Use of negative quartet cosine invariants as a phasing figure of merit: NQEST

Abstract

472UNIVALENT (MONODENTATE) SUBSTITUTION ON CONVEX POLYHEDRA completely overwhelms f/for q=0 and 1, thus falls off very rapidly with q. If the cubic or icosahedral p.g. is purely rotational, 432 or 532, then at q= V/2 for any polyhedron (or assembly of points) of this symmetry with no vertex (point) on a rotation axis ½(1-V)log 2-(3 log e)/4V+log k<log R <½(1-V) log 2+ log k, where k=9 for 432 and 15 for 532. The linearity of log R improves asymptotically as V increases. This expression shows that the effect of symmetry on N tends to vanish even in point groups of high symmetry if V is sufficiently large. For V=240 and p.g. 532, for example, log R ~ -34-80, which means that N(A120B120)" C(240,120),-~ 1072, so that the effect of symmetry relative to N is completely negligible.We are indebted to Professor J. D. H. Donnay for a number of constructive comments on the draft manuscript. The costs of computing were defrayed by the National Research Council of Canada through a grant in aid of research, and by a grant from IBM Canada Ltd. Recent theoretical advances in the identification of those cosine invariants cos (Oh + Ok + 01-~-Ore) which are probably negative suggest algorithms for the calculation of a figure of merit which is sensitive to the integrity of a phase set. The negative quartet figure of merit, NQEST, defined here is of particular utility in conjunction with fast multi-solution tangent formula techniques. Development of the methods and applications to both known and unknown crystal structures are presented.

Structure–activity relationships of antiarrhythmic agents: crystal structure of amiodarone hydrochloride and two derivatives, and their conformational comparison with thyroxine

“…Data were corrected for Lorentz and polarization effects, but not absorption. The structures were determined by multisolution procedures (Main, Lessinger, Woolfson, Germain & Declercq, 1977;DeTitta, Edmonds, Langs & Hauptman, 1975) and the non-H atoms refined anisotropically by full-matrix least-squares methods on F, minimizing ~[w (F o --Fc) 2], where w--1/o'2(Fo). H-atom coordinates were located in Fourier difference maps for amiodarone (I) and benziodarone (III) and refined isotropically and were calculated for desethylamiodarone (II), and their isotropic thermal parameters derived from their attached C parameters.…”

Structure of (7S)-N-acetyldemecolcine, C23H27NO6

“…The solution involved selection of planes occurring most frequently in negative quartets (Silverton, Kabuto & Akiyama, 1978) and use of 9 of these as magic-integer variables in the multisolution technique. The reliability of the solutions was assessed by both a weighted figure of merit and the NQEST test (DeTitta, Edmonds, Langs & Hauptman, 1975). The solution with the best value of NQEST, which was also one of the best on the combined figure of merit, gave an E map showing most of the heavier atoms.…”

The use of non-local constraints in maximum-entropy electron density reconstruction

“…The numerical methods used to determine the AL'S in order to satisfy the constraints were explained in the previous paper. The method was first applied to the structure of prostaglandin (De Titta, Langs, Edmonds & Duax, 1980). Three cases were considered (0 denotes the empty set):…”