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An idea due to D. Rogers [Computing Methods in Crystallography (1965), edited by J. S. Rollett, pp. 117-148. Oxford: Pergamon Press] has been developed and implemented. The method is an advantageous alternative to Wilson plot or K-curve scaling of intensity data. On the relative experimental scale the structure factor can be written in matrix notation as F(h) = k-1Σjfj(h) exp (2πihTxj) exp (-hTbjh); and the squared structure-factor magnitude can be written as |F(h)|2 = k-2 exp (-2hTbh){Σjf2j + 2Σj Σk>jfjfk exp [2πihT(xj - xk)]}, if a common, or average, anisotropic temperature factor is factored out of the atomic summations. The fj2 summation corresponds to the Patterson origin peak, and the fj fk double summation to the off-origin Patterson peaks. A trivariate Gaussian density function, P(u) - Pmin = p0 exp (-uTpu), is fitted by least squares to the origin peak from a Patterson synthesis with coefficients |F|2measjf2j. Fourier inversion of the fitted Gaussian gives the scale and thermal parameters, k2 = (det p)1/2/(π3/2VcellP0) and b = (π2/2)p-1. The fit of the parameter Pmin is constrained by the condition that Pmin = -F(000)2/(k2 VcellΣjZ2j), and thus only P0 and the six coefficients Pij (i < j = 1, 2, 3) are independent parameters.
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