NEW DEVELOPMENTS OF THE TWIN VARIABLES APPROACH TO THE CRYSTAL STRUCTURE DETERMINATION. G. Tsoucaris, A. Mishnev*, A. Hountas#, Universite de Paris-Sud, Centre Pharmaceutique, Chatenay-Malabry, France, *Latvian Institute of Organic Synthesis, Riga, Latvia, #Agricultural University of Athens, Athens, Greece
In the development of a new approach to the crystal structure solution based on the concept of twin variables (Hountas & Tsoucaris (1995), Acta Cryst. A51, 754-763) we investigate: 1) dependence of the procedure on the parameters involved, 2) the role of random starts for [[Psi]]-sets, 3) an attempt for transferring of phase information from low (LR) to high (HR) resolution. The basic procedure implies gradient search of the minimum of the global minimization function in the [[Psi]]-variables space. Relation between Es and [[Psi]]s is expressed by convolution eq. E(H) = [[Sigma]][[Psi]](K) [[Psi]]*(K-H) (1) and regression eq. [[Psi]](H) = [[Sigma]] [[Epsilon]](K) [[Psi]](H-K) (2).
1. Parameter optimization. To control the number of accepted Es in the extension process we calculate the acceptance criterion AMIN for the value of _E_ by empirical formula AMIN = 0.5 + N/1000, where N is the current number of Es. We also introduce a) Sim-type weights in eq.(2) and gradient expression for Mmod, b) recombination formula in the form [[Psi]]new = ([[Psi]]old + [[Psi]]new)/2.
2. Multisolution algorithm. 100-150 random starts for [[Psi]]-sets produced several good solutions with the mean phase errors (MPE) in the range of 25-35 for 150-200 Es. The best set contained 210 phases with MPE of 27 (test structure with 41 nonhydrogen atoms in P1).
3. From LR to HR. An important characteristic of the method is the decoupling of E-set, containing the moduli information, and primitive [[Psi]]-variables. Thus part of the [[Psi]]-set can be located outside the observed sphere. This amounts to modeling LR E-data with HR [[Psi]]-set, and thus introducing a bias towards atomicity. After transferring of information from the LR Es to the [[Psi]]-set containing HR components, one extends the phase and modulus information to the HR Es in the next step by means of eq. (1).