A multisolution procedure via tendentially maximally entropical starting sets

Large starting sets of random phases are in general inconsistent with positivity and atomicity of the electron density. A correct solution can be achieved from them because the tangent formula is a process which maximizes entropy under physical constraints involving the positivity and atomicity of electron density. Starting sets which are themselves tendentially maximally entropical can be created by associating phase shifts Δ, generated according to the von Mises distribution of each triplet phase, to some (from 50 to 300) triplet invariants. Then the phases generated via these perturbed triplets are samples of the phase population expected to be maximally entropical on the basis of the prior information. Experimental tests show that the method may be a useful alternative to other conventional multisolution methods.