreatic trypsin inhibitor. II. Crystallographic refinement at 1.9 Å resolution. J. Mol. Biol. 89, 73–101.
Takano, T. (1977a). Structure of myoglobin refined at 2.0 Å resolution. I. Crystallographic refinement of metmyoglobin from sperm whale. J. Mol. Biol. 110, 537–568.
Takano, T. (1977b). Structure of myoglobin refined at 2.0 Å resolution. II. Structure of deoxymyoglobin from sperm whale. J. Mol. Biol. 110, 569–584.