The two-channel maximum entropy method

At a given rj in the unit cell, either p + (r) or p (r) is significant, excess and lack of scattering density being mutually exclusive. As described by Papoular et al. (1966), the related probabilities p + (rj) and p (rj) are defined as 

The entropic densities then follow from equations equivalent to Eqs. (5.56) 

It follows that in a given pixel r, either pj or pj can have a value larger than A, which is taken as a measure of the significance level. The relation of Eq. (5.63) reduces the number of unknowns to one per pixel as in the one-channel maximum entropy method. 

In the application of the two-channel method to a-glycine, use of a uniform prior density sharpens and enhances the bond peaks relative to the observed deformation density, but suppresses the lone-pair peaks to much lower levels. The use of the multipole refinement deformation density as a nonuniform prior gives better results and some increase in detail. 

The electrostatic properties of the molecule may be used as a criterion for judging the MEM enhancement. Using the uniform prior density, the MEM molecular dipole moment derived by the discrete boundary partitioning of space (chapter 6) is only 1.3 D, compared with 9.1 D based on the experimental density, 

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Papoular, R.J., Vekhter, Y. and Coppens, P. (1996) The two-channel maximum-entropy method applied to the charge density of a molecular crystal a-glycine, Acta Cryst., A52, 397 107. 

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